Hand Motions
Certain hand motions are required in order to acquire technique. For example we discussed parallel sets above, but did not specify what types of hand motions are needed to play them. It is important to emphasize from the start that the required hand motions can be extremely small, almost imperceptible. After you have become expert, you can exaggerate them to any extent you desire. Thus during a concert by any famous performer, most of the hand motions will not be discernible (they also tend to happen too fast for the audience to catch) so that most of the visible motions are exaggerations. Thus two performers, one with apparently still hands, and one with flair and aplomb, may in fact be using the same hand motions of the type we discuss here. The major hand motions are pronation and supination, thrust (or push) and pull, claw and throw, flick, and wrist motions. They are almost always combined into more complex motions. Note that they always come in pairs (there is a right and left flick, and similarly for wrist motions). They are also the major natural motions of the hands and fingers.
All finger motions must be supported by the major muscles of the arms, the shoulder blades in the back, and the chest muscles in front that are anchored to the center of the chest. The slightest twitch of the finger, therefore, involves all of these muscles. There is no such thing as just moving one finger -- any finger motion involves the entire body. Stress reduction is important for relaxing these muscles so that they can respond to, and assist in, the movement of the fingertips. The major hand motions are discussed only briefly here; for more details, please consult the references (Fink, Sandor).
Pronation and Supination
The hand can be rotated around the axis of the forearm. The inward rotation (thumbs downward) is called pronation and the outward rotation (thumbs upward) is called supination. These motions come into play, for example, when playing octave tremolos. There are two bones in your forearm, the inside bone (radius, connecting to the thumb) and the outside bone (ulna, connecting to the pinky). Hand rotation occurs by rotation of the inner bone against the outer one (hand position referenced to that of the piano player with palm facing down). The outer bone is held in position by the upper arm. Therefore, when the hand is rotated, the thumb moves much more than the pinky. A quick pronation is a good way to play the thumb. For playing the octave tremolo, moving the thumb is easy, but the pinky can only be moved quickly using a combination of motions. Thus the problem of playing fast octave tremolos boils down to solving the problem of how to move the pinky.
Thrust and Pull
Thrust is a pushing motion, towards the fallboard, usually accompanied by a slightly rising wrist. With curved fingers, the thrust motion causes the vector force of the hand moving forward to be directed along the bones of the fingers. This adds control and power. It is therefore useful for playing chords. The pull is a similar motion away from the fallboard. In these motions, the total motion can be larger than or smaller than the vector component downward (the key drop), allowing for greater control. Thrust is one of the main reasons why the standard finger position is curved. Try playing any large chord with many notes, first lowering the hand straight down as in a gravity drop, then using the thrust motion. Note the superior results with the thrust. Pull is useful for some legato and soft passages. Thus, when practicing chords, always experiment with adding some thrust or pull.
Claw and Throw
Claw is moving your fingertips into your palm and throw is opening the fingers out to their straight position. Many students do not realize that, in addition to moving the fingertips up and down, they can also be moved in and out during play. These are useful additional motions. They add greater control, especially for legato and soft passages, as well as for playing staccato. Just as for the thrust and pull, these motions allow a large motion with a much smaller keydrop. Thus, instead of always trying to lower the fingers straight down for the key drop, try experimenting with some claw or throw action to see if it will help. Note that the claw movement is much more natural and easier to conduct than a straight down. The straight down motion of the fingertip is actually a complex combination of a claw and a throw. The key drop action can sometimes be simplified by flaring the fingers out flat and playing with only a small claw movement. This is why you can sometimes play better with flat fingers than curved.
Flick
The flick is one of the most useful motions. It is a quick rotation and counter-rotation of the hand; a fast pronation-supination combination, or its reverse. We have seen that parallel sets can be played at almost any speed. When playing fast passages, the problem of speed arises when we need to connect parallel sets. There is no single solution to this connection problem. The one motion that comes closest to a universal solution is the flick, especially when the thumb is involved, as in scales and arpeggios. Single flicks can be conducted extremely quickly with zero stress, thus adding to the speed of play; however, quick flicks need to be "re-loaded"; i.e., continuous fast flicks is difficult. But this is quite suitable for connecting parallel sets because the flick can be used to play the conjunction and then be re-loaded during the parallel set. To re-emphasize what was pointed out at the beginning of this section, these flicks and other motions do not need to be large and are in general imperceptibly small; thus the flick can be considered more as a momentum flick than an actual motion.
Wrist Motion
We already saw that the wrist motion is useful whenever the thumb or pinky is played; the general rule is to raise the wrist for the pinky and lower it to play the thumb. Of course, this is not a hard rule; there are plenty of exceptions. The wrist motion is also useful in combination with other motions. By combining wrist motion with pronation-supination, you can create rotary motions for playing repetitive passages such as LH accompaniments, or the first movement of Beethoven's Moonlight Sonata. The wrist can be moved both up and down, and side-to-side. Every effort should be made such that the playing finger is parallel to the forearm; this is accomplished with the side-to-side wrist motion. This configuration puts the least amount of lateral stress on the tendons moving the fingers and reduces the chances of injuries such as Carpal Tunnel Syndrome. If you find yourself habitually playing (or typing) with the wrist cocked at a sideways angle, this may be a warning sign to expect trouble. A loose wrist is also a pre-requisite for total relaxation.
Summary
The above is a very brief review of hand motions. An entire book can be written on this subject. And we did not even touch on the topics of adding other motions of the elbow, upper arm, shoulders, body, feet, etc. The student is encouraged to research this topic as much as possible because it can only help. The motions just discussed are seldom used alone. Parallel sets can be played with any combination of most of the above motions without even moving a finger (relative to the hand). This was what was meant, in the HS practice section, with the recommendation to experiment with and to economize the hand motions. Knowledge of each type of motion will allow the student to try each one separately to see which is needed. It is in fact the key to the ultimate in technique.