Fact Check - 5. Music, Temperament, and Social Concord
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Query: 5. Music, Temperament, and Social Concord
Fact Check
Quoted text:
A whole tone scale can be made by proceeding by whole tones. On the piano, we would get the series C, D, E, F♯, G♯, A♯ (=B♭), then back to C. But we would not get the other six tones. To do this, we must continue tuning by fifths.
For ease of visualizing this on the black keys of a piano, let us begin by a fifth below middle C: F. This gives us what musicians call the “circle of fifths,” consisting of F, C, G, D, A, E, B, F♯, C♯, G♯, D♯, A♯—and then, a fifth above A♯, E♯. (Alternatively, if we begin with C, we will end up with B♯.)
However, as every pianist knows, there really is no E♯ (or B♯). That is F. We would seem to have arrived back at our starting point.
But in fact, we have not done so, for a very good reason. To return to a higher octave of our starting F (or C), we would need some doubling, that is, power of 2 in the denominator of whatever fractional system we are using. Its powers are 9, 27, 81, 243, and so forth, with the power always ending in an odd number—a 9, a 7, a 3, or a 1. Thus, as we reach the circle’s return at the seventh octave, we get a slight dissonance, an out-of-tuneness. Since antiquity, musicians have called this a “comma” (Greek “komma”). This represents the ratio of tuning by odd-numbered intervals relative to even ones.
Can a music expert check that this makes sense?
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