### Thrust and Pull, Beethoven's Moonlight

For those who are learning Beethoven's Moonlight Sonata for the first time, the most difficult section is the two-hand arpeggic ending of the 3rd movement (bars 196-198; this movement has 200 bars). By illustrating how to practice this difficult passage, we can demonstrate how arpeggios should be played. Let's try the RH first. In order to simplify the practice, we skip the first note of bar 196 and practice only the following 4 ascending notes (E, G#, C#, E), which we will cycle. As you cycle, make an elliptical, clockwise motion (as seen from above) of the hand. We divide this ellipse into two parts: the upper part is the half towards the piano and the lower part is the half towards your body. When playing the upper half, you are "thrusting" your hand towards the piano, and when playing the lower half, you are "pulling" the hand away from it. First, play the 4 notes during the upper half and return the hand to its original position using the lower half. This is the thrust motion for playing these 4 notes. Your fingers tend to slide towards the piano as you play each note. Now make a counter clockwise motion of the hand and play the same 4 ascending notes during the lower half of the ellipse. Each finger tends to slide away from the piano as it plays each note. Those who have not practiced both motions may find one much more awkward than the other. Advanced players should find both motions equally comfortable.

The above was for the RH ascending arp. For the RH descending arp, let's use the first 4 notes of the next bar (same notes as in preceding paragraph, an octave higher, and in reverse order). Here, the pull motion is needed for the lower half of the clockwise motion, and the thrust is used for the upper half of the counter clockwise rotation. For both ascending and descending arps, practice both thrust and pull until you are comfortable with them. Now see if you can figure out the corresponding exercises for the LH. Notice that these cycles are all parallel sets and therefore can eventually be played extremely fast.

Having learned what the thrust and pull motions are, you might reasonably ask, "why do you need them?" First, it should be pointed out that the thrust and pull motions use different sets of muscles. Therefore, given a specific application, one motion has to be better than the other. We will learn below that one motion is stronger than the other. Students who are not familiar with these motions may randomly pick one or switch from one to the other without even knowing what they did. This can result in unexpected flubs, unnecessary stress, or speed walls. The existence of the thrust and pull is analogous to the situation with TU and TO. Recall that by learning both TU and TO, you get to fully utilize all the capabilities of the thumb. In particular, at high speed, the thumb is used in a way which is about midway between TU and TO; however, the important thing to keep in mind is that the thumb motion must be on the TO side of dead center. If you are even slightly on the TU side, you hit a speed wall.

The analogy of thrust and pull to TU and TO go even further, because thrust and pull also have a neutral motion, just as TU and TO have a range of motions in between. You get the neutral motion by reducing the minor axis of the ellipse to zero; i.e., you simply translate the hand right and left without any apparent elliptical motion. But here again, it makes a big difference whether you approach the neutral position from the thrust side or the pull side, because the seemingly similar neutral motions (approached from thrust or pull side) are actually being played using a different set of muscles. Let me illustrate this with a mathematical example. Mathematicians will be horrified if you tell them that 0 = 0, which at first glance seems to be correct. Reality, however, dictates that we must be very careful. This is because we must know the true meaning of zero; i.e., we need a mathematical definition of zero. It is defined as the number 1/N, when N is allowed to go to infinity. You get to the "same" number zero, whether N is positive or negative! Unfortunately, if you try to divide by zero: 1/0, you get a different answer depending on whether N is positive or negative. 1/0 = +infinity when N is positive, and 1/0 = -infinity when N is negative! If you had assumed the two zeros to be the same, your error after the division could have been as big as two infinities depending on which zero you used! In a similar way, the "same" neutral position achieved by starting with TU or TO are fundamentally different, and similarly with thrust and pull. That is, under certain circumstances, a neutral position approached from either thrust or pull is better. The difference in feel is unmistakable when you play them. This is why you need to learn both.

This point is so universally important, especially for speed, that I will illustrate it with another example. The Samurai's life depends on the speed of his sword. In order to maximize this speed, the sword must always be in motion. If he simply raises the sword, stops, and lowers it, the motion is too slow and his life is endangered. The sword must continually move in some circular, elliptical, or curved motion, even when it looks like he is simply raising and lowering it. This is one of the first lessons in swordsmanship. Thus the use of generically circular motions to increase speed has universal validity, and applies to the piano also.

OK, so we have established that thrust and pull are both needed, but how do we know when to use which? In the case for TU and TO, the rules were clear; for slow passages you can use either one, and for certain legato situations, you need TU; for all others you should use TO. For arps, the rule is to use the strong motions as a first choice and the weak motions as a secondary choice. Each person has a different strong motion, so you should first experiment to see which is strongest for you. The pull motions should be stronger because our pulling muscles in the arms are stronger than the pushing muscles. Also, the pull motions use the fleshy parts of the fingers whereas the thrust motions tend to use the fingertips which tends to injure the fingertips and to strain the attachment of the fingernails.

Finally, one can ask the question, "why not always play neutral - neither thrust nor pull?" Or just learn one (pull only), and simply become very good at it? Here again, we are reminded of the fact that there are two ways to play neutral depending on whether you approach it from the thrust side or pull side, and for a particular application, one is often better than the other. As for the second question, a second motion may be useful for endurance because it uses a different set of muscles. Not only that, but in order to play the strong motions well, you must know how to play the weak motions. That is, you play best when the hand is balanced in the sense that it can play both motions. Therefore, whether you decide to use thrust or pull for a particular passage, you should always practice the other one also. That is the only way that you will know which motion is best for you. For example, as you practice this ending of Beethoven's sonata, you should find that you make faster technical progress by practicing every cycle using both thrust and pull. In the end, most students should end up playing very close to neutral, although a few may decide to use exaggerated thrust or pull motions.

There is much more new material to practice in this 3rd movement before we should be playing HT, so at this stage, you probably do not need to practice anything HT, except as experimentation to see what you can or cannot do. In particular, trying HT at the highest speeds will be counter-productive and is not recommended. However, cycling a single cycle HT can be quite beneficial, but this also should not be over-practiced if you still cannot play it satisfactorily HS. The main difficulties in this movement are concentrated in the arps and Alberti accompaniments ("do-so-mi-so" type); once these are mastered, you have conquered 90% of this movement. For those without sufficient technical skill, you should be satisfied with getting up to about quarter-note = MM120. Once you can play the entire movement comfortably at that speed, you might try to mount an effort towards presto (above 160). It is probably not a coincidence that with the 4/4 signature, presto corresponds to the rapid heart beat rate of a very excited person. Note how the LH accompaniment of bar 1 actually sounds like a beating heart.

It should be clear by now that playing arpeggios is technically very complex. Thrust and pull also apply to scales, and the rules for scales are the same as for the arps (the strong motion is the first choice but both strong and weak should be practiced). However, with scales, the difference between thrust and pull is more difficult to illustrate for novice players; this is why we demonstrated them using arps above. Note that both thrust and pull become awkward when playing TU. This is another reason for avoiding TU. In fact, thrust and pull are very basic motions and apply to practically anything you play, including parallel sets. Therefore, it pays to practice them well, and to think about which one you are using whenever you play anything. The complexity of arps results from the fact that you can combine thrust, pull, the cartwheel motion, TU, TO, pronation, and supination in any permutation. This is a mind boggling array of combinations. If you did not know the various components and simply let your hand pick its own movement, the chances of hitting the optimum combination are practically zero. The result is often a speed wall, confusion, or inconsistency.

We shall now outline our plan of attack for learning this movement. We started with the most difficult part, the two-hand arp at the end. Most students will have more difficulty with the LH than the RH; therefore, once the RH is fairly comfortable, start practicing the RH arp of the first two bars of this movement, while still practicing the LH part of the ending. One important rule for playing arps rapidly is to keep the fingers near the keys as much as possible, almost touching them. Do not lift the fingers off the keys. Note that we are looking for short practice segments for both hands so that we can alternate rapidly between the two hands. Do not cycle one hand for too long because of the danger of injury. After some practice, you will be able to cycle one hand for long periods of time; however, the effects of any injury are sometimes not felt until several days later, so it is a good insurance policy to develop the habit of changing hands frequently even if you feel no fatigue or pain.

Another important point to remember is to know when to use curled or flat finger positions. In general, use flat finger positions for black keys and the curled position for white keys. Thus in the first 2 bars of this 3rd movement, only the note D is played with curled fingers. This habit of curling only specific fingers for each ascending arp is best cultivated by cycling parallel sets. Clearly, a major technical skill you must learn is the ability to quickly change any finger from flat to curl, independently of the others.

The pedal is used in only two situations in this piece: (1) at the end of bar 2, at the double staccato chord and all following similar situations, and (2) bars 165-166, where the pedal plays a critical role. The next segment to practice is the tremolo type RH section starting at bar 9. Work out the fingering of the LH carefully -- those with smaller hands may not be able to hold the 5th finger down for the duration of the 2 bars. If you have difficulty interpreting the rhythm of this section, listen to several recordings to get some ideas. Then come the LH Alberti accompaniment starting at bar 21, and similar RH parts that appear later. The Alberti accompaniment can be practiced using parallel sets, as explained starting at section II.8. The next difficult segment is the RH trill of bar 30. This first trill is best performed using 3,5 fingering and the second one requires 4,5. For those with small hands, these trills are just as difficult as the ending arps, so they should be practiced from the very beginning, when you first start learning this movement. These are the basic technical requirements of this piece. The cadenza of bar 186 is an interesting combination of a "scale" and an arp; if you have difficulty interpreting it, listen to several recordings to get some ideas. Don't overlook the fact that bars 187 and 188 are adagio.

Start HT practice after all these technical problems are solved HS. There is no need to practice using the pedal until you start HT. Note that bars 163, 164, are played without pedal. Then application of the pedal to bars 165, 166, gives meaning to these last 2 bars. Because of the fast pace, there is a tendency to practice too loud. This is not only musically incorrect, but technically damaging. Practicing too loud can lead to fatigue and speed walls; the key to speed is relaxation. It is the P sections that create most of the excitement. For example, the FF of bar 33 is just a preparation for the following P, and in fact, there are very few FF's in the entire movement. The whole section from bar 43 to 48 is played P, leading to just one bar, #50, played F. Whereas the objective during HS practice was to get up to speed (or faster) quickly, slow practice becomes paramount during HT play. Except when cycling HT, always practice HT slower than your maximum speed. You will make faster progress by practicing at a speed at which your fingers want to go faster, than to force the fingers to play faster than they can. Thus the choice of practice speed for HS and HT practice is diametrically opposite: the objective is speed for HS and accuracy for HT. There is no need to push for speed HT because (if you had practiced correctly), that was already achieved HS, so that HT speed will automatically come as soon as the two hands become coordinated. In HT practice, you are working for coordination, not speed.

Finally, if you have practiced correctly, you should find certain speeds at which it is easier to play faster than slower. This is completely natural in the beginning, and is one of the best signs that you have learned the lessons of this book well. Of course, once you have become technically proficient, you should be able to play at any speed with equal ease.