Fundamentals of Piano Practice

A common problem seen with many pianos is compacted hammers. I raise this point because the condition of the hammer is much more important to the proper development of piano technique and for cultivating performance skills, than many people realize. Numerous places in this book refer to the importance of practicing musically in order to acquire technique. But you can't play musically if the hammer can't do its job, a critical point that is overlooked even by many tuners (often because they are afraid that the extra cost will drive customers away). For a grand piano, a sure sign of compacted hammers is that you find the need to close the lid at least partially in order to play soft passages. Another sure sign is that you tend to use the soft pedal to help you play softly. Compacted hammers either give you a loud sound or none at all. Each note tends to start with an annoying percussive bang that is too strong, and the sound is overly bright. It is these percussive bangs that are so damaging to the tuners' ear. A properly voiced piano enables control over the entire dynamic range and produces a more pleasing sound.

Let's first see how a compacted hammer can produce such extreme results. How do small, light hammers produce loud sounds by striking with relatively low force on strings under such high tension? If you were to try to push down on the string or try to pluck it, you will need quite a large force just to make a small sound. The answer lies in an incredible phenomenon that occurs when tightly stretched strings are struck at right angles to the string. It turns out that the force produced by the hammer at the instant of impact is theoretically infinite! This nearly infinite force is what enables the light hammer to overcome practically any achievable tension on the string and cause it to vibrate.

Here is the calculation for that force. Imagine that the hammer is at its highest point after striking the string (grand piano). The string at this point in time makes a triangle with its original horizontal position (this is just an idealized approximation, see below). The shortest leg of this triangle is the length between the agraffe and the impact point of the hammer. The second shortest leg is from the hammer to the bridge. The longest is the original horizontal configuration of the string, a straight line from bridge to agraffe. Now if we drop a vertical line from the hammer strike point down to the original string position, we get two right triangles back-to-back. These are two extremely skinny right triangles that have very small angles at the agraffe and at the bridge; we will call these small angles "theta"s.

The only thing we know at this time is the force of the hammer, but this is not the force that moves the string, because the hammer must overcome the string tension before the string will yield. That is, the string cannot move up unless it can elongate. This can be understood by considering the two right triangles described above. The string had the length of the long legs of the right triangles before the hammer struck, but after the strike, the string is the hypotenuse, which is longer. That is, if the string were absolutely inelastic and the ends of the string were rigidly fixed, no amount of hammer force will cause the string to move.

It is a simple matter to show, using vector diagrams, that the extra tension force F (in addition to the original string tension) produced by the hammer strike is given by f = Fsin(theta), where f is the force of the hammer. It does not matter which right triangle we use for this calculation (the one on the bridge side or on the agraffe side). Therefore, the string tension F = f/sin(theta). At the initial moment of the strike, theta = 0, and therefore F = infinity! This happens because sin(0) = 0. Of course, F can get to infinity only if the string cannot stretch and nothing else can move. What happens in reality is that as F increases towards infinity, something gives (the string stretches, the bridge moves, etc.) so that the hammer begins to move the string and theta increases from zero, making F finite.

This force multiplication explains why a small child can produce quite a loud sound on the piano in spite of the hundreds of pounds of tension on the strings. It also explains why an ordinary person can break a string just playing the piano, especially if the string is old and has lost its elasticity. The lack of elasticity causes the F to increase far more than if the string were more elastic, the string cannot stretch, and theta remains close to zero. This situation is greatly exacerbated if the hammer is also compacted so that there is a large, flat, hard groove that contacts the string. In that case, the hammer surface has no give and the instantaneous "f" in the above equation becomes very large. Since all this happens near theta = 0 for a compacted hammer, the force multiplication factor is also increased. The result is a broken string.

The above calculation is a gross over-simplification and is correct only qualitatively. In reality, a hammer strike initially throws out a traveling wave towards the bridge, similarly to what happens when you grab one end of a rope and flick it. The way to calculate such waveforms is to solve certain differential equations that are well known. The computer has made the solution of such differential equations a simple matter and realistic calculations of these waveforms can now be made routinely. Therefore, although the above results are not accurate, they give a qualitative understanding of what is happening, and what the important mechanisms and controlling factors are.

For example, the above calculation shows that it is not the transverse vibration energy of the string, but the tensile force on the string, that is responsible for the piano sound. The energy imparted by the hammer is stored in the entire piano, not just the strings. This is quite analogous to the bow and arrow -- when the string is pulled, all the energy is stored in the bow, not the string. And all of this energy is transferred via the tension in the string. In this example, the mechanical advantage and force multiplication calculated above (near theta = 0) is easy to see. It is the same principle on which the harp is based.

The easiest way to understand why compacted hammers produce higher harmonics is to realize that the impact occurs in a shorter time. When things happen faster, the string generates higher frequency components in response to the faster event.

The above paragraphs make it clear that a compacted hammer will produce a large initial impact on the string whereas a properly voiced hammer will be much gentler on the string thus imparting more of its energy to the lower frequencies than the harmonics. Because the same amount of energy is dissipated in a shorter amount of time for the compacted hammer, the instantaneous sound level can be much higher than for a properly voiced hammer, especially at the higher frequencies. Such short sound spikes can damage the ear without causing any pain. Common symptoms of such damage are tinnitus (ringing in the ear) and hearing loss at high frequencies. Piano tuners, when they must tune a piano with such worn hammers, would be wise to wear ear plugs. It is clear that voicing the hammer is at least as important as tuning the piano, especially because we are talking about potential ear damage. An out-of-tune piano with good hammers does not damage the ear. Yet many piano owners will have their pianos tuned but neglect the voicing.

The two most important procedures in voicing are hammer re-shaping and needling.

When the flattened strike point on the hammer exceeds about 1 cm, it is time to re-shape the hammer. Note that you have to distinguish between the string groove length and flattened area; even in hammers with good voicing, the grooves may be over 5 mm long. In the final analysis you will have to judge on the basis of the sound. Shaping is accomplished by shaving the "shoulders" of the hammer so that it regains its previous rounded shape at the strike point. It is usually performed using 1 inch wide strips of sandpaper attached to strips of wood or metal with glue or double sided tape. You might start with 80 grit garnet paper and finish it off with 150 grit garnet paper. The sanding motion must be in the plane of the hammer; never sand across the plane. There is almost never a need to sand off the strike point. Therefore, leave about 2 mm of the center of the strike point untouched.

Needling is not easy because the proper needling location and needling depth depend on the particular hammer (manufacturer) and how it was originally voiced. Especially in the treble, hammers are often voiced at the factory using hardeners such as lacquer, etc. Needling mistakes are generally irreversible. Deep needling is usually required on the shoulders just off the strike point. Very careful and shallow needling of the strike point area may be needed. The tone of the piano is extremely sensitive to shallow needling at the strike point, so that you must know exactly what you are doing. When properly needled, the hammer should allow you to control very soft sounds as well as produce loud sounds without harshness. You get the feeling of complete tonal control. You can now open your grand piano fully and play very softly without the soft pedal! You can also produce those loud, rich, authoritative tones.

b. Polishing the Capstans

Polishing the capstans can be a rewarding maintenance procedure. They may need polishing if they have not been cleaned in over 10 years, sometimes sooner. Press down on the keys slowly to see if you can feel a friction in the action. A frictionless action will feel like sliding an oily finger along a smooth glassware. When friction is present, it feels like the motion of a clean finger on squeaky clean glass. In order to be able to get to the capstans, you will need to lift the action off from the keys by unscrewing the screws that hold the action down for the grand. For uprights you generally need to unscrew the knobs that hold the action in place; make sure that the pedal rods, etc., are disengaged.

When the action is removed, the keys can be lifted out after removing the key stop rail. First make sure that all the keys are numbered so that you can replace them in the correct order. This is a good time to remove all the keys and clean any previously inaccessible areas as well as the sides of the keys. You can use a mild cleaning agent such as a cloth dampened with Windex for cleaning the sides of the keys.

See if the top, spherical contact areas of the capstans are tarnished. If they do not have a shiny polish, they are tarnished. Use any good brass/bronze/copper polish (such as Noxon) to polish and buff up the contact areas. Reassemble, and the action should now be much smoother.

Equal Temperament

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I present here the easiest, approximate, equal temperament scheme. More accurate algorithms can be found in the literature (Reblitz, Jorgensen). No self-respecting professional tuner would use this scheme; however, when you get good at it, you can produce a decent equal temperament. For the beginner, the more complete and precise schemes will not necessarily give better results. With the more complex methods, a beginner can quickly get confused without any idea of what he did wrong. With the method shown here, you can quickly develop the ability to find out what you did wrong.

Mute the side strings from G3 to C#5. Tune A4 to the A440 fork. Tune A3 to A4. Then tune up in contracted 5ths from A3 until you cannot go up any more without leaving the muted range, then tune one octave down, and repeat this up-in-5ths and down-one-octave procedure until you get to A4. For example, you will start with a contracted A3-E4, then a contracted E4-B4. The next 5th will take you above the highest muted note, C#4, so you tune one octave down, B4-B3. All octaves are, of course, just. The contracted 5ths should beat a little under 1 Hz at the bottom of the muted range and about 1.5 Hz near the top. The beat frequencies of the 5ths between these highest and lowest limits should increase smoothly with increasing pitch.

When going up in 5ths, you tune flat from just to create a contracted 5th. Therefore you can start from just and tune flat in order to increase the beat frequency to the desired value and set the pin correctly at the same time. If you had done everything perfectly, the last D4-A4 should be a contracted 5th with a beat frequency of 1 Hz without any tuning. Then, you are done. You have just done a "circle of 5ths". The miracle of the circle of 5ths is that it tunes every note once, without skipping any within the A3-A4 octave!

If the final D4-A4 is not correct, you made some errors somewhere. In that case, reverse the procedure, starting from A4, going down in contracted 5ths and up in octaves, until you reach A3, where the final A3-E4 should be a contracted 5th with a beat frequency slightly under 1 Hz. For going down in 5ths, you create a contracted 5th by tuning sharp from just. However, this tuning action will not set the pin. Therefore, in order to set the pin correctly, you must first go too sharp, and then decrease the beat frequency to the desired value. Therefore, going down in 5ths is a more difficult operation than going up in 5ths.

An alternative method is to start with A and tune to C by going up in 5ths, and checking this C with a tuning fork. If your C is too sharp, your 5ths were not sufficiently contracted, and vice versa. Another variation is to tune up in 5ths from A3 a little over half way, and then tune down from A4 to the last note that you tuned coming up.

Once the bearings are set, continue as described in the Kirnberger section above.

What is Stretch?

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Harmonic tuning is always associated with a phenomenon called stretch. Harmonics in piano strings are never exact because real strings attached to real ends do not behave like ideal mathematical strings. This property of inexact harmonics is called inharmonicity. The difference between the actual and theoretical harmonic frequencies is called stretch. Experimentally, it is found that most harmonics are sharp compared to their ideal theoretical values, although there can be a few that are flat.

According to one research result (Young, 1952), stretch is caused by inharmonicity due to the stiffness of strings. Ideal mathematical strings have zero stiffness. Stiffness is what is called an extrinsic property -- it depends on the dimensions of the wire. If this explanation is correct, then stretch must also be extrinsic. Given the same type of steel, the wire is stiffer if it is fatter or shorter. One consequence of this dependence on stiffness is an increase in the frequency with harmonic mode number; i.e., the wire appears stiffer to harmonics with shorter wavelengths. Stiffer wires vibrate faster because they have an extra restoring force, in addition to the string tension. This inharmonicity has been calculated to within several percent accuracy so that the theory appears to be sound, and this single mechanism appears to account for most of the observed stretch.

These calculations show that stretch is about 1.2 cents for the second mode of vibration at C4 and doubles about every 8 semitones at higher frequency (C4 = middle C, the first mode is the lowest, or fundamental frequency, one cent is one hundredth of a semitone, and there are 12 semitones in an octave). The stretch becomes smaller for lower notes, especially below C3, because the wire wound strings are quite flexible. Stretch increases rapidly with mode number and decreases even more rapidly with string length. In principle, stretch is smaller for larger pianos and larger for lower tension pianos if the same diameter strings are used. Stretch presents problems in scale design since abrupt changes in string type, diameter, length, etc., will produce a discontinuous change in stretch. Very high mode harmonics, if they happen to be unusually loud, present problems in tuning because of their large stretch -- tuning out their beats could throw the lower, more important, harmonics audibly out of tune.

Since larger pianos tend to have smaller stretch, but also tend to sound better, one might conclude that smaller stretch is better. However, the difference in stretch is generally small, and the tone quality of a piano is largely controlled by properties other than stretch.

In harmonic tuning you tune, for example, the fundamental or a harmonic of the upper note to a higher harmonic of the lower note. The resulting new note is not an exact multiple of the lower note, but is sharp by the amount of stretch. What is so interesting about stretch is that a scale with stretch produces "livelier" music than one without! This has caused some tuners to tune in double octaves instead of single octaves, which increases the stretch.

The amount of stretch is unique to each piano and, in fact, is unique to each note of each piano. Modern electronic tuning aids are sufficiently powerful to record the stretch for all the desired notes of individual pianos. Tuners with electronic tuning aids can also calculate an average stretch for each piano or stretch function and tune the piano accordingly. In fact, there are anecdotal accounts of pianists requesting stretch in excess of the natural stretch of the piano. In aural tuning, stretch is naturally, and accurately, taken into account. Therefore, although stretch is an important aspect of tuning, the tuner does not have to do anything special to include stretch, if all you want is the natural stretch of the piano.

Precision, Precision, Precision

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The name of the game in tuning is precision. All tuning procedures are arranged in such a way that you tune the first note to the tuning fork, the second to the first, etc., in sequence. Therefore, any errors will quickly add up. In fact, an error at one point will often make some succeeding steps impossible. This happens because you are listening for the smallest hint of beats and if the beats were not totally eliminated in one note, you can't use it to tune another as those beats will be clearly heard. In fact, for beginners, this will happen frequently before you learn how precise you need to be. When this happens, you will hear beats that you can't eliminate. In that case, go back to your reference note and see if you hear the same beat; if you do, there is the source of your problem -- fix it.

The best way to assure precision is by checking the tuning. Errors occur because every string is different and you are never sure that the beat you hear is the one you are looking for, especially for the beginner. Another factor is that you need to count beats per second (bps), and your idea of, say 2bps, will be different on different days or at different times of the same day until you have those "beat speeds" well memorized. Because of the critical importance of precision, it pays to check each tuned note. This is especially true when "setting the bearings" which is explained below. Unfortunately, it is just as difficult to check as it is to tune correctly; that is, a person who cannot tune sufficiently accurately is usually unable to perform a meaningful check. In addition, if the tuning is sufficiently off, the checking doesn't work. Therefore, I have provided methods of tuning below that use a minimum of checks. The resulting tuning will not be very good initially, for equal temperament. The Kirnberger temperament (see below) is easier to tune accurately. On the other hand, beginners can't produce good tunings anyway, no matter what methods they use. At least, the procedures presented below will provide a tuning which should not be a disaster and which will improve as your skills improve. In fact, the procedure described here is probably the fastest way to learn. After you have improved sufficiently, you can then investigate the checking procedures, such as those given in Reblitz, or "Tuning" by Jorgensen.

Harmonic Tuning

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Once you are satisfied with your ability to tune unisons, start practicing tuning octaves. Take any octave near middle C and mute out the upper two side strings of each note by inserting a wedge between them. Tune the upper note to the one an octave below, and vice versa. As with unisons, start near middle C, then work up to the highest treble, and then practice in the bass. Repeat the same practice with 5ths, 4ths, and major 3rds.

After you can tune perfect harmonics, try de-tuning to see if you can hear the increasing beat frequency as you deviate very slightly from perfect tune. Try to identify various beat frequencies, especially 1bps (beat per second) and 10bps, using 5ths. These skills will come in handy later.

Rumblings in the Bass

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The lowest bass strings are second in difficulty (to the highest notes) to tune. These strings produce sound composed mostly of higher harmonics. Near the tuning point, the beats are so slow and soft that they are difficult to hear. Sometimes, you can "hear" them better by pressing your knee against the piano to feel for the vibrations than by trying to hear them with your ears, especially in the single string section. You can practice unison tuning only down to the last double string section. See if you can recognize the high pitched, metallic, ringing beats that are prevalent in this region. Try eliminating these and see if you need to de-tune slightly in order to eliminate them. If you can hear these high, ringing, beats, it means that you are well on your way. Don't worry if you can't even recognize them at first-- beginners are not expected to.

Rocking It in the Treble

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The most difficult notes to tune are the highest ones. Here you need incredible accuracy in moving the strings and the beats are difficult to hear. Beginners can easily lose their bearing and have a hard time finding their way back. One advantage of the need for such small motions is that now, you can use the pin-rocking motion to tune. Since the motion is so small, rocking the pin does not damage the pinblock. To rock the pin, place the lever parallel to the strings and pointing towards the strings (away from you). To tune sharp, pull up on the lever, and to tune flat, press down. First, make sure that the tuning point is close to the center of the rocking motion. If it is not, rotate the pin so that it is. Since this rotation is much larger than that needed for the final tuning, it is not difficult, but remember to correctly set the pin. It is better if the tuning point is front of center (towards the string), but bringing it too far forward would risk damaging the pinblock when you try to tune flat. Note that tuning sharp is not as damaging to the pinblock as tuning flat because the pin is already jammed up against the front of the hole.

Equalizing String Tension

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Pounding is also helpful for distributing the string tension more evenly among all the non-speaking sections of the string, such as the duplex scale section, but especially in the section between the capo bar and the agraffe. There is controversy as to whether equalizing the tension will improve the sound. There is little question that the even tension will make the tuning more stable. However, whether it makes a material difference in stability may be debatable, especially if the pins were correctly set during tuning. In many pianos, the duplex sections are almost completely muted out using felts because they might cause undesirable oscillations. In fact, the over-strung section is muted out in almost every piano. Beginners need not worry about the tension in these "non-speaking" sections of the strings. Thus heavy pounding, though a useful skill to learn, is not necessary for a beginner.

My personal opinion is that the sound from the duplex scale strings does not add to the piano sound. In fact, this sound is inaudible and is muted out when they become audible in the bass. Thus the “art of tuning the duplex scale” is a myth although most piano tuners (including Reblitz!) have been taught to believe it by the manufacturers, because it makes for a good sales pitch. The only reason why you want to tune the duplex scale is that the bridge wants to be at a node of both the speaking and non-speaking lengths; otherwise, tuning becomes difficult, sustain may be shortened, and you lose uniformity. Using mechanical engineering terminology, we can say that tuning the duplex scale optimizes the vibrational impedance of the bridge. In other words, the myth does not detract from the tuners’ ability to do their job. Nonetheless, a proper understanding is certainly preferable. The duplex scale is needed to allow the bridge to move more freely, not for producing sound. Obviously, the duplex scale will improve the quality of the sound (from the speaking lengths) because it optimizes the impedance of the bridge, but not because it produces any sound. The facts that the duplex scale is muted out in the bass and is totally inaudible in the treble prove that the sound from the duplex scale is not needed. Even in the inaudible treble, the duplex scale is “tuned” in the sense that the aliquot bar is placed at a location such that the length of the duplex part of the string is a harmonic length of the speaking section of the string in order to optimize the impedance (“aliquot” means fractional or harmonic). If the sound from the duplex scale were audible, the duplex scale would have to be tuned as carefully as the speaking length. However, for impedance matching, the tuning need only be approximate, which is what is done in practice. Some manufacturers have stretched this duplex scale myth to ridiculous lengths by claiming a second duplex scale on the pin side. Since the hammer can only transmit tensile strain to this length of string (because of the rigid Capo bar), this part of the string cannot vibrate to produce sound. Consequently, practically no manufacturer specifies that the non-speaking lengths on the pin side be tuned.

Making that Final Infinitesimal Motion

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We now advance to the next level of difficulty. Find a note near G5 that is slightly out of tune, and repeat the above procedure for G3. The tuning motions are now much smaller for these higher notes, making them more difficult. In fact you may not be able to achieve sufficient accuracy by rotating the pin. We need to learn a new skill. This skill requires you to pound on the notes, so put on your ear muffs or ear plugs.

Typically, you would get through motion (4) successfully, but for motion (5) the pin would either not move or jump past the tuning point. In order to make the string advance in smaller increments, press on the lever at a pressure slightly below the point at which the pin will jump. Now strike hard on the note while maintaining the same pressure on the lever. The added string tension from the hard hammer blow will advance the string by a small amount. Repeat this until it is in perfect tune. It is important to never release the pressure on the lever and to keep the pressure constant during these repeated small advances, or you will quickly lose track of where you are. When it is in perfect tune, and you release the lever, the pin might spring back, leaving the string slightly flat. You will have to learn from experience, how much it will spring back and compensate for it during the tuning process.

The need to pound on the string to advance it is one reason you often hear tuners pounding on the piano. It is a good idea to get into the habit of pounding on most of the notes because this stabilizes the tuning. The resulting sound can be so loud as to damage the ear, and one of the occupational hazards of tuners is ear damage from pounding. Use of ear plugs is the solution. When pounding, you will still easily hear the beats even with ear plugs. The most common initial symptom of ear damage is tinnitus (ringing in the ear). You can minimize the pounding force by increasing the pressure on the lever. Also, less pounding is required if the lever is parallel to the string instead of perpendicular to it, and even less if you point it to the left. This is another reason why many tuners use their levers more parallel to the strings than perpendicular. Note that there are two ways to point it parallel: towards the strings (12 o'clock) and away from the strings (6 o'clock). As you gain experience, experiment with different lever positions as this will give you many options for solving various problems. For example, with the most popular 5-degree head on your lever, you may not be able to point the lever handle to the right for the highest octave because it may hit the wooden piano frame.

Sympathetic Vibrations

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The accuracy required to bring two strings into perfect tune is so high that it is a nearly impossible job. It turns out that, in practice, this is made easier because when the frequencies approach within a certain interval called the "sympathetic vibration range", the two strings change their frequencies towards each other so that they vibrate with the same frequency. This happens because the two strings are not independent, but are coupled to each other at the bridge. When coupled, the string vibrating at the higher frequency will drive the slower string to vibrate at a slightly higher frequency, and vice versa. The net effect is to drive both frequencies towards the average frequency of the two. Thus when you tune 1 and 2 unison, you have no idea whether they are in perfect tune or merely within the sympathetic vibration range (unless you are an experienced tuner). In the beginning, you will most likely not be in perfect tune.

Now if you were to try to tune a third string to the two strings in sympathetic vibration, the third string will bring the string closest to it in frequency into sympathetic vibration. But the other string may be too far off in frequency. It will break off the sympathetic vibration, and will sound dissonant. The result is that no matter where you are, you will always hear beats -- the tuning point disappears! It might appear that if the third string were tuned to the average frequency of the two strings in sympathetic vibration, all three should go into sympathetic vibration. This does not appear to be the case unless all three frequencies are in perfect tune. If the first two strings are sufficiently off, a complex transfer of energy takes place among the three strings. Even when the first two are close, there will be higher harmonics that will prevent all beats from disappearing when a third string is introduced. In addition, there are frequent cases in which you cannot totally eliminate all beats because the two strings are not identical. Therefore, a beginner will become totally lost, if he were to try to tune a third string to a pair of strings. Until you become proficient at detecting the sympathetic vibration range, always tune one string to one; never one to two. In addition, just because you tuned 1 to 2 and 3 to 2, it does not mean that the three strings will sound "clean" together. Always check; if it is not completely "clean", you will need to find the offending string and try again.

Note the use of the term "clean". With enough practice, you will soon get away from listening to beats, but instead, you will be looking for a pure sound that results somewhere within the sympathetic vibration range. This point will depend on what types of harmonics each string produces. In principle, when tuning unisons, you are trying to match the fundamentals. In practice, a slight error in the fundamentals is inaudible compared to the same error in a high harmonic. Unfortunately, these high harmonics are generally not exact harmonics but vary from string to string. Thus, when the fundamentals are matched, these high harmonics create high frequency beats that make the note "muddy" or "tinny". When the fundamentals are de-tuned ever so slightly so that the harmonics do not beat, the note "cleans up". Reality is even more complicated because some strings, especially for the lower quality pianos, will have extraneous resonances of their own, making it impossible to completely eliminate certain beats. These beats become very troublesome if you need to use this note to tune another one.

Tuning Unisons

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Now engage the tuning lever on the pin for string 1. We will tune string 1 to string 2. The motion you will practice is: (1) flat, (2) sharp, (3) flat, (4) sharp and (5) flat (tune). Except for (1), each motion must be smaller than the previous one. As you improve, you will add or eliminate steps as you see fit. We are assuming that the two strings are almost in tune. As you tune, you must follow two rules: (a) never turn the pin unless you are simultaneously listening to the sound, and (b) never release the pressure on the tuning lever handle until that motion is complete.

For example, let's start with motion (1) flat: keep playing the note every second or two with the LH, so that there is a continuous sound, while pushing the end of the lever handle away from you with the thumb and 2nd finger. Play the note in such a way as to maintain a continuous sound. Don't lift the key for any length of time, as this will stop the sound. Keep the key down and play with a quick up-and-down motion so that there is no break in the sound. The pinky and the rest of your RH should be braced against the piano. The required motion of the lever is just a few millimeters. First, you will feel an increasing resistance, and then the pin will start to rotate. Before the pin begins to rotate, you should hear a change in the sound. As you turn the pin, listen for string 1 going flat, creating a beat with the center string; the beat frequency increasing as you turn. Stop at a beat frequency of 2 to 3 per second. The tip of the tuning lever should move less than one cm. Remember, never rotate the pin when there is no sound because you will immediately lose track of where you are with respect to how the beats are changing. Always maintain constant pressure on the lever until that motion is completed for the same reason.

What is the rationale behind the above 5 motions? Assuming that the two strings are in reasonable tune, you first tune string 1 flat in step (1) to make sure that in step (2) you will pass the tuning point. This also protects against the possibility that you had placed the lever on the wrong tuning pin; as long as you are turning flat, you will never break a string.

After (1) you are flat for sure, so in step (2) you can listen to the tuning point as you pass through it. Go past it until you hear a beat frequency of about 2 to 3 per second on the sharp side, and stop. Now you know where the tuning point is, and what it sounds like. The reason for going so far past the tuning point is that you want to set the pin, as explained above.

Now go back flat again, step (3), but this time, stop just past the tuning point, as soon as you can hear any incipient beats. The reason why you don't want to go too far past the tuning point is that you don't want to undo the "setting of the pin" in step (2). Again, note exactly what the tuning point sounds like. It should sound perfectly clean and pure. This step assures that you did not set the pin too far.

Now conduct the final tuning by going sharp (step 4), by as little as you can beyond perfect tune, and then bringing it into tune by turning flat (step 5). Note that your final motion must always be flat in order to set the pin. Once you become good, you might be able to do the whole thing in two motions (sharp, flat), or three (flat, sharp, flat).

Ideally, from step (1) to final tune, you should maintain the sound with no stoppage, and you should always be exerting pressure on the handle; never letting go of the lever. Initially, you will probably have to do this motion by motion. When you become proficient, the whole operation will take just a few seconds. But at first, it will take a lot longer. Until you develop your "tuning muscles" you will tire quickly and may have to stop from time to time to recover. Not only the hand/arm muscles, but the mental and ear concentration required to focus on the beats can be quite a strain and can quickly cause fatigue. You will need to develop "tuning stamina" gradually. Most people do better by listening through one ear than through both, so turn your head to see which ear is better.

The most common mistake beginners make at this stage is to try to listen for beats by pausing the tuning motion. Beats are difficult to hear when nothing is changing. If the pin is not being turned, it is difficult to decide which of the many things you are hearing is the beat that you need to concentrate on. What tuners do is to keep moving the lever and then listening to the changes in the beats. When the beats are changing, it is easier to identify the particular beat that you are using for tuning that string. Therefore, slowing down the tuning motion doesn't make it easier. Thus the beginner is between a rock and a hard place. Turning the pin too quickly will result in all hell breaking loose and losing track of where you are. On the other hand, turning too slowly will make it difficult to identify the beats. Therefore work on determining the range of motion you need to get the beats and the right speed with which you can steadily turn the pin to make the beats come and go. In case you get hopelessly lost, mute strings 2 and 3 by placing a wedge between them, play the note and see if you can find another note on the piano that comes close. If that note is lower than G3, then you need to tune it sharp to bring it back, and vice versa.

Now that you have tuned string 1 to string 2, reposition the wedge so that you mute 1, leaving 2 and 3 free to vibrate. Tune 3 to 2. When you are satisfied, remove the wedge and see if the G is now free of beats. You have tuned one note! If the G was in reasonable tune before you started, you haven't accomplished much, so find a note nearby that is out of tune and see if you can "clean it up". Notice that in this scheme, you are always tuning one single string to another single string. In principle, if you are really good, strings 1 and 2 are in perfect tune after you finish tuning 1, so you don't need the wedge any more. You should be able to tune 3 to 1 and 2 vibrating together. In practice this doesn't work until you become really proficient. This is because of a phenomenon called sympathetic vibration.

Setting the Pin

2006-02-24T09:43:00.000-08:00

It is important to "set the pin" correctly in order for the tuning to hold. If you look down on the pin, the string comes around the right side of the pin (grands -- it is on the left for uprights) and twirls around it. Therefore if you rotate the pin cw (clockwise), you will tune sharp and vice versa. The string tension is always trying to rotate the pin ccw (counter clock-wise, or flat). Normally, a piano de-tunes flat as you play it. However, because the grip of the pinblock on the pin is so strong, the pin is never straight but is always twisted.

If you rotate it cw and stop, the top of the pin will be twisted cw with respect to the bottom. In this position, the top of the pin wants to rotate ccw (the pin wants to untwist) but can't because it is held by the pinblock. Remember that the string is also trying to rotate it ccw. The two forces together can be sufficient to quickly de-tune the piano flat when you play something loud.

If the pin is turned ccw, the opposite happens -- the pin will want to untwist cw, which opposes the string force. This reduces the net torque on the pin, making the tuning more stable. In fact, you can twist the pin so far ccw that the untwisting force is much larger than the string force and the piano can then de-tune itself sharp as you play. Clearly, you must properly "set the pin" in order produce a stable tuning. This requirement will be taken into account in the following tuning instructions.

Engaging and Manipulating the Tuning Lever

2006-02-24T09:42:00.000-08:00

If your tuning lever has adjustable length, pull it out about 3 inches and lock it in place. Hold the handle of the tuning lever in your RH and the socket in your LH and engage the socket over the pin. Orient the handle so that it is approximately perpendicular to the strings and pointing to your right. Lightly jiggle the handle around the pin with your RH and engage the socket with your LH so that the socket is securely engaged, as far down as it will go. From day one, develop a habit of jiggling the socket so that it is securely engaged. At this point, the handle is probably not perfectly perpendicular to the strings; just choose the socket position so that the handle is as close to perpendicular as the socket position will allow. Now find a way to brace your RH so that you can apply firm pressure on the lever. For example, you can grab the tip of the handle with the thumb and one or two fingers, and brace the arm on the wooden piano frame or brace your pinky against the tuning pins directly under the handle. If the handle is closer to the plate (the metal frame) over the strings, you might brace your hand against the plate. You should not grab the handle like you hold a tennis racket and push-pull to turn the pin -- this will not give enough control. You may be able to do that after years of practice, but in the beginning, grabbing the handle and pushing without bracing against something is too difficult to control accurately. So develop a habit of finding good places to brace your hand against, depending on where the handle is. Practice these positions making sure that you can exert controlled, constant, powerful pressure on the handle, but do not turn any pins yet.

The lever handle must point to the right so that when you turn it towards you (the string goes sharp), you counteract the force of the string and free the pin from the front side of the hole (towards the string). This allows the pin to turn more freely because of the reduction in friction. When you tune flat, both you and the string are trying to turn the pin in the same direction. Then the pin would turn too easily, except for the fact that both your push and the string's pull jam the pin against the front of the hole, increasing the pressure (friction) and preventing the pin from rotating too easily. If you had placed the handle to the left, you run into trouble for both the sharp and flat motions. For the sharp motion, both you and the string jam the pin against the front of the hole, making it doubly difficult to turn the pin, and damaging the hole. For the flat motion, the lever tends to lift the pin off from the front edge of the hole and reduces the friction. In addition, both the lever and string are turning the pin in the same direction. Now the pin now turns too easily. The lever handle must point to the left for uprights. Looking down on the tuning pin, the lever should point to 3 o'clock for grands and to 9 o'clock for uprights. In both cases, the lever is on the side of the last winding of the string.

Professional tuners do not use these lever positions. Most use 1-2 o'clock for grands and 10-11 o'clock for uprights and Reblitz recommends 6 o'clock for grands and 12 o'clock for uprights. In order to understand why, let's first consider positioning the lever at 12 o'clock on a grand (it is similar at 6 o'clock). Now the friction of the pin with the pinblock is the same for both the sharp and flat motions. However, in the sharp motion, you are going against the string tension and in the flat motion, the string is helping you. Therefore, the difference in force needed between sharp and flat motions is much larger than the difference when the lever is at 3 o'clock, which is a disadvantage. However, unlike the 3 o'clock position, the pin does not rock back and forth during tuning so that when you release the pressure on the tuning lever, the pin does not spring back -- it is more stable -- and you can get higher accuracy.

The 1-2 o'clock position is a good compromise that makes use of both of the advantages of the 3 o'clock and 12 o'clock positions. Beginners do not have the accuracy to take full advantage of the 1-2 o'clock position, so my suggestion is to start with the 3 o'clock position, which should be easier at first, and transition to the 1-2 o'clock position as your accuracy increases. When you become good, the higher accuracy of the 1-2 o'clock position can speed up your tuning so that you can tune each string in just a few seconds. At the 3 o'clock position, you will need to guess how much the pin will spring back and over-tune by that amount, which takes more time. Clearly, exactly where you place the lever will become more important as you improve.

Pythagorean, Equal, Meantone, and “Well” Temperaments

2006-02-24T09:37:00.001-08:00

Historical developments are central to discussions of temperament because the music of the time is tied to the temperament of the time. Pythagoras is credited with inventing the Pythagorean Temperament at around 550 BC, in which the chromatic scale is generated by tuning in perfect 5ths, using the circle of 5ths. The twelve perfect fifths in the circle of fifths do not make an exact factor of two. Therefore, the final note you get is not exactly the octave note but is too high in frequency by what is called the "Pythagorean comma", which is about 23 cents (a cent is one hundredths of a semitone). Since a 4th plus a 5th make up an octave, the Pythagorean temperament results in a scale with perfect 4ths and 5ths, except at the end where you get a very bad dissonance. It turns out that tuning in perfect 5ths leaves the 3rds in bad shape. This is another disadvantage of the Pythagorean temperament. Now if we were to tune by contracting each 5th by 23/12 cents, we would end up with exactly one octave and that is one way of tuning an Equal Temperament (ET) scale. In fact, we shall use just such a method in the section on tuning. The ET scale was already known within a hundred years or so after invention of the Pythagorean temperament. Thus ET is not a "modern temperament".

Following the introduction of the Pythagorean temperament, all newer temperaments were efforts at improving on it. The first method was to halve the Pythagorean comma by distributing it among two final 5ths. One major development was Meantone Temperament, in which the 3rds were made just instead of the 5ths. Musically, 3rds play more prominent roles than 5ths, so that meantone made sense, especially during an age when music made greater use of 3rds. Unfortunately, meantone has a wolf worse than Pythagorean.

The next milestone is represented by Bach's Well Tempered Clavier in which he wrote music for various Well Temperaments (WT). These were temperaments that struck a compromise between meantone and Pythagorean. This concept worked because Pythagorean tuning ended up with notes that were too sharp, while meantone is too flat. In addition, WT presented the possibility of not only good 3rds, but also good 5ths. The simplest WT was devised by Kirnberger, a student of Bach. Its biggest advantage is its simplicity. Better WTs were devised by Werkmeister and by Young. If we broadly classify tunings as Meantone, WT, or Pythagorean, then ET is a WT because ET is neither sharp nor flat. There is no record of the temperaments Bach used. We can only guess at the temperaments from the harmonies in his compositions, especially his “Well Tempered Clavier”, and these studies indicate that essentially all the details of tempering were already worked out by Bach’s time (before 1700) and that Bach used a temperament not very different from Werkmeister.

The violin takes advantage of its unique design to circumvent these temperament problems. The open strings make intervals of a 5th with each other, so that the violin naturally tunes Pythagorean. Since the 3rds can always be fingered just (meaning exact), it has all the advantages of the Pythagorean, meantone, and WT, with no wolf in sight! In addition, it has a complete set of frequencies (infinite) within its frequency range. Little wonder that the violin is held in such high esteem by musicians.

In the last 100 years or so, ET had been almost universally accepted because of its musical freedom and the trend towards increasing dissonance. Piano tuners liked it because it can hide minor changes in tuning that can occur just a few days after tuning. All the other temperaments are generically classified as "historical temperaments", which is clearly a misnomer. The historical use of WT gave rise to the concept of key color in which each key, depending on the temperament, endowed specific colors to the music, mainly through the small de-tunings that create "tension" and other effects. This greatly complicated issues because now musicians were dealing not only with pure chords versus wolves, but with colors that were not easily defined. The extent to which the colors can be brought out depends on the piano, the pianist, the listener, and the tuner. Note that the tuner can blend stretch (see "What is stretch?" near the end of section 5) with temperament to control color. After listening to music played on pianos tuned to WT, ET tends to sound more muddy and bland. Thus key color does matter. More important are the wonderful sounds of pure (stretched) intervals in WT. On the other hand, there is always some kind of a wolf in the WTs which is reduced in ET.

For playing most of the music composed around the times of Bach, Mozart, and Beethoven, WT works best. As an example, Beethoven chose chords for the dissonant ninths in the first movement of his Moonlight Sonata that are least dissonant in WT, and are much worse in ET. These great composers were acutely aware of temperament. Most works from Chopin's and Liszt's time were composed with ET in mind and key color is not an issue. Although these compositions sound different in ET and WT to the trained ear, it is not clear that WT is objectionable (for Chopin, etc.) because pure intervals always sound better than detuned ones. The conclusion is that Bach was right: WT should be used for everything, although some musicians might complain that Chopin sounds too bright in WT.

My personal view for the piano is that we should get away from ET because it deprives us of one of the most enjoyable aspects of music -- pure intervals, that was the motivation for creating the chromatic scale. You will see a dramatic demonstration of this if you listen to the last movement of Beethoven's Waldstein played in ET and WT. Meantone can be somewhat extreme unless you are playing music of that period (before Bach), so that we are left with the WTs. For simplicity and ease of tuning, you cannot beat Kirnberger. I believe that once you get used to WT, ET will not sound as good even for Chopin, once you get used to it. Therefore, the world should standardize to the WTs. Which one you choose (Kirnberger, Werckmeister, Valloti, Young) does not make a big difference for most people because those not educated in the temperaments will generally not notice a big difference even among the major temperaments, let alone among the different WTs. This is not to say that we should all use Kirnberger but that we should be educated in the temperaments and have a choice instead of being straight-jacketed into the bland ET. This is not just a matter of taste or even whether the music sounds better. We are talking about developing our musical sensitivity and knowing how to use those really pure intervals.

The biggest disadvantage of WT is that if the piano is out of tune by even a small amount, the dissonance becomes audible, whereas it is much less audible in ET. In fact, most acoustic pianos today will require more frequent tunings if tuned to WT. Therefore, WT will become more practical when the self-tuning pianos become available. There are no such problems with the electronic pianos, and in addition, you can change temperament with the flick of a switch. Another problem with WT is that transposition can change the key color. Of course, WT does not produce all pure intervals – every WT is a compromise just as ET is a compromise.

I believe that these WT drawbacks are minor compared to the advantages; I would be happy if all piano students developed their sensitivity to the point at which they can notice that a piano is very slightly out of tune. And music teachers should be even happier if their students start arguing about which WT is the best. It is about time we listened to Bach, who knew all about ET, but has been trying to tell us to use WT for the last 200 years.

Temperament, Music, and the Circle of Fifths

2006-02-24T09:37:00.000-08:00

The above mathematical approach is not the way in which the chromatic scale was historically developed. Musicians first started with chords and tried to find a music scale with the minimum number of notes that would produce those chords. The requirement of a minimum number of notes is obviously desirable since it determines the number of keys, strings, holes, etc. needed to construct a musical instrument. Chords are necessary because if you want to play more than one note at a time, these notes will create dissonances that are unpleasant to the ear unless they form harmonious chords. The reason why dissonances are so unpleasant to the ear may have something to do with the difficulty of processing dissonant information through the brain. It is certainly easier, in terms of memory and comprehension, to deal with harmonious chords than dissonances. Some dissonances are nearly impossible for most brains to figure out if two dissonant notes are played simultaneously. Therefore, if the brain is overloaded with the task of trying to figure out complex dissonances, it becomes impossible to relax and enjoy the music, or follow the musical idea. Clearly, any scale must produce good chords if we are to compose advanced, complex music requiring more than one note at a time.

We saw above that the optimum number of notes in a scale turned out to be 12. Unfortunately, there isn’t any 12-note scale that can produce exact chords everywhere. Music would sound better if a scale with perfect chords everywhere could be found. Many such attempts have been made, mainly by increasing the number of notes per octave, especially using guitars and organs, but none of these scales have gained acceptance. It is relatively easy to increase the number of notes per octave with a guitar-like instrument because all you need to do is to add strings and frets. The latest schemes being devised today involve computer generated scales in which the computer adjusts the frequencies with every transposition; this scheme is called adaptive tuning (Sethares).

The most basic concept needed to understand temperaments is the concept of the circle of fifths. To describe a circle of 5ths, take any octave. Start with the lowest note and go up in 5ths. After two 5ths, you will go outside of this octave. When this happens, go down one octave so that you can keep going up in 5ths and still stay within the original octave. Do this for twelve 5ths, and you will end up at the highest note of the octave! That is, if you start at C4, you will end up with C5 and this is why it is called a circle. Not only that, but every note you hit when playing the 5ths is a different note. This means that the circle of 5ths hits every note once and only once, a key property useful for tuning the scale and for studying it mathematically.

Mathematics of the Chromatic Scale and Chords

2006-02-24T09:32:00.000-08:00

Three octaves of the chromatic scale are shown in Table 2.2a using the A, B, C, . . . notation. Black keys on the piano are shown as sharps, e.g. the # on the right of C represents C#, etc., and are shown only for the highest octave. Each successive frequency change in the chromatic scale is called a semitone and an octave has 12 semitones. The major chords and the integers representing the frequency ratios for those chords are shown above and below the chromatic scale, respectively. The word chord is used here to mean two notes whose frequency ratio is a small integer. Except for multiples of these basic chords, integers larger than about 10 produce chords not readily recognizable to the ear. In reference to Table 2.2a, the most fundamental chord is the octave, in which the frequency of the higher note is twice that of the lower one. The interval between C and G is called a 5th, and the frequencies of C and G are in the ratio of 2 to 3. The major third has four semitones and the minor third has three. The number associated with each chord, e.g. four in the 4th, is the number of white keys, inclusive of the two end keys for the C-major scale, and has no further mathematical significance. Note that the word "scale" in "chromatic scale", "C-major scale", and "logarithmic or frequency scale" (see below) has different meanings; the second is a subset of the first.

TABLE 2.2a: Frequency Ratios of Chords in the Chromatic Scale

|--Octave--
CDEFGAB
1

|--5th--
C D E F
2

|--4th--
G A B
3

|-Maj.3rd-
C # D #
4

|-Min.3rd-
E F #
5

|
G # A # B
6

|
C
8

We can see from the above that a 4th and a 5th "add up" to an octave and a major 3rd and a minor 3rd "add up" to a 5th. Note that this is an addition in logarithmic space, as explained below. The missing integer 7 is also explained below.

The "equal tempered" (ET) chromatic scale consists of "equal" half-tone or semitone rises for each successive note. They are equal in the sense that the ratio of the frequencies of any two adjacent notes is always the same. This property ensures that each note is the same as any other note (except for pitch). This uniformity of the notes allows the composer or performer to use any key without hitting bad dissonances, as further explained below. There are 12 equal semitones in an octave of an ET scale and each octave is an exact factor of two in frequency. Therefore, the frequency change for each semitone is given by

semitone¹² = 2 or
semitone = 2^1/12 = 1.05946. . . . . . . . . . . . . . . . . . Eq. (2.1)

Eq. (2.1) defines the ET chromatic scale and allows the calculation of the frequency ratios of "chords" in this scale. How do the "chords" in ET compare with the frequency ratios of the ideal chords? The comparisons are shown in Table 2.2b and demonstrate that the chords from the ET scale are extremely close to the ideal chords.

TABLE 2.2b: Ideal Chords versus the Equal Tempered Scale

Chord	Freq. Ratio	Eq. Tempered Scale	Difference
Min.3rd:	6/5 = 1.2000	semitone³ = 1.1892	+0.0108
Maj.3rd:	5/4 = 1.2500	semitone⁴ = 1.2599	-0.0099
Fourth:	4/3 = 1.3333	semitone⁵ = 1.3348	-0.0015
Fifth:	3/2 = 1.5000	semitone⁷ = 1.4983	+0.0017
Octave:	2/1 = 2.0000	semitone¹² = 2.0000	0.0000

The errors for the 3rds are the worst, over five times the errors in the other chords, but are still only about 1%. Nonetheless, these errors are readily audible, and some piano aficionados have generously dubbed them "the rolling thirds" while in reality, they are unacceptable dissonances. It is a defect that we must learn to live with, if we are to adopt the ET scale. The errors in the 4ths and 5ths produce beats of about 1 Hz near middle C, which is barely audible in most pieces of music; however, this beat frequency doubles for every higher octave.

The integer 7, if it were included in Table 2.2a, would have represented a chord with the ratio 7/6 and would correspond to a semitone squared. The error between 7/6 and a semitone squared is over 4% and is too large to make a musically acceptable chord and was therefore excluded from Table 2.2a. It is just a mathematical accident that the 12-note chromatic scale produces so many ratios close to the ideal chords. Only the number 7, out of the smallest 8 integers, results in a totally unacceptable chord. The chromatic scale is based on a lucky mathematical accident in nature! It is constructed by using the smallest number of notes that gives the maximum number of chords. No wonder early civilizations believed that there was something mystical about this scale. Increasing the number of keys in an octave does not result in much improvement of the chords until the numbers become quite large, making that approach impractical for most musical instruments.

Note that the frequency ratios of the 4th and 5th do not add up to that of the octave (1.5000 + 1.3333 = 2.8333 vs 2.0000). Instead, they add up in logarithmic space because (3/2)x(4/3) = 2. In logarithmic space, multiplication becomes addition. Why might this be significant? The answer is because the geometry of the cochlea of the ear seems to have a logarithmic component. Detecting acoustic frequencies on a logarithmic scale accomplishes two things: you can hear a wider frequency range for a given size of cochlea, and analyzing ratios of frequencies becomes simple because instead of dividing or multiplying two frequencies, you only need to subtract or add their logarithms. For example, if C3 is detected by the cochlea at one position and C4 at another position 2mm away, then C5 will be detected at a distance of 4 mm, exactly as in the slide rule calculator. To show you how useful this is, given F5, the brain knows that F4 will be found 2mm back! Therefore, chords (remember, chords are frequency divisions) are particularly simple to analyze in a logarithmically constructed cochlea. When we play chords, we are performing mathematical operations in logarithmic space on a mechanical computer called the piano, as was done in the 1950's with the slide rule. Thus the logarithmic nature of the chromatic scale has many more consequences than just providing a wider frequency range. The logarithmic scale assures that the two notes of every chord are separated by the same distance no matter where you are on the piano. By adopting a logarithmic chromatic scale, the piano keyboard is mathematically matched to the human ear in a mechanical way! This is probably one reason for why harmonies are pleasant to the ear - harmonies are most easily deciphered and remembered by the human hearing mechanism.

Suppose that we did not know Eq. 2.1; can we generate the ET chromatic scale from the chord relationships? If the answer is yes, a piano tuner can tune a piano without having to make any calculations. These chord relationships, it turns out, completely determine the frequencies of all the notes of the 12 note chromatic scale. A temperament is a set of chord relationships that provides this determination. From a musical point of view, there is no single "chromatic scale" that is best above all else although ET has the unique property that it allows free transpositions. Needless to say, ET is not the only musically useful temperament, and we will discuss other temperaments below. Temperament is not an option but a necessity; we must choose a temperament in order to accommodate these mathematical difficulties. No musical instrument based on the chromatic scale is completely free of temperament. For example, the holes in wind instruments and the frets of the guitar must be spaced for a specific tempered scale. The violin is a devilishly clever instrument because it avoids all temperament problems by spacing the open strings in fifths. If you tune the A(440) string correctly and tune all the others in 5ths, these others will be close, but not tempered. You can still avoid temperament problems by fingering all notes except one (usually A-440). In addition, the vibrato is larger than the temperament corrections, making temperament differences inaudible.

The requirement of tempering arises because a chromatic scale tuned to one scale (e.g., C-major with perfect chords) does not produce acceptable chords in other scales. If you wrote a composition in C-major having many perfect chords and then transposed it, terrible dissonances can result. There is an even more fundamental problem. Perfect chords in one scale also produce dissonances in other scales needed in the same piece of music. Tempering schemes were therefore devised to minimize these dissonances by minimizing the de-tuning from perfect chords in the most important chords and shifting most of the dissonances into the less used chords. The dissonance associated with the worst chord came to be known as “the wolf”.

The main problem is, of course, chord purity; the above discussion makes it clear that no matter what you do, there is going to be a dissonance somewhere. It might come as a shock to some that the piano is a fundamentally imperfect instrument! We are left to deal forever with some compromised chords in almost every scale.

The name "chromatic scale" generally applies to any 12-note scale with any temperament. Naturally, the chromatic scale of the piano does not allow the use of frequencies between the notes (as you can with the violin), so that there is an infinite number of missing notes. In this sense, the chromatic scale is incomplete. Nonetheless, the 12-note scale is sufficiently complete for the majority of musical applications. The situation is analogous to digital photography. When the resolution is sufficient, you cannot see the difference between a digital photo and an analog one with much higher information density. Similarly, the 12-note scale apparently has sufficient pitch resolution for a sufficiently large number of musical applications. This 12-note scale is a good compromise between having more notes per octave for greater completeness and having enough frequency range to span the range of the human ear, for a given instrument or musical notation system with a limited number of notes.

There is healthy debate about which temperament is best musically. ET was known from the earliest history of tuning. There are definite advantages to standardizing to one temperament, but that is probably not possible or even desirable in view of the diversity of opinions on music and the fact that much music now exist, that were written with particular temperaments in mind. Therefore we shall now explore the various temperaments.

Beethoven (5th Symphony, Appassionata, Waldstein)

2006-02-24T09:06:00.000-08:00

The use of mathematical devices is deeply embedded in Beethoven's music. Therefore, this is one of the best places to dig for information on the relationship between mathematics and music. I'm not saying that other composers do not use mathematical devices. Practically every musical composition has mathematical underpinnings. However, Beethoven was able to extend these mathematical devices to the extreme. It is by analyzing these extreme cases that we can find more convincing evidence on what types of devices he used.

We all know that Beethoven never really studied advanced mathematics. Yet he incorporates a surprising amount of math in his music, at very high levels. The beginning of his Fifth Symphony is a prime case, but examples such as this are legion. He "used" group theory type concepts to compose this famous symphony. In fact, he used what crystallographers call the Space Group of symmetry transformations! This Group governs many advanced technologies, such as quantum mechanics, nuclear physics, and crystallography that are the foundations of today's technological revolution. At this level of abstraction, a crystal of diamond and Beethoven's 5th symphony are one and the same! I will explain this remarkable observation below.

The Space Group that Beethoven "used" (he certainly had a different name for it) has been applied to characterize crystals, such as silicon and diamond. It is the properties of the Space Group that allow crystals to grow defect free and therefore, the Space Group is the very basis for the existence of crystals. Since crystals are characterized by the Space Group, an understanding of the Space Group provides a basic understanding of crystals. This was neat for materials scientists working to solve communications problems because the Space Group provided the framework from which to launch their studies. It's like the physicists needed to drive from New York to San Francisco and the mathematicians handed them a map! That is how we perfected the silicon transistor, which led to integrated circuits and the computer revolution. So, what is the Space Group? And why was this Group so useful for composing this symphony?

Groups are defined by a set of properties. Mathematicians found that groups defined in this way can be mathematically manipulated and physicists found them to be useful: that is, these particular groups that interested mathematicians and scientists provide us with a pathway to reality. One of the properties of groups is that they consist of Members and Operations. Another property is that if you perform an Operation on a Member, you get another Member of the same Group. A familiar group is the group of integers: -1, 0, 1, 2, 3, etc. An Operation for this group is addition: 2 + 3 = 5. Note that the application of the operation + to Members 2 and 3 yields another Member of the group, 5. Since Operations transform one member into another, they are also called Transformations. A Member of the Space Group can be anything in any space: an atom, a frog, or a note in any musical space dimension such as pitch, speed, or loudness. The Operations of the Space Group relevant to crystallography are Translation, Rotation, Mirror, Inversion, and the Unitary operation. These are almost self explanatory (Translation means you move the Member some distance in that space) except for the Unitary operation which basically leaves the Member unchanged. However, it is somewhat subtle because it is not the same as the equality transformation, and is therefore always listed last in textbooks. Unitary operations are generally associated with the most special member of the group, which we might call the Unitary Member. In the integer group noted above, this Member would be 0 for addition and 1 for multiplication (5+0 = 5x1 = 5).

Let me demonstrate how you might use this Space Group, in ordinary everyday life. Can you explain why, when you look into a mirror, the left hand goes around to the right (and vice versa), but your head doesn't rotate down to your feet? The Space Group tells us that you can't rotate the right hand and get a left hand because left-right is a mirror operation, not a rotation. Note that this is a strange transformation: your right hand becomes your left hand in the mirror; therefore, the wart on your right hand will be on your left hand image in the mirror. This can become confusing for a symmetric object such as a face because a wart on one side of the face will look strangely out of place in a photograph, compared to your familiar image in a mirror. The mirror operation is why, when you look into a flat mirror, the right hand becomes a left hand; however, a mirror cannot perform a rotation, so your head stays up and the feet stay down. Curved mirrors that play optical tricks (such as reversing the positions of the head and feet) are more complex mirrors that can perform additional Space Group operations, and group theory will be just as helpful in analyzing images in a curved mirror. The solution to the flat mirror image problem appeared to be rather easy because we had a mirror to help us, and we are so familiar with mirrors. The same problem can be restated in a different way, and it immediately becomes much more difficult, so that the need for group theory to help solve the problem becomes more obvious. If you turned a right hand glove inside out, will it stay right hand or will it become a left hand glove? I will leave it to you to figure that one out (hint: use a mirror).

Let's see how Beethoven used his intuitive understanding of spatial symmetry to compose his 5th Symphony. That famous first movement is constructed largely by using a single short musical theme consisting of four notes, of which the first three are repetitions of the same note. Since the fourth note is different, it is called the surprise note, and carries the beat. This musical theme can be represented schematically by the sequence 5553, where 3 is the surprise note. This is a pitch based space group; Beethoven used a space with 3 dimensions, pitch, time, and volume. I will consider only the pitch and time dimensions in the following discussions. Beethoven starts his Fifth Symphony by first introducing a Member of his Group: three repeat notes and a surprise note, 5553. After a momentary pause to give us time to recognize his Member, he performs a Translation operation: 4442. Every note is translated down. The result is another Member of the same Group. After another pause so that we can recognize his Translation operator, he says, "Isn't this interesting? Let's have fun!" and demonstrates the potential of this Operator with a series of translations that creates music. In order to make sure that we understand his construct, he does not mix other, more complicated, operators at this time. In the ensuing series of bars, he then successively incorporates the Rotation operator, creating 3555, and the Mirror operator, creating 7555. Somewhere near the middle of the 1st movement, he finally introduces what might be interpreted as the Unitary Member: 5555. Note that these groups of 5 identical notes are simply repeated, which is the Unitary operation.

In the final fast movements, he returns to the same group, but uses only the Unitary Member, and in a way that is one level more complex. It is always repeated three times. What is curious is that this is followed by a fourth sequence -- a surprise sequence 7654, which is not a Member. Together with the thrice repeated Unitary Member, the surprise sequence forms a Supergroup of the original Group. He has generalized his Group concept! The supergroup now consists of three members and a non-member of the initial group, which satisfies the conditions of the initial group (three repeats and a surprise).

Thus, the beginning of Beethoven's Fifth symphony, when translated into mathematical language, reads just like the first chapter of a textbook on group theory, almost sentence for sentence! Remember, group theory is one of the highest forms of mathematics. The material is even presented in the correct order as they appear in textbooks, from the introduction of the Member to the use of the Operators, starting with the simplest, Translation, and ending with the most subtle, the Unitary operator. He even demonstrates the generality of the concept by creating a supergroup from the original group.

Beethoven was particularly fond of this four-note theme, and used it in many of his compositions, such as the first movement of the Appassionata piano sonata, see bar 10, LH. Being the master that he is, he carefully avoids the pitch based Space Group for the Appassionata and uses different spaces -- he transforms them in tempo space and volume space (bars 234 to 238). This is further support for the idea that he must have had an intuitive grasp of group theory and consciously distinguished between these spaces. It seems to be a mathematical impossibility that this many agreements of his constructs with group theory just happened by accident, and is virtual proof that he was somehow playing around with these concepts.

Why was this construct so useful in this introduction? It certainly provides a uniform platform on which to hang his music. The simplicity and uniformity allow the audience to concentrate only on the music without distraction. It also has an addictive effect. These subliminal repetitions (the audience is not supposed to know that he used this particular device) can produce a large emotional effect. It is like a magician's trick -- it has a much larger effect if we do not know how the magician does it. It is a way of controlling the audience without their knowledge. Just as Beethoven had an intuitive understanding of this group type concept, we may all feel that some kind of pattern exists, without recognizing it explicitly. Mozart accomplished a similar effect using repetitions.

Knowledge of these group type devices that he uses is very useful for playing his music, because it tells you exactly what you should and should not do. Another example of this can be found in the 3rd movement of his Waldstein sonata, where the entire movement is based on a 3-note theme represented by 155 (the first CGG at the beginning). He does the same thing with the initial arpeggio of the 1st movement of the Appassionata, with a theme represented by 531 (the first CAbF). In both cases, unless you maintain the beat on the last note, the music loses its structure, depth and excitement. This is particularly interesting in the Appassionata, because in an arpeggio, you normally place the beat on the first note, and many students actually make that mistake. As in the Waldstein, this initial theme is repeated throughout the movement and is made increasingly obvious as the movement progresses. But by then, the audience is addicted to it and does not even notice that it is dominating the music. For those interested, you might look near the end of the 1st movement of the Appassionata where he transforms the theme to 315 and raises it to an extreme and almost ridiculous level at bar 240. Yet most in the audience will have no idea what device Beethoven was using, except to enjoy the wild climax, which is obviously ridiculously extreme, but by now carries a mysterious familiarity because the construct is the same, and you have heard it hundreds of times. Note that this climax loses much of its effect if the pianist does not bring out the theme (introduced in the first bar!) and emphasize the beat note.

Beethoven tells us the reason for the inexplicable 531 arpeggio in the beginning of the Appassionata when the arpeggio morphs into the main theme of the movement at bar 35. That is when we discover that the arpeggio at the beginning is an inverted and schematized form of his main theme, and why the beat is where it is. Thus the beginning of this piece, up to bar 35, is a psychological preparation for one of the most beautiful themes he composed. He wanted to implant the idea of the theme in our brain before we heard it! That may be one explanation for why this strange arpeggio is repeated twice at the beginning using an illogical chord progression. With analysis of this type, the structure of the entire 1st movement becomes apparent, which helps us to memorize, interpret, and play the piece correctly.

The use of group theoretical type concepts might be just an extra dimension that Beethoven wove into his music, perhaps to let us know how smart he was, in case we still didn't get the message. It may or may not be the mechanism with which he generated the music. Therefore, the above analysis gives us only a small glimpse into the mental processes that inspire music. Simply using these devices does not result in music. Or, are we coming close to something that Beethoven knew but didn't tell anyone?

Mozart (Eine Kleine Nachtmusik, Sonata K300)

2006-02-24T09:05:00.000-08:00

When I first heard of Mozart's formula, I felt a great excitement, because I thought that it might shed light on music theory and on music itself. You may at first be disappointed, as I was, when you find out that Mozart's formula, as we know it today, appears to be strictly structural. Structural analyses have so far not yet provided much information on how you come up with famous melodies; but then, music theory doesn't either. Today's music theory only helps to compose "correct" music or expand on it once you have come up with a musical idea. Music theory is a classification of families of notes and their arrangements in certain patterns. We can not yet rule out the possibility that music is ultimately based on certain identifiable types of structural patterns. I first learned of Mozart's formula at a lecture given by a music professor. I have since lost the reference -- if anyone reading this book knows of a reference (professor’s name, his institution), please let me know.

It is now known that Mozart composed practically all of his music, from when he was very young, according to a single formula that expanded his music by over a factor of ten. That is, whenever he concocted a new melody that lasted one minute, he knew that his final composition would be at least ten minutes long. Sometimes, it was a lot longer. The first part of his formula was to repeat every theme. These themes were generally very short -- only 4 to 10 notes, much shorter than you would think when you think of a musical theme. These themes, that are much shorter than the over-all melody, simply disappear into the melody because they are too short to be recognized. This is why we do not normally notice them, and is almost certainly a conscious construct by the composer. The theme would then be modified two or three times and repeated again to produce what the audience would perceive as a continuous melody. These modifications consisted of the use of various mathematical and musical symmetries such as inversions, reversals, harmonic changes, clever positioning of ornaments, etc. These repetitions would be assembled to form a section and the whole section would be repeated. The first repetition provides a factor of two, the various modifications provide another factor of two to six (or more), and the final repetition of the entire section provides another factor of two, or 2x2x2 = 8 at a minimum. In this way, he was able to write huge compositions with a minimum of thematic material. In addition, his modifications of the original theme followed a particular order so that certain moods or colors of music were arranged in the same order in each composition.

Because of this pre-ordained structure, he was able to write down his compositions from anywhere in the middle, or one voice at a time, since he knew ahead of time where each part belonged. And he did not have to write down the whole thing until the last piece of the puzzle was in place. He could also compose several pieces simultaneously, because they all had the same structure. This formula made him look like more of a genius than he really was. This naturally leads us to question: how much of his reputed "genius" was simply an illusion of such machinations? This is not to question his genius -- the music takes care of that! However, many of the wonderful things that these geniuses did were the result of relatively simple devices and we can all take advantage of that by finding out the details of these devices. For example, knowing Mozart's formula makes it easier to dissect and memorize his compositions. The first step towards understanding his formula is to be able to analyze his repetitions. They are not simple repetitions; Mozart used his genius to modify and disguise the repetitions so that they produced music and, more importantly, so that the fact of the repetition will not be recognized.

As an example of repetitions, let's examine the famous melody in the Allegro of his Eine Kleine Nachtmusik. This is the melody that Salieri played and the pastor recognized in the beginning of the movie, "Amadeus". That melody is a repetition posed as a question and an answer. The question is a male voice asking, "Hey, are you coming?" And the reply is a female voice, "OK, OK, I'm coming!" The male statement is made using only two notes, a commanding fourth apart, repeated three times (six notes), and the question is created by adding three rising notes at the end (this appears to be universal among most languages -- questions are posed by raising the voice at the end). Thus the first part consists of 9 notes. The repetition is an answer in a female voice because the pitch is higher, and is again two notes, this time a sweeter minor third apart, repeated (you guessed it!) three times (six notes). It is an answer because the last three notes wiggle down. Again, the total is 9 notes. The efficiency with which he created this construct is amazing. What is even more incredible is how he disguises the repetition so that when you listen to the whole thing, you would not think of it as a repetition. Practically all of his music can be analyzed in this way. If you are not yet convinced, take any of his music and analyze it, and you will find this pattern.

Let's look at another example, the Sonata #16 in A, K300 (or KV331, the one with the Alla Turca ending). The basic unit of the beginning theme is a quarter note followed by an eighth note. The first introduction of this unit in bar 1 is disguised by the addition of the 16th note. This introduction is followed by the basic unit, completing bar 1. Thus in the first bar, the unit is repeated twice. He then translates the whole double unit of the 1st bar down in pitch and creates bar 2. The 3rd bar is just the basic unit repeated twice. In the 4th bar, he again disguises the first unit by use of the 16th notes. Bars 1 to 4 are then repeated with minor modifications in bars 5-8. From a structural viewpoint, every one of the first 8 bars is patterned after the 1st bar. From a melodic point of view, these 8 bars produce two long melodies with similar beginnings but different endings. Since the whole 8 bars is repeated, he has basically multiplied his initial idea embodied in the 1st bar by 16! If you think in terms of the basic unit, he has multiplied it by 32. But then he goes on to take this basic unit and creates incredible variations to produce the first part of the sonata, so the final multiplication factor is even larger. He uses repetitions of repetitions. By stringing the repetitions of modified units, he creates a final melody that sounds like a long melody until you break it up into its components.

In the 2nd half of this exposition, he introduces new modifications to the basic unit. In bar 10, he first adds an ornament with melodic value to disguise the repetition and then introduces another modification by playing the basic unit as a triplet. Once the triplet is introduced, it is repeated twice in bar 11. Bar 12 is similar to bar 4; it is a repetition of the basic unit, but structured in such a way as to act as a conjunction between the preceding 3 related bars and the following 3 related bars. Thus bars 9 to 16 are similar to bars 1 to 8, but with a different musical idea. The final 2 bars (17 and 18) provide the ending to the exposition. With these analyses as examples, you should now be able to dissect the remainder of this piece. You will find that the same pattern of repetitions is found throughout the entire piece. As you analyze more of his music you will need to include more complexities; he may repeat 3 or even 4 times, and mix in other modifications to hide the repetitions. What is clear is that he is a master of disguise so that the repetitions and other structures are not usually obvious when you just listen to the music without any intent to analyze it.

Mozart's formula certainly increased his productivity. Yet he may have found certain magical (hypnotic? addictive?) powers to repetitions of repetitions and he probably had his own musical reasons for arranging the moods of his themes in the sequence that he used. That is, if you further classify his melodies according to the moods they evoke, it is found that he always arranged the moods in the same order. The question here is, if we dig deeper and deeper, will we just find more of these simple structural/mathematical devices, just stacked one on top of each other, or is there more to music? Almost certainly, there must be more, but no one has yet put a finger on it, not even the great composers themselves -- at least, as far as they have told us. Thus it appears that the only thing we mortals can do is to keep digging.

The music professor mentioned above who lectured on Mozart’s formula also stated that the formula is followed so strictly that it can be used to identify Mozart’s compositions. However, elements of this formula were well known among composers. Thus Mozart is not the inventor of this formula and similar formulas were used widely by composers of his time. Some of Salieri’s compositions follow a very similar formula; perhaps this was an attempt by Salieri so emulate Mozart. Thus you will need to know some details of Mozart’s specific formula in order to use it to identify his compositions.

There is little doubt that a strong interplay exists between music and genius. We don't even know if Mozart was a composer because he was a genius or if his extensive exposure to music from birth created the genius. The music doubtless contributed to his brain development. It may very well be that the best example of the "Mozart effect" was Wolfgang Amadeus himself, even though he did not have the benefit of his own masterpieces. Today, we are just beginning to understand some of the secrets of how the brain works. For example, until recently, we had it partly wrong when we thought that certain populations of mentally handicapped people had unusual musical talent. It turns out that music has a powerful effect on the actual functioning of the brain and its motor control. This is one of the reasons why we always use music when dancing or exercising. The best evidence for this comes from Alzheimer's patients who have lost their ability to dress themselves because they cannot recognize each different type of clothing. It was discovered that when this procedure is set to the proper music, these patients can often dress themselves! "Proper music" is usually music that they heard in early youth or their favorite music. Thus mentally handicapped people who are extremely clumsy when performing daily chores can suddenly sit down and play the piano if the music is the right type that stimulates their brain. Therefore, they may not be musically talented; instead, it is the music that is giving them new capabilities. It is not only music that has these magical effects on the brain, as evidenced by savants who can memorize incredible amounts of information or carry out mathematical feats normal folks cannot perform. There is a more basic internal rhythm in the brain that music happens to excite. Therefore, these savants may not be talented but are just using some of the methods of this book, such as mental play. Just as good memorizers have brains that are automatically memorizing everything they encounter, some savants may be repeating music or mathematical thoughts in their heads all the time, which would explain why they cannot perform ordinary chores – because their brains are already preoccupied with something else.

If music can produce such profound effects on the handicapped, imagine what it could do to the brain of a budding genius, especially during the brain's development in early childhood. These effects apply to anyone who plays the piano, not just the handicapped or the genius.

Mozart's Formula, Beethoven and Group Theory

2006-02-24T09:04:00.000-08:00

There is an intimate, if not absolutely essential, relationship between mathematics and music. At the very least, they share a large number of the most fundamental properties in common, starting with the fact that the chromatic scale is a simple logarithmic equation (see Chapt. Two, Section 2) and that the basic chords are ratios of the smallest integers. Now few musicians are interested in mathematics for mathematics' sake. However, practically everyone is curious and has wondered at one time or other whether mathematics is somehow involved in the creation of music. Is there some deep, underlying principle that governs both math and music? In addition, there is the established fact that every time we succeeded in applying mathematics to a field, we have made tremendous strides in advancing that field. One way to start investigating this relationship is to study the works of the greatest composers from a mathematical point of view. The following analyses contain no inputs from music theory.

Future Research Topics

2006-02-24T08:13:00.000-08:00

Every subsection in this section is incomplete; I am just putting down some initial ideas.

This book is based on the scientific approach, which ensures that errors are corrected as soon as possible, that all known facts are explained, documented, and organized in a useful way, and that we only make forward progress. The past situation of one piano teacher teaching a very useful method and another knowing nothing about it, or two teachers teaching completely opposite methods, should not occur. An important part of the scientific approach is a discussion of what is still unknown and what still needs to be researched. The following is a collection of such topics.

Momentum Theory of Piano Playing

Slow play in piano is called “playing in the static limit”. This means that when depressing a key, the force of the finger coming down is the main force used in the playing. As we speed up, we transition from the static limit to the momentum limit. This means that the momenta of the hand, arms, fingers, etc., play much more important roles than the force in depressing the keys. Of course, force is needed to depress the key, but when in the momentum limit, the force and motion are usually 180 degrees out of phase. That is, your finger is moving up when your finger muscles are trying to press it down! This happens at high speed because you had earlier lifted the finger so rapidly that you have to start depressing it on its way up so that you can reverse its action for the next strike. The actual motions a complex because you use the hand, arms, and body to impart and absorb the momenta. This is one of the reasons why the entire body gets involved in the playing, especially when playing fast. Note that the swing of the pendulum and the dribbling of the basketball are in the momentum limit. In piano playing, you are generally somewhere between the static and momentum limits with increasing tendency towards momentum limit with increasing speed.

In static play, the force vector and motion of the finger are in phase. As we transition to momentum play, a phase difference develops, until, in the pure momentum regime, the phase difference is 180 degrees, as it is in the pendulum.

The importance of momentum play is obvious; it involves many new finger/hand motions that are not possible in static play. Thus knowing which motions are of the static or momentum type will go a long way toward understanding how to execute them and when to use them. Because momentum play has never been discussed in the literature until now, there is a vast area of piano play for which we have very little understanding.

The Physiology of Technique

We still lack even a rudimentary understanding of the bio-mechanical processes that underlie technique. It certainly originates in the brain, and is probably associated with how the nerves communicate with the muscles, especially the rapid muscles. What are the biological changes that accompany technique? when fingers are “warmed up”?

Brain Research (HS vs HT Play, etc.)

Brain research will be one of the most important fields of medical research in the near future. This research will initially concentrate on preventing mental deterioration with age (such as curing Alzheimer’s disease). Then concurrent efforts at actually controlling the growth of mental capabilities will surely develop. Music should play an important role in such developments because we can communicate aurally with infants long before any other method, and it is already clear that, the earlier you start the control process, the better the results.

We are all familiar with the fact that, even if we can play HS quite well, HT may still be difficult. Why is HT so much more difficult? One of the reasons may be that the two hands are controlled by the different halves of the brain. If so, then learning HT requires the brain to develop ways to coordinate the two halves. This would mean that HS and HT practice use completely different types of brain functions and supports the contention that these skills should be developed separately so that we work on one skill at a time. One intriguing possibility is that we may be able to develop HT parallel sets that can solve this problem.

What Causes Nervousness?

In piano pedagogy, nervousness has been “swept under the rug” (ignored) for too long. We need to study it from medical and physiological points of view. We need to know if some individuals can benefit from proper medication. Moreover, is there a medical or psychological regiment whereby it can eventually be eliminated? Finally, from a formal psychological point of view, we must develop a teaching procedure that will reduce nervousness. Nervousness is clearly the result of a mental attitude/reaction/perception, and is therefore very amenable to active control. For example, pianists who play popular/jazz type music seem to be much less nervous in general than those who play classical. There is no reason why we shouldn’t investigate why this is so, and take advantage of this phenomenon.

Causes and Remedies for Tinnitus

Cochlea structure, high and low frequency tinnitus.

There is evidence that moderate intake of aspirin can slow down hearing loss with age. However, there is also evidence that aspirin, under certain conditions, can aggravate tinnitus. There does not appear to be any evidence that tinnitus is caused purely by age; instead, there is ample evidence that it is caused by infection, disease, accidents, and abuse of the ear. Therefore, in most of these cases, the causes and the types of damage can be directly studied.

What is Music?

Cochlea structure vs music scales and chords. Parameters: timing (rhythm), pitch, patterns (language, emotions), volume, speed. Musical information processing in brain.

At What Age to Start Piano?

We need medical/psychological/sociological studies into how/when we should start youngsters. This type of research is already starting to be conducted in sports, at least informally, by individual sports organizations that have developed methods for teaching youngsters down to about 2 years of age. In music, we can start as soon as the babies are born, by letting them listen to the appropriate types of music. In music, we are probably interested more in the development of the brain than in acquiring motor skills. Because we expect brain research to explode in the near future, this is an opportune time to take advantage of that research and use the results for learning piano.

The Future of Piano

Finally, we look into the future. The “Testimonials” section gives ample evidence that our new approach to piano practice will enable practically anyone to learn piano to her/is satisfaction. It will certainly increase the number of pianists. Therefore, the following questions become very important: (1) can we calculate the expected increase in pianists? (2) what will this increase do to the economics of the piano: performers, teachers, technicians, and manufacturers, and (3) if piano popularity explodes, what will be the main motivation for such large numbers of people to learn piano?

Piano teachers will agree than 90% of piano students never really learn piano in the sense that they will not be able to play to their satisfaction and basically give up trying to become accomplished pianists. Since this is a well known phenomenon, it discourages youngsters and their parents from deciding to start piano lessons. Since serious involvement with piano will interfere materially with the business of making a living, the economic factor also discourages entry into piano. There are many more negative factors that limit the popularity of the piano (lack of good teachers, high expense of good pianos and their maintenance, etc.), almost all of which are eventually related to the fact that piano has been so difficult to learn. Probably only 10% of those who might have tried piano ever decide to give it a try. Therefore, we can reasonably expect the popularity of the piano to increase by 100 times if the promise of this book can be fulfilled.

Such an increase would mean that a large fraction of the population in developed countries would learn piano. Since it is a significant fraction, we do not need an accurate number, so let’s just pick some reasonable number, say 30%. This would require at least a 10 fold increase in the number of piano teachers. This would be great for students because one of the big problems today is finding good teachers. In any one area, there are presently only a few teachers and the students have little choice. The number of pianos sold would also have to increase, probably by something in excess of 300%. Although many homes already have pianos, many of them are not playable. Since most of the new pianists will be at an advanced level, the number of good grand pianos needed will increase by an even larger percentage.

By using this book as a basic starting point for practice methods, piano teachers can concentrate on what they do best: teaching how to make music. Since this is what teachers have been doing all along, there will be only minor new changes needed in how teachers teach. The only new element is the addition of practice methods that take very little time to learn. The biggest change, of course, is that teachers will be liberated from the old slow process of teaching technique. It will be much easier for teachers to decide what to teach because technical difficulties will be much less of an impediment. Within a few teacher/student generations, the quality of teachers will improve dramatically which will further accelerate the learning rates of future students.

Is an increase of 100 times in the population of pianists reasonable? What would they do? They certainly can’t all be concert pianists and piano teachers. The very nature of how we view piano playing will change. First of all, the piano will, by then, become a standard second instrument for all musicians, because it will be so easy to learn and there will be pianos everywhere. The joy of playing piano will be enough reward for many. The zillions of music lovers who could only listen to recordings can now play their own music -- a much more satisfying experience. As anyone who has become an accomplished pianist will tell you, once you get to that level, you cannot help but compose music. Thus a piano revolution will also ignite a revolution in composition, and new compositions will be in great demand because many pianists will not be satisfied with playing “the same old things”. Pianists will be composing music for every instrument because of the development of keyboards with powerful software and every pianist will have an acoustic piano and an electronic keyboard, or a dual instrument (see below). The large supply of good keyboardists would mean that entire orchestras will be created using keyboard players. Another reason why the piano would become universally popular is that it will be used as a method for increasing the IQ of growing infants. Brain research will certainly reveal that the intelligence can be improved by proper brain stimulation during its early developmental stages. Since there are only two inputs into the infant’s brain, auditory and visual, and the auditory is initially much more advanced than visual, music is the most logical means for influencing the brain during early development.

With such huge forces at work, the piano itself will evolve rapidly. First, the electronic keyboard will increasingly intrude into the piano sector. The shortcomings of the electronic pianos will continue to decrease until the electronics become indistinguishable from the acoustics. Regardless of which instrument is used, the technical requirements will be the same. By then, the acoustic pianos will have many of the features of the electronics: they will be in tune all the time (instead of being out of tune 99% of the time, as they are now), you will be able to change temperaments by flicking a switch, and midi capabilities will be easily interfaced with the acoustics. The acoustics will never completely disappear because the art of making music using mechanical devices is so fascinating. In order to thrive in this new environment, piano manufacturers will need to be much more flexible and innovative.

Piano tuners will also need to adapt to these changes. All pianos will be self-tuning, so income from tuning will decrease. However, pianos in tune 100% of the time will need to be voiced more frequently, and how hammers are made and voiced will need to change. It is not that today’s pianos do not need voicing just as much, but when the strings are in perfect tune, any deterioration of the hammer becomes the limiting factor to sound quality. Piano tuners will finally be able to properly regulate and voice pianos instead of just tuning them; they can concentrate on the quality of the piano sound, instead of just getting rid of dissonances. Since the new generation of more accomplished pianists will be aurally more sophisticated, they will demand better sound. The greatly increased number of pianos and their constant use will require an army of new piano technicians to regulate and repair them. Piano tuners will also be much more involved in adding and maintaining electronic (midi, etc.) capabilities to acoustics. Therefore, the piano tuners’ business will extend into the maintenance and upgrading of electronic pianos. Thus most people will either have a hybrid or both an acoustic and electronic piano.

The Future of Education

The Internet is obviously changing the nature education. One of my objectives in writing this book on the WWW is to explore the possibilities of making education much more cost effective than it has been. Looking back to my primary education and college days, I marvel at the efficiency of the educational processes that I had gone through. Yet the promise of much greater efficiency via the internet is staggering by comparison. My experience thus far has been very educational. Here are some of the advantages of internet based education:
(i) No more waiting for school buses, or running from class to class; in fact no more cost of school buildings and associated facilities.
(ii) No costly textbooks. All books are up-to-date, compared to many textbooks used in universities that are over 10 years old. Cross referencing, indexing, topic searches, etc., can be done electronically. Any book is available anywhere, as long as you have a computer and internet connection.
(iii) Many people can collaborate on a single book, and the job of translating into other languages becomes very efficient, especially if a good translation software is used to assist the translators.
(iv) Questions and suggestions can be emailed and the teacher has ample time to consider a detailed answer and these interactions can be emailed to anyone who is interested; these interactions can be stored for future use.
(v) The teaching profession will change drastically. On the one hand, there will be more one-on-one interactions by email, video-conferencing, and exchange of data (such as audio from a piano student to the teacher) but on the other, there will be fewer group interactions where the group of students physically assembles in one classroom. Any teacher can interact with the “master text book center” to propose improvements that can be incorporated into the system. And students can access many different teachers, even for the same topic.
(vi) Such a system would imply that an expert in the field cannot get rich writing the best textbook in the world. However, this is as it should be -- education must be available to everyone at the lowest cost. Thus when educational costs decrease, institutions that made money the old way must change and adopt the new efficiencies. Wouldn’t this discourage experts from writing textbooks? Yes, but you need only one such “volunteer” for the entire world; in addition, the internet has already spawned enough such free systems as Linux, browsers, Adobe Acrobat, etc., that this trend is not only irreversible but well established. In other words, the desire to contribute to society becomes a large factor in contributing to education. For projects that provide substantial benefits to society, funding mechanisms (government, philanthropists, and sponsoring businesses) will certainly evolve.
(vii) This new paradigm of contributing to society may bring about even more profound changes to society. One way of looking at business as conducted today is that it is highway robbery. You charge as much as you can regardless of how much or how little good your product does to the buyer. In an accurate accounting paradigm, the buyer should always get his money’s worth. That is the only situation in which that business can be viable in the long run. This works both ways; well-run businesses should not be allowed to go bankrupt simply because of excessive competition. In an open society in which all relevant information is immediately available, we can have financial accounting that can make pricing appropriate to the service. The philosophy here is that a society consisting of members committed to helping each other succeed will function much better than one consisting of robbers stealing from each other. In particular, in the future, practically all basic education should be essentially free. This does not mean that teachers will lose their jobs because teachers can greatly accelerate the learning rate and should be paid accordingly.

It is clear from the above considerations that free exchange of information will transform the educational (as well as practically every other) field. This book is one of the attempts at taking full advantage of these new capabilities.

Learning Rate Calculation

2006-02-24T08:11:00.000-08:00

Here is my crude attempt to mathematically calculate the piano learning rate of the methods of this book. The result indicates that it is about 1000 times faster than the intuitive method. The huge multiple of 1000 makes it unnecessary to calculate an accurate number in order to show that there is a big difference. This result appears plausible in view of the fact that many students who worked hard all their lives using the intuitive method are not able to perform anything significant, whereas a fortunate student who used the correct learning methods can become a concert pianist in less than 10 years. It is clear that the difference in practice methods can make the difference between a lifetime of frustration and a rewarding career in piano. Now, “1000 times faster” does not mean that you can become a pianist in a millisecond; all it means is that the intuitive methods are 1000 times slower than the good methods. The conclusion we should draw here is that, with the proper methods, our learning rates should be pretty close to those of the famous composers such as Mozart, Beethoven, Liszt, and Chopin. Remember that we have certain advantages not enjoyed by those past geniuses. They did not have those wonderful Beethoven sonatas, Liszt and Chopin etudes, etc., with which to acquire technique, or those Mozart compositions with which to benefit from the “Mozart effect”, or books like this one with an organized list of practice methods. Moreover, there are now hundreds of time-proven methods for using those compositions for acquiring technique (Beethoven often had difficulty playing his own compositions because nobody knew the correct or wrong way to practice them). An intriguing historical aside here is that the only common material available for practice for all of these great pianists was Bach’s compositions. Thus, we are led to the idea that studying Bach may be sufficient for acquiring most basic keyboard skills.

I will try to make a detailed calculation starting with the most fundamental precepts and progressing to the final result without jumping over unknown gaps. In this way, if there are errors in this calculation, it can be refined as we improve our understanding of how we acquire technique. This is, obviously, the scientific approach. There is nothing new in these calculations except for their application to musical learning. The mathematical material is simply a review of established algebra and calculus.

Mathematics can be used to solve problems in the following way. First, you define the conditions that determine the nature of the problem. If these conditions have been correctly determined, they allow you to set up what are called differential equations; these are accurate, mathematical statements of the conditions. Once the differentials equations are set up, mathematics provides methods for solving them to provide a function which describes the answers to the problems in terms of parameters that determine these answers. The solutions to the problems can then be calculated by inserting the appropriate parameter values into the function.

The physical principle we use to derive our learning equation is the linearity with time. Such an abstract concept may seem to have nothing to do with piano and is certainly non-biological, but it turns out that, that is exactly what we need. So let me explain the concept of “the linearity with time”. It simply means proportional to time. For example, if we learn an amount of technique L (stands for Learning) in time T, then if we repeat this process again a few days later, we should learn another increment L in the same T. Thus we say that L is linear with respect to T in the sense that they are proportional; in 2T, we should learn 2L. Of course, we know that learning is highly non-linear. If we practice the same short segment for 4 hours, we are likely to gain a lot more during the first 30 minutes than during the last 30 minutes. However, we are talking about an optimized practice session averaged over many practice sessions that are conducted over time intervals of years (in an optimized practice session, we are not going to practice the same 4 notes for 4 hours!). If we average over all of these learning processes, they tend to be quite linear. Certainly within a factor of 2 or 3, linearity is a good approximation, and that amount of accuracy is all we need. Note that linearity does not depend, to first approximation, on whether you are a fast learner or a slow learner; this changes only the proportionality constant. Thus we arrive at the first equation:

L = kT (Eq. 1.1),

where L is an increment of learning in the time interval T and k is the proportionality constant. What we are trying to find is the time dependence of L, or L(t) where t is time (in contrast to T which is an interval of time). Similarly, L is an increment of learning, but L(t) is a function.

Now comes the first interesting new concept. We have control over L; if we want 2L, we simply practice twice. But that is not the L that we retain because we lose some L over time after we practice. Unfortunately, the more we know, the more we can forget; that is, the amount we forget is proportional to the original amount of knowledge, L(O). Therefore, assuming that we acquired L(O), the amount of L we lose in T is:

L = -kTL(O) (Eq. 1.2),

where the k’s in equations 1.1 and 1.2 are different, but we will not re-label them for simplicity. Note that k has a negative sign because we are losing L. Eq. 1.2 leads to the differential equation

dL(t)/dt = -kL(t) (Eq. 1.3)

where “d” stands for differential (this is all standard calculus), and the solution to this differential equation is

L(t) = Ke(expt.-kt) (Eq. 1.4),

where “e” is a number called the natural logarithm which satisfies Eq. 1.3, and K is a new constant related to k (for simplicity, we have ignored another term in the solution that is unimportant at this stage). Eq. 1.4 tells us that once we learn L, we will immediately start to forget it exponentially with time if the forgetting process is linear with time.

Since the exponent is just a number, k in Eq. 1.4 has the units of 1/time. We shall set k = 1/T(k) where T(k) is called the characteristic time. Here, k refers to a specific learning/forgetting process. When we learn piano, we learn via a myriad of processes, most of which are not well understood. Therefore, determining accurate values for T(k) for each process is generally not possible, so in the numerical calculations, we will have to make some “intelligent guesses”. In piano practice, we must repeat difficult material many times before we can play them well, and we need to assign a number (say, “i”) to each practice repetition. Then Eq. 1.4 becomes

L(i,t,k) = K(i)e(expt.-t[i]/T[k]) (Eq. 1.5),

for each repetition i and learning/forgetting process k. Let’s examine some relevant examples. Suppose that you are practicing 4 parallel set notes in succession, playing rapidly and switching hands, etc., for 10 minutes. We assign i = 0 to one parallel set execution, which may take only about half a second. You might repeat this 10 or 100 times during the 10 minute practice session. You have learned L(0) after the first parallel set. But what we need to calculate is the amount of L(0) that we retain after the 10 minute practice session. In fact, because we repeat many times, we must calculate the cumulative learning from all of them. According to Eq. 1.5, this cumulative effect is given by summing the L’s over all the parallel set repetitions:

L(Total) = Sum(over i)K(i)e(expt.-t[i]/T[k]) (Eq.1.6).

Now let’s put in some numbers into Eq. 1.6 in order to get some answers. Take a passage that you can play slowly, HT, in about 100 seconds (intuitive method). This passage may contain 2 or 3 parallel sets that are difficult and that you can play rapidly in less than a second, so that you can repeat them over 100 times in those 100 seconds (method of this book). Typically, these 2 or 3 difficult spots are the only ones holding you back, so if you can play them well, you can play the entire passage at speed. Of course, even with the intuitive method, you will repeat it many times, but let’s compare the difference in learning for each 100 second repetition. For this quick learning process, our tendency to “lose it” is also fast, so we can pick a “forgetting time constant” of around 30 seconds; that is, every 30 seconds, you end up forgetting almost 30% of what you learned from one repetition. Note that you never forget everything even after a long time because the forgetting process is exponential -- exponential decays never reach absolute zero. Also, you can make many repetitions in a short time for parallel sets, so these learning events can pile up quickly. This forgetting time constant of 30 seconds depends on the mechanism of learning/forgetting, and I have chosen a relatively short one for rapid repetitions; we shall examine a much longer one below.

Assuming one parallel set repetition per second, the learning from the first repetition is e(expt.-100/30) = 0.04 (you have 100 seconds for forget the first repetition), while the last repetition gives e(expt.-1/30) = 0.97, and the average learning is somewhere in between, about 0.4 (we don’t have to be exact, as we shall see). and with over 100 repetitions, we have over 40 units of learning for the use of parallel sets. For the intuitive method, we have a single repetition or e(expt. -100/30) = 0.04. The difference is a factor of 40/0.04 = 1,000! With such a large difference factor, we do not need much accuracy to demonstrate that there is a big difference. The actual difference in learning may be even bigger because the intuitive method repetition is at slow speed whereas the parallel set repetition rate is at, or even faster than, the final speed.

The 30 second time constant used above was for a “fast” learning process, such as that associated with learning during a single practice session. There are many others, such as technique acquisition by PPI (post practice improvement). After any rigorous conditioning, your technique will improve by PPI for a week or more. The rate of forgetting, or technique loss, for such slow processes is not 30 seconds, but much longer, probably several weeks. Therefore, in order to calculate the total difference in learning rates, we must calculate the difference for all known methods of technique acquisition using the corresponding time constant, which can vary considerably from method to method. PPI is largely determined by conditioning, and conditioning is similar to the parallel set repetition calculated above. Thus the difference in PPI should also be about 1,000 times.

Once we calculate the most important rates as described above, we can refine the results by considering other factors that influence the final results. There are factors that make the methods of this book slower (initially, memorizing may take longer than reading, or HS may take longer than HT because you need to learn each passage 3 times instead of once, etc.) and factors that make them faster (such as learning in short segments, getting up to speed quickly, avoiding speed walls, etc.). There are many more factors that make the intuitive method slower, so that the above “1000 times faster” result may be an under-estimate. However, it is probably not possible to take full advantage of the 1000 times factor, since most students may already be using some of the ideas of this book.

The effects of speed walls are difficult to calculate because speed walls are artificial creations of each pianist and I do not know how to write an equation for them. Experience tells us that the intuitive method is susceptible to speed walls. The methods of this book provide many ways of avoiding them. Moreover, speed walls are clearly defined here so that it is possible to pro-actively avoid them during practice. Parallel sets are the most powerful tools for avoiding them because speed walls do not generally form when you decrease speed from high speed. Therefore, speed walls greatly retard the learning rate for intuitive methods. Some teachers who do not understand speed walls adequately will prohibit their students from practicing anything risky and fast, thus slowing progress even more, even when this slow play succeeds in completely avoiding speed walls. When all these factors are taken into account we come to the conclusion that the “up to 1000 times faster” result is basically correct. We also see that the use of parallel sets, practicing difficult sections first, practicing short segments, and getting up to speed quickly, are the main factors that accelerate learning. HS practice, relaxation, and early memorization are some of the tools that enable us to optimize the use of these accelerating methods.

Thermodynamics of Piano Playing

2006-02-24T08:08:00.000-08:00

An important field of mathematics is the study of large numbers. Even when single events of a particular type are not predictable, large numbers of such events often behave according to strict laws. Although the energies of individual molecules of water in a glass may differ considerably, the temperature of the water can stay very constant and can be measured with high accuracy. Does piano playing have an analogous situation that would allow us to apply the laws of large numbers and thereby draw some useful conclusions?

Piano playing is a complex process because of a large number of variables that enter into the production of music. The study of large numbers is accomplished by counting the "number of states" of a system. The grand total of meaningful states so counted might be called the "canonical ensemble", a meaningful assembly that sings together a tune that we can decipher. Believe it or not, "canonical ensemble" (see Statistical Mechanics by Kerson Huang, Wily, 1963, P. 75) is legitimate thermodynamic terminology! Therefore, all we need to do is to calculate the canonical ensemble, and when finished, we simply apply the known mathematical rules of large systems (i.e., thermodynamics) and voila! We are done!

The variables in question here are clearly the different motions of the human body, especially those parts important in playing the piano. Our job is to count all the ways in which the body can be moved in playing the piano; this is clearly a very large number; the question is, is it large enough for a meaningful canonical ensemble?

Since no one has ever attempted to calculate this canonical ensemble, we are exploring new territory here, and I will attempt only a very approximate estimate. The beauty of canonical ensembles is that, in the end, if the calculations are correct (a legitimate concern for something this new), the method used to arrive at it is usually immaterial -- you always arrive at the same answers. We calculate the ensemble by listing all the relevant variables, and counting the total parameter space of these variables. So here we go.

Let's start with the fingers. Fingers can move up and down, sideways, and be curled or straight (three variables). Say there are 10 measurably different positions for each variable (parameter space = 10); counting only the number of 10s, we have 4 so far, including the fact that we have 10 fingers. There are actually many more variables (such as rotating the fingers around each finger axis) and more than 10 measurable parameters per variable, but we are counting only those states that can be reasonably used to play the piano, for a given piece of music. The reason for this restriction is that we will be using the results of these calculations for comparing how two persons play the same piece, or how one person would play it twice in a row. This will become clearer later on.

Now the palms can be raised or lowered, flexed sideways, and rotated around the axis of the forearm. That's 3 more 10s for a total of 7. The forearm can be raised or lowered, and swung sideways; new total is 9. The upper arm can be swung forward-backwards, or sideways; new total is 11. The body can be moved forwards-backwards, and sideways: new total is 13. Then there are the variables of force, speed, and acceleration, for a total of at least 16. Thus the total parameter space of a pianist has many more than 10(exp)16 states (one followed by 16 zeros!). The actual number for a given piece of music is many orders of magnitude larger because of the above calculation is only for one note and a typical piece of music contains thousands or tens of thousands of notes. The final parameter space is therefore about 10(exp)20. This is approaching the ensemble space for molecules; for example, one cc of water has 10(exp)23 molecules, each with several degrees of freedom of motion and many possible energy states. Since thermodynamics applies to volumes of water very much smaller than 0.0001 cc, the canonical ensemble of the pianist is pretty close to thermodynamic conditions.

If the canonical ensemble of the pianist is nearly thermodynamic in nature, what conclusion can we draw? The most important result is that any single point in this phase space is totally irrelevant, because the chances of your reproducing this particular point is essentially zero. From this result, we can draw some immediate conclusions:

First Law of Pianodynamics: no two persons can play the same piece of music in exactly the same way. A corollary to this first law is that the same person, playing the same piece of music twice, will never play it exactly the same way.

So what? Well, what this means is that the notion that listening to someone play might decrease your creativity by your imitating that artist is not a viable idea, since it is never possible to imitate exactly. It really supports the school of thought which claims that listening to good artists play cannot hurt. Each pianist is a unique artist, and no one will ever reproduce her/is music. The corollary provides a scientific explanation for the difference between listening to a recording (which reproduces a performance exactly) and listening to a live performance, which can never be reproduced (except as a recording).

Second Law of Pianodynamics: we can never completely control every aspect of how we play a given piece.

This law is useful for understanding how we can unconsciously pick up bad habits, and how, when we perform, the music takes on its own life and in some ways, goes out of our own control. The powerful laws of pianodynamics take over in these cases and it is useful to know our limitations and to know the sources of our difficulties in order to control them as much as possible. It is a truly humbling thought, to realize that after a long, hard practice we could have picked up any number of bad habits without ever even suspecting it. This may in fact provide the explanation of why it is so beneficial to play slowly on the last run-through during practice. By playing slowly and accurately, you are greatly narrowing the ensemble space, and excluding the "bad" ones that are far away from the "correct" space of motions. If this procedure does indeed eliminate bad habits, and is cumulative from practice session to practice session, then it could produce a huge difference in the rate at which you acquire technique in the long run.

Increasing Speed

2006-02-24T08:07:00.000-08:00

These results also provide the mathematical basis for explaining the well known trick of alternating fingers when playing the same note many times. One might think at first that using just one finger would be easier and offer more control, but that note can be played repetitively faster by playing parallel using as many fingers as you can for that situation, than playing serially.

The need for parallel play also singles out trills as a particularly difficult challenge to play fast because trills must in general be executed with only two fingers. If you tried to trill with one finger, you will hit a speed wall at, say, speed M; if you trill with two fingers, the speed wall will be at 2M (again, ignoring momentum balance). Does mathematics suggest any other way of attaining even higher speeds? Yes: phase truncation.

What you can do is to lower the finger to play the note but then raise the finger only sufficiently to reset the repetition mechanism, before playing the next note. You may need to raise the finger by only 90 degrees instead of the normal 180 degrees. This is what I mean by phase truncation; the unnecessary part of the total phase is truncated off. If the original amplitude of finger travel for the 360 degree motion was 2 cm, with a 180 degree truncation, the finger now moves only 1 cm. This 1 cm can be further reduced until the limit at which the repetition mechanism stops working, at about 5 mm. Phase truncation is the mathematical basis for the fast repetition of the grand and explains why the rapid repetition is designed to work with a short return distance.

A good analogy to gaining speed in this way is the dribbling action of a basketball, as contrasted to the swinging action of a pendulum. A pendulum has a fixed frequency of swing regardless of the swing amplitude. A basketball, however, will dribble faster as you dribble closer to the ground (as you reduce the dribble amplitude). A basketball player will generally have a hard time dribbling until s/he learns this change in dribble frequency with dribble height. A piano acts more like a basketball than a pendulum (fortunately!), and the trill frequency increases with decreasing amplitude until you reach the limit of the repetition mechanism. Note that even with the fastest trill, the backcheck is engaged for a correct trill, because the keys must always be depressed completely. The trill is possible because the mechanical response of the backcheck is faster than the fastest speed that the finger can achieve.

The trill speed is not limited by the piano mechanism except for the height at which the repetition stops working. Thus it is more difficult to trill rapidly with most uprights because phase truncation is not as effective. These mathematical conclusions are consistent with the fact that to trill fast, we need to keep the fingers on the keys and to reduce the motions to the minimum necessary for the repetition mechanism to work. The fingers must press "deeply into the piano" and just lifted sufficiently to activate the repetition mechanism. Furthermore, it helps to use the strings to bounce the hammer back, just as you bounce the basketball off the floor. Note that a basketball will dribble faster, for a given amplitude, if you press down harder on it. On the piano, this is accomplished by pressing the fingers firmly down on the keys and not letting them "float up" as you trill.

Another important factor is the functional dependence of finger motion (purely trigonometric, or hyperbolic, etc.) for controlling tone, staccato, and other properties of the piano sound relating to expression. With simple electronic instruments, it is an easy task to measure the exact finger motion, complete with key speed, acceleration, etc. These characteristics of each pianist's playing can be analyzed mathematically to yield characteristic electronic signatures that can be identified with what we hear aurally, such as angry, pleasant, boisterous, deep, shallow, etc. For example, the motion of the key travel can be analyzed using FFT (fast Fourier transform), and it should be possible, from the results, to identify those motion elements that produce the corresponding aural characteristics. Then, working backwards from these characteristics, it should be possible to decipher how to play in order to produce those effects. This is a whole new area of piano play that has not been exploited yet. This kind of analysis is not possible by just listening to a recording of a famous artist, and may be the most important topic for future research.

Speed Walls

2006-02-24T08:04:00.000-08:00

Let's assume that a person starts practicing a piece of music by first playing slowly, using mostly serial play, since that is the easiest way (let's ignore chords for the time being). As the finger speed is gradually increased, s/he will naturally hit a speed wall because human fingers can move only so fast. Thus we have mathematically discovered one speed wall, and that is the speed wall of serial play. How do we break this speed wall? We need to find a play method that has no speed limit. That is parallel play. In parallel play, you increase the speed by decreasing the phase difference. That is, speed is numerically proportional to the inverse of the phase difference. Since we know that the phase difference can be decreased to zero (which gives you a chord), we know that parallel play has the potential give you infinite speed and therefore it has no theoretical speed limit. We have arrived at a mathematical foundation for the chord attack!

The distinction between serial and parallel play is somewhat artificial and oversimplified. In reality, practically everything is played parallel. Thus the above discussion served only as an illustration of how to define or identify a speed wall. The actual situation with each individual is too complex to describe (because speed walls are caused by bad habits, stress and HT play), but it is clear that wrong playing methods are what create speed walls and each person has her/is own mistakes that result in speed walls. This is demonstrated by the use of parallel set exercises which overcome the speed walls. This means that speed walls are not always there by themselves, but are created by the individual. Therefore, there is any number of possible speed walls depending on each individual and every individual has a different set of speed walls. There are, of course common classes of speed walls, such as those created by stress, by wrong fingering, by lack of HS technique, lack of HT coordination, etc. It would be, in my opinion, very counterproductive to say that such complex concepts will never be scientifically or mathematically treated. We have to. For example, in parallel play, phase plays a very important part. By decreasing the phase to zero, we can play infinitely fast, in principle.

Can we really play infinitely fast? Of course not. So then what is the ultimate parallel speed limit, and what mechanism creates this limit? We know that different individuals have different speed limits, so the answer must include a parameter that depends on the individual. Knowing this parameter will tell us how to play faster! Clearly, the fastest speed is determined by the smallest phase difference that the individual can control. If the phase difference is so small that it cannot be controlled, then "parallel play speed" loses its meaning. How do we measure this minute phase difference for each individual? This can be accomplished by listening to her/is chords. The accuracy of chord play (how accurately all the notes of the chord can be played simultaneously) is a good measure of an individual's ability to control the smallest phase differences. Therefore, in order to be able to play parallel fast, you must be able to play accurate chords. This means that, when applying the chord attack, you must first be able to play accurate chords before proceeding to the next step.

It is clear that there are many more speed walls and the particular speed wall and the methods for scaling each wall will depend on the type of finger or hand motion. For example you can attain infinite speed with parallel play only if you have an infinite number of fingers (say, for a long run). Unfortunately, we have only ten fingers and often only five are available for a particular passage because the other five are needed to play other parts of the music. As a rough approximation, if serial play allows you to play at a maximum speed of M, then you can play at 2M using two fingers, 3M using three fingers, etc., serially. The maximum speed is limited by how rapidly you can recycle these fingers. Actually, this is not quite true because of momentum balance (it allows you to play faster), which will be treated separately below. Thus each number of available fingers will give you a different new speed wall. We therefore arrive at two more useful results. (1) there can be any number of speed walls, and (2) you can change your speed wall by changing your fingering; in general, the more fingers you can use in parallel before you need to recycle them, the faster you can play. Putting it differently, most conjunctions bring with them their own speed walls.

Serial, Parallel Play

2006-02-24T07:58:00.000-08:00

The finger motions for playing the piano can be classified at the most basic level as serial or parallel. In serial play, each finger is lowered in succession in order to play. A scale is an example of something that can be played serially. In parallel play, all fingers move together. A chord is an example of parallel play. As we shall see later, a scale can also be played parallel.

Serial play can be described by any oscillatory function such as a trigonometric function of hyperbolic function. It is basically characterized by an amplitude (the distance you move the finger up and down) and a frequency (how fast you play). Except for chords and rapid rolls, most slow pieces can be played serially, and beginners tend to start by playing serially. In parallel play, there is a well defined phase relationship between different fingers. Therefore, we must now discuss phase in some detail.

Phase is a measure of where the finger is, in relation to the other fingers. Suppose that we use the trigonometric function (sine, cosine, etc.) to describe finger motion. Then in its rest position, the finger is, say, at zero degrees in phase space. Since we know how pianos should be played, we will build some of that knowledge into our definition of phase. Since lifting the fingers off from the keys is in general not the correct way to play, we will define the zero of the phase as the upper rest positions of the keys. Thus the zero phase position of the black keys will be higher than the zero phase position of the white keys by the extra height of the black keys. Furthermore, we assume that if you lift the fingers off the keys, this extra motion does not count as far as the phase is concerned. These conventions are in accord with good technique and also simplify the mathematics. Then the phases of this motion can be defined as: finger depressing half way down = 90 degrees; depressing to bottom position = 180 degrees, rising half way up = 270 degrees, and rising back to the original position = 360 degrees, which is also zero degrees again. Now in parallel play, if the second finger starts its motion when the first finger is at 90 degrees, the third finger starts off when the first finger is at 180 degrees, etc., then this parallel play will play notes 4 times faster than serial play at the same finger speed. In this case the phase difference between fingers is 90 degrees. If you were to decrease the phase difference to 9 degrees, the notes will be played 40 times faster -- this example illustrates the power of parallel playing for speeding up your play. In a chord, the phase difference is zero.

Serial play can be defined as parallel play in which the phase difference between successive fingers is about 360 degrees or larger, or in which the phases are not inter-related. Hand motion helps both serial and parallel play, but in different ways. It helps serial play by adding to the amplitude. But it affects parallel play in a most important way by helping you to control the phase. With these simple definitions, we can start to generate some useful results.

Why do we need a Mathematical Theory?

2006-02-24T07:56:00.000-08:00

Any discipline can benefit from a basic mathematical theory if a valid theory can be formulated. Every field that was successfully mathematized has inexorably advanced by leaps and bounds. This is because once the theory is correctly formulated, the powerful mathematical tools and conclusions can all be applied with great certainty. Below is my first attempt at such a formulation for piano. As far as I know, it is the first of its kind in the history of man. Such virgin territory has historically yielded enormous benefits very quickly. I was surprised myself by how many useful, and sometimes hitherto unknown, conclusions we can draw from some very rudimentary theories, as you will see. Whatever math I use below is truly simple math. At this early stage, we can do a lot with the simplest concepts. Further advances are obviously possible by application of higher mathematics. I will also discuss some of those possibilities.

There is little question that the art of piano playing suffers from a total lack of mathematical analysis. In addition, no one doubts that speed, acceleration, momentum, force, etc., play critical roles in piano play. No matter what genius lies behind the artist, the music must be transmitted, through flesh and bone, and via a mechanical contraption consisting of wood, felt, and metal. Therefore, we are dealing with not only a mathematical, but also a total scientific approach that involves human physiology, psychology, mechanics and physics that all tie together to represent what we do at the piano.

The need for such an approach is demonstrated by the fact that there are many questions for which we still have no answers. What is a speed wall? How many are there? What causes them? Is there a formula for overcoming speed walls? What are pianists doing when they play harsh versus sweet, or shallow versus deep? Is it possible to teach two different pianists to play the same passage in exactly the same way? Is there any way to classify different finger motions like there is for the horse's gaits? We answer all of these questions below.

The advantages of a mathematical theory are obvious. For example, if we can mathematically answer the question of what a speed wall is (or what they are -- if the theory predicts more than one!), then the theory should immediately provide us with possible solutions on how to break the speed wall(s). Today, no one knows how many speed walls there are. Just knowing how many there are would be a terrific advance. It may be important to prove mathematically that no two pianists (or one pianist) can ever play the same piece exactly the same way. This is because, in that case, listening to someone else play may not be harmful because you cannot imitate it exactly anyway (assuming that exact imitation is not desirable), and trying to teach a student to imitate a famous artist exactly is then proven to be impossible. This will clearly affect how teachers teach students using examples of recordings from famous artists.

Until quite recently, chemists scoffed at physicists who were able to apply equations to lots of things but couldn't even come close explaining simple chemical reactions. Biology and medicine also initially developed in their own ways, with little math and using methods that were far removed from fundamental science. Medicine, biology, and chemistry, all started initially as pure art. Now, all three disciplines are intensely mathematical and rely on the most advanced scientific principles. The ensuring accomplishments in these fields are too numerous to discuss here. One example: in chemistry, the chemists' most basic foundation, the periodic table of the elements, was explained by physicists using quantum mechanics. As a result of becoming more scientific, all three disciplines are enormously successful and are advancing in leaps and bounds. The "scientification" of any discipline is inevitable; it is only a matter of time, because of the enormous benefits that can follow. The benefits of scientification will also apply to music.

So how do we apply the exact science of mathematics to something that is perceived as art? Certainly, in the beginning, it will be crude, but refinements are certain to follow. Already, piano technicians know that the piano itself is a marvel in the use of basic physics in its design. Piano technicians must be familiar with an enormous amount of science, math, and physics in order to ply their "art". A mathematical theory of piano playing must start with a scientific approach in which each item under discussion is clearly defined and classified; see "The Scientific Method" in Chapter Three. Once this is accomplished, we search for all relevant relationships between these objects. These procedures comprise the essence of Group Theory. It is elementary! Let us begin.

The Psychology of Piano

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We are all aware that psychology plays a major role not only in music, but also in piano learning. There are numerous ways for taking advantage of our understanding of psychology and we will discuss some of these methods in this section. However, the more important immediate task is to uncover the psychological pitfalls that have created seemingly insurmountable obstacles to learning piano, such as “lack of talent”, or “nervousness” when performing. Another example is the phenomenon of the great artists’ inability to teach discussed in section 16.e above. This phenomenon was explained in terms of the artists’ psychological approach to teaching which mirrored their approach to composing music. Since the psychology of music is only minimally understood, composers simply create music in their minds “out of nothing” -- there is no such thing as a formula for creating music. They similarly acquired technique by imagining the musical output and letting the hands find a way to accomplish it. It is a terrific shortcut to a complex result, when it works, and is still the only way for composing music. However, for most students, it is a most inefficient way for acquiring technique and we now know that there are better approaches. Therefore, an analysis of these psychological approaches is a necessary component of piano pedagogy.

Psychology is mostly controlled by knowledge and it is often difficult to distinguish between psychology and knowledge. In most cases, it is knowledge that controls how we psychologically approach a subject. What we are discussing here is clearly psychology because knowledge is not enough -- you need to actually change the mental approach in order to accomplish the objective. Knowledge makes this change possible, or even easy. It is now time to examine some specific items.

Perhaps the most important one is how we view piano learning, or our general attitude towards the process of learning to play. The methods of this book are diametrically opposite to most other older methods. For example, when a student fails to learn, it was because of a lack of talent according to the old system, so failure was the student’s fault. In the system of this book, failure is the teacher’s fault because the teacher’s job is to provide all the information necessary for success. This new assignment of fault is possible only if there is sufficient information so that all reasonably competent students (over 90% of the human population) can succeed; but that is indeed the case with the material available here. Previously, the teacher was the master of the art, and the student had to follow strict rules provided by the teacher. In our new system, the student is the employer and master of the learning process and the teacher must provide what the student needs; in other words, the teacher supplies the necessary information and the student designs her/is own practice routines using this information. Now the responsibility for understanding the learning process falls on the student because s/he is in charge of the learning process -- there is no more blind faith that practicing Hanon for one hour every day will transform you into a virtuoso. In fact, nothing should be taken on faith and it is the teacher’s responsibility to explain each method so that the student understands it. This will require the teacher to be knowledgeable in a wide variety of disciplines, especially the sciences. We have come to a point in history when art teachers cannot ignore science any more. Therefore, the psychology of piano learning requires profound changes in the requirements for both the student and the teacher.

In short, the old system was a system of rules based on historical practices; the new one is a system of methods based on knowledge.

For the students, especially those trained in the old system with rules, the transition from the old to the new ranges from “very easy” to complete confusion. Some students will instantly enjoy the new empowerment and freedom and, within a week, are enjoying the full benefits of the methods. On the other extreme are those students who don’t immediately realize that there are no more rules and are still looking for “new rules” to follow. They are full of questions: When I cycle one hand, is 10 times enough, or do I need 10,000 times? Do I cycle as fast as I can, or at a slower, more accurate speed? Is HS practice necessary, even if I can already play HT? For simple music, HS practice can be awfully boring -- why do I need it? Such questions reveal the extent to which the student has adapted to the new psychology, or failed to adapt. To illustrate, let us psycho-analyze the last question. In order to ask such a question, that person must have been practicing blindly because s/he read that it was necessary to practice HS. In other words, s/he was blindly following a rule. That is not the method of this book. Here, we first define an objective, and then use HS practice to achieve it. This objective might be more secure memory in order to avoid blackouts during performances, or technical development so that when you play HT, you can hear that the playing is based on superior technical skills. When these objectives are achieved, the practice is not boring at all!

For the teacher, there is no question that everything in modern society is based on broad education. There is no need to become a scientist or to study advanced concepts in psychology. Success in the real world is not tied to academic achievements; most successful business entrepreneurs don’t have an MBA. Perhaps the most important advance of modern society is that all these concepts that used to be considered specialized knowledge in advanced fields are becoming easier to understand, not because they have changed, but because a better understanding always simplifies and the teaching methods are always improving. Moreover, we are becoming more familiar with them because we need them more and more in our daily lives. This information age is also making such knowledge more easily accessible. Thus a teacher simply needs to expend the necessary energy to explore, and the results will follow automatically. What will not work is the attitude that a method has been developed for 30 years and therefore should work indefinitely without modification. The teacher needs to adopt a new psychology of open communications and perpetual learning.

Many of us need a psychological device to overcome the unfounded fear of the inability to memorize. In this book, we are not talking about memorizing Fur Elise only. We are talking about a repertoire of over 5 hours of real music, most of which you can just sit down and play at a moment’s notice. Some people have no difficulty memorizing, but most have preconceived notions that memorizing significant repertoires is only for the “gifted” few. For them, accepting the idea that “memorizing large repertoires can be routine” will only come in stages. The main reason for this unfounded fear is the past experience in which students are first taught to play a piece well, then taught to memorize which, as explained in section III.6, is one of the most difficult ways to memorize. Because so many students were taught in this way, and had tremendous difficulties, there is a general perception that memorizing is difficult. For students who were taught correctly from the beginning, memorizing is like second nature; it is an integral part of learning any new composition. For those who have not learned to memorize, the first stage is to incorporate the memorizing into the learning routine, and to understand the concept that learning and memorizing at the same time is actually faster than learning alone -- this concept is often a difficult psychological barrier to overcome. The second stage is to develop a maintenance routine, such as practicing cold, and using finished pieces to warm up your hands instead of exercises, or playing finished pieces for polishing your technique and practicing musical playing. The third stage is to find ways to maintain a large repertoire without forgetting it, such as making sure that you can still play them HS, that you can play them in your head, away from the piano, or that you can play the piece from anywhere in the middle.

Note that with each stage, you will improve your psychological health. For example, the first stage tells you that there is a better way, there is hope. In the second stage, you eliminate the fear of forgetting -- after all, it is just another stage in the memorizing process. In the third stage, you will feel a pride in your achievements and enjoy the real fruits of your efforts -- making music. Thus memorizing is just one example of how knowledge contributes to the psychological health of the pianist.

Nervousness is a particularly difficult psychological barrier to overcome. In order to succeed, you must understand that nervousness is a purely mental process. The present system of railroading young students into recitals without proper psychological preparation is counter productive, and generally produces students that are more prone to nervousness problems than when they started their lessons. Once a student experiences intense nervousness from their piano experience, it can negatively influence anything else that they do that is similar, such as appearing in plays or any other type of public performance. Therefore, the present system is bad for psychological health in general. As discussed in section 15 above, nervousness is an eminently solvable problem for most people and a good program for overcoming nervousness will contribute to mental health because of the pride, joy, and sense of accomplishment that you will feel.

In summary, this new method is devoid of faith (in rules), mystique (of great masters or established schools), or even “talent” (so often fictitious or arbitrary); instead, it is based on psychological devices derived from knowledge. These psychological devices help to nurture a healthy brain. For the student, a healthy psychological approach is an important key to successfully learning to play the piano. A piano teacher must have a deep understanding of the psychology of the piano.

Bach: the Greatest Composer and Teacher (15 Inventions and their Parallel Sets)

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In this section, we briefly analyze Bach’s fifteen 2-part Inventions (from simple structural points of view) in order to explore how and why he composed them. The objective is to better understand how to practice and benefit from Bach’s compositions. As a by-product, we can use these results to speculate on what music is and how Bach produced such incredible music out of what (we will demonstrate) is basic “teaching material” that should be no different from Czerny or Cramer-Bulow. Clearly, Bach used advanced musical concepts in harmony, counterpoint, etc., that music theoreticians are still debating to this day, while others wrote “lesson music” mainly for their finger training value. Here, we only examine the Inventions at the simplest structural level. Even at this basic level, there are some educational and intriguing ideas that we can explore and arrive at the realization that music and technique are inseparable.

There is a nice essay on Bach’s Inventions and their history, etc., by Dr. Yo Tomita of Queen’s University in Belfast, Ireland. This is one of the best analysis of the Inventions and what they contain. The name “Inventions” does not seem to have any specific meaning in terms of the contents of the Inventions. Each Invention uses a different scale (in ascending order by key) that was important in the Well Temperaments favored during Bach’s time. They were initially written for his oldest son Wilhelm Friedemann Bach when Friedemann was 9 years old, around 1720. They were subsequently upgraded and taught to other students.

The single most striking feature common to all the Inventions is that each one concentrates on a small number of parallel sets, usually less than three. Now, you might say, “That’s not fair -- since practically every composition can be decomposed into parallel sets, of course, the Inventions must be all parallel sets, so what’s new?” The new element is that each Invention is based on only one to three specific parallel sets that Bach chose for practice. To demonstrate this, we list these parallel sets below for each Invention. In order to concentrate entirely on simple parallel sets, Bach completely avoids the use of thirds and more complex chords (in one hand), that Hanon uses in his highest numbered exercises. Thus Bach wanted his students to master parallel sets before chords.

Single parallel sets are almost trivial from a technical point of view. That is why they are so useful -- they are easy to learn. Anyone with a some piano experience can learn to play them pretty fast. The real technical challenges arise when you have to join two of them with a conjunction in between. Bach obviously knew this and therefore used only combinations of parallel sets as his building blocks. Thus the Inventions teach how to play parallel sets and conjunctions -- learning parallel sets is of no use if you can’t connect them. Below, I use the term “linear” parallel set to denote sets in which the fingers play sequentially (e.g., 12345), and “alternating” sets when alternate fingers play (132435). These joined parallel sets form what is normally called “motifs” in these Inventions. However, the fact that they are created using the most basic parallel sets suggests that the “motifs” were not chosen because of their musical content, but were chosen for their pedagogical value and the music was then added with the genius of Bach. Thus only Bach could have achieved such a feat; this explains why Hanon failed. Only one representative combination of parallel sets is listed below for each Invention; Bach used them in many variations, such as reversed, inverted, etc. Note that Hanon based his exercises on essentially the same parallel sets, although he probably accomplished this by accident, by extracting these motifs from Bach's works. Perhaps the most convincing evidence that Bach knew about parallel sets is the beautiful progressive complexity of the sets he chose with increasing Invention number.

List of the parallel sets in each Invention (for the RH):
#1: 1234 and 4231 (linear followed by alternating); in a later modification of this Invention, Bach replaced the 4231 alternating set with two linear sets, 432,321. This change is logical because it converts this Invention from one that teaches two different types of parallel sets to one that concentrates on only one, since these inventions are arranged in order of increasing parallel set complexity. Thus the alternating parallel set 4231 was out of order for the first Invention. However, the order of difficulty of each Invention may not follow the same order as parallel set complexity for most people, because the structural simplicity of the parallel sets does not always equate to easier playing.

#2: Linear sets as in #1, but with a wider variety of conjunctions. An added complexity is that the same motif, appearing at different times, requires a different fingering. Thus the first two inventions deal mainly with linear sets, but the second one is more complex.

#3: 324 and 321 (alternating followed by linear). A short alternating set is introduced.

#4: 12345 and 54321 with an unusual conjunction. These longer linear sets with the unusual conjunction increase the difficulty.

#5: 4534231; full blown alternating sets.

#6: 545, 434, 323, etc., the simplest example of the most basic 2-note parallel sets joined by one conjunction; these are difficult when the weak fingers are involved. Although they are simple, they are an extremely important basic technical element, and alternating them between the two hands is a great way to learn how to control them (using one hand to teach the other, section II.20). It also introduces the arpegic sets.

#7: 543231; this is like a combination of #3 and #4 and is therefore more complex than either one.

#8: 14321 and first introduction of the “Alberti” type combination 2434. Here, the progression in difficulty is created by the fact that the initial 14 is only one or two semitones which makes it difficult for combinations involving the weaker fingers. It is amazing how Bach not only knew all the weak finger combinations, but was able to weave them into real music.

#9: The lessons here are similar to those in #2 (linear sets), but are more difficult.

#10: This piece consists almost entirely of arpegic sets. Because arpegic sets involve larger finger travel distances between notes, they represent another progression in difficulty.

#11: Similar to #2 and #9; again, difficulty is increased, by making the motif longer than for the preceding pieces. Note that in all the other pieces, there is only a short motif followed by a simple counterpoint section which makes it easier to concentrate on the parallel sets.

#12: This one combines linear and arpegic sets, and is played faster than previous pieces.

#13: Arpegic sets, played faster than #10.

#14: 12321, 43234; a more difficult version of #3 (5 notes instead of 3, and faster).

#15: 3431, 4541, difficult combinations involving finger 4. These finger combinations become especially difficult to play when many of them are strung together.

The above list shows that:
(i) There is a systematic introduction of increasingly complex parallel sets.
(ii) There tends to be a progressive increase in difficulty, with emphasis on developing the weaker fingers.
(iii) The “motifs” are, in reality, carefully chosen parallel sets and conjunctions, chosen for their technical value just as in the Hanon series. However, Bach succeeded where Hanon failed because Bach understood the difference between music and noise, and that music and technique cannot be learned separately.

The fact that motifs, chosen simply for their technical usefulness, can be used to create some of the greatest music ever composed is intriguing. This fact is nothing new to composers. To the average music aficionado who has fallen in love with Bach’s music, these motifs seem to take on special significance with seemingly deep musical value because of the familiarity created by repeated listening. In reality, it is not the motifs themselves, but how they are used in the composition that produces the magic. If you look simply at the barest, basic motifs, you can hardly see any difference between Hanon and Bach, yet no one would consider the Hanon exercises as music. The complete motif actually consists of the parallel sets and the attached counterpoint section, so-called because it acts as the counterpoint to what is being played by the other hand. Bach’s clever use of the counterpoint obviously serves many purposes, one of which is to create the music. The counterpoint (which is missing in the Hanon exercises) might appear to add no technical lessons (the reason why Hanon ignored it), but Bach uses it for practicing skills such as trills, ornaments, staccato, etc., and the counterpoint certainly makes it much easier to compose the music and adjust its level of difficulty.

Thus music is created by some “logical” sequence of notes or sets of notes that is recognized by the brain, just as ballet, beautiful flowers, or magnificent scenery is recognized visually. What is this “logic”? A large part of it is automatic, almost hard-wired brain data processing, as in the visual case; it starts with an inborn component (newborn babies will fall asleep when they hear a lullaby), but a large component can be cultivated (e.g., Bach versus Rock and Roll). But even the cultivated component is mostly automatic. In other words, when any sound enters the ears, the brain instantaneously begins to process and interpret the sounds whether we consciously try to process the information or not. An enormous amount of this automatic processing goes on without our even noticing it, such as depth perception, eye focusing, direction of origin of sounds, walking/balancing motions, etc. Most of that processing is inborn and/or cultivated but is basically out of our conscious control. The result of that mental processing is what we call music appreciation. Chord progressions and other elements of music theory give us some idea of what that logic is. But most of that “theory” today is a simple compilation of various properties of existing original music. They do not provide a sufficiently basic theory to allow us to create new music, though they allow us to avoid pitfalls and extend/complete a composition once you have somehow generated a viable motif. Thus it appears that music theory today is still very incomplete. Hopefully, by further analyzing music from the great masters, we can, slowly, step by step, approach that goal of developing a better understanding of music.

Finally, it is clear that the Inventions were created for technique development. However, Bach’s music has not been utilized as much as they should have been in the past because of the difficulty of learning to play them for students unfamiliar with effective practice methods. The methods of this book should eliminate those difficulties and allow more widespread use of this most valuable resource for healthy technique acquisition. Hopefully, this section illustrates the synergy between Bach’s teachings and the methods of this book which will allow more students to benefit from the world’s greatest music composed by the world’s greatest teacher.

“Normal” Practice Routines and Bach’s Teachings

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After 3 or 4 days, you can return to your “normal” practice routine. For the “memorizing” routine, we basically did nothing but memorize because mixing memorizing with other practice will slow down the memorizing process. In the “normal” routine, we can take advantage of the beginning, when the hands are still “cold”. If you had never done this before, you must practice playing your finished pieces “cold”. Of course, you cannot play difficult, fast pieces cold. Either play easier pieces, or play the difficult ones slowly. A good procedure is to start with easier ones and gradually play the harder ones. Once you become a strong enough performer so that you have no trouble playing cold (this may take a year), this step becomes optional, especially if you play the piano every day. If you do not play every day, you may lose the ability to play cold if you stop practicing it. Another thing that can be practiced during this warming-up period is scales and arpeggios; see sections III.4.b and III.5 for details on how to practice them. You might also try the finger independence and lifting exercises of III.7.d. Start practicing other compositions in addition to the Bach.

By this time, you should be able to play the entire Bach Invention in your mind, HS, with no trouble. This is a good time to conduct maintenance on pieces you had memorized previously, because learning a new piece will often result in forgetting portions of previously learned pieces. Alternate practice between the Bach Invention and your old pieces. You should practice the Bach HS most of the time until you have acquired all the necessary technique. Increase speed as quickly as you can, to speeds faster than the final speed. Practice mostly those sections that give you difficulty; there is no need to practice sections that are easy for you. Once you get to a certain speed HS, start practicing HT at a slower speed. As soon as you feel comfortable HT at a slow speed, bring it up to a faster speed. To increase speed (HS or HT), do not use the metronome or force your fingers to play faster. Wait until you get the feeling that the fingers WANT to go faster, and then increase the speed by a comfortable amount. This will allow you to practice relaxed and avoid all speed walls.

The most important function of HS practice is technique acquisition; therefore, do not try to acquire technique HT, because you can waste a lot of time trying to do that. In order to transition successfully from HS to HT practice, cultivate the feeling that the two hands need each other in order to play. This will help you to find those motions that help HT play. Thus HT play is not just a superposition of HS play, but a new mode of play. HS play is useful even during HT play; for example, if you make a mistake playing HT, you can correct it without interrupting the music by going back to HS play for the hand that made the error while continuing uninterrupted with the other hand. Without extensive HS practice, such a feat would be impossible.

In order to acquire the specific techniques that Bach had in mind, we must analyze this Invention in some detail. Bach’s Inventions were composed mainly as practice pieces for technique and each Invention teaches you specific new sets of techniques. Therefore, we must know what types of skills this Invention is intended to teach us. Bach teaches us not only specific skills, but also HOW TO PRACTICE THEM! That is, by analyzing the Inventions, we can learn many of the practice methods of this book!!

The main theme of this Invention is given by the first 4 bars of the RH. This is then repeated by the LH. The structure of these Inventions, consisting of 2 voices, has a dual purpose. The first is that it teaches us hand independence. The second, less obvious one, is that it is telling us to practice HS! Both hands play basically the same things, giving us the opportunity to balance the technical levels of the two hands; this can only be achieved by HS practice and giving the weaker hand more work. There is no better way to practice hand independence, the principal lesson of the Inventions, than by practicing the hands separately. The section where one hand is trilling would be devilishly difficult to practice HT from the beginning, whereas it is quite easy, HS. Some students who do not know HS practice will try to “match” the two hands by figuring out the trill notes ahead of time and then slowing it down for HT practice. This may be appropriate for beginners or youngsters who have not yet learned to trill. Most students should trill (HS) from the beginning, and work on accelerating the trill as soon as possible. There is no need to mathematically match the two hands; this is art, not mechanics! Bach wants you to trill one hand independently of the other. The reason why you should not match the notes is that these trills are just a device to sustain the notes for a long time, and the individual notes have no rhythmic value. What do you do, then, if you happen to end up with the wrong trill note at the end? You should be able to compensate for that by either waiting briefly or changing the speed of the trill near the end -- that is the type of skill that this Invention teaches. Therefore, matching the trill to the other hand for practice defeats the lesson of this Invention. The staccato in bars 3 and 4 of the RH is another device for practicing hand independence; staccato in one hand versus legato in the other requires more control than both legato. The staccato should be used throughout the piece although, in many editions, they are indicated only at the beginning.

Most Bach lesson pieces teach not only independence between the hands but also independence of the fingers within one hand, and especially the 4th finger. Thus in bars 11 and 13, there are 6 notes in the RH that can be played as two triplets but are actually three doublets because of the 3/8 time signature. These bars can be difficult for beginners because they require the coordination of three difficult motions: (i) the RH fingering symmetry is that of 2 triplets (345345 rhythm), but it must be played as 3 doublets (345345), (ii) at the same time, the LH must play something completely different, and (iii) all this must be accomplished using mostly the three weakest fingers, 3, 4, and 5. Bach frequently used this device of forcing you to play a rhythm that is different from the fingering symmetry in order to cultivate finger independence. He also tries to give the 4th finger as much work as possible, as in the final 45.

The triplets are easier to play using 234 fingering instead of 345, especially for larger hands, and most editions suggest the 234 fingering. Knowledge of parallel set exercises indicates that Bach’s original intent was 345 (for maximum technical development value), and it is a “musical license” to change it to 234 in order to facilitate musicality. That is, in any composition other than these Inventions, 234 would be the correct fingering. Use of 234 can be further justified here because it teaches the student the principle of choosing the fingering with the greatest control. Therefore, the student can justifiably choose either fingering. A similar situation arises in bar 38 where Bach’s original intention for the LH was probably 154321 (a more complete parallel set) whereas musical license would indicate 143212 which is technically less demanding. Without help from parallel set exercises, the obvious choice is the musical license. By using parallel set exercises, the student can learn to use either fingering with equal ease.

The “triplets in 3/8 signature” is a good example of how reading the music incorrectly makes it difficult to get up to speed and how speed walls form. When playing HT, you will encounter problems if you play the RH triplets in two beats (wrong way) and the LH in three (correct). Even if you made a second mistake of playing the LH in two beats in order to match the RH, there will be a problem with the rhythmic change from adjacent bars. You might manage to play through these mistakes at slow speed, but when speeded up, they become impossible to play and you begin to build a speed wall. This is an example of the importance of rhythm. It is amazing how many lessons Bach can cram into something that looks so simple, and these complexities partly explain why, without proper practice methods or guidance from knowledgeable teachers, many students find it impossible to memorize Bach or to play his compositions beyond a certain speed. The lack of proper practice methods is the main reason why so many students end up playing so few Bach pieces.

The Inventions are excellent technical lesson pieces. Hanon, Czerny, etc., tried to achieve the same ends using what they thought were simpler, more systematic approaches but they failed because they tried to simplify something that is infinitely complex. By contrast, Bach squeezed as many lessons as he could into every bar, as demonstrated above. Hanon, Czerny, etc., must have been aware of the difficulties of learning Bach but were unaware of good practice methods, and tried to find simpler methods of acquiring technique by following their intuitive instincts. This is one of the best historical examples of the pitfalls of the intuitive approach.

Because the Inventions were composed for teaching specific skills, they can sound somewhat constrained. In spite of this constraint, all of Bach’s lesson pieces contain more music than practically anything ever composed and there are enough of them to satisfy the needs of students at any level, including beginners. If the inventions are too difficult, consider studying the very large number of delightful (and eminently performable) simpler lesson pieces Bach composed. Most of them can be found in the “Clavier Book of Anna Magdalena Bach” (his second wife). Because there are so many, most books will contain only a small number of selections. Because the Inventions are lesson pieces, almost every edition has the critical fingerings indicated. Therefore, figuring out the fingerings, which is extremely important, should not be a problem.

The Inventions were composed by assembling well defined segments that are usually only a few bars long. This makes them ideal for using HS segmental practice, another key element of the methods of this book. This, and many other properties of Bach’s compositions make them ideal music to learn using the methods of this book, and it is quite probable that they were composed with these practice methods in mind. Bach may have been aware of most of the material of this book!

Another important lesson of Bach’s Inventions is parallel sets. The main technical lesson of this Invention #4 is the parallel set 12345, the basic set needed to play the scale and runs. However, Bach knew that a single parallel set is too dangerous from a technical point of view because you can cheat by phase locking without acquiring technique. In order to prevent phase locking, he added one or two notes to the parallel set. Now if you tried to cheat, you will be caught immediately because the music will not come out even: Bach has given you no choice but to acquire the required technique if you want to play this musically! Here is another example of Bach teaching us why music and technique are inseparable (by using music as a criterion for technique acquisition). Therefore, the quickest way to learn to play this Invention is to practice the 12345 and 54321 parallel sets. As soon as you test your fingers using these parallel sets, you will understand why Bach composed this Invention. If you can do these parallel set exercises satisfactorily, this piece will be quite easy, but you will find that the parallel sets are not easy at all, and will probably require lots of work even if you are at an intermediate level. First work on these sets using only white keys; then work on others that include black keys, as suggested by Bach. A good example is the LH 12345 parallel set of bars 39-40, with the difficult 4th finger on a white key following 3 on black. Bach extracts the most difficult part of this parallel set, 2345, and repeats it in bar 49.

Bach clearly saw the value of playing a small number of notes very quickly, such as ornaments and trills, for developing technique (velocity). Thus his ornaments are another key device for acquiring technique, and they are essentially a small assemblage of parallel sets. There are numerous discussions on how to play Bach’s ornaments; these discussions are important from the point of view of correct musical expression, but we must not miss the point that technically, ornaments in lesson pieces are an essential device for acquiring velocity, and are not just musical ornaments. Play both the RH and LH trills with fingers 1 and 3, which will make the LH trill easier to learn. Most students will be able to play the RH trill better than the LH trill in the beginning; in that case, use the RH to teach the LH. This “technique transfer” from one hand to the other is easier if both hands use similar fingering. Because the purpose of the trill is simply to sustain the notes, there is no specific trill speed that is required; however, try to trill the two hands at the same speed. If you want to trill very fast, use the parallel sets to practice them as described in section III.3.a. It is extremely important to start the first two notes rapidly if you want to trill fast. The easiest way to do this is to phase lock them. This phase-locked “non-musical play” will not be noticeable because it comes so quickly at the beginning of the trill. In fact, if the first 2 notes are faster than the rest of the trill, the audience will think that the entire trill is faster than it actually is. Watch the positions of fingers 2, 4, and 5 while trilling. They should be stationary, close to the keys, and slightly curved.

Most students find it difficult to play these Inventions beyond a certain speed, so let’s visit a practice routine for increasing speed. Using this type of routine, you should be able to eventually play at practically any reasonable speed, including speeds at least as fast as those of Glen Gould and other famous pianists. We will learn to play bars 1 and 2 fast, and after that, you should be able to figure out how to accelerate the rest. Note that these two bars are self-cycling (see section III.2). Try cycling it rapidly. Chances are, you will fail because stress develops rapidly with speed. Then just practice 212345 of bar 1 until it is smooth and fast. Then practice 154, then 54321 of the 2nd bar. Then connect them, and finally, cycle the two bars. You may not be able to complete everything the first day, but the PPI will make it easier on the second day. Using similar methods, solve all your technical difficulties in the entire piece. The key difficulty in the LH is the 521 of bar 4, so practice 521 parallel set until you can play it at any speed, completely relaxed. Note that the 212345 of the RH and the 543212 of the LH are thumb-passing exercises. Clearly, Bach recognized that thumb over and thumb under are critical technical elements at high speed and created numerous ingenious opportunities for you to practice them. Before you can play HT fast, you must get up to HS speeds that are much faster than the HT speed you want. “Getting up to speed” doesn’t mean just being able to attain the speed, but you must be able to feel the quiet hands and have complete control of each individual finger. Beginners may need months of HS practice for the higher speeds. Many students tend to extract more speed from their fingers by playing loud; this is also not true speed, so play everything softly for these practice sessions. When starting to play HT fast, exaggerate the rhythm -- this might make it easier. You cannot really accelerate until you can play musically; we will discuss this below. Although most Bach compositions can be played at different speeds, the minimum speed for the Inventions is the speed at which you can feel the quiet hands when you acquire the necessary technique, because if you don’t get up to that speed, you have missed one of his most important lessons.

An intermediate level player should be able to conquer the technical difficulties of this Invention in about a week. Now we are ready to practice playing it as a piece of music! Listen to several recordings in order to get an idea of what can be done and what you want to do. Try different speeds and decide on your own final speed. Video-tape your own playing and see if the result is visually and musically satisfactory; usually, it is not, and you will find many improvements you will want to make. You may never be completely satisfied even if you practiced this piece all your life.

In order to play musically, you must feel each note before playing it, even if it is just for a split second. This will not only give you more control and eliminate errors, but also allow you to accelerate continuously through the keydrop so that the hammer shank is flexed by just the right amount when the hammer strikes the strings. Pretend that there is no bottom to the keydrop and let the bottom of the keydrop stop your finger. You can do this and still play softly. This is called “playing deeply into the piano”. You cannot “raise your finger high and plonk it down” as Hannon recommended and expect to make music. Such a motion can cause the hammer shank to oscillate instead of flexing and produce an unpredictable and harsh sound. Therefore, as you practice HS, practice for musicality also. Use the “flat finger positions” of section III.4.b. Combine these with a supple wrist. Play as much as possible with the flat, fleshy part of the finger (opposite the fingernail), not the bony finger tip. If you video tape your playing, the curled finger position will look childish and amateurish. You cannot play relaxed until you can completely relax the extensor muscles of the first 2 or 3 phalanges of fingers 2 to 5. This relaxation is the essence of the flat finger positions. At first, you will be able to include all these considerations only at slow speed. However, as soon as you develop quiet hands, you will gain the ability to include them at higher speeds. In fact, because these finger positions allow complete relaxation and control, you will be able to play at much faster speed. This is one of the (many) reasons why quiet hands is so important. If you have not been paying attention to musicality, you should hear an immediate change in the tonality of your music when you adopt these principles, even at slow speeds.

Tone and color: The improved tonality will be most clearly evident when playing softly; the softer play also helps relaxation and control. The flat finger position is what enables softer play with control. How soft is soft? This depends on the music, speed, etc., but for practice purposes one useful criterion is to play softer and softer until you start to miss some notes; this level (or slightly louder) is usually the best for practicing softly. Once you have control over tonality (sound of each individual note), try to add color to your music (effect of groups of notes). Color for each composer is different. Chopin requires legato, special staccato, rubato, etc. Mozart requires the utmost attention to the expression markings. Beethoven requires uninterrupted rhythms that run continuously over many, many bars; therefore, you need to develop the skill for “connecting” consecutive bars. Bach’s Inventions are somewhat contrived and “boxed in” because they are mostly confined to simple parallel sets. You can easily overcome this handicap by emphasizing the multitude of musical concepts that give his music almost infinite depth. The most obvious musicality comes from the harmony/conversation between the two hands. The ending of every piece must be special, and Bach’s endings are always convincing. Therefore, don’t just let the ending catch up to you; make sure that the ending is purposeful. In this Invention, pay special attention to bar 50, in which the two hands move in opposite directions as you enter the authoritative ending. When you bring the music up to speed and develop quiet hands, the 6-note runs (e.g., 212345, etc.) should sound like rising and falling waves. The RH trill is bell-like because it is a full note, while the LH trill is more sinister because it is a half note. When practicing HS, note that the RH trill is not just a trill but it comes crashing down at the end. Similarly, the LH trill is an introduction to the ensuing counterpoint to the RH. You cannot bring out color unless you lift each finger at precisely the right moment. Most of Bach’s lesson pieces contain lessons in lifting the fingers accurately. Of course, the coloration should initially be investigated HS. Quiet hands is also most easily acquired HS; therefore adequate HS preparation before HT practice is of critical importance for tone and color. Once the preparation work is done, you can start HT and bring out the incredible richness of Bach’s music!

Tone and color have no limits in the sense that once you succeed, it becomes easier to add more, and the music actually becomes easier to play. All of a sudden, you may discover that you can play the entire composition without a single audible mistake. This is probably the clearest illustration of the statement that you cannot separate music from technique. The act of producing good music actually makes you a better pianist. This provides one of the explanations of why you have good days and bad days -- when your mental mood and finger conditioning are just right so that you can control the tone and color, you will have a good day. This teaches us that on bad days, you may be able to “recover” by trying to remember the fundamentals of how you control tone and color. This ends the discussions on Invention #4. We now return to the practice routine.

You have been practicing for over one hour by now, and the fingers are flying. This is the time when you can really make music! You must make every effort to practice making music during at least half of the total practice time. Once you have built up a sufficiently large repertoire, you should try to increase this “music time” from 50% to 90%. Therefore, you must consciously set aside this portion of your practice routine for music. Play your heart out, with all the emotion and expression you can muster. Finding musical expression is very difficult and exhausting; therefore, initially, it will require much more conditioning and effort than anything you can do with Hanon. If you don’t have a teacher, the only known ways to learn musicality are to listen to recordings and to attend concerts. If you are scheduled to perform a particular composition in the near future, play it slowly, or at least at a comfortable and fully controllable speed once, before going on to something different. Expression is not important when playing slowly. In fact, it may be beneficial to purposely play with little expression when playing slowly before moving on to something else.

Learning Bach is strongly emphasized in this book. Why? Because Bach’s music written for technical development is unique in piano pedagogy in its healthy, complete, efficient, and correct approach to technique acquisition -- there is nothing else like it. Every experienced teacher will assign some Bach pieces for study. As mentioned above, the only reason why students do not learn more Bach pieces is because, without the proper practice methods, they seem so difficult. You can demonstrate to yourself the benefits of the Bach lessons by learning five of his technical compositions and practicing them for half a year or more. Then go back and play the most difficult pieces that you had learned previously, and you will be amazed at the greater ease and control that you have gained. Bach’s compositions were designed to create concert pianists with sound fundamental technique. Chopin’s etudes were not designed for gradual, complete technical development and many of Beethoven’s compositions can cause hand injury and ear damage if you don’t get proper guidance (they appear to have damaged Beethoven’s hearing). Neither of them teaches you how to practice. Therefore, Bach’s compositions stand out above all others for technical development. With the practice methods of this book, we can now take full advantage of Bach’s resources for technical development that has been sadly under-utilized in the past.

In summary, there is no magical practice routine for faster learning. Only practitioners of intuitive methods who do not know how to teach practice methods need the concept of a “standard practice routine” which is a poor substitute for the missing practice methods. To those who know the practice methods, the concept of a standard practice routine becomes a somewhat silly idea. For example, a typical standard routine might start with Hanon exercises; however, you can easily bring the Hanon exercises up to ridiculous speeds by applying the methods of this book. And once you accomplish that, you begin to wonder why you are doing this. Now, what will you gain by playing these ridiculously fast Hanon pieces every day?? Instead of a standard practice routine, you must define what your objective for the practice session is, and select the practice methods needed to achieve that goal. In fact, your practice routine will constantly evolve during each practice session. Thus the key for designing a good practice routine is an intimate knowledge of all the practice methods. How different this is, from the intuitive routine described in section II.1! No more extensive finger exercises, or Czerny and other pieces just for technical work with no music. No more structured practice sessions with interminable repetitions with the brain shut off. No more speed limits, speed walls, or the boring slow practice with the metronome. Our method is pure empowerment, freeing us to quickly master the technical material so that we can concentrate on music, and even to learn as many Bach pieces as we desire.

Routine for Learning a New Piece (Invention #4)

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In this book, “Learning a new piece” is synonymous with memorizing it. Therefore, without any warm-ups, etc., immediately start memorizing Bach’s Invention #4, RH first, starting with segments of one to three bars that make up a distinct phrase, then the LH. Continue this process until you have memorized the entire piece, HS only. See section III.6 for more details on memorizing. Those already good at using the methods of this book should be able to memorize the entire Invention (not perfectly), HS, on the first day, after one or two hours of practice (for an average person with an IQ of about 100). Concentrate only on memorizing, and don’t worry about anything that you “cannot play satisfactorily” (such as the 1,3 trill in the LH), and play at any speed that is comfortable for you. If you want to memorize this piece as quickly as possible, it is best to concentrate only on this piece and not play other pieces. Instead of one long session of 2 hrs, you might practice 1 hr, twice during the day.

Memorizing is easier at faster speed. Therefore, as you memorize in segments, accelerate it as much as you can, even if this makes the playing a little sloppy. However, play it slowly once before switching hands, making sure that you play each note accurately. Play each segment just a few times, then switch hands. From the first day, try to play HS in your mind, away from the piano; if you get stuck and have a complete blackout, don’t worry, this is normal. You will re-memorize this part during the next practice session. Practice until you can play the entire composition, each hand separately.

Play Thumb Over everywhere except for the 21 in 212345 of bar 1, and other similar places, where Thumb Under is much easier. It is amazing how Bach found a way to make you practice Thumb Under in a fast passage; in practically all fast passages, you need to play Thumb Over. The choice of Thumb Under or Over will become very important later on, when we increase the velocity.

On the second day, start HT slowly, still in segments of a few bars, and then connecting them. Again, don’t practice anything else; even playing finger exercises to warm up will cause you to forget some of what you just memorized. Note that from the first day, you had started technique acquisition, which is inseparable from memory. Technique acquisition/memory is almost a purely brain process (although many people call it “hand memory”), and is composed of short term memory that is stored in a specific part of the brain, and several forms of permanent memory that are permanent changes in the brain. Short term memory is almost instantaneous, but the first form of permanent memory takes about 5 minutes to complete (even for those who can “instantly” memorize many things), and after that, the memory is in your brain essentially forever. However, there is no guarantee that you can recall it later on. This process of writing from “volatile memory” to “non-volatile memory” is automatic, and you have no control over it. The difference between good memorizers and bad memorizers is that the bad memorizers cannot recall what is already in their brain. Therefore, when you practice memorizing, you must practice recalling information rather than inputting information into the brain. The second form of permanent memory is associated with post practice improvement and actually changes your ability to play that segment, in addition to storing it in memory -- this is the technique acquisition part. Most of the permanent improvement in technique occurs during sleep, and this is one of the reasons why we need to sleep -- so that the brain can make the necessary repairs and improvements to adapt to our changing environment. Our brain is more complicated than an automobile; therefore, it is not surprising that you cannot make repairs or modifications until you bring it into a garage and shut the engine off (sleep). A good night’s sleep, including REM sleep, is necessary for making maximum progress for learning piano. REM (Rapid Eye Movement) sleep is an important stage of sleep in which the eyes move rapidly, although you are asleep. This is why sleep is so important for babies -- because there is so much construction going on in their brains.

Learning the Rules

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Therefore, the first “practice routine” you should use is to follow Chapter One, starting from the beginning and applying the concepts to a composition you want to play. The objective is to become familiar with all the available practice methods. You can choose a piece that you have never played before, but the best choice is probably a composition that you have already practiced a little so that you can concentrate more on learning the practice methods than learning the composition. Choose a piece that is not too long and not too difficult. Before you start on the piano, read the entire Chapter One (or the whole book) once quickly. Don’t even try to learn anything the first time because this book contains so many ideas, and they are described so concisely, that most people need to read it several times. You will be surprised at how well the key ideas will register permanently in your brain when you read something without trying to memorize everything in it. Read it the first time as if you are reading a novel or some fun story and skip sections that you think have too much detail; after you pass all the major ideas through your brain once, it will become much easier to understand the beginning of the book even if you don’t remember most of what you read previously. You will also have a good idea of the outline of the book and how it is organized: all the basics are presented in Chapter One, section II, and the more advanced concepts are discussed in section III.

There is no need to practice each method until you become good at it, before going on to the next one. The idea is to try each one several times and to understand the purposes of the methods and to get a rough idea of how the objectives are achieved. You will have plenty of time to practice them later on! Of course, you might have fun applying them and end up spending a lot of time on some particularly rewarding methods. There is nothing wrong with that!

Once you have some familiarity with most of the practice methods, we are ready to design practice routines. In order to design generally useful routines, we assume that you have had at least one year of serious piano practice. Our objective is to learn Bach’s Invention #4.

The “Ideal” Practice Routine (Bach’s Teachings and Invention #4)

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Is there an ideal, universal practice routine? No, because each person must design her/is own practice routine at each practice session. In other words, this book is all about designing your own practice routines. Some differences between a well designed routine and the intuitive routine of section II.1 are discussed in the last paragraph of this section. A good piano teacher will discuss the appropriate practice routines for the lesson pieces during the lesson. Those who already know how to create practice routines might still find this section interesting, as we will discuss many useful points (such as Bach’s teachings and specifics on how to practice his Invention #4) in addition to practice routines.

Many students who learn the numerous useful ideas of this book for the first time feel lost and wonder if there are magical practice routines, like the magical practice methods described here. They would like some guidance on typical practice routines that use these methods. Therefore, I describe a few sample practice routines below. Practice routines depend on the skill level, what the person wants to accomplish, the composition being practiced, what the person was practicing the day before, etc. A practice session for preparing for performances is different from that for learning a new piece, which is different from that for polishing a piece that you have been practicing for some time.

A universal routine, such as “Practice Hanon for 30 minutes, then scales/arpeggios for 20 minutes, then Cramer-Bulow (or Czerny, etc.), followed by lesson pieces” does not make any practical sense; it is the epitome of the intuitive method and reveals a general ignorance of how to practice. The question “What is a good practice routine?” is answered by “How do you design practice routines?” Instead of asking “What must I do?” you should ask “What do I want to accomplish?” You design a practice routine by (i) defining your objective and (ii) assembling the resources to accomplish it. In order to do this, you must first become familiar with all the practice methods. Since there is so much material in this book, you should not wait until you understand the last page before applying the methods. This book is written like a practice routine: you can pick a composition you want to play, and start practicing it by reading from the beginning of Chapter One and applying each principle in the order in which it is presented.

Beginners: Age 0 to 65+

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A frequent concern of many parents is "At what age can our children start piano?", while the primary concerns of older beginners are "Am I too old to learn piano? How proficient can I expect to be? How long will it take?" So let's briefly survey what we might be able to expect if you started piano at different ages. Of course, there are significant differences in "talent" among individuals, so that you may not fit into any of the categories below. However, we are increasingly beginning to recognize that what we had attributed to "talent" was in reality a result of our history. In other words, "talent" was a way for us to hide our ignorance of what really happened. This relatively recent "discovery" is radically changing the landscape of piano pedagogy. The old, intuitive system followed the sequence typified by: Beyer, Hanon, Czerny, small pieces, classics, and finally major pieces. In our new system, we eliminate the first three; i.e., we are back to what Mozart, Beethoven, etc. did. Surprise! What they did was perfectly legitimate! They may be the norm, not the exception, if you know what you are doing. Therefore, we can legitimately question whether talent is such an important factor in how quickly you can learn to play. So then, what IS an important factor? Age is one, because learning piano is a process of developing nerve cells, especially in the brain. The process of nerve growth slows down with age. So let's examine categories of beginners according to their ages, and the consequences of slowing brain growth with age. In the classifications below, we assume that the practice methods of this book are available to these individuals. It is still difficult to predict the learning rate because the methods of this book have not been widely adopted until now, these methods allow students to learn practically anything they want, within reason, at any skill level, and these methods have solved many problems that were traditionally almost insurmountable.

Ages 0-6. Babies can hear as soon as they are born, and most maternity wards test babies for hearing right after birth in order to detect abnormalities as early as possible. Up to about age 6, they acquire new skills in stepwise fashion; that is, they suddenly acquire a new skill such as language and rapidly become good at it. But each individual acquires these skills at different times and in a different order. These skills will be discussed in the next section. The most important topic in this age range is listening to music. Most parents make the mistake of giving the baby only baby music. That might be appropriate for a very short time (a few months), but you should quickly transition to adult music. It is not a good idea to expose them immediately to loud blaring trumpets and thunderous drum rolls that can frighten the baby, but most babies can understand Bach, Chopin, etc. Music is an acquired taste; therefore, how the babies' brains develop musically will depend on the type of music they hear. Older classical music started with simpler chord structures and harmonies that are easily and naturally appreciated by the human brain. Then more complex chords and dissonances were added later on as we became accustomed to them over the ages. Therefore, the older classical music is more appropriate for babies because they are more compatible with the fundamental brain processes that produce music appreciation. The piano is particularly appropriate because it is like an entire orchestra that is nonetheless based on a single chromatic scale that can lead to perfect pitch, which babies can acquire without even trying.

Ages 3-12. Below age 3, most children's hands are too small to play the piano, the fingers cannot bend or move independently, and the brain and body (vocal chords, muscles, etc.) may not yet be sufficiently developed to deal with concepts in music. Above age 4, most children are able to receive some type of music education, especially if they have been exposed to music since birth; thus they should be constantly tested for their sense of pitch (relative and perfect pitch; can they "carry a tune?"), rhythm, loud-soft, fast-slow, and reading music, which is easier than any alphabet. This group can take full advantage of the enormous brain growth that takes place during this age interval; learning is effortless and limited more by the ability of the teacher to provide the appropriate material than by the student's ability to absorb it. One remarkable aspect of this age group (there are many!) is their "malleability"; their "talents" can be molded. Thus, even if they would not have naturally become musicians if left alone, they can be made into musicians by proper training. This is the ideal age group for starting piano.

Ages 13-19, the "teen" ages. This group still has an excellent chance of becoming concert level pianists. However, they may have lost the chance to become those super stars that the younger beginners can become. Although brain development has slowed down, the body is still growing rapidly until about age 15, and at a slower rate thereafter. The most important factors here are the love of music and the piano. This age group can achieve practically anything they want to, as long as they have an intense interest in music. However, they are not malleable any more; encouraging them to learn piano does not work if they are more interested in cello or saxophone, and the parents' role changes from giving direction to giving support for whatever the teens want to do. This is the age interval in which the teens learn what it means to take responsibility and what it means to become an adult -- all lessons that can be learned from the piano experience. In order to influence them, you need to use more advanced methods, such as psychology. This age group should not be considered "too late to start" for becoming concert pianists; they still definitely have a good chance. They will probably never forget anything they memorized at these ages or younger. Above this age group, age classifications become difficult because there is so much variation among individuals depending on their history.

Ages 20-35. Some individuals in this age group still have a chance of becoming concert level pianists. They can use the experience they learned in life to acquire piano skills more efficiently than younger students. Those who decide to learn piano in this age group generally have greater motivation and a clearer understanding of what they want. But they will have to work very hard, because progress will come only after a sufficient amount of work. At this age group, nervousness can start to become a major problem for some. Although younger students can become nervous, nervousness seems to increase with age. This happens because severe nervousness arises from fear of failure, and fear arises from mental associations with memories of terrible events, whether imagined or real. These terrifying memories/ideas tend to accumulate with age. Therefore, if you want to perform, you should do some research into controlling nervousness, by becoming more confident, or by practicing public performance at every opportunity, etc. Nervousness can arise from both the conscious and subconscious brain; therefore, you will need to deal with both in order to learn to control it. For those who just want to become sufficiently technically proficient to enjoy playing major piano compositions, starting in this age group should not present any problems. Although some maintenance will be required, you can keep anything you memorized in this age group, for life.

Ages 35-45. This age group cannot develop into concert level pianists, but can still perform adequately for simpler material. They can acquire enough skill to play most famous compositions for personal enjoyment and informal performances. The most demanding material will probably be out of reach. Nervousness reaches a maximum somewhere between the ages of 40 and 60 and then often declines slowly. This might explain why many famous pianists stopped performing somewhere in this age interval. Memorizing starts to become a problem in the sense that, although it is possible to memorize practically anything, you will tend to forget it, almost completely, if not properly maintained. Reading the music can start to become a problem for some who require strong corrective lenses. This is because the distance from the eyes to the keyboard or music stand is intermediate between reading and distant vision. Thus you may want a set of eye glasses for intermediate vision. Progressive lenses might solve this problem, but some find them bothersome because of their small field of focus.

Ages 45-65. This is the age range in which, depending on the person, there will be increasing limitations on what you can learn to play. You can probably get up to the level of the Beethoven Sonatas, although the most difficult ones will be a huge challenge that will take many years to learn. Acquiring a sufficiently large repertoire will be difficult, and at any time, you will be able to perform only a few pieces. But for personal enjoyment, there is still a limitless number of compositions that you can play. Because there are more wonderful compositions to learn than you have time to learn them, you may not necessarily feel a limit to what you can play. There is still no major problems in learning new pieces, but they will require constant maintenance if you want to keep them in your repertoire. This will greatly limit your playable repertoire, because as you learn new pieces, you will completely forget the old ones, unless you had learned them at much younger ages. In addition, your learning rate will definitely start to slow down. By re-memorizing and re-forgetting several times, you can still memorize a significant amount of material.

Ages 65+. There is no reason why you can't start learning piano at any age. Those who start at these ages are realistic about what they can learn to play and generally do not have unattainable expectations. There are plenty of simple but wonderful music to play and the joy of playing remains just as high as at younger ages. As long as you are alive and not terribly handicapped, you can learn piano and make satisfactory progress at any age. Memorizing a composition you are practicing is not a problem for most. The greatest difficulty in memorizing will come from the fact that it will take you a long time to get up to speed for difficult material, and memorizing slow play is the most difficult memory work. Therefore, if you choose easy pieces that can be brought up to speed quickly, you will memorize those more quickly. Stretching the hands to reach wide chords or arpeggios, and fast runs will become more difficult, and relaxation will also be more difficult. If you concentrate on one composition at a time, you can always have one or two compositions that can be performed. There is no reason to modify your practice methods -- they are the same as those used for the youngsters. And you may not feel as much nervousness as you might have in the middle ages. Learning piano, especially memory work, is one of the best exercises for the brain; therefore, serious efforts at learning piano should delay the aging process, just as proper physical exercise is necessary to maintain health.

Starter Books and Keyboards

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The first order of business when starting is to decide which lesson books to use. For those who want to start by learning general technique (not specialties such as jazz or gospel), you can use any of a number of beginner books such as Michael Aaron, Alfred, Bastien, Faber and Faber, Schaum, or Thompson. Of these, many people prefer Faber and Faber. Most of them have beginner books designed for young children or adults. There is an excellent piano site at:

http://www.amsinternational.org/piano_pedagogy.htm

which lists most of these teaching books and reviews many of them. Depending on your age and past musical education, you can skip through these books at your pace and optimize your learning rate.

These starter books will teach you the fundamentals: reading music, various common fingerings such as scales, arpeggios and accompaniments, etc. As soon as you are familiar with most of the fundamentals, you can start learning pieces that you want to play. Here again, teachers are invaluable because they know most of the pieces that you might want to play and can tell you whether they are at the level that you can handle. They can point out the difficult sections and show you how to overcome those difficulties. They can play the lesson pieces to demonstrate what you are trying to achieve; obviously, avoid teachers who cannot or refuse to play for you. After a few months to about a year of such study, you will be ready to continue by following the material of this book. In order to avoid the numerous pitfalls that await you, it is a good idea to read this book, at least quickly once through, before you begin your first lesson.

At the very beginning, perhaps up to a year, it is possible to start learning using keyboards, even the smaller ones with less than the 88 keys of the standard piano. If you plan to play electronic keyboards all your life, it is certainly permissible to practice only on keyboards. However, practically all keyboards have actions that are too light to truly simulate an acoustic piano. As soon as possible, you will want to transition to a 88-key digital piano with weighted keys, see section 17 above.

Do You Need a Teacher?

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Many beginners would like to start learning piano on their own, and there are valid reasons for this. However, there is no question that, for the first 6 months (and probably much longer), there is no faster way to start than taking lessons from a teacher, even one who teaches the intuitive method. The only teachers to avoid completely are those who cannot teach what you want (you may want pop, jazz, and blues while the teacher teaches only classical), or those who teach strict, inflexible methods not appropriate for the student (one method might be designed for very young children but you may be an older beginner). Why are teachers so helpful in the beginning? Firstly, the most fundamental things that you do every time you play, such as hand position, sitting position, hand movements, etc., are difficult to explain in a textbook, whereas a teacher can show you instantly, what is right and what is wrong. You don’t want to pick up these wrong habits and have to live with them all your life. Secondly, a beginner sitting down at the piano and playing for the first time is usually making at least 20 mistakes at the same time (left-right coordination, volume control, rhythm, arm and body movements, speed, timing, fingering, trying to learn the wrong things first, total neglect of musicality, etc., etc.). It is the teacher’s job to identify all the mistakes and make a mental priority list of which ones must be corrected first, so that the worst offenders can be eliminated quickly. Most teachers also know which basic skills you need and teach them to you in the correct order. Teachers are also helpful in finding the appropriate teaching material for you. Teachers provide a structured learning environment, without which the student can end up doing the wrong things and not realizing that they are not making any progress. In short, teachers are definitely cost effective for beginners.

Piano Care

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All new pianos need at least a year of special care and tuning after purchase, in order for the strings to stop stretching and the action and hammers to equilibrate. Most piano dealers will try to minimize the cost of servicing the new pianos after delivery. This is assuming that the piano was properly prepped prior to delivery. Many dealers postpone a lot of the prep work until after delivery, and if the customer does not know about it, may omit some steps entirely. In this regard, among the less expensive models, Yamaha, Kawai, Petroff, and a few others may be easier to buy because most of the prep work is completed at the factory. A new piano will need at least 4 tunings the first year in order to stabilize the stretching of the strings.

All pianos require maintenance in addition to regular tuning. In general, the better the quality of the piano, the easier it is to notice the deterioration caused by normal wear and tear, and therefore the more maintenance it should require. That is, more expensive pianos are more expensive to maintain. Typical maintenance chores are: leveling the keys, reducing friction (such as polishing the capstans), eliminating extraneous sounds, re-shaping the hammers and voicing them (needling), checking the innumerable bushings, etc. Voicing the hammer is probably the most neglected maintenance procedure. Worn, hard, hammers can cause string breakage, loss of musical control (bad for technical development), and difficulty in playing softly. It also ruins the tonal quality of the piano, making it harsh and unpleasant to the ear. If the action is sufficiently worn, it may need a general regulation job, which means restoring all parts of the action to their original specifications.

For old pianos with visibly rusted strings, the sound can sometimes be improved significantly by replacing the strings. If the bass wire-wound strings are very rusted, this can deaden those notes. Replacing these strings can be quite worthwhile if those bass notes are weak and have no sustain. The upper, non-wound strings generally do not need replacing. However, for extremely old pianos, these strings can be so stretched out that they have lost all longitudinal elasticity. Such strings are prone to breakage and cannot vibrate properly, and should be replaced.

Pianists should familiarize themselves with some of the basic knowledge about tuning, such as the parts of a piano, temperaments, stability of tuning, and effects of temperature and humidity changes, in order to be able to communicate with the tuner and to understand what s/he needs to do. Too many piano owners are ignorant of these basics; consequently, they frustrate the tuner and in fact work against her/im, with the result that the piano is not properly maintained. Some owners get so accustomed to their deteriorated piano that, when the tuner does a good job of restoring it to its original glory, the owner is very unhappy about the strange new sound and feel of the piano. Worn hammers tend to produce overly bright and loud sounds; this has the unexpected effect of making the action feel light. Therefore, properly voiced hammers may initially give the impression that the action is now heavier and less responsive. Of course, the tuner did not change the force required to depress the keys. Once the owners become accustomed to the newly voiced hammers, they will find that they have much better control of expression and tone, and they can now play very softly. With worn hammers, it is very difficult to play evenly and softly.

Pianos need to be tuned at least once a year and preferably twice, during the fall and spring, when the temperature and humidity are midway between their yearly extremes. Many advanced pianists have them tuned even more frequently. In addition to the obvious advantages of being able to create better music and to sharpen your musicality, there are many compelling reasons for keeping the piano tuned. One of the most important is that it can affect your technical development. Compared to an out-of-tune piano, a well-tuned piano practically plays itself -- you will find it surprisingly easier to play. Thus a tuned piano can actually accelerate technical development. An out-of-tune piano can lead to flubs and the stuttering habit of pausing at every mistake. Many important aspects of expression can be brought out only on well-tuned pianos. Since we must always pay attention to practicing musically, it does not make sense to practice on a piano that cannot produce proper music. This is one of the reasons why I prefer Well Temperaments (with their crystal clear chords) to the Equal Temperament, in which only the octaves are clear. See Chapter Two for more discussions on the merits of various temperaments. Higher quality pianos have a distinct edge because they not only hold the tuning better, but can also be tuned more accurately. Lower quality pianos often have extraneous beats and sounds that make accurate tuning impossible. In this respect, good grands are far superior to run-of-the-mill uprights.

Those who have perfect pitch are very much bothered by pianos that are out of tune. If you have perfect pitch, severely out of tune pianos can accelerate the gradual loss of perfect pitch with age. Babies and very young children can automatically acquire perfect pitch if they hear the piano sound sufficiently frequently, even if they have no idea what perfect pitch is. In order for them to acquire the correct perfect pitch, the piano must be in tune.

If you always practice on a tuned piano, you will have a difficult time playing on one that is out of tune. The music doesn't come out, you make unexpected mistakes, and have memory blackouts. This holds true even if you know nothing about tuning and can't even tell if a particular note is out of tune. Conversely, the best way to test the tuning is to play a piece of music. Good tuning is like magic to any pianist. By playing a piece of music, most pianists can readily hear the difference between a poor tuning and an excellent one, even if they cannot tell the difference by playing single notes or test chords (assuming they are not also piano tuners). Therefore, along with technical development, every pianist must learn to hear the benefits of good tuning. It may be a good idea to practice on an out-of-tune piano once in a while in order to know what to expect in case you are asked to play on one with questionable tuning. For recitals, it is a good idea to tune the recital piano just before the recital, so that the recital piano is in better tune than the practice piano. Try to avoid the reverse case in which the practice piano is in better tune than the recital piano. This is another reason why students who practice on inexpensive uprights have little problem with playing recitals on large, unfamiliar grands, as long as the grands are in tune.

In summary, grands are not necessary for technical development up to about the intermediate level, although they will be beneficial at any level. Above intermediate level, the arguments in favor of grands over uprights become compelling. Grands are better because their actions are faster, they can be tuned more accurately, have a larger dynamic range, have a true soft pedal, can enable more control over expression and tone (you can open the lid), and can be regulated to provide more uniformity from note to note (by use of gravity instead of springs). These advantages, however, are initially minor compared to the student's love for music, diligence, and correct practice methods. Grands become more desirable for advanced students because technically demanding material is easier to execute on a grand. For such advanced pianists, proper tuning, regulation, and hammer voicing become essential because if the piano maintenance is neglected, practically all of the advantages will be lost.

Purchasing an Acoustic Piano

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Buying an acoustic piano can be a trying experience for the uninitiated, whether they buy new or used. If a reputable dealer can be found, it is certainly safer to buy new but even then the cost of the initial depreciation is large. Many piano stores will rent you the piano with an agreement that the rental will be applied to the purchase price in case you decide to keep it. In that case, make sure that you negotiate for the best purchase price before you even discuss rental; after you agree to a rental, you will have very little negotiating power. You will end up with a higher initial price so that, even after subtracting the rental, the final price is not a bargain. Even with expensive pianos, many dealers find it too costly to keep them prepped and in tune. At such dealers, it is difficult to test the piano by playing it. Thus buying a piano is usually a hit-or-miss proposition. For mass produced pianos such as Yamaha or Kawai, the quality of their new pianos tends to be uniform, so that you know pretty much what you will get. The sound quality of the more expensive "hand made" pianos can vary considerably so that buying these pianos is more difficult if you want to pick a good one.

Good used acoustic pianos are difficult to find in piano stores because playable pianos sell first and most stores are left with an excess inventory of unplayable ones. Obviously, the best bargains are to be found among the private sales. For the uninitiated, you will need to hire a piano tuner/technician to evaluate the used pianos in the private market. You will also need a lot of patience because good private sales are not always there when you need them. However, the wait can be worthwhile because the same piano will cost only half as much at a private sale compared to the store. There is a steady demand for good, reasonably priced pianos. This means that it is not easy to find bargains at widely accessible sites, such as the internet piano markets, because good pianos sell quickly. Conversely, such sites are excellent places to sell. The best place to find bargains is the classified section of newspapers, especially at large metropolitan areas. Most such advertisements are placed on Friday, Saturday, or Sunday.

Only a few name brand pianos "hold their value" when kept for many years. The rest quickly lose their value so that trying to sell them years after purchase is not a worthwhile alternative. “Hold value” means that their resale value will keep up with inflation; it does not mean that you can sell them for a profit. Thus if you bought a piano for $1,000 and sold it 30 years later for $10,000, you have made no profit if inflation is 10X during those 30 years. In addition, you will incur the cost of tuning and maintenance of at least $2000 for this example. It is cheaper to buy a brand new 7 ft Yamaha grand every 50 years than to buy a new Steinway M and completely restore it every 50 years; therefore, the choice of which piano to buy does not depend on economics but on what type of piano you need. With very few exceptions, pianos are not good investments; you have to be an experienced piano technician in order to find bargains in the used piano market that can be resold for a profit. Even if you find such a bargain, selling pianos is a time consuming, labor-intensive task. For more details on how to buy a piano, consult Larry Fine's book. Even with the most famous brands, a newly purchased piano will immediately lose 20% to 30% of its purchase price upon delivery, and will in general depreciate to half of the price of an equivalent new piano in about 5 years. As a very rough "rule of thumb" a used piano will cost about half the price of the new one of the same model in a piano store and about 1/4 at a private sale.

The price of pianos can be roughly classified according to whether they are worth rebuilding. Those worth rebuilding tend to cost at least twice as much when new. Practically all uprights and all mass produced grands (Yamaha, Kawai, etc), are not rebuilt because the rebuilding cost is about as high as the price of a new piano of the same model. Rebuilding such pianos is often impossible because the rebuilding trade and necessary parts are non-existent. Pianos worth rebuilding are Steinway, Bosendorfer, Bechstein, Mason and Hamlin, some Knabe, and a few others. Roughly speaking, it costs about 1/4 of the price of a new piano to rebuild and the resale value is about 1/2 of new; this is why rebuilding such pianos can be cost effective, for both the rebuilder and the buyer.

Grands

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The advantages of most grands are: greater dynamic range (loud/soft), open structure allowing the sound to escape freely (which provides more control and expression), richer sound, faster repetition, smoother action (use of gravity instead of springs), a "true" soft pedal (see section II.24), clearer sound (easier to tune accurately) and more impressive appearance. An exception is the class of "baby" grands (less than about 5'-2") whose sound output is usually unsatisfactory and should be considered mainly as decorative furniture. A few companies (Yamaha, Kawai) are beginning to produce baby grands with acceptable sound, so for these very new pianos, don't write them off without testing them. Larger grands can be classified into two main classes, the "student grands" (those below about 6 to 7 ft), and the concert grands. The concert grands provide more dynamic range, better sound quality, and more tonal control.

As an example of this "quality versus size" issue, consider the Steinway pianos. The baby model, model S (5'-2"), is essentially a decorative furniture and very few produce sufficient quality sound to be considered playable and are inferior to many uprights. The next larger size group consists of models M, O, and L (5'-7" to 5'-11"). These models are quite similar and are excellent student pianos. However, advanced pianists would not consider them to be true grands because of poorer sustain, too much percussive sound, and notes with too much harmonic content. The next model, A (6'-2"), is borderline, and B(6'-10"), C(7'-5"), and D(9') are true grands. One problem with evaluating Steinways is that the quality within each model is extremely variable; however, on average, there is a significant improvement in sound quality and output with each increase in size.

One of the biggest advantages of grand pianos is the use of gravity as the return force of the hammer. In uprights the restoring force for the hammer is supplied by springs. Gravity is always constant and uniform across the entire keyboard whereas non-uniformities in the springs and friction can create non-uniformities in the feel of the keys of an upright. Uniformity of feel is one of the most important properties of well-regulated, quality pianos. Many students are intimidated by the appearance of huge grands at recitals and competitions, but these grands are actually easier to play than uprights. One fear that these students have concerning these grands is that their actions may be heavier. However, touch weight is something that is adjusted by the technician regulating the piano and can be adjusted to any number regardless of whether the piano is an upright or a grand. Advanced students will of course find it easier to play demanding pieces on grands than uprights, mainly because of the faster action and uniformity. Consequently, grands can save you a lot of time when you try to acquire advanced skills. The main reason for this is that it is easy to develop bad habits when struggling with difficult material on uprights. Challenging material is even more difficult on electronic pianos (and impossible on models without proper touch weight) because they do not have the robustness and response to touch that are required at high speeds.

Some people with small rooms agonize over whether a large grand would be too loud in such a space. Loudness is usually not the most important issue, and you always have the option of closing the lid to different degrees. The maximum loudness of the medium and large grands is not that different, and you can play softer with the larger grands. It is the multiple sound reflections that are most bothersome. Multiple reflections can be easily eliminated by a carpet on the floor and sound-insulation on one or two walls. Thus if the piano physically fits into a room with no obvious difficulties, then it may be acceptable from the sound point of view.

Uprights

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Acoustic uprights have their own advantages. They are less expensive than grands. They take up less space, and for small rooms, large grands may produce too much sound so that they cannot be played full blast with the lid fully open without hurting or even damaging the ears. Grands, with the lid open, are very sensitive to touch. Thus grands require hammer voicing more frequently than uprights; otherwise, they become too "brilliant" or "harsh", at which point most owners will end up playing the grand with the lid closed. Many homeowners ignore voicing entirely. The result is that such grands produce too much and too harsh sound, and are therefore played with the lid down. There is nothing technically wrong with playing a grand with the lid closed. However, some purists will express great dismay at such practice, and you are certainly throwing away something wonderful for which you made a significant investment. Performances at recitals almost always require the lid to be open. Therefore you should always practice with the lid open before a performance even if you normally practice with it closed. However, in a larger room, or in a recital hall, there is much less multiple reflection of the sound so that you do not hear the deafening roar that can result in a small room. A concert hall will absorb the sound from the piano so that, if you are accustomed to practicing in a small room, you will have difficulty hearing your own playing in a concert hall. Since uprights are essentially closed instruments, the neglect of voicing is less noticeable. Uprights also tend to be less expensive to maintain, mainly because expensive repairs are not worthwhile and are therefore not performed. Of course, there are quality uprights that are competitive with grands in feel and sound quality, but their number is small.

Among uprights, spinets are the smallest and generally the least expensive pianos; most do not produce satisfactory sound, even for students. The small height of spinets limits the string length, which is the main limitation on sound output. In theory, the treble should produce satisfactory sound (there is no limitation on string length even for spinets), but most spinets are weak in the treble because of poor quality of construction; therefore, be sure to test the higher notes if you are evaluating a spinet. Uprights larger than console size can be very good student pianos. Old uprights with poor sound are generally not salvageable, no matter what their size. At such an age, the value of the piano is less than the cost of restoring them; it is cheaper to buy a newer upright with satisfactory sound.

Electronic Pianos

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Today's electronic pianos are still inferior to good grands for technical development but are improving rapidly. Even the best electronics are inadequate for advanced pianists; their mechanical response is poorer, the musical output and dynamic range are inferior, and fast, technically advanced material becomes difficult to execute. Most affordable speakers can not compete with the sound board of a grand. The electronic pianos do not allow the control of tone, color, pianissimo, staccato, and the special manipulations of the damper and soft pedals, that good grands provide. Thus there is no question that an advanced pianist will prefer a grand piano over an electronic. Most uprights do not provide sufficient advantage for technical development to warrant their use over quality electronics that are readily available.

The electronic pianos have some unique advantages, so we discuss them here. Because of these advantages, most serious pianists will own both an acoustic and an electronic.
(1) For less than half the price of an average acoustic upright, you can buy a new electronic piano with all the features you need: headphone and volume control, touch control, organ, string, harpsichord, metronome, recording and midi/analog out, transposition, different tunings and canned accompaniments. Most electronics provide much more, but these are the minimum features you can expect. The argument that an acoustic piano is a better investment than an electronic is false because an acoustic piano is not a good investment, especially when the initial cost is so much higher. The electronic piano requires no maintenance, whereas the maintenance costs of acoustics are substantial, since they require tuning, voicing, and regulation about twice a year, plus occasional repairs.
(2) The electronics are always in perfect tune. Very young children exposed sufficiently to perfectly tuned pianos acquire perfect pitch automatically, although most parents never discover this because, if it is not discovered and maintained, it is lost during the teen years. The acoustic piano begins to go out of tune the minute the tuner leaves your house, and some notes will be out of tune most of the time (in fact, most of the notes will be out of tune most of the time). However, these small deviations from tuning will not affect the learning of perfect pitch unless the piano is allowed to go way out of tune. Because too many acoustic pianos are inadequately maintained, the fact that the electronics are always in tune can be a huge advantage. The importance of a well tuned piano for musical and technical development cannot be over-emphasized, because without the musical development, you will never learn how to perform.
(3) You can use headphones or adjust the volume so that you can practice without disturbing others. The ability to turn down the volume is also useful for reducing ear damage when practicing loud passages: an important factor for anyone over 60 years old, when many will start to suffer from hearing loss or tinnitus. If you are an advanced player, even an electronic will create considerable "playing noise" (with the volume turned off) that can be quite loud to anyone nearby and these vibrations can transmit through the floor to rooms under the piano. Therefore it is a mistake to think that the sound from an electronic (or an acoustic with "silent" feature) can be completely turned off.
(4) They are more portable than acoustics. Although there are light keyboards with similar features, it is best for piano practice to use the heavier electronics so that they do not shift while playing loud, fast music. Even these heavier electronics can be easily moved by two persons, and will fit in many cars.
(5) Variable touch weight is more important than many people realize. However, you have to know what "touch weight" means before you can use it to advantage; see the following paragraphs for details. In general, the touch weight of electronics is a little lighter than that of acoustics. This lighter weight was chosen for two reasons: to make it easier for keyboard players to play these electronics (keyboards are even lighter), and to make them easier to play compared to the acoustics. The disadvantage of the lighter weight is that you may find it slightly more difficult to play an acoustic after practicing on an electronic. The touch weight of acoustics needs to be heavier in order to produce a richer tone. One advantage of heavier weight is that you can feel the keys of an acoustic while playing, without inadvertently playing some wrong notes. However, this can also lead to careless playing with some inadvertent finger motions because you can lightly hit a key of an acoustic without making any sound. You can practice getting rid of these uncontrolled motions by using an electronic and choosing a light touch weight so that an inadvertent strike will produce a sound. Many people who practice only on acoustics don't even know that they have such uncontrolled motions until they try to play on an electronic. The light touch is also useful for acquiring difficult technique quickly. Then, if you need to play on an acoustic later on, you can practice with increased weight after you acquire the technique. This two-step process is usually faster than trying to acquire technique at heavy key weight.
(6) Recording piano music is one of the most difficult things to do using conventional recording equipment. With an electronic piano, you can do it with the push of a button! You can easily build up an album of all the pieces you learned. Recording is one of the best ways not only to really finish and polish your pieces but also to learn how to perform for an audience. Everyone should cultivate a habit of recording every finished piece from the very beginning of their lessons. Of course, the initial performances will not be perfect, so you may want to go back and re-record them as you improve. Too many students never record their performances, which is the main reason for excessive nervousness and difficulties during performances.
(7) Most pianists who follow good practice methods and become proficient when young will end up composing their own music. Electronic pianos are helpful for recording these compositions so that you don't need to write them down, and for playing them in different instruments, as appropriate for each composition. With some additional software or hardware, you can even compose entire symphonies and play every instrument yourself. There is even software that will transcribe (though imperfectly) your music onto sheet music.
(8) If you can acquire technique rapidly, there is nothing stopping you from broadening your horizon beyond classical music and playing popular music, jazz, blues, etc. You will appeal to a wider audience if you can mix music genres and you will have more fun. The electronic piano can help by providing the accompaniments, drums, etc., for those types of music. Thus these extra capabilities of the electronic pianos can be very useful and should not be ignored.
(9) Buying electronic pianos is very simple, especially when compared to buying acoustics (see below). All you need to know is your price range, the features you want, and the manufacturer. You don't need an experienced piano technician to help you evaluate the piano. There are no questions about whether the piano dealer made all the proper "prepping", whether the dealer will honor the agreements to ensure that the piano functions after delivery, whether the piano was properly "stabilized" during the first year of ownership, or whether you got one with good or inferior tone and touch. Many established manufacturers, such as Yamaha, Roland, Korg, Technic, Kawai, and Kurzweil, produce electronics of excellent quality.

The touch weight of a piano is not a simple matter of adding or subtracting lead weights to the keys to change the force required to depress them. The touch weight is a combination of the down weight, the inertia of the keys and hammers, and the force required to produce a certain volume of sound. The down weight is the maximum weight that the key will support before it will start to move down. This is the weight that is adjusted using lead weights. The down weight of all pianos, including the "weighted key" electronics, is standardized at about 50 grams and varies little from piano to piano regardless of touch weight. When playing a piano, this 50 gram weight is a small fraction of the force required to play -- most of the force is used to produce the sound. In acoustics, this is the force needed to impart velocity to the hammer. In electronics, it is the electronic reaction to the key motion and a fixed mechanical resistance. In both cases, you also have to overcome the inertia of the mechanism in addition to supplying the force for producing the sound. For example, when playing staccato, most of the force required is for overcoming the inertia whereas when playing legato, the inertial component is small. Electronics have a smaller inertial component because they have only the inertia of the keys whereas the acoustics have the additional inertia of the hammers; this makes the acoustics less sensitive to inadvertent hitting of the keys. Therefore, you will feel the most difference between acoustics and electronics when playing fast or staccato and little difference when playing legato. For the pianist, touch weight is simply the effort required to produce a certain volume of sound and has little to do with down weight. For acoustics, touch weight is determined mostly by hammer mass and voicing (hardness of the hammer). There is only a narrow range of hammer masses that is ideal because you want heavier hammers for larger sound but lighter ones for faster action. Thus a lot of the touch weight can be adjusted by the piano technician by hammer voicing, rather than by changing weights. For electronic pianos, touch weight is controlled in the software in the following way, in order to simulate what happens in a grand. For heavier touch weight, the sound is switched to that of a softer hammer, and vice versa. There is no mechanical change to the down weight of the keys or the inertial component. Thus if you switch to the heaviest key weight, you might feel that the sound is somewhat muffled and if you switch to the lightest weight, the sound might be too brilliant. In electronic pianos, it is easier to decrease the touch weight without adversely affecting the sound because there is no hammer to move. On the other hand, the maximum dynamic range of most electronic pianos is limited by the electronics and speakers, so that for the loudest sounds, the grand piano can have a lighter touch weight. In summary, touch weight is a subjective judgment by the pianist about how much effort is required to produce a certain volume of sound; it is not the fixed weight or resistance of the keys to the keydrop.

You can demonstrate this subjective judgment by turning the volume up or down using the electronic piano. Thus if you practice on an electronic for a long time with the volume turned down, and then play an acoustic, the acoustic can feel downright light. Unfortunately, things are a little more complicated because when you switch to a heavier touch weight with the electronic piano, it also gives you the sound of a softer hammer. In order to reproduce the sound of a properly voiced hammer, you need to strike harder. This adds to the perception of a heavier key weight, and this effect cannot be simulated by changing the volume control. From these discussions, we can draw the following conclusions: there are small differences in the touch weight between grands and electronics, with the grands tending to be heavier, but those differences are not sufficient to cause major problems when switching from one to the other.

Grand, Upright, or Electronic?

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Grands have certain advantages over uprights. However, these advantages are minor compared to the importance of the skill level of the pianist. There are great pianists who became technically advanced practicing mostly on uprights. There is no evidence that you need a grand for initial technical development, although a few piano teachers will insist that any serious student must practice on a grand. An argument can be made in favor of uprights, at least for beginners, because uprights require firmer playing and may be better for early finger development (you need to press harder in order to make louder sounds). They may be superior even for intermediate students because uprights are less forgiving and require greater technical skill to play. These arguments are controversial, but do illustrate the point that, for students up to intermediate level, any differences among uprights and grands are small compared to other factors such as student motivation, talent, quality of teachers, practice methods, and proper piano maintenance. Another factor is piano quality: good uprights are superior to low quality grands (which includes most grands under 5.2 feet). In general, students above intermediate level will need a grand piano.

Electronic (also called digital) pianos have capabilities that the acoustics (the mechanical uprights and grands) cannot provide and therefore fill a niche of their own, as explained below. They cost much less, are easier to purchase, maintain and transport, and make excellent starter or second pianos. The electronics have basically rendered the uprights obsolete. Therefore, if you are buying your first piano, it is easiest if you start with a quality electronic and then purchase a grand later on, when you are certain that the piano is going to be a big part of your life. Thus the rule concerning uprights is simple: if you already have one, there is no reason to get rid of it until you buy an electronic or a grand; if you don't have a piano, there is no compelling reason to buy an upright.

Why the Greatest Pianists Could Not Teach

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Very few of the greatest pianists were good teachers. This is eminently natural because artists train all their lives to be artists, not teachers. I experienced an analogous situation as a graduate physics student at Cornell University where I took courses taught by professors who specialized in teaching, and where I also attended weekly lectures by famous physicists including numerous Nobel Prize winners. Some of those renowned physicists could certainly present exciting lectures that attracted great interest, but I learned most of the skills needed to find a job as a physicist from the teaching professors, not the Nobel laureates. This difference in teaching ability between teaching and practicing scientists pales in comparison with the chasm that exists in the arts world because of the nature of the scientific discipline (see Chapter Three). Learning and teaching are an integral part of being a scientist. By contrast, the greatest pianists were either reluctantly, or by economic necessity, pushed into teaching for which they received no meaningful training. Thus there are plenty of reasons why the great performers may not have been good teachers.

Unfortunately, we have historically looked to the famous artists for guidance, under the rationale that if they can do it, they should be able to show us how. Typical historical accounts reveal that, if you were to ask a famous pianist how to play a certain passage, s/he will sit at the piano and play it out because the language of the pianist is spoken by the hands and the piano, not the mouth. That same great artist may have little idea about how the fingers are moving or how they are manipulating the piano keys. In order to move the hands in the proper way, you must learn to control thousands of muscles and nerves, and then train the hands to execute those motions. There are two extremes among the ways to acquire technique. One extreme is the analytical one, in which every motion, every muscle and every physiological information is analyzed. The other extreme is the artist’s approach, in which the person simply imagines a certain musical output and the body responds in different ways until the desired result is obtained. This artist's approach can not only be a quick shortcut, but can also yield unexpected results that may exceed the original idea. It also has the advantage that a genius without analytical training can be successful. The disadvantage is that there is no assurance of success. Technique acquired in this way cannot be taught analytically, except by saying that “you must feel the music this way” in order to play it. Unfortunately, for those who do not know how to do it yet, this kind of instruction is of little help, except as a demonstration that it can be done. Also, even knowing the practice methods isn’t enough. You need the correct explanation of why they work. This requirement is often outside the expertise of the artist or piano teacher. Thus there is a fundamental impediment to proper development of piano teaching tools: artists and piano teachers do not have the training to develop such tools; on the other hand, scientists and engineers who may have such training have insufficient piano experience to teach piano.

The old masters were geniuses, of course, and had some remarkable insights and inventiveness as well as intuitive feel of mathematics and physics which they applied to their piano playing. Therefore, it is incorrect to conclude that they had no analytical approaches to technique; practically every analytical solution to piano practice that we know of today was re-invented many times by these geniuses or at least used by them. It is therefore unbelievable that no one ever thought of documenting these ideas in a systematic way. It is even more amazing that there does not seem to have been even a general realization by both teachers and students that practice methods were the key to acquiring technique. The main difficulty seems to have been the inability of the artist approach to identify the correct theoretical basis (explanation) for why these practice methods work. Without a sound theoretical explanation or basis, even a correct method can be misused, misunderstood, changed, or degraded by different teachers so that it may not always work and be viewed as unreliable or useless. These historical facts prevented any orderly development of piano teaching methods. Thus the understanding, or the explanation of why a method works, is at least as important as the method itself.

In addition, piano teachers tended to be poor communicators in the sense that they tended not to share teaching ideas. Only at large conservatories was there any significant mixing of ideas so that the quality of teaching at conservatories was better than elsewhere. However, the problems of the preceding paragraph prevented any truly systematic developments of teaching methods even at these organizations. An additional factor was the stratification of piano learning into beginners and advanced students. Conservatories generally accepted only advanced students; yet, without conservatory type teaching, few students attained the advanced levels necessary to be accepted. This gave piano learning a reputation as something far more difficult than it really was. The bottleneck created by a lack of good teaching methods was historically attributed to lack of “talent”. When all these historical facts are assembled, it is easy to understand why the great masters could not teach, and why even dedicated piano teachers did not have all the tools they needed.

Although I started writing this book as just a compilation of some remarkably effective teaching tools, it has evolved into a project that deals directly with the historical deficiencies responsible for most of the difficulties of acquiring technique. Fate has suddenly turned the future of piano into a wide, open unknown with limitless possibilities. We are entering a brave, new, exciting era that can finally be enjoyed by everyone.

Some Elements of Piano Lessons

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The piano lesson should not be a routine in which the student plays the lesson piece and the teacher assigns a new piece. It is the teacher's job, when starting a new piece, to go through it in segments, examining the fingerings, analyzing the music, and basically bringing the student up to speed during the lesson, at least HS or in segments. After the technical problems are solved, the job shifts into playing it musically -- examining the musical content, bringing out the expression, the attributes of the composer (Mozart is different from Chopin, etc.), the color, etc. A good teacher can save the students a tremendous amount of time by demonstrating all the necessary elements of technique. It should not be left to the student to try to find these out by trial and error. Because of these requirements, lessons beyond beginner level can become quite intense and time consuming. Scales should be taught thumb-under for beginners but, within a year, they should be taught thumb-over also. Although most exercises such as Hanon are now considered unhelpful, it is very important to be able to play scales and arpeggios (in all transpositions) well; this will require many years of hard work.

Practicing 30 minutes every 2 or 3 days is the absolute minimum necessary to make any progress. Half an hour every day is adequate for significant progress for youngsters. As they get older, they will need progressively more time. These are minimum practice times; more time will be needed for faster progress.

The best way to motivate students to practice, and the best way to teach the art of making music, is to hold recitals. When the students must perform, all the teacher's instructions, the necessary practice time, etc., take on an entirely new meaning and urgency. The students will become self-motivated. It is a mistake to teach piano without any program of performance. There are numerous possibilities for such programs and experienced teachers will be able to design an appropriate one for each student at every level. Formal recitals and music competitions are full of pitfalls and must be approached with care and a lot of planning. However, teachers can organize informal recitals using much less stressful formats, with tremendous benefits to the students.

Although recitals and competitions are important, it is even more important to avoid their pitfalls. The main pitfall is that recitals can be self-defeating because the stress, nervousness, extra effort and time, and sense of failure after even small mistakes, can do more harm than good in molding the performance capability/psychology of the student at any age. Therefore teachers must have a clearly defined program or approach to teaching the art of performing in addition to the art of playing. The preparatory methods for recitals discussed in section 14 above should be part of this program. Popular, or "fun" music is especially useful for performance training. Above all, the program must be designed to produce a rewarding atmosphere of accomplishment and not a competitive one where anything short of miraculous perfection, playing the most difficult pieces the student can manage, is a failure. In competitions, students must be taught early on that judging is never perfect or fair; that it is not the winning, but the participatory process, that is most important for its pedagogical value. Given the same piece of music to play, a relaxed and less nervous student will perform better, and develop a better attitude towards performing. Students must understand that it is the process, not the final winning, that is the final objective of having competitions. One of the most important components of this objective is to cultivate the ability to enjoy the experience instead of becoming nervous. One of the worst pitfalls of most competitions is the emphasis on the most difficult material that the student can play. The correct emphasis should be on the music, not the technique.

Of course we must aim to win competitions and play flawless recitals. But there are stressful and less stressful approaches to these objectives. It is the teacher's job to teach stress control. Unfortunately, the majority of teachers today totally ignore performance stress control or worse, parents and teachers frequently pretend that there is no such thing as nervousness even when they themselves are nervous. This can have the effect of creating a permanent problem with nervousness. See section 15 above for discussions on controlling nervousness.

It is important to first teach a student all about nervousness and stress and not to shove them out on a stage to perform with no preparation in the vain hope that they will somehow learn to perform on their own. Such action is quite analogous to throwing a person into the middle of a deep lake to teach them how to swim; that person can end up with a lifelong fear of water. Playing for the teacher at every lesson is a good start, but is woefully insufficient preparation. Thus the teacher should design a "performance training" routine in which the student is gradually introduced to performances. This training must start with the first piano lessons. Various skills, such as recovering from blackouts, preventing blackouts, covering mistakes, sensing mistakes before they occur, snippet playing, starting from arbitrary places in a piece, choice of pieces to perform, audience communication, etc., should be taught. Above all, they must learn mental play. We saw that HS practice, slow play, and "playing cold" are the important components of preparation. Most students do not know which "finished" pieces they can perform satisfactorily until they actually play them in recitals several times; therefore, even among finished pieces, every student will have a "performable" and a "questionable" repertoire. One of the best ways to train for performances is to record the student's finished pieces and produce an album of finished repertoire that is periodically updated as the student advances. This should be done from the very beginning of lessons so as to cultivate the skill as early as possible. The first mistake most pianists make is to think that "I am still a beginner, so my playing is not worth recording". Once you buy that argument in the beginning, you will end up following it the rest of your life because it becomes a self-fulfilling prophesy. That argument is false because music is supreme -- easy compositions, played musically, is as good as it gets; Horowitz cannot play "chopsticks" any better than a well-taught beginner.

Clearly, performance is a complex field and must be systematically taught before a student is asked to walk out on a stage and play. Without such training, even good performers will not perform to their best ability, and the majority of students will end up thinking that piano performance as a kind of hell that is associated with music or piano. Once that attitude is ingrained in youth, they will carry it into adulthood. The real truth should be the exact opposite. Performance should be the final goal, the final reward for all the hard work. It is the demonstration of the ability to sway an audience, the ability to convey the grandest designs of the greatest musical geniuses that every lived. Secure mental play is the surest way to achieve these objectives.

One way to introduce students to performing at recitals is to hold mock recitals among the students themselves and to have them discuss their fears, difficulties, weaknesses, and strengths to get them all acquainted with the main issues. How do you play mentally? Do you do it all the time? Do you use photographic memory or keyboard memory, or just music memory? Does it happen automatically or do you do it at certain times? They will understand the issues better when they can actually feel them and then discuss them openly with their peers. Any stress or nervousness they might feel becomes less scary when they realize that everyone experiences the same things, that nervousness is perfectly natural, and that there are various ways to combat them. In particular, once they go through the entire process from start to finish of a mock recital, the whole procedure becomes much less mysterious and frightening. Students must be taught that learning to enjoy performing is part of the art of piano. That "art of performing" also requires study and practice, just like finger technique. In a group of students, there is always one that is good at performing. The others can learn by watching and discussing how these good ones cope with each issue.

Another way to introduce students to performances and at the same time have some fun is to schedule an informal recital in which the students play a game of "who can play fastest". In this game, every student plays the same piece, but the amount of practice time is limited, say, to three weeks. Note that in this ruse, the hidden agenda is to teach the students how to enjoy giving recitals, not to teach them how to play fast. The students themselves vote for the winner. At first, the teacher gives no instructions; students must choose their own practice methods. After the first recital, the teacher holds a group lesson in which the winner describes her/is practice methods and the teacher adds any useful information. Note that HS practice and parallel sets are major concepts that help to play fast. Of course, clarity, accuracy, and music must be considered in choosing a winner. There will be wide differences in the practice methods and achievements of the various students and, in this way, they will learn from each other and will understand the basic teachings better. While the students are participating in a "contest", it is the teacher's job to ensure that it is a fun experience, a way to experience the joy of performing, a way to completely forget about nervousness. Mistakes evoke laughter, they are not to be frowned upon. And refreshments might be served afterwards. The teacher must not forget to intersperse instructions for learning to perform, together with the "contest" skills.

Once the students are taught the basics of performance, how should recitals be organized? They should be designed to strengthen performance capability. One of the hardest things to do is to perform the same composition several times on the same day or on successive days. Therefore, such repeat performances provide the best training for strengthening the performance capability. For teachers or schools with a sufficient number of students, the following is a good scheme to use. Group the students into beginner, intermediate, and advanced. On Friday, hold a recital of the beginners, with their parents and friends as audience. Beginners should participate in recitals from their first year of lessons, as early as 4 or 5 years of age. At the end of this recital, the advanced students also play, which makes it really worthwhile for the audience to attend. On Saturday, the intermediate students play, with their parents and friends as audience; again, the advanced students play at the end. On Sunday, the advanced students hold their recital, with their parents as the audience; some special guests might be invited. In this way, the advanced students get to perform the same piece three days in a row. The Sunday recital of the advanced students should be recorded and copied onto CD's, as they make great souvenirs. If this type of recital is held twice a year, each advanced student will have six recitals under their belt every year. If these students are also entered into competitions (typically involving an audition, a final, and, if they win, a winner's concert), they will have adequate performance training (at least 9 performances a year). Since most pieces are not "secure" until they are performed 3 times, this recital scheme will also serve to make the recital piece "secure" so that it can now be included in the "performable" repertoire, after just one weekend of recitals.

Teachers should be willing to communicate with other teachers, exchange ideas, and learn from each other. There is nothing as potentially damaging to a student as a teacher whose teaching methods are inflexible and frozen in time. In this information age, there is no such thing as secret methods of teaching piano, and the success of the teacher depends on open communications. An important topic of communication is the exchange of students. Most students can benefit greatly by having been taught by more than one teacher. Teachers of beginners should pass their students to higher level teachers as soon as they are ready. Of course, most teachers will try to keep their best students and to teach as many students as they can. One way to solve this problem is for teachers to form groups consisting of teachers with different specialties so that the group forms a complete school. This also helps the teachers because it will make it much easier for them to find students. For students looking for good teachers, it is clear from these considerations that it is best to look for groups of teachers rather than teachers who operate individually. Teachers can also benefit by banding together and sharing students and costs of facilities.

Starting teachers often have difficulty finding their first students. Joining a group of teachers is a good way to get started. Also many established teachers often have to turn away students because of a lack of time, especially if the teacher has a good reputation in that local area. Those teachers are good sources of students. One way to increase the pool of potential students is to offer to go to the students' homes to teach. For at least the first few years when a new teacher starts to teach, this might be a good approach for increasing the potential student pool.

Memorizing, Reading, Theory, Mental Play, Absolute Pitch

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The teacher must choose, at an early stage, whether the student should be taught to play from memory or learn to read music. This choice is necessitated by the fact that the details of the teaching program and how the teacher interacts with the students depend on it. The Suzuki violin method emphasizes playing from memory at the expense of reading, especially for youngsters, and this is the best approach for piano also. It is easier to practice reading after you can play reasonably well. The reason for this order of learning is simple; it is also the way children learn language: they first learn to speak, then to read. The abilities to speak and to make music are natural evolutionary traits that we all have; reading is something that was added later as a consequence of our civilization. Learning to speak is simply a process of memorizing all the sounds and logical constructs of each language. Therefore, reading is more "advanced" and less "natural", and therefore cannot logical precede memory. For example, there are many concepts in memory that can never be written down, such as color, playing with authority and confidence, etc. A single "crescendo" indication can be played in a large number of ways. You cannot "read" a crescendo indication unless you have heard many crescendos and know what they sound like.

However, reading should not be totally neglected in the beginning. It is only a matter of priority. Since music notation is simpler than any alphabet, young children should be able to learn to read music even before they can learn to read books. Thus reading should be taught from the very beginning, but only enough to read music for practicing a piece and memorizing it. Reading should be encouraged as long as it does not interfere with playing from memory. This means that, once a piece is memorized, the music should not be used for daily practice. However, the teacher must make sure that this lack of emphasis on reading does not result in a poor reader who automatically memorizes everything and can't read. There is a tendency in most beginners to become either good readers (and poor memorizers) or vice versa, because when you become good at one, you need less of the other. By monitoring the student carefully, a teacher can prevent the student from becoming a poor reader or a poor memorizer. Parental help is often necessary for this monitoring to succeed because the teacher is not always there when the student is practicing. In fact, many parents unwittingly create poor memorizers or readers by helping their children out instead of forcing them to practice their weaker skills. Because becoming a poor reader or memorizer happens over a long period of time, usually many years, there is ample time to detect the trend and correct it. A negligible number of people are born good or bad readers or memorizers. The vast majority became good memorizers or good readers because of the way they learned throughout their life.

Reading is an indispensable teaching tool for teachers; the teacher's job can be made easier if the student can be taught to read. Teachers who emphasize reading are certainly justified because of the enormous amount of information that is contained in even the simplest printed music, and practically every beginning student will miss a large fraction of that information. Even advanced pianists often return to the music score to make sure that they haven't missed anything. Very often, you have to improve your skill to a certain level before you can fully execute all the markings on the score so that, in the beginning, some of the markings may be effectively meaningless; thus you need the score at every stage of development. Therefore, there is no question that reading is essential. In addition, learning to read is not a simple task; not only do you have to learn the complex language of the music score, but you also have to learn to recognize and execute the instructions in real time. This is why reading must be taught from the very beginning. However, too many teachers depend too much on reading, which causes confusion among the students because the students are more interested in learning piano than simplifying the teacher's task. Asking a student to read the score is not the most efficient way to correct mistakes. All these conflicting factors cause great confusion and controversy in piano pedagogy about whether is it better to teach memory or reading. Clearly, the best program is one based on memory, but with enough reading training so that the student does not become a poor reader.

How much reading training is enough? The normal amount of reading needed to learn your new pieces is generally sufficient. Especially for beginners, it does not pay to embark upon a reading program just to be able to read (because your fingers can't play them anyway), although the initial slow reading speed can be awfully frustrating. A major learning trick in piano pedagogy is to learn several skills simultaneously, especially because many of them take a long time to learn. Thus memorizing, reading, theory, etc., can all be learned simultaneously, saving you a lot of time in the long run.

As students advance, a distinction should be made between compositions that they "sight read" and those that they memorize. "Sight reading" is used here in a loose terminology to mean playing music by looking at the score, without memorizing it. All significant lesson pieces should be memorized. These are pieces that the students can be expected to perform for an audience. As the students advance, therefore, they will acquire two types of repertoire; those they memorize and those they sight read, such as easy pieces and accompaniments. In later stages, the student may decide to learn true sight reading (section 11 above), which is the ability to play music, that they had never heard before, by reading a music score that they had not previously seen. Thus every student should have a program for technical development based on memorization and a sight reading program.

You can never teach too much music theory (solfege), notation, dictation, etc. Learning theory helps the students to acquire technique, memorize, understand the structure of the composition, and perform it correctly. It will also help with improvisation and composition. It should be noted that, statistically, the majority of successful piano students will end up composing music. Modern music (pop, jazz, etc.) nowadays uses very advanced musical concepts and the underlying theory is helpful for understanding chord progressions, music structure and improvisation. Therefore, there are advantages to learning both classical and modern music. Modern music provides contemporary theory and helps develop rhythm, and also appeals to a wider audience. It is easier to learn performance skills and to suppress stage fright using modern music, and learning both classics and pop greatly increases the size of your audience.

Mental play should be taught from the very beginning in order to train the students to play music in their minds all the time. If this is done at the correct pitch, young students who have been sufficiently exposed to music will acquire perfect pitch after only a few lessons with no effort. This is a good time to identify those students who have little idea of pitch and to devise programs to help them. Advanced students automatically develop mental playing skills because they are so necessary; however, if they are taught from the beginning, it will speed their learning rates for everything else. If mental playing is not taught, the students may not even realize that they are doing it, and not develop it properly. Moreover, because they are not aware of what they are doing, they will tend to neglect mental playing as they get older and their brains get bombarded with other pressing matters. As they neglect the mental playing, they will lose their perfect pitch, and their ability to perform with ease.

Teaching Youngsters, Parental Involvement

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Children should be tested for their readiness to take piano lessons at ages between 3 and 5. The first lessons for beginners, especially young children under 7 years old, should be brief, 10 to 15 minutes at most. Increase the lesson time only as their attention time span and stamina increase. If more time is necessary, divide the lesson into sessions with breaks in between ("cookie time", etc.). The same rules apply to practice times at home. You can teach a lot in 10 min.; it is better to give 15 min. lessons every other day (3 days/wk) than to give hour long lessons every week. This principle applies at any age, although the time between lessons increases with age and skill level.

It is important for youngsters to listen to recordings. Even if they can't truly interpret Chopin until they demonstrate some maturity, they can listen to Chopin at any age. They should also listen to recordings of their own playing; otherwise, they may not understand why you are criticizing their mistakes. Do not feed them music just because it is classical or it was written by Bach. Play what you and the youngsters enjoy.

Youngsters should learn counting by counting out loud -- without hearing their counting, the teacher may have no idea whether the child understands the concept. Youngsters develop in spurts, both physically and mentally, and they can only learn what they are mature enough to learn. In other words, you can't teach them something until they are ready for it. Therefore, part of the teaching must consist of a constant testing of their level of readiness. On the other hand, most youngsters are ready for many more things than most adults realize and once they are ready, the sky is the limit. Therefore, it is also a mistake to assume that all kids must be treated as kids all the time. They can be surprisingly advanced in many respects so that treating them as kids only holds them back (for example, by letting them listen only to “kiddie music”) and deprives them of the opportunity to fulfill their potential.

For at least the first 2 years of lessons (longer for youngsters) teachers must insist that the parents participate in the teaching/learning process. The parents' first job is to understand the methods that the teacher is teaching. Since so many practice methods and recital preparation procedures are counter-intuitive, the parents must be familiar with them so that they can not only help to guide the students, but also avoid negating the teacher's instructions. Unless the parents participate in the lessons, they will fall behind after just a few lessons and can actually become a hindrance to the child's development. The parents must participate in deciding how long the students practice each day, since they are most familiar with all the time demands of the students. The parents also know the students' ultimate objectives best -- are the lessons just for casual playing, or for advancing to much higher levels? What types of music do the students eventually want to play? Beginning students always need help at home in working out the optimum routine for daily practice as well as keeping track of weekly assignments. Once the lessons start, it is surprising how often the teachers need the parents' help -- where and how to buy sheet music, how often to tune the piano, or when to upgrade to a better piano, etc. The teachers and parents need to agree on how fast the students are expected to learn and to work towards attaining that learning rate. The parents need to be informed of the students' strengths and weaknesses so as to be able to match their expectations and plans with what is or is not achievable. Most importantly, it is the parents' job to evaluate the teacher and to make proper decisions on switching teachers at the appropriate time.

Students need a lot of help from their parents, and the kinds of help change with age. When young, the students need constant help with daily practice routines: are they practicing correctly and following the teacher's instructions? It is most important at this stage to establish correct practice habits. The parents must make sure that during practice, the students make it a habit to play through mistakes instead of backtracking, which will create a stuttering habit and makes the student mistake-prone during performances. Most youngsters will not understand the teacher's instructions given hurriedly during their lessons; the parents can more readily understand those instructions. As the students advance, they need feedback on whether they are playing musically, whether their tempo and rhythm are accurate or if they need to use the metronome, and whether they should stop practicing and start listening to recordings.

Parental involvement should go much farther than just helping the teacher. Piano or music education can start at home as soon as the child is born. Listening to the "right" kind of music, and listening to the sound of well tuned pianos, can have the most profound effects on the child's brain and its development. In addition to supplying the musical stimuli, it is also the parents' job to keep testing the child for when s/he becomes receptive to the different stages of musical development. Is the child ready to start pressing piano keys? Can the child sing or hum a tune? Is the child ready to start (music) reading lessons? Note that music notation is much simpler than the alphabet. Does the child have rhythm? Does the child have perfect pitch? What kind of music or instrument does the child like? You never know until you test them. It is generally counterproductive to try to push children into something for which they are not yet ready or do not show interest. You cannot just push children in some direction; the only thing you can do is to arrange the environment so that they will develop an interest in that direction. Familiarity, good, pleasant experiences, and success are factors that can lead a child in those directions. Before they are ready, the only thing you can do is to provide these environments and to test them; but if they are ready, watch out! They can progress far faster than you ever dreamed.

Mental development is the main reason for letting youngsters listen to classics -- the "Mozart Effect". The reasoning goes something like this. Assume that the average parent has average intelligence; then there is a 50% chance that the child is smarter than the parents. That is, the parents cannot compete on the same intellectual level as their baby! Mozart (or any other genius composer) is different - few babies will be able to challenge those intellectual levels. In addition, music is a universal language; unlike the crazy adult languages that we speak, music is inborn, so babies can communicate in music long before they can say "dada". Therefore, classical music can stimulate a baby's brain long before the parents can communicate with the baby even on the most basic levels. And these communications are conducted at the levels of the genius composers, something few parents can hope to match!

Parents must also balance the physical and mental developments of their children. Because learning piano can be so fast, those olden days -- when dedicated pianists had insufficient time for sports and other activities -- are over. Techies and artists don't have to turn into wimps. There is this disturbing tendency to classify each youngster as brainy or brawny, creating a wall or even antagonism between art and physical activity. Actually, the two follow eerily similar principles. As an example, the rules for learning golf and piano are so similar that this book can be turned into a golf manual with just a few changes. The Greeks had it right a long time ago -- mental and physical development must proceed in parallel. If the parents do not provide proper guidance, some youngsters will devote all their time in one direction, neglecting everything else and wasting precious time. Health and injury is another issue. Those music players with earphones can damage the ears so that you begin to lose hearing and suffer maddening tinnitus before age 40. Parents must educate their children to turn the volume down on those earphones, especially if they are listening to those genres of music that are often played extremely loud.

Types of Teachers

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Teaching piano is a difficult profession because practically everything you try to do contradicts something else that should be done. If you teach reading, the student may end up unable to memorize. If you teach slow, accurate play, the student may not acquire sufficient technique in any reasonable amount of time. If you push them too fast, they may forget all about relaxation. If you concentrate on technique, the student might lose track of musical playing. You need to devise a system that successfully navigates through all these types of contradictory requirements and still satisfies the individual wishes and needs of each student. There was no standard text book until this book was written, and starting teachers had to invent their own teaching systems with very little guidance. Teaching piano is a Herculean task that is not for the faint of heart.

Historically, teachers generally fell into at three categories: teachers for beginners, intermediate students, and advanced students. This specialization developed because each student had to spend a considerable amount of time at each stage, and made it difficult for any one teacher to teach successfully, independently of other teachers. The most successful approach involved a group of teachers composed of all three categories; the teachers were coordinated in such a way that their teachings were mutually compatible, and the appropriate students were directed or passed on to the appropriate teachers. This assembly of different teachers into a group was necessary because teaching methods were inefficient and not standardized. Thus many teachers of advanced students often refused to take students from certain teachers because the latter "do not teach the proper fundamentals". This should not happen if the fundamentals are standardized.

The three categories of teachers were needed because it was a waste of resources for teachers capable of teaching intermediate students to be teaching beginners. In addition, most advanced teachers have not been good teachers of beginners. The last thing an advanced teacher wanted was a student who was initially taught all the "wrong" methods. This is not the ideal situation. In the ideal scenario, any teacher should be able to teach any student at any level and quickly bring them up through the different levels. If the students progress sufficiently rapidly, it will not make any sense for teachers to specialize at each level, and the student can progress to the end using only one teacher's system. Hopefully, with the advent of this book, and the vast amount of information now available on the internet, most piano teachers will be able to adopt the more ideal model of teaching.

Origin and Control of Nervousness

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Nervousness is a natural human emotion just as happiness, fear, sadness, etc., are emotions. Nervousness arises from a mental perception of a situation in which performance is critical. Therefore, nervousness, like all emotions, is a performance enhancing reaction to perceived critical situations. Happiness feels good, so we try to create happy situations, which helps us; fear helps us to escape danger, and sadness makes us avoid sad situations which tends to improve our chances of survival. Nervousness makes us concentrate all our energies towards the critical task at hand and is therefore another survival tool. Most people dislike nervousness because it is too often accompanied, or is caused, by fear of failure. Therefore, although nervousness is necessary for a great performance, it needs to be kept under control; in particular, it should not be allowed to interfere with the performance. In other words, we need to develop a healthy attitude towards nervousness. The history of the great artists is full of legends of extremely nervous as well as totally non-nervous performers, indicating that this phenomenon is not understood at all.

Emotions are basic, primitive, animal reactions, somewhat like instinct, and are not totally rational. Under normal circumstances, emotions guide our daily, moment-by-moment actions nicely. However, under extreme conditions, emotions can get out of control, and becomes a liability. Clearly, emotions were designed to work only under normal circumstances. For example, fear makes the frog escape long before a predator can catch it. However, when cornered, the frog freezes in fear and this makes it an easier meal for the snake than if the overwhelming fear hadn't paralyzed it. Likewise, nervousness normally is mild and helps us to perform a critical task better than if we were lackadaisical. However, under extreme conditions, it can spin out of control and hinder our performance. The requirement to perform a difficult piano solo flawlessly in front of a large audience eminently qualifies as an extreme condition. It is no surprise that nervousness can grow out of control, unless our name is Wolfie or Franz (Freddy apparently didn't qualify, as he was a nervous wreck and disliked public performances). Thus, although violinists do get nervous, it does not spin out of control when they are playing in an orchestra because the conditions are not as extreme as for solo performances. Youngsters, who are too frightened to perform solo, almost always enjoy performing in a group. This shows the over-riding importance of the mental perception of the situation.

Clearly, the way to control nervousness is to first study its cause and nature and to develop methods for controlling it based on this knowledge. Since it is an emotion, any method for controlling emotions will work. Some have claimed that, under a doctor's supervision, medications such as Inderal and Atenolol, or even Zantac will work to calm nerves. Conversely, you can make it worse by drinking coffee or tea, not getting enough sleep, or taking certain cold medications. Emotions can also be controlled by use of psychology, training, or conditioning. Knowledge is the most effective means of control. For example, experienced snake handlers do not suffer any of the emotions most of us would experience when we come close to a poisonous snake because of their knowledge of snakes.

By the time nervousness becomes a problem, it is usually a compound emotion spinning out of control. In addition to nervousness, other emotions such as fear and worry, join in. A lack of understanding of nervousness also creates fear because of the fear of the unknown. As the symptoms worsen, you worry that the extreme nervousness will interfere with the performance. Thus just the simple knowledge of what stage fright is, can be a calming factor by reducing the fear of the unknown.

How does nervousness grow out of control, and are there ways to prevent it? One way to approach this question is to visit some principles of fundamental science. Practically anything in our universe grows by a process known as the Nucleation-Growth (NG) mechanism. The NG theory states that an object forms in two stages, nucleation and growth. This theory became popular and useful because it is in fact the way in which the majority of objects in our universe form, from raindrops to cities to stars. It is amazing that this theory, which has many intricate parts, describes the formation of so many things so accurately. Two key elements of NG theory are: (1) nucleation - nuclei are always forming and disappearing. However, there is a thing called a critical nucleus which, when formed, becomes stable -- it does not disappear. In general, the critical nucleus does not form unless there is a supersaturation of the material that aggregate to form it, or it is "seeded", and (2) growth - for the object to grow to its final size, the critical nucleus needs a growth mechanism by which to increase its size. One of the most interesting aspects of nucleation is that there is almost always a barrier to nucleation -- otherwise, everything would have nucleated a long time ago. Growth is a two-way street: it can be positive or negative.

Let's examine one example: rain. Rain occurs when water droplets form critical nuclei in air that is supersaturated with water vapor (relative humidity greater than 100%). The oft misquoted "scientific truth" that relative humidity never exceeds 100% is routinely violated by Nature because that "truth" is valid only under equilibrium conditions, when all forces have been allowed to equilibrate. Nature is almost always dynamic, and it can be far from equilibrium. This happens, for example, when the air cools rapidly and becomes supersaturated with water vapor; that is, relative humidity higher than 100%. Even without supersaturation, water vapor is constantly forming water droplets, but these evaporate before they can form critical nuclei. With supersaturation, critical nuclei can suddenly form, especially if there are hydrophilic dust particles (the seeds) in the air or a compressive disturbances such as thunderclaps that bring the molecules closer together. The air filled with critical nuclei is what we call a cloud or fog. If the formation of the cloud reduces the supersaturation to zero, a stable cloud is created; if not, the nuclei will keep growing to reduce the supersaturation. Nuclei can grow by other mechanisms. This is the growth stage of the NG process. The nuclei can bump into each other and aggregate, or start to fall and hit other water molecules and nuclei, until rain drops form.

Let's apply NG theory to nervousness. In everyday life, your sense of nervousness comes and goes, without becoming anything serious. However, in an unusual situation such as just before a performance, there is a supersaturation of factors that cause nervousness: you must perform flawlessly, you didn't have enough time to practice the piece, there is a big audience out there, etc. However, this still may not cause any problem because there are natural barriers to nucleating nervousness, such as a flow of adrenalin, a sense of accomplishment, or even just a lack of the realization that there is nervousness, or you might be too busy finalizing the preparations for the recital. But then, a fellow performer says, "Hey, I got butterflies in my stomach," (the seed) and you suddenly feel a lump in your throat and realize that you are nervous -- the critical nucleus has formed! This may still not be that bad, until you start to worry that perhaps your piece is not yet ready to perform or the nervousness might start to interfere with the playing -- these worries cause the nervousness to grow. These are exactly the processes described by NG theory. The nice thing about any scientific theory is that it not only describes the process in detail, but also provides solutions. So how does NG theory help us?

First of all we can attack nervousness at the nucleation stage; if we can prevent nucleation, it will never form a critical nucleus. Just merely delaying the nucleation will be helpful because that will reduce the time available for it to grow. Playing easier pieces will reduce the supersaturation of worry. Mock recitals will give you more experience and confidence; both will reduce the fear of the unknown. Generally, you need to perform a piece 3 or more times before you know whether you can perform it successfully or not; thus playing pieces that had been performed several times will also help. Nervousness is generally worst before a performance; once you start playing, you are so busy with the task at hand that there is no time to dwell on nervousness, thus reducing the growth factor. This knowledge helps because it alleviates the fear that things might get worse during the performance. Not dwelling on nervousness is another way of delaying the nucleation as well as slowing the growth stage. Thus it is a good idea to keep yourself occupied while waiting for the recital to begin. Mental play is useful because you can check your memory and keep yourself occupied at the same time by playing the piece in your mind. See the following section on Teaching for suggestions on how teachers can provide performance training.

For an important recital, avoiding nucleation is probably not possible. Therefore we should also consider ways to discourage growth. Since nervousness generally decreases after the performance starts, this knowledge can be used to reduce the worry and therefore the nervousness. This can feed on itself, and as you feel more assured, nervousness can often dissipate entirely, if you can reduce it below the critical nucleus. Another important factor is mental attitude and preparation. A performance is always an interactive process, with yourself and with the audience. When the music comes out well, it is easier to perform well; conversely, if you make a mistake, it can feed back psychologically and further degrade the performance. Thus it is important to be mentally prepared so as not to be adversely affected by mistakes or perceived poor performance. Instead of grimacing at a mistake, you might put on a smile. Remember that you are your worst critic and even casual playing sounds terrific to the audience. They generally hear less than half of the mistakes and remember even less, whereas the performer remembers every mistake. Inexperienced performers often try to play too fast which is almost always counterproductive. Playing musically, of course, is always the answer -- when you can involve your entire brain in the business of creating music, there is very little brain resources left to worry about nervousness. These are all measures for reducing the growth of nervousness.

It is not a good idea to pretend that nervousness does not exist, especially with youngsters who can more easily suffer long term psychological damage. Kids are smart and they can easily see through the pretense, and the need to play along with the pretense can only increase the stress. This is why performance training, in which nervousness is discussed openly, is so important. For the case of young students, their parents and friends attending the recital need to be educated also. Statements like "I hope you aren't nervous!" or "How can you perform without getting nervous?" are almost certain to cause nucleation and growth. On the other hand, to completely ignore nervousness and send kids out to perform with no performance training is also irresponsible and can even cause lifelong psychological damage.

Developing the proper mental attitude is the best way for controlling stage fright. If you can get into the frame of mind that performing is a wonderful experience of making music for others and develop proper reactions when you do make mistakes, nervousness will not be problematic. There is this huge difference between, for example, creating humor out of a mistake or recovering nicely from it and letting that mistake look like a disaster that mars the entire performance. Here again, we must know what not to do. That is why it is so important, early in a student's career, to play very easy pieces that can be performed without nervousness; even just one such experience can provide the existence proof that performing without nervousness is possible. That single experience can influence your performance attitude for the rest of your life. The best way to guarantee such a flawless performance is to develop a secure mental play, which will allow you to start playing from any note in the piece, stay ahead of the music, create the musicality in your mind, develop absolute pitch, recover from flubs or cover them up, play mental music all day, practice any part of the music at any time or place, etc.; these achievements will give you the confidence of an accomplished musician.

In summary, stage fright is nervousness that has spiraled out of control. A certain amount of nervousness is normal and necessary. You can minimize nervousness by delaying its nucleation by keeping busy and reducing its growth by playing musically. Thus it doesn't make sense to ask "do you get nervous when you perform?" Everyone does, and should. Such a question can actually nucleate nervousness. We only need to contain nervousness so that it does not grow out of control. Thus realizing that a certain amount of nervousness is normal is the best starting point for learning how to control it. Of course, there is a wide range of individuals from those who don't get nervous at all, to those who suffer terribly from stage fright. The best policy for nervousness is honesty -- we must acknowledge its effect on each individual and treat it accordingly. Gaining confidence in your ability to perform can usually eliminate nervousness, and perfecting the art of mental play is the only way to really achieve such confidence.

After the Recital

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Review the recital results and evaluate your strengths and weaknesses so that you can improve your practice/recital preparation routines. A few students will be able to play consistently without audible mistakes. Most of the others will make several mistakes every time they play. Some will tend to bang on the piano while others may be too timid. There is a cure for every problem. Those who make mistakes probably have not yet learned to play sufficiently musically and almost always cannot play in their minds. Those who tend to play flawlessly invariably have learned mental play, whether they do it consciously or not.

As noted elsewhere, playing several recitals in succession is the hardest thing to do. But if you must, then you will need to recondition the recital pieces immediately following the recital. Play them with little or no expression, medium speed, then slow. If certain sections or pieces did not come out satisfactorily during the recital, you can work on them, but only in small segments. If you want to work on the expression at full speed, do this also in small segments. Experienced teachers know the difficulty of playing consecutively and will purposely use this to strengthen the students' performance ability by scheduling recitals on consecutive days. However, it is my personal opinion that it is more important to train the student to enjoy performing than to give them too many difficult tasks. The joy of performance should not emphasize "showing off" the technical skills of playing difficult pieces but should instead concentrate on making music.

That Unfamiliar Piano

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Some students fret that the recital piano is a huge grand whereas they practice on a small upright. Fortunately, the larger pianos are easier to play than the smaller ones. Therefore the issue of a different piano is usually not something to worry about for the typical student recital. Larger pianos generally have better action, and both louder and softer sounds are easier to produce on them. In particular, grands are easier to play than uprights, especially for fast, difficult passages. Thus the only time you may have to be concerned about the piano is when the recital piano is decidedly inferior to your practice piano. The worst situation is the one in which your practice piano is a quality grand, but you must perform using low quality upright. In that case, technically difficult pieces will be very difficult to play on the inferior piano and you may need to take that into account, for example, by playing at a slower tempo, or shortening or slowing down the trill, etc. The actions of grands can be slightly heavier than those of uprights, which may give some beginners problems, so it is advisable to practice on the grand before the recital. On average, the key weight feel of grands and uprights is about the same because, although most grands have heavier action, they produce more sound, and the two effects tend to cancel each other out. Of course, it is impossible to generalize about pianos because there is so much variation from piano to piano, even within the same model piano from the same manufacturer. Therefore, you should always try to practice on the recital piano before the recital.

Another important factor is the tuning of the piano. Pianos in good tune are significantly easier to play than one out of tune. Therefore, it is a good idea to tune the recital piano just before the recital. Conversely, it is not a good idea to tune the practice piano just before the recital unless it is badly out of tune. Therefore, if the recital piano is out of tune, it may be best to play slightly faster and louder than you intended. Because of the tendency of out of tune pianos to cause flubs and blackouts, the practice piano should always be in reasonable tune. Otherwise, the students may develop a habit of stuttering or lose their confidence in their ability to memorize.

Proper voicing of the hammers (see Chapt. Two, section 7) is more critical than most people realize. The importance of practicing musically, and especially of being able to play softly, is mentioned repeatedly in this book. You can't do any of that without properly voiced hammers. Hammer voicing is too often neglected in practice pianos with the result that musical playing becomes nearly impossible. How can you practice performing on a piano with which it is impossible to perform? There are many students who think that they cannot perform, simply because their pianos were not properly maintained. The folklore that a great pianist can produce great music using any piano is not true. Please read the section on voicing.

During the Recital

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Nervousness is usually worst just before you start to play. Once you start, you will be so busy with the playing that the nervousness will tend to be forgotten and nervousness subsequently decreases. This knowledge can be quite reassuring, so there is nothing wrong with starting play as soon as you sit down at the piano for the recital. Some people will delay starting by adjusting the bench or some clothing item in order to have time to double check that the starting tempo, etc., are correct; this procedure is also acceptable, as it reassures the audience that you are not too nervous and is in no hurry to start. You should also mentally play the beginning at this time, with emphasis on the musical output. It is a good idea to practice starting, from several days prior to the recital. Whenever you have time, just pretend that it is recital time, and play the first few bars.

You can't assume that you won't make any mistakes because that assumption can only get you into more trouble. Be ready to react correctly with each mistake, or more importantly an impending mistake that you can avoid. It is amazing how often you can feel an impending mistake before it hits, especially if you are good at mental play. The worst thing that most students do when they make a mistake or when they anticipate one is to get scared and start playing more slowly and softly. This can lead to disaster. Although finger memory is not something you want to depend on, this is one time you can take advantage of it. Finger memory depends on habit and stimuli -- the habit of having practiced many times, and the stimuli of previous notes leading to succeeding notes. Therefore, in order to enhance finger memory, you must play slightly faster and louder, exactly the opposite of what an anxious person would do during a recital (another counter-intuitive situation!). The faster play makes better use of the playing habit, and leaves less time for moving some wrong muscle that might derail you from the habit. The firmer play increases the stimuli for the finger memory. Now playing faster and louder are scary things to do during a recital, so you should practice this at home just as you practice anything else. Learn to anticipate mistakes and to avoid them by using these avoidance methods. The important lesson here is that one trick for "playing through mistakes" is to play it slightly faster and louder. Another method is to make sure that the melodic line is not broken, even at the cost of missing some "accompaniment" notes. With practice, you will find that this is easier than it sounds; the best time to practice this is when you are sight reading. Another way to play through mistakes is to at least keep the rhythm. Of course, none of this would be needed if you have a really secure mental play, especially if you also have perfect pitch.

Performance Preparation Routines

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All successful piano teachers hold recitals of their students. Therefore, attending these recitals is a good way to find good teachers and to learn about how they teach. There is a direct correlation between how good the teacher is and how many recitals s/he schedules. Obviously, the better teachers hold more recitals, some as many as six or more a year. See the section on "Teaching" for how you can schedule so many recitals every year. Have you noticed that student recitals tend to be either terrific or terrible? This happens because some teachers know how to prepare their students for recitals while others do not. This explanation is supported by the observation that, when the recital is good, all the students play well, and vice versa.

Even if a student can play perfectly during practice, s/he can make all kinds of mistakes during a recital if the preparation is incorrect. Most students intuitively practice hard and at full speed during the week preceding the recital, and especially on the day of the recital. In order to simulate the recital, they imagine an audience listening nearby and play their hearts out, playing the entire piece from beginning to end, many times. This practice method is the single biggest cause of mistakes and poor performance. The most telling remark I hear so often is, "Strange, I played so well all morning but during the recital, I made mistakes that I don't made during practice!" To an experienced teacher, this is a student practicing out of control without any guidance about right and wrong methods of recital preparation.

Teachers who hold those recitals in which the students perform wonderfully keep a tight leash on their students and control their practice routines closely. Why all this fuss? Because during a recital, the most stressed element is the brain, not the playing mechanism. And this stress cannot be replicated in any kind of simulated performance. Thus the brain must be rested and fully charged for a one-time performance; it cannot be drained by playing your heart out. All mistakes originate in the brain. All the necessary information must be stored in an orderly manner in the brain, with no confusion. This is why improperly prepared students always play worse in a recital than during practice. When you practice at full speed, a large amount of confusion is introduced into the memory. It is analogous to a computer that has been used for a long time without defragmenting the main disk and deleting duplicate and useless files. In addition, the environment of the recital is different from that of the practice piano, and can be very distracting. Therefore, you must have a simple, mistake-free memory of the piece that can be retrieved in spite of all the added distractions. This is why it is extremely difficult to perform the same piece twice on the same day, or even on successive days. The second performance is invariably worse than the first, although intuitively, you would expect the second performance to be better because you had one extra experience performing it. As elsewhere in this section, these types of remarks apply only to students. Professional musicians should be able to perform anything any number of times at any time; this skill comes from continuous exposure to performing, and honing the proper rules of preparation.

Through trial and error, experienced teachers have found practice routines that work. The most important rule is to limit the amount of practice on recital day, so as to keep the mind fresh. The brain is totally unreceptive on recital day. It can only become confused. Only a small minority of talented students have sufficiently "strong" musical brains to assimilate something new on recital day. By the way, this also applies to tests and exams at school. Most of the time, you will score better in an exam by going to a movie the night before the exam than by cramming. A typical recommended piano practice routine is to play nearly full speed once, then medium speed once and finally once slowly. That's it! No more practice! Never play faster than recital speed. Notice how counter intuitive this is. Since parents and friends will always use intuitive methods, it is important for the teacher to make sure that any person associated with the student also knows these rules, especially for the younger students. Otherwise, in spite of anything the teacher says, the students will come to the recital having practiced all day at full speed, because their parents made them do it.

Of course, this is just the starting point. It can be altered to fit the circumstances. This routine is for the typical student and is not for professional performers who will have much more detailed routines that depend not only on the type of music being played, but also on the particular composer or particular piece to be played. Clearly, for this routine to work, the piece will have had to be ready for performance way ahead of time. However, even if the piece has not been perfected and can be improved with more practice, this is still the best routine for the recital day. If you make a mistake that you know is stubborn and which you are almost certain that it will occur during the recital, fish out just the few bars containing the mistake and practice those at the appropriate speeds (always ending with slow play), staying away from fast playing as much as possible. If you are not sure that the piece is completely memorized, you can play it very slowly several times. Again, the importance of secure mental play must be emphasized -- it is the ultimate test of whether you are ready to perform.

Since you are allowed only one practice at speed (or close to it), what do you do if you make a mistake during that one practice? Play right through! Don't stop to correct it or even hesitate. Unfortunately, any mistake you make at this time has a high probability of reappearing during the recital. Therefore, after you have finished the piece, go back and fish out the phrase containing the mistake and play it slowly several times. You will generally find that in mental play, the same place will be insecure -- therefore, practice it very fast and very slowly mentally.

Also, avoid extreme exertion, such as playing a football game or lifting or pushing something heavy (such as a concert grand!). This can suddenly change the response of your muscles to a signal from the brain and you can end up making totally unexpected mistakes when you play at the recital. Of course, mild warm-up exercises, stretching, calisthenics, Tai Chi, Yoga, etc., can be very beneficial.

For the week preceding the recital, always play medium speed, then slow speed, before quitting practice. You can substitute medium speed for slow speed if you are short of time, or the piece is particularly easy, or if you are a more experienced performer. Actually, this rule applies to any practice session, but is particularly critical before a recital. The slow play erases any bad habits that you might have picked up, and re-establishes relaxed playing. Therefore, during these medium/slow plays, concentrate on relaxation. There is no fixed number such as half speed, etc., to define medium and slow, although medium is generally about 3/4 speed, and slow is about half speed. More generally, medium speed is the speed at which you can play comfortably, relaxed, and with plenty of time to spare. Slow is the speed at which you need to pay attention to each note separately.

Blackouts are different from mistakes and must be dealt with differently. Never try to restart from where you blacked out unless you know exactly how to restart. Always restart from a preceding section or a following section that you know well (preferably a following section because mistakes usually cannot be corrected during the recital). Secure mental play will eliminate practically all blackouts.

Up to the last day before the recital, you can work on improving the piece. But within the last week, adding new material or making changes in the piece (such as fingering) is not recommended, although you might try it as a training experiment to see how far you can push yourself. Being able to add something new during the last week is a sign that you may be a strong performer. For working on long pieces such as Beethoven Sonatas, avoid playing the entire composition many times. It is best to chop it into short segments of a few pages at most and practice the segments. Practicing HS is also an excellent idea because no matter who you are, you can always improve technically. Although playing too fast is not recommended in the last week, you can practice at any speed HS. Avoid learning new pieces during this last week. That does not mean that you are limited to the recital pieces; you can still practice any piece that you have previously learned. New pieces are unpredictable and will often cause you to learn new skills that affect or alter how you play the recital piece. In general, you will not be aware that this happened until you play the recital piece and wonder how some new mistakes crept in.

Make a habit of playing your recital pieces "cold" (without any warming up) when you start any practice session. The hands will warm up after one or two pieces, so you may have to rotate the recital pieces with each practice session, if you are playing many pieces. Of course, "playing cold" has to be done within reason. If the fingers are totally sluggish from inaction, you cannot, and should not try to, play difficult material at full speed; it will lead to stress and even injury. Some pieces can only be played after the hands are completely limbered up, especially if you want to play it musically. However, the difficulty of playing musically must not be an excuse for not playing cold because the effort is more important than the result in this case. You need to find out which ones you can play cold at full speed, and which ones you should not.

Recording your playing is a good way to practice playing before an audience. Videotaping is far better than just audio recording; it is by far the best way to simulate a performance -- the only better way is to recruit a bunch of people to listen to you. Videotaping has the advantage that you can alternate practicing with taping so that you can immediately correct any mistakes you find. The magic of videotaping works in two ways. First, it is such a good simulation of the actual recital that, if you can play satisfactorily during videotaping, you will have no trouble during the recital -- you will gain the confidence to perform. The second magic is that, if you gain sufficient confidence, the nervousness can be almost completely eliminated. Of course, in order to eliminate nervousness, you must also follow all the other points discussed in this book, starting with the attitude that you are a performing pianist and therefore is expected to perform. Finally, as stated repeatedly in this book, secure mental playing is the most important skill that will improve your performance immeasurably. Once you have performed after mastering mental playing, you will wonder how you ever had the courage to perform without it.

Casual Performances

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Now let's talk about casual performances. Common types of casual performances are playing pieces for testing pianos in stores or playing for friends at parties, etc. These are different from formal recitals because of their greater freedom. There is usually no set program, you just pick anything you think appropriate for the moment, and it may in fact be full of changes and interruptions midway through the playing. Nervousness should not even be an issue, and casual performances provide one of the best ways to practice methods for avoiding nervousness. Even with the alleviating factors, this is not easy in the beginning. One thing you can do to get an easy start is to play little snippets (short segments from a composition) from various pieces you know. You can start with easy ones. You can pick out just the best sounding sections. If it doesn't work out too well, start on another one. Same, if you get stuck. You can start and quit at any time. This is a great way to experiment and find out how you perform and which snippets work. Do you tend to play too fast? It is better to start too slow and speed up than the other way round. Can you adjust to a different piano -- especially one that is out of tune or difficult to play? Can you keep track of the audience reaction? Can you make the audience react to your playing? Can you pick the right types of snippets for the occasion? Can you put yourself in the right frame of mind to play? What is your level of nervousness, can you control it? Can you play and talk at the same time? Can you gloss over mistakes without being bothered by them?

Playing snippets has one interesting advantage which is that most audiences are very impressed by your ability to stop and start anywhere in the middle of a piece. Most people assume that all amateur pianists learn pieces by finger memory from beginning to end, and that somehow, the ability to play snippets requires special talent. Since the methods of this book are based on practicing segments, this should be an easy thing to do. Start with short snippets, and then gradually try longer ones. Once you have done this type of casual snippet performance on 4 and 5 different occasions, you should be ready to perform longer sections. Obviously, one of the routines you should practice "cold" are snippet playing routines.

There are a few rules for preparing for snippet performances. Don't perform a piece you had just learned. Let it stew for at least 6 months; preferably one year. If you had just spent 2 weeks learning a difficult new piece, don't expect to be able to play snippets you had not played at all in those 2 weeks -- be prepared for all kinds of surprises, such as blackouts. In that case, try out the snippets at home before attempting to perform them. Don't practice the snippets fast on the day on which you might be performing them. Practicing them very slowly will help. It is a good idea to double check that you can still play them HS. You can break a lot of these rules for very short snippets. You should experiment to see which rules you need to follow for snippet performances. Above all, make sure that you can mentally play them (away from the piano) -- that is the ultimate test of your readiness.

Because casual performances are much more relaxed, it provides an avenue for easing your way gradually into performing, in preparation for recitals. This is because recitals are often high pressure affairs with the attendant nervousness. Students suddenly thrust into formal recitals often end up becoming nervous at any performance. Nervousness is a purely mental thing and is a feedback mechanism that feeds on itself. Therefore it is quite possible that it can be mostly avoided depending on the person's history. For example, by going through enough casual performances without developing any nervousness, a person can get to perform at recitals with much less nervousness than if s/he were suddenly thrust into formal recitals. Thus one thing you should work on, is to learn how to suppress nervousness during casual performances. Learning to enjoy the occasion, to use it as a way to demonstrate how you can express yourself, etc., will reduce nervousness, whereas fear of performing, making mistakes, etc., will increase it.

Clearly, it is a mistake for a teacher to take a student and enter her/im into a recital without any preparation. Students must be gradually introduced to performing through a well planned program. They should be taught the art of snippet playing at informal occasions. They should practice performing by videotaping. Students need to take a course on nervousness. They should play very simple pieces for the first few recitals. Students and their parents must know the details of the recital preparation routines (see below). In summary, even if we know the art of making music, we can't perform without training in the art of performing.

In general, don't expect to perform anything well, casual or otherwise, unless you have performed the piece at least three times, and some claim, at least 5 times. Sections that you thought were simple may turn out to be difficult to perform, and vice versa. Thus the first order of business is to lower your expectations and start planning on how you are going to play this piece, especially when unexpected things happen. It is certainly not going to be like the best run you made during practice.

A few mistakes or missed notes goes unnoticed in practice, and your assessment of how they sound during practice is probably much more optimistic than your own assessment if you had played exactly the same way for an audience. After a practice, you tend to remember only the good parts, and after a performance, you tend to remember only the mistakes. Usually, you are your worst performance critic; every slip sounds far worse to you than to the audience. Most audiences will miss half of the mistakes and forget most of what they do catch after a short period of time.

Practicing Musically

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Although the ideas of this paragraph apply to all practice sessions, this is the most appropriate place to bring up this subject: how musically you practice and how loud you practice, especially the more exciting loud, passages. Many students hate to practice when others are around to listen. Others are of the opinion that piano practice is necessarily unpleasant and punishing to the ear. These are symptoms of a common misconception. If you are using the correct practice methods and making terrific progress, and quickly transitioning to making music, there is nothing unpleasant about piano practice sessions.

A common mistake is to practice loud passages loud all the time when learning a new composition. There is no need to play a loud passage loud until you can play it satisfactorily; loudness is added later. By separating the loudness from the technique, you acquire technique faster and with less fatigue, and reduce stress. Once the technique is attained with full relaxation, you can add much more power than you could before, without picking up bad habits. Students who have not completely eliminated stress often practice everything too loud. Thus practicing too loud is frequently an indication of some underlying problem. Of course, there are students who never play sufficiently firmly to produce a solid, clear, tone, and these have the opposite problem of having to firm up their playing. Both problems, either playing too loudly or too softly, can be helped by practicing the gravity drop. The best criterion that you are practicing correctly is the reaction of others -- if your practice sounds good to them, or at least it doesn't bother them, then you are probably doing it right.

The benefits of practicing musically all the time becomes obvious when it comes time to perform. Looking at this another way, practicing without regard to musicality will certainly make switching to "performance mode" an impossible task. What does it mean to play musically? This question can only be answered definitively by application of the myriad micro-rules that apply to specific passages of specific compositions. If you have incorporated all of the musical notations and markings into your music, you have built a sound foundation. Then there are the useful general rules:
(i) carefully connect each bar to the next bar (or measure, or phrase). These bars/measures do not stand alone; one logically flows into the other and they all support each other. They are connected rhythmically as well as conceptually. You might think that this point is trivially obvious; however, when you do this consciously, you might be surprised by the improvement in your music.
(ii) there must always be a conversation between the RH and LH. They don't play independently. And they won't talk to each other automatically just because you timed them perfectly. You must consciously create a conversation between the two hands, or voices, in the music.
(iii) "cresc." means that most of the passage should be played softly; only the last few notes are loud, which means that it is important to start softly. Similarly, for other indications of this nature (rit., accel., dim., etc); make sure that you have reserved space for the action to take place and don't start the action immediately, wait until the last moment.
(iv) strive more for accuracy than expressive rubato; rubato is often too easy, incorrect, and not in tune with the audience. This is the time to use the metronome to check your timing and rhythm.
(v) when in doubt, start and end each musical phrase softly, with the louder notes near the middle. It is usually incorrect to have loud notes at the beginning.

Musical playing feeds on itself. Thus a good performance begets a better performance. This also applies to practicing. Musicality also has no limit -- you can improve no matter where you are on the scale of musicality. The terrifying part of this is the flip side. If you do not pay attention, you can develop non-musical playing habits that can keep on destroying your musicality. This is why it is so important to focus on musicality and not only on technique; it can make the difference between whether you can perform or not. The above points [(i) to (v)] are not trivial. If you focus on them, several things will automatically happen. Firstly, you will be so preoccupied by trying to get them all to come out right that you will have less opportunity to make non-musical mistakes. Secondly, they will set your playing on a sound basis from which to improve. As you hear the music coming out correctly, it will become much easier to further enhance the music than if you had started it wrong.

Practicing for Performances

2006-02-21T12:59:00.001-08:00

Most students do not listen to themselves sufficiently during practice; they often practice as if on auto-pilot. This does not mean that you can put yourself on auto-pilot for a performance in the hopes that you can perform like you did during practice. You can't just run with a piece of music and expect the audience to follow you; if you did, you will lose them because they will sense that the music is not communicating. The correct way is to listen to your own music (always) and to let your music lead you -- that is the only way it is going to attract the audience's attention. During a performance, your music will always lead you, whether you let it or not; this is why students who make mistakes become so depressed and the depression makes it harder to play well. On the other hand, if you get a good start, the audience will be drawn in, and the music will feed on itself and the performance becomes much easier. For the music to lead you, you must not just listen to the music coming out of the piano; you must first play it mentally and to anticipate what you want to produce.

Lowering your expectations generally means playing a little slower than your practice speeds and paying more attention to every note. As we saw earlier, playing slowly is not necessarily easier, and this illustrates the importance of slower practice. Remember that the audience hasn't heard this piece hundreds of times like you have and so are not as familiar with every detail; chances are, it will sound much faster to them than to you. And you will need to spoon feed every note to them or they won't hear it. During practice you will probably even hear notes that you missed, as if you had played it correctly, because you know that it is supposed to be there. Clearly, the science of performing is complex and experienced performers can give you plenty of useful advice.

Basics of Flawless Performances

2006-02-21T12:59:00.000-08:00

The basic requirements for a flawless performance are: technical preparation, musical interpretation, and a good performance preparation routine. After these are completed, then the only missing ingredient is good mental play (memorization). When all these elements come together, you can virtually guarantee a perfect performance. Here, we review these important elements and discuss how to know that you have met the requirements, as well as add the necessary ideas not discussed elsewhere.

Of course, there are plenty of excuses for not being able to perform. Knowing these excuses is one of the prerequisites for learning how to perform. Perhaps the most common excuse is that you are always learning new pieces so that there is insufficient time to really finish a piece or maintain the finished pieces in playable condition. We saw that learning a new piece is the best way to mess up old pieces. For those who have never performed, the second most important reason is that they probably never really finished anything. There is always that one difficult section you can't quite manage in every "interesting" piece worth performing. If you haven't performed the piece, you have no idea whether it is finished or not. Another excuse is that pieces that are easy for you are somehow always uninteresting. Note that the learning methods of this book are designed to counter every one of these excuses, mainly by accelerating the learning process and by encouraging memorization. By the time you can play your piece well in your mind, none of these excuses will be valid. The technical methods are discussed in II and III. The musical training and memorization, that culminate in mental playing, are also covered elsewhere, especially in III.6.

Benefits and Pitfalls of Performances/Recitals

2006-02-21T12:58:00.000-08:00

We need to discuss the benefits and pitfalls of performing because this knowledge determines how we design our daily piano learning program. For the amateur pianist, the benefits of performances, even casual ones, are immeasurable. The most important benefit is that technique is never really demonstrated until you can demonstrate it in a performance. That is, music and technique are inseparable, so that if you perform successfully, it means that you practiced correctly. This works both ways: if you practice correctly, performing shouldn't be a problem. This point draws a clear line between practicing musically, relaxed, on the one hand and, on the other, repeating mindlessly just to be able to play a difficult passage, working like a dog, mistaking piano for some type of calisthenics.

For young students, the benefits are even more fundamental. They learn what it means to complete a real task, and they learn what "making music" means. Most youngsters don't learn these skills until they go to college; piano students must learn them at their first recital, regardless of age. Students are never as self-motivated as when preparing for a recital. Teachers who have held recitals know the enormous benefits. Their students become focused, self-motivated, and results oriented; they listen intently to the teacher and really try to understand the meaning of the teachers' instructions. The students become deadly serious about eliminating all errors and learning everything correctly -- it is capitalism at its best, because it is their recital. Teachers without recitals often end up with students who practice maybe a few times just before lesson day -- the difference is like night and day.

Because the psychology and sociology of piano playing is not well developed, there are pitfalls that we must seriously consider. The most important one is nervousness and its impact on the mind, especially for the young. Nervousness can make recitals a frightful experience that requires careful attention in order to avoid not only unhappy experiences but also lasting psychological damage. At the very least, reducing nervousness will alleviate stress and fright. There is not enough attention paid to making recitals a pleasant experience and reducing the tension and stress, especially for piano competitions. This whole subject will be treated more completely in the section on nervousness. The point here is that any treatment on performing must include a discussion of stage fright. Even great artists have stopped performing for long periods of time for one reason or another. Therefore, although good piano teachers always hold recitals of their students and enter them into competitions, it is the job of the parents to look out for the social and psychological welfare of their children, since piano teachers are not necessarily good sociologists or psychologists. It is important for any person guiding youngsters through recitals and competitions to learn the fundamentals of what causes nervousness, how to deal with it, and its psychological consequences. Therefore, the following section (section 15) on nervousness is a necessary companion to this section.

There are numerous other psychological and sociological implications of recitals and competitions. The judging systems in music competitions are notoriously unfair, and judging is a difficult and thankless job. Thus students entered into competition must be informed of these shortcomings of the "system" so that they do not suffer mental damage from perceived unfairness and disappointment. It is difficult, but possible, for students to understand that the most important element of competitions is that they participate, not that they win. There is too much emphasis on technical difficulty and not enough on musicality. The system does not encourage communication among teachers to improve teaching methods. It is no wonder that there is a school of thought that favors eliminating competitions. There is no question that recitals and competitions are necessary; but the present situation can certainly be improved.

Videotaping and Recording Your Own Playing

2006-02-16T13:24:00.000-08:00

One of the best ways to improve your musical playing and to practice for recitals is to videotape/record it and watch/listen to it. You will be surprised at how good and how bad the different parts of your playing are. They are often very different from what you imagine yourself to be doing. Do you have a good touch? Do you have rhythm? What are you doing, that is breaking up the rhythm? Is your tempo accurate and constant? What are your strengths and weaknesses? Do you clearly bring out the melodic lines? Is one hand too loud/soft? Are the arm/hands/fingers in their optimum positions? Are you using the whole body -- i.e., is the body in synch with the hands or are they fighting each other? All these and much more become immediately obvious. The same music sounds quite different when you are playing it or listening to its recording. You hear much more when you are listening to a recording than when playing it. Video taping is the best way to prepare for recitals and can sometimes eliminate nervousness almost completely.

Until recently, most pianists tried mainly to make audio recordings, thinking that the musical output was the most important; in addition, the older camcorders could not adequately record music. Audio recording has the disadvantage that proper recording of the piano sound is more difficult than most people realize and such attempts usually result in failure and abandonment of the effort. Camcorders have become so affordable and versatile that videotaping is now unquestionably the better method. Although the resulting sound may not be CD quality (don't believe the claims of digital video camera manufacturers), you do not need such quality to achieve all the useful pedagogical objectives. Only when you have a properly voiced, high quality grand piano (Steinway B or better) and you become an advanced player, do you need the necessary equipment for satisfactory audio recording. Even then, you will get better results more cost effectively by seeking out a recording studio.

Initially, start by making a one-to-one map between what you think you are playing and the actual output. That way, you can modify your general playing tendencies so that the output will come out right. For example, if you are playing faster than you think in easy sections and slower in difficult sections, you can make the proper adjustments. Are your pauses long enough? Are the endings convincing? The recording is also helpful in deciding whether you want or need a better piano; your inability to perform satisfactorily may in fact be caused by the piano, not you. With old, worn hammers, you can't play pianissimo. Once you become a good enough pianist, factors such as the quality of the piano and proper voicing of the hammers will show up more obviously in the recordings.

There is no question that you must record your playing if you want to progress beyond just playing for yourself. The recording session will test how you might react in an actual performance, for example, if you make a mistake or have a blackout. Watching yourself react to mistakes will give you an opportunity to see what types of reactions are "proper" and what types are "improper". Also, during a performance, you tend to get blackouts, etc., at unexpected places where you generally had no trouble during practice. Recording sessions will bring out most of these problem spots.

In general, your pieces are not "finished" unless you can record them satisfactorily; that is, to the degree of perfection that you desire. Videotaping turns out to be a very good simulation of playing in recitals. Thus, if you can play satisfactorily during videotaping, you will have little trouble playing that piece in a recital. You will also find that you are not nervous performing pieces that you can record with acceptable results; we will discuss this in more detail in the section on nervousness (stage fright). Thus videotaping is one of the best tools for polishing a piece and getting it ready for performing.

What are the disadvantages? The main disadvantage is that it will take a lot of time, because you must watch or listen to the recordings. You might be able to save some time by listening while you are doing some other chore. The recording session itself takes little extra time because that counts as part of practice time. However, every time you correct a section, you must re-record and listen again. Thus there is no escaping the fact that watching/listening to yourself is going to be a time consuming operation. However, it is something that every piano student must do. Another disadvantage is that, without a really super recording system, you may need to use more pedal than you would like because the percussive component of the piano sound is picked up more efficiently by the audio system than by the human ear.

I describe some methods for audio and video recording below.

Audio Recording

Audio recording piano music is one of the most demanding of recording tasks. Things like portable cassette recorders for recording voice will not do, because the volume and frequency ranges of the piano exceed the capabilities of most inexpensive recording systems under about $1000.00. Modern equipment is sufficient to pick up most of the frequency range, and what small distortions are introduced, are not generally bothersome. However, the frequency response is not sufficiently flat, the highest and lowest frequencies are missed, and the dynamic range is insufficient. There is a surprising amount of audio power in ambient noise that the human ear/brain excludes (for example, the ears are shaped in such a way as to act as a noise filter), which microphones will pick up. Therefore, you will have to put up with some hiss for the softest playing and/or distortion for the loudest sounds, and all background noise (such as someone walking around or washing dishes) must be minimized. And unless you purchase very good mikes and/or put a lot of effort into their proper placement, etc., the piano sound will not be faithfully reproduced.

The following is an audio recording system that I have set up for myself. The components are:

(1) Sony MiniDisc ($150).
(2) Small mixer ($150 to $250).
(3) Boundary or PZM (Pressure Zone Microphone) mike ($50 to $300 each). You will need one for mono recording and two for stereo.
(4) Connecting cables.

I am assuming that you have a HiFi system into which you can plug the output; if not, use your TV (via the mixer). The Sony MD is readily available at electronics stores. In the US, Sam Ash may be the best place to buy a mixer, cables and mike, or you can get them at Radio Shack.

The MD is convenient because it is easy to edit, label, erase, and to quickly locate different recordings, is portable (fits in a small pocket), operates on its own rechargeable battery and comes with headphones. You can record 74 minutes on one disk, which can be rewritten any number of times. It also has many features such as optical and analog input/output, and most of the important functions (volume [both for record and playback], recording modes [mono/stereo], etc.), are programmable. The greatest disadvantage of the MD (I don't know if this has been corrected with the newer models) is that, although it is a digital device, it has no digital output. Within its dynamic range, the sound quality is almost as good as a CD so that the sound quality will be limited by the mike. Make sure to bring all the components with you when shopping around for the cables.

If you have a versatile HiFi system, you may not need the mixer. However, because the mixer allows you to try many more options and to optimize the system, I highly recommend it. You might first set up the system without the mixer and then buy it if necessary. The mixer has many built-in functions and just about any type of connector you might have, allowing you to connect practically any device to any other device and perform some signal processing. It contains pre-amps, signal attenuators, equalizers, balancers, etc. It has inputs for mono and stereo so that you can put in a mono signal and distribute it to both inputs of your stereo system. This is useful if you have only one mike. However, stereo recording gives audibly better results. For example, one mike placed towards the treble will not pick up sufficient bass sound; however, you can correct for this using the mixer. Most mixers will even supply power to your mike. Since the MD has both a line-in and mike inputs, you can record either with or without the mixer; however, you will usually sacrifice quite a bit of dynamic range, resulting in distortion or excessive noise. For playback, the same mixer will allow you to plug the output into any HiFi system. For many HiFi systems, the MD output may not have sufficient power.

Camcorders

Digital camcorders are better than the older analog types because you can make copies without degradation, they provide more options for editing, etc., and you can copy them directly to CDs or DVDs. Once you start taping, you may want to send the tapes to other people! However, analog camcorders are more affordable and are quite adequate. The biggest problem with camcorders is that they all have motors that make noise which is picked up by the built-in mike. Find a model with either an attachable mike of good quality, or a mike input and buy a separate quality mike. This will produce better results than the built-in mike. Also, make sure that the AGC (automatic gain control) can be turned off. Especially with classical music, you want to record the entire dynamic range of your playing. Some AGCs in high end camcorders do such a good job that you barely notice them, but you should make every effort to turn them off because the dynamic range is such an important characteristic of the piano. Most camcorders have plugs for connecting to a TV, which makes viewing simple. You will also need a fairly sturdy tripod; a light one might shake if you really pound away at the piano.

Learning Relative Pitch and Perfect Pitch (Sight Singing)

2006-02-16T13:22:00.000-08:00

Relative pitch is the ability to identify a note, given a reference. Perfect pitch (also called absolute pitch) is the ability to identify a note without being given a reference note. How good you are is determined by how accurately you can reproduce a pitch, how quickly you can identify a note, and how many notes you can identify when they are played simultaneously. People with good perfect pitch will instantly (within 3 seconds)identify 10 notes played simultaneously as a chord. The standard test for absolute pitch uses 2 pianos; the teacher sits at one and the student at the other, and the student tries to repeat the note played by the teacher. If there is only one piano, the student names the note played by the teacher (do, re, mi . . . . or C, D, E, . . ..). In the following exercises you can use either system; there is no real advantage of using one over the other. However, once you choose one system, don't use the other one until you have acquired a strong perfect pitch because the use of two systems can add unnecessary confusion and slow down your learning. I use the doremi system because the alphabet system is used in so many other places that the doremi system is less confusion. Nobody is born with relative or perfect pitch; these are learned skills. This is because the chromatic scale is a human invention - there is no physical relationship between the pitches of the chromatic scale and nature. The only physical relationship between the chromatic scale and the ear is that both operate on a logarithmic scale in order to accommodate a large frequency range. The effect of the logarithmic human hearing is that the ear hears a large difference in pitch between 40 and 42.4 Hz (a semitone or 100 cents), but hears almost no difference between 2000Hz and 2002.4 Hz (about 2 cents), for the same difference of 2.4 Hz. The human ear responds to all frequencies within its range and is not calibrated on an absolute scale at birth. This is in contrast to the eye, which responds to color on an absolute scale (everyone sees red as red) because color detection is achieved using chemical reactions that respond to specific wavelengths of light. Some people who can identify certain pitches with specific colors can acquire perfect pitch by the color that the sound evokes. They are effectively calibrating the ear to an absolute reference.

Perfect and relative pitch are best learned in very early youth. Babies who cannot understand a single word will respond appropriately to a soothing voice or a lullaby or an angry sound, which demonstrates their readiness for musical training. The best way for toddlers to acquire perfect pitch is to be exposed almost daily to well tuned pianos from birth. Therefore, every parent who has a piano should keep it tuned and play it for the baby from birth. Then they should test the child from time to time for perfect pitch. This test can be performed by playing a note (when the child is not looking) and then asking her/im to find that note on the piano. If the child can find it after several tries, s/he has relative pitch; if s/he can find it the first time every time, s/he has perfect pitch. The particular temperament to which the piano is tuned (equal, Well temperament, etc.) is not important; in fact most people with perfect pitch know nothing about temperaments and when notes on pianos tuned to different temperaments are played, they have no trouble in identifying the notes. Perfect pitch and relative pitch can be acquired later in life but becomes more difficult after age 20 to 30. In fact, even those with perfect pitch will slowly lose it starting around age 20, if it is not maintained. Many piano schools routinely teach perfect pitch to all their students. Although the success rate is not 100%, over 90% of the students succeed. The problem with teaching a group of older students is that there is always a certain percentage of "pitch deprived" students who had never been trained in pitch and who will have difficulty learning even relative pitch.

Babies can hear right after birth. Many hospitals routinely screen babies immediately after birth in order to identify hearing impaired babies who will need special treatments immediately. Because the hearing impaired babies do not receive sound stimuli, their brain development is retarded; this is another evidence that music can help brain development. For babies, the memory of external sound in the brain is initially empty. Thus any sound heard at that stage is special, and all subsequent sounds are referenced to those initial sounds. In addition, babies (of most species, not only humans) use sound to identify and bond to the parents (usually the mother). Of all the sound characteristics that the baby uses for this identification, absolute pitch is probably a major characteristic. These considerations explain why almost every youngster can readily pick up absolute pitch. Some parents expose babies to music before birth to accelerate the babies' development, but I wonder if this will help perfect pitch, because the sound velocity in amniotic fluid is different from that in air with a resultant change in apparent frequency. Therefore, this practice might confuse the perfect pitch, if it works at all. For implanting perfect pitch, the electronic piano is better than an acoustic because it is always in tune.

Having perfect pitch is clearly an advantage. It is a great help for memorizing, sight reading, and recovering from blackouts, and for composing music. You can be the pitch pipe for your choir, and easily tune a violin or wind instrument. It is a lot of fun because you can tell how fast a car is going by just listening to the tires whine, you can tell the differences between different car horns and locomotive whistles, especially by noting whether they use thirds or fifths. You can remember telephone numbers easily by their tones. However, there are disadvantages. Music played off tune does not sound right. Since so much music is played off tune, this can present quite a problem. The person can sometimes react strongly to such music; physical reactions such as teary eyes or clammy skin can occur. Transposed music is OK because every note is still correct. Out-of-tune pianos become difficult to play. Perfect pitch is a mixed blessing.

There is a method that makes learning relative and perfect pitch quick and easy! This method is not generally taught at music schools or in the literature, although it has been used by those with perfect pitch (usually without their explicit knowledge of how they acquired it), since the beginning of music. With the method described here, the pitch skills become simple by-products of the memory process. You expend little extra effort to acquire pitch recognition because memorizing is necessary anyway, as explained in III.6. In that section we saw that the final objective of memorizing is to be able to play the music in your mind (mental playing). It turns out that, by paying attention to relative and perfect pitch during the process of practicing mental playing, you naturally acquire the pitch skills! Thus, you do not only play music in your mind, but you must always play it at the correct pitch. This makes perfect sense because, without playing at the correct pitch, you lose so many of the benefits of mental play. For most, memorizing two significant compositions is sufficient to acquire perfect pitch to within a semi-tone, which is faster than any known method being taught today; for most, this should take a few weeks to a few months. Young children will accomplish this with zero effort, almost automatically; as you grow older, you will need more effort to cultivate perfect pitch because of all the other confusing sounds that are already in memory. In the following paragraphs, I will flesh out the details of how this is done. It may be helpful to read section III.6, and especially III.6j.

Therefore, the fastest way to learn relative/perfect pitch is to practice playing music in your mind at the correct pitch. Most schools teach pitch recognition by training students to sing their solfege lessons at the correct pitch. However, practicing in your mind is a more powerful and useful method than singing out loud because you are not limited by your singing abilities. I am not saying that solfege and singing are useless; they are necessary for learning the basics of music, and every pianist should learn some solfege if at all possible. What I am saying is that mental play is an even more necessary skill, which is often neglected by teachers. One of the reasons why teachers neglect this is that when you are playing music in your mind, the teacher cannot hear it. The assumption in solfege is that when you finish the solfege lessons, you will have learned perfect pitch, etc., and therefore, be able to play in your mind. But that takes too long, and can waste a lot of time because solfege lessons extend over many years. Mental play is such a necessary skill that it should be taught, starting at the first few piano lessons. Teaching early is critical, especially for youngsters, because learning pitch recognition rapidly becomes more difficult with age. The teacher can "hear" the effects of mental play by the benefits it bestows on memory, reduction in flubs, perfect pitch, compositional skills, etc.

Two useful pieces for practicing relative/perfect pitch are, Bach's Invention #1 and Beethoven's Moonlight Sonata, 1st Movement. The Moonlight has compelling melodies that make the memorizing process easy and enjoyable. Yet the complex chord transitions provide a variety of notes and intervals and the complexity prevents you from guessing the notes -- you need a considerable amount of practice and repetition before you can play it in your mind perfectly. It is also technically simple enough for everybody. The Bach Invention gives you middle C (its first note) and the C Major scale; these are the most useful note and scale to recognize in perfect pitch. Both compositions should be practiced HS for pitch practice. Later on, you should try HT in your mind, at least for the Moonlight which is easier.

Start with the Bach; the objective here is to master all the white keys first. As you memorize it and practice playing it in your mind, pay attention to each note and every interval: a semi-tone, a full note, a third, fifth, etc. The first 4 RH notes give you doremifa, 2 full tones and a semi-tone. Practice relative and absolute pitch at the same time; therefore, listen to the notes in your mind: the music, the emotions, the visualization of the keyboard, etc., will all help you to place the notes very close to the correct pitches on the piano. Here again, playing musically will be very beneficial. With practice, any error will decrease progressively with time. Therefore, test yourself at the piano frequently at first, and measure your progress.

When creating notes in your mind as you play the music, do not try to hum or sing them using the vocal chords because the dynamic range of the piano is much larger than your singing range and you need to train the mind to deal with these higher and lower notes. Also, the memory of each note for perfect pitch must initially include everything -- the harmonics, timbre, and other characteristics of your piano -- you need as many memory associations as possible in order to hasten the memory process. Therefore, use the same piano until you feel that you have perfect pitch and try to memorize every characteristic of your piano sound. Unless you have an electronic piano, you will need to make sure that the piano is not out of tune. Once you acquire a strong perfect pitch, it will work with any source of sound. Unless you are a trained singer who can sing on pitch (in which case you don't need to practice perfect pitch), you will not be able to accurately reproduce the pitch you hear in the mind. The resultant incorrect sound from the vocal chords will confuse the brain and destroy any absolute pitch that you might have acquired. The perfect pitch you initially acquire is fragile and you will probably gain and lose it several times. Just as playing in the mind frees the pianist from the limitations of the piano, mental play (instead of singing them) frees you from the limitations of the vocal chords. Our brains are incredibly powerful and, as musicians, we must learn to use all its powers, free from any artificial limitations. Too many people make the mistake of thinking that their brains have imaginary limits, thus missing out on many natural capabilities of the brain (such as perfect pitch).

After you have completely memorized the Bach, and can play the entire piece in your mind, start memorizing the C major scale in absolute pitch, the C4-C5 octave. Concentrate on learning C4; every time you walk by the piano, try to guess C4 and test it. You can try to recall just a single C4, but you will have more success if you mentally play the first few bars of the Bach, and concentrate hard on how it sounds on the piano. You can succeed with only the C4, by concentrating on exactly how it sounds at the piano, but it is easier with real music. After a few days of intense practice, start testing your pitch recognition by playing notes randomly all over the piano (without looking at the piano) and trying to guess what they are. At first, you may fail miserably. There are just too many notes on the piano. In order to improve your success rate, guess the notes by referencing to the C4-C5 octave. If you press C2, you should recognize it as C4, two octaves down. When you hear a low note, bring it up in octaves until it is in the C4-C5 range. In this way, you reduce the task of memorizing 88 notes on the keyboard to just 8 notes and one interval (octave). This simplification is possible because of the logarithmic nature of the chromatic scale; further simplification of the octave using smaller intervals is not profitable because of the strange nature of the octave. Acquaint yourself with all the notes on the piano by playing them in octaves and training the mind to recognize all octave notes of the same key; all octave C's, D's, etc. Until you gain some rudimentary absolute pitch, you will need to perform most of your practice at the piano so that you can correct yourself as soon as you wander off key. Do not practice mentally with the wrong pitch for extended periods; always have the piano nearby to correct yourself. You can start practicing more away from the piano as soon as you can keep the pitch as long as you have the first note right.

Then memorize the Moonlight and start work on the black keys. Successful pitch recognition depends strongly on how you test yourself at the piano. You should be able to think of any number of ways to test, but I will describe some so that you get an idea of how to create your own. Let's use the first 3 RH notes of the Moonlight. Memorize the sound of these notes in your mind and try to recall them later. At first, you might be several notes off if you had not touched the piano for a few hours. With practice, this error will decrease. See if you can get the first note (G#) right when you first sit down at the piano. Practice relative pitch by first making sure that one note is correct (say the second note -- C#) by checking it on the piano, then mentally play a half tone down -- middle C, and check it with the piano. Go to the 3rd note -- E, check it, come down a full tone -- D, and check it. Now go back to the first note (G#), come down half a step (G) and then, mentally, go all the way up to C4 and check it. When you test your absolute pitch after not playing the piano for a while, see if you tend to be too high or too low. See if you can compensate for this error the next time. Another way of testing is to make sure that you start on the right note by checking it with the piano, then mentally play the music for while and then check the last note you played mentally. Most people find that they tend to go flat.

Progress may seem slow at first, but your guesses should get closer with practice. Then suddenly, one day, you should experience that magical moment when you are able to identify any note on the piano, without using the center octave as a reference. Until you experience this, you do not really have perfect pitch; your guesses will not always be close, and you can easily lose it. If that magic happens, strengthen your perfect pitch by practicing to identify the notes as rapidly as you can. The strength of your perfect pitch is measured by the speed with which you can identify notes. After that, start practicing with 2-note chords, then 3, etc. Once you have a strong perfect pitch, you can practice humming the notes, and singing on pitch. That's about all the instruction you need! Congratulations, you have done it!

The biological mechanism underlying perfect pitch is not well understood. It appears to be entirely a memory function. Therefore, in order to truly acquire perfect pitch, you will need to change your mental habits, just as you have to, when memorizing. In memorizing, we saw that the change you needed was to develop a mental habit of constantly inventing associations (the more outrageous or shocking, the better!) and repeating them automatically in the brain. For good memorizers, this process occurs naturally, or effortlessly, and that is why they are good. The brains of poor memorizers either become quiescent when not needed, or wander into logical or other interests instead of performing memory work. People with perfect pitch tend to make music mentally; music keeps running around in their heads, whether it is their own compositions or music they had heard. This is why most people with perfect pitch automatically start to compose music. The brain always returns to music when it has nothing else to do. Therefore, once you learn mental playing, you may find yourself playing music in your head a lot more than you used to do. This is probably a helpful prerequisite to acquiring perfect pitch. This explains why you acquire perfect pitch all of a sudden, just as you acquire technique or quiet hands all of a sudden. You reach this point at which there are enough reference melodies in your head so that you can accurately reference your pitch. In that case, there is nothing absolute about absolute pitch -- which seems to be true. Those with perfect pitch are always adjusting their pitch because they tend to be sharp or flat at different times. If they go flat, then, how do they know? The answer is music! They play some critical music mentally, and it will sound wrong unless the pitch is right. That is why the method described here is the "natural" and probably the only way to really learn perfect pitch. That is, you need to be an experienced mental player before you can gain absolute pitch. You can't just go to the piano for a few seconds 10 times a day, practice perfect pitch, and expect to learn it if you don't keep doing it mentally while away from the piano, for a good fraction of your time. Therefore, as with memorization, the hardest part of learning absolute pitch is not the practice, but the changing of your mental habits. In principle, it's easy -- just start mental playing as much as you can.

This easy way to naturally acquire perfect pitch illustrates the importance of mental play. That is how everybody who "was born with perfect pitch" acquired it! Mozart had to play music in his mind because it was so necessary to practically everything he did -- for memorizing, for perfect performances, for composing, for dealing with music all day whether he had access to a piano or not, for saving enormous amounts of time, and a zillion other reasons. What I am saying is that mental play frees the musician from the physical/mechanical limitations of musical instruments and endows her/im with new powers. Now we can understand how youngsters, just by listening to music, can acquire perfect pitch -- they naturally tend to repeat the music in their minds, because there are few other sounds in their heads at this stage.

We saw above that you can start to lose perfect pitch after about age 20, if it is not maintained. Again, the explanation is simple: our lives become more complex as we age, and we have less time to devote to mentally playing music. We also tend to fill our minds with confusing sounds outside the chromatic scale.

Our method of memorizing using mental play needs to be periodically maintained as part of the memory maintenance program. This program automatically performs maintenance on pitch recognition. You only need to check, from time to time, that your mental play is on pitch. This too, should happen automatically because you should always mentally play at least the beginning of every piece just before actually playing it at the piano. By first playing it in your mind, you ensure that the speed, rhythm, and expression are correct. Music sounds more exciting when you mentally lead it, and less exciting if you play it and wait for the piano to make the music.

Note the similarities between "memorizing before you learn" (III. 6) which saves a lot of time and at the same time results in superior memory, and learning pitch by "playing in your mind" which also saves time and results in more powerful perfect pitch. The conventional methods of learning perfect pitch (described below) generally start with learning one note, and expanding the range using relative pitch. In our method, we learn the entire keyboard at once. This makes sense because that is the end product you want. Not only do you learn perfect pitch, but you also learn the location of that note on the keyboard (because it is combined with keyboard memory). Knowing the location of every note on the keyboard will become an indispensable skill when you start composing and improvising. We have come to the realization that, in the past, many students could not advance to concert level pianists because they were never taught mental playing.

This method works because learning pitch is a memory process. Moreover, memory is an associative process (read III.6). By playing and remembering the entire music, you instantly create a huge number of associations (melody, rhythm, emotions, keyboard location, fingering, music structure, etc.) with every note -- this huge number of associations make the exact pitch impossible to forget -- any wrong note is guaranteed to violate some association. Now that we have learned the fastest way, let's examine some conventional methods. These will be useful as supplemental exercises to help you better execute the faster method.

Conventional methods of learning perfect pitch take a long time, typically more than 6 months, and often, much longer. One way to start is by memorizing one note. You might pick A440 because you hear it every time you go to a concert and can perhaps recall it most easily. However, A is not a useful note for getting to the various chords of the C major scale, which is the most useful scale to memorize. Therefore, pick C, E, or G, whichever you tend to remember best; C is probably the best. Your accuracy may be atrocious in the beginning; you might be easily off by 3 or 4 semitones, but it should improve with time. Devise ways to increase your accuracy. One way is to identify the highest and lowest notes you can hum; for me, they are F3 and F5. In that case, F4 may be the best note to memorize. By trying to sing one octave up or down, you can find out if your F4 is too high or too low; if you started with F4 that was too high, you can't hum F5. If you practice that single note every day, at least once a day, you will eventually learn it. Of course, you can try several notes at once.

Then learn the C major scale. Given middle C (C4), can you sing all the other notes in the octave (white keys) up to C5? Given any note, can you sing another note, one full tone or a semitone up or down? Can you start with any note between C4 and C5 and sing up to C5 or down to C4? Check frequently with the piano. Next, learn the chromatic scale. Then learn the intervals: given any note, can you sing a third, fourth, fifth, or octave up or down? Learning relative pitch is fairly easy for most piano students because they have heard the scales and intervals so many times. For non-singers, it may be easier to just imagine the notes instead of actually singing them. Practice these exercises first at the piano and then away from the piano.

You can now graduate to sight singing actual music. Read some easy pieces, without the piano and see if you can play the music correctly in your mind. You might begin using music you already know, to make it easier to start. Then gradually practice on music you never played before. If you do not have absolute pitch yet, always use the piano to help you start at the correct note. Do not practice relative pitch using the wrong absolute pitch. How long it takes to learn relative pitch and sight singing depends greatly on the individual and can vary from weeks to over 6 months. After enough practice, congratulations! You have acquired relative pitch that is not only useful in its own right, but will also be helpful in sight reading.

The standard way to learn absolute pitch in music classes is via the solfege (singing exercises) route. Solfege books are readily available in stores or over the internet. It consists of increasingly complex series of exercises involving different scales, intervals, time signatures, rhythms, accidentals, etc, for voice training. It also covers pitch recognition and dictation. Solfege books are best used in a class environment with a teacher. Absolute pitch is taught as an adjunct to these exercises by learning to sing them at the correct pitch. Therefore, there are no special methods for acquiring absolute pitch -- you just repeat until the correct pitch is implanted in memory.

In summary, every pianist must learn perfect pitch because it is so easy, useful, and even necessary in many situations. Perfect pitch will not only help you to avoid flubs, but also to recover from them. Learning perfect pitch is inseparably associated with playing in your mind. Mental play frees you from having to sit at the piano in order to play your favorite pieces, and you can practice anywhere, at any time. Most importantly, mental playing is what enables you to transition from an amateur pianist to a true musician with the potential to advance to the concert level.

Sight Reading

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It is useful to classify sight reading into three levels so that we know what we are talking about. At the novice sight reading level, we are talking about playing compositions that we have not memorized, and which we play by looking at the score. We may already be familiar with the melodies in the composition, and have played it before. At the intermediate level, we can sight read music we have never seen or heard before and can sight sing it, although we are not trained in music theory. This level is what is generally considered to be sight reading, and this type of sight reading is the topic of this section. At the advanced level, we are able to apply basic music theory to the sight reading and we are reading music at a much higher level of understanding. How pianists at each of these levels approach sight reading is obviously different. Below, we discuss sight reading rules that are fairly generally applicable.

(1) Keep the eyes on the music; do not look at the keyboard/fingers. You may glance at the hands when it is necessary for large jumps. Try to develop a peripheral vision towards the keyboard so that you have some idea of where the hands are while still looking at the score. Peripheral vision has the advantage that you can keep track of both hands simultaneously. It is particularly beneficial to develop a habit of feeling the keys before playing them. Although this rule applies whether you are sight reading or not, it becomes critical in sight reading. It also helps to "get there ahead of time" for jumps, see section 7.e and 7.f above; therefore, you should practice the jump maneuvers in conjunction with the sight reading practice.

(2) Play through mistakes and make them as inaudible as possible. The best way to do this is to make it sound as if you had modified the music -- then the audience does not know whether you made a mistake or changed it. This is why students with basic music theory training have such an advantage in sight reading. Three ways to make mistakes less audible are (i) keep the rhythm intact, (ii) maintain a continuous melody (if you can't read everything, carry the melody and omit the accompaniment), and (iii) practice simplifying those parts that are too complicated to sight read. The first thing that must be done is to eliminate the habits of stopping and backtracking (stuttering), at every mistake. The best time to develop the skill of not stopping at every mistake is when you begin your first piano lessons. Once the stuttering habit is ingrained, it will take a lot of work to eliminate it. For those with a stuttering habit, the best thing to do is to decide that you will never backtrack again (whether you succeed or not) -- it will slowly go away. Learning to anticipate flubs is a great help, and this will be discussed below. The most powerful tool, is the ability to simplify the music. Eliminate ornamentals, fish out the melody from fast runs, etc.

(3) Learn all the common musical constructs: major and minor scales and their fingerings as well as their corresponding arpeggios, common chords and chord transitions, common trills, ornaments, etc. When sight reading, you should recognize the constructs and not read the individual notes. Memorize the locations of those very high and very low notes as they appear on the score so that you can find them instantly. Start by memorizing all the octave C's, then fill in the others, beginning with notes closest to the C's.

(4) Look ahead of where you are playing; at least one bar ahead, but even more, as you develop the skill at reading the music structure. Get to the point where you can read one structure ahead. By looking ahead, you can not only prepare ahead of time but also anticipate flubs before they occur. You can also anticipate fingering problems and can avoid painting yourself into impossible situations. Although fingering suggestions on the music are generally helpful, they are often useless because, although they may be the best fingerings, you may not be able to use them without some practice. Therefore, you should develop your own set of fingerings just for sight reading.

(5) "Practice, practice, practice". Although sight reading is relatively easy to learn, it must be practiced every day in order to improve. It will take most students from one to two years of diligent practice to become good. Because sight reading depends so heavily on recognition of structures, it is closely related to memory. This means that you can lose the sight reading ability if you stop practicing. However, just as with memory, if you become a good sight reader when young, this ability will stay with you all your life. After practicing sight reading, try to play in your mind (section III.6j), some of the common structures that you encountered.

Of course, you should keep adding to the "tricks of the trade" as you improve. You can acquire the art of scanning through a composition before sight reading it, in order to get some feel for how difficult it is. Then you can figure out ahead of time how to get around the "impossible" sections. You can even practice it quickly, using a condensed version of the learning tricks (HS, shorten difficult segments, use parallel sets, etc.), just enough to make it sound passable. I have met sight readers who would talk to me about some sections of a new piece for a while, then play through it with no trouble. I later figured out that they were practicing those sections in the few seconds they had while they were distracting me with their "discussions".

In order to practice sight reading, you will need to gather several books with many easy pieces and read through them. Because it is initially easier to practice "sight reading" with familiar pieces, you can use the same composition to practice sight reading several times, a week or more apart. There are numerous "Sonatina" books, Mozart's easier sonatas, and books of easy popular songs, are good books for practicing. For the easiest pieces, you might use Beyer, the beginner books listed in III.18c, or the easiest Bach pieces for beginners. Although you can develop a lot of sight reading skills with familiar pieces, you should also practice with pieces that you had never seen before in order to develop true sight reading skills. The most useful skill for help with true sight reading is sight singing, which we now discuss.