If you were asked to determine how a piano, or any instrument, should be tuned, the most important factor to begin with would be your own musical goals and tastes. Keyboard tunings are compromises arising from the intersection of different (sometimes opposing) influences. Likewise there are no absolute boundaries that separate one 'color-class' from another. We have names for individual colors (e.g., red, blue, etc.) but define them to be inclusive of an array of shades and hues. We think of it as natural and appropriate to think of the visual spectrum as continuous, and have no great compulsion to limit the number of colors or the 'distance' between them. Our conception of colors is likewise in 'broad strokes'. Painting (before pointilism) involved continuous motions produced by the wrist and elbow (not button-pushing produced by the fingers). We can choose which button to press, but otherwise, the quality of the physical action has no impact whatsoever on the frequency of the pitch. One presses a button with a finger to get a pitch. With regard to the piano, pitch control is a decidedly digital activity. Most people accept this as natural and inevitable, rather than as a result of how we use our bodies to make music. While the audible frequency spectrum is continuous, we generally conceive of the pitch-universe as a relatively limited number of fixed frequencies, with absolute boundaries differentiating pitches from 'non-pitches', and a significant amount of separation between adjacent pitches.
In this essay, I will discuss the musical and cultural problems which occurred as a result of the widespread use of the piano and its tuning system. Just by singing we can hear that the frequency spectrum has an infinite number of pitches, and thus there are also an infinite number of possible tuning systems. All of these scales, in turn, belong to a particular tuning system, which is itself a selection of pitches from the frequency spectrum. Even a piano, however, does not contain all possible pitches.
A particular piano piece, for example, may be confined to the notes of one particular scale-say G major-one of many scales possible on the piano. We are, naturally, aware that each piece of music is really only a selection or arrangement of individual pitches from among a larger pool of available tones. When we listen to a piece of music, we do not normally think about the tuning system upon which it is based. Piano's Ivory Cage The Piano's Ivory Cage
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