### Scales: Origin, Nomenclature and Fingerings

Repeating scales and exercises mindlessly is discouraged in this book. However, it is critically important to develop the skill to play exquisite scales and arpeggios, in order to acquire some basic techniques and standard fingerings for routine playing and sight reading. Scales and arpeggios in all the major and minor keys should be practiced until you are familiar with their fingerings. They should sound crisp and authoritative, not loud but confident; just listening to them should lift up one's spirits.

Before proceeding with the fingerings, let's discuss some basic properties of scales: the key nomenclature and the question: what is a scale? There is nothing magical or even musical about the C major scale; it arises simply from the desire to include as many chords as possible into an interval that can be played with one hand. This is just a convenience design feature (just as the most modern features are incorporated into every new car design) that makes it easier to learn/play the keyboard. From the size of the human fingers/hand, we can assume that the largest interval should span 8 keys. How many chords can these keys accommodate? We need the octave, plus thirds, fourths, fifths, and sixths. Starting from C4, we have now placed E4, F4, G4, A4, and C5, a total of 6 notes, leaving space for only 2 more notes, a full tone and a semitone. Note that even the minor third is already present as A4-C5. If you place the semitone near C4, you end up with one accidental (black key) near C4 and 4 near C5 in order to complete the chromatic scale, so it is better to place the semitone near C5 so that the octave is better balanced with 2 accidentals near C4 and 3 near C5. This completes the construction of the C major scale, with its accidentals.

In the nomenclature process, it is unfortunate that the keyboard was designed with the C major scale at C instead of A. Thus the octave numbers change at C, not A; therefore, at C4, the notes are numbered . . . A3,B3,C4,D4,E4, . . . For any scale, the first note is called the tonic, so C is the tonic of the C major scale.

The standard major scale ascending fingerings are 12312341 (RH), 54321321(LH) for C,G,D,A,E major scales (with 0,1,2,3,4 sharps, respectively); these fingerings will be abbreviated as S1 and S2, where S stands for "standard". The sharps increase in the order F,C,G,D,A, (G-major has F#, D-major has F# and C#, A-major has F#, C#, and G#, etc.) and for the F,Bb,Eb,Ab,Db,Gb, major scales, the flats increase in the order B,E,A,D,G,C; every interval between adjacent letters is a fifth. They are therefore easy to remember, especially if you are a violinist (the violin's open strings are G,D,A,E). The letters always appear in the sequence GDAEBFC which represents the complete circle of fifths, and this sequence is worth memorizing. Look at B or Gb major scales in a music book and you will see how the 5 sharps or 6 flats line up with the same sequence. Thus 2 sharps will have sharps at F, C, three sharps will be F, C, G, and so on. The flats increase in reverse order compared to the sharps. Each scale is identified by its key signature; thus the key signature of the G major scale has one sharp (F#). Once you learn to recognize the interval of a fifth, you can generate all the scales in order of increasing sharps (by going up in fifths from C) or in order of increasing flats (by going down in fifths); this is useful when you want to practice all the scales in sequence without having to refer to the printed scales. See table below for the ascending major scales (reverse the fingerings for descending scales):

 RH LH Scale Sharps/Flats S1=12312341 S2=54321321 C,G,D,A,E 0,1,2,3,4 Sharps S1 43214321321 B 5 Sharps 12341231 S2 F 1 Flat 41231234 32143213 Bb 2 Flats 31234123 32143213 Eb 3 Flats 34123123 32143213 Ab 4 Flats 23123412 32143213 Db 5 Flats 23412312 43213214 Gb 6 Flats

The minor scales are complex because there are 3 of them, and can be confusing because they are often just called "minor" without specifying which of the three, or worse, they have been given several different names. They were created because they produce moods different from the others. The simplest minor scale is the relative minor (also called natural minor); it is simple because it shares the same key signature as its major relative, but its tonic moves up to the sixth note of its major relative. Thus the relative minor of G major has its tonic at E and the key signature is F#, and is called E (relative) minor. Another minor is the melodic minor; it is created by raising the 6th and 7th notes of the relative minor only when ascending; the descending part is unchanged. The third, and the most frequently used, minor is the harmonic minor which is created from the relative minor by raising the 7th note a semitone.

Fingerings for the harmonic minor scales (the last column lists the raised note for the minor scale); thus A (harmonic) minor is ABCDEFG#A, and its relative major is C major:

 S1 S2 A 0 Sharp G sharp S1 S2 E 1 Sharp D Sharp S1 43214321 B 2 Sharps A Sharp 34123123 43213214 F# 3 Sharps E Sharp 34123123 32143213 C# 4 Sharps B Sharp 34123123 32143213 G# 5 Sharps F dSharp S1 S2 D 1 Flat C Sharp S1 S2 G 2 Flats F Sharp S1 S2 C 3 Flats B Nat. 12341231 S2 F 4 Flats E Nat. 21231234 21321432 Bb 5 Flats A Nat. 31234123 21432132 Eb 6 Flats D Nat.

As stated earlier, there is nothing magical about scales; they are simply human creations constructed for convenience -- just a framework on which to hang your music. Therefore, you can create any number of them, and the ones covered here, though widely used, are not the only ones.

We can never play scales too well. When practicing scales, always try to accomplish something -- smoother, softer, clearer, faster. Make the hands glide, the scale sing; add color, authority or an air of excitement. Quit as soon as you start to lose concentration. There is no such thing as a maximum speed in parallel playing. Therefore, in principle, you can keep increasing the speed and accuracy all your life -- which can be quite a bit of fun, and is certainly addicting. If you want to demonstrate your speed to an audience, you can probably do that using scales and arpeggios at least as well as with any piece of music.