Thumb: the Most Versatile Finger; Examples of Scale/Arpeggio Practice Routines
The thumb is the most versatile finger; it lets us play scales, arpeggios, and wide chords (if you don't believe it, try playing a scale without the thumb!). Most students do not learn how to use the thumb correctly until they practice scales. Therefore it is important to practice scales as soon as possible. Repeating the C major scale over and over, or even including the B major, is not the way to practice scales. It is important to practice all the major and minor scales and arpeggios; therefore we will examine an example of a scale practice routine and point out what needs to be done and what the benefits are.
For simplicity, we will consider only the major scales here, but you should devise similar exercises for the minor scales and corresponding exercises with the arpeggios. Practice the harmonic minor scales.
First, a reminder of fundamentals. Play with the tip of the thumb, not the first joint. This makes the thumb effectively as long as possible, which is needed because it is the shortest finger from the wrist joint. In order to produce a smooth scale, all the fingers need to be as similar as possible. In order to play with the tip of the thumb, you may have to raise the wrist slightly. Using the tip is helpful at high speeds and for better control. Playing with the tip is absolutely necessary when playing arpeggios and chords. It is also important to cultivate the "glissando motion" in which the fingers point away from the direction of motion of the hand. Do not exaggerate the glissando motion, you only need a small amount. Playing with the tip also facilitates TO. Three octaves is probably an optimum span to practice, and the RH span should be one or two octaves above the LH span; in other words, choose a comfortable span for each hand. The objective of these exercises is to build the necessary motions and hand positions into your playing so that they become a permanent part of how you play anything. Thus these are some of the few exercises that must be repeated many times until the motions and positions are habituated so that you don't have to think about them.
There are many ways to generate all the scales but the simplest, and one of the most interesting, is to use the circle of fifths. Start with C major, practice it a few times, then go up a fifth and practice G major. You will notice that it has one sharp. If you go up another fifth, you will need two sharps, etc.; with every move up a fifth, you add a sharp. If moving up in fifths brings the span too high in the treble for comfort, go down one octave. What is interesting is that when you add a sharp (using the circle of fifths), you keep all the previously used sharps; not only that, but the order in which they appear is the same as the order in which they are written on the music staff. The maximum number of sharps comes at B major (5 sharps), and the next one is 6 flats at G-flat major. These flats decrease with successive fifths, again in the same orderly manner, until you return to C major. Thus the circle of fifths takes you to every scale once and only once, in an orderly way, which is what you want. TEST: If you go down in fifths, what is the order of increase or decrease of sharps and flats?
Now you can devise similar practice routines for the arps.