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. . . Assume that we have
two melodies moving parallel
to each other, the first written in whole notes, and the second in half-notes.
If the time for each note were to be indicated by the tapping of a stick,
the taps for the second melody would recur with double the rapidity of
those for the first. If now the taps were to be increased greatly in rapidity
without changing the relative speed, it will be seen that when the taps
for the first melody reach sixteen to the second, those for the second
melody will be thirty-two to the second. In other words, the vibrations
from the taps of one melody will give the musical tone C, while those of
the other will give the tone C one octave higher. Time has been translated,
as it were, into musical tone. Or, as has been shown above, a parallel
can be drawn between the ratio of rhythmical beats and the ratio of musical
tones by virtue of the common mathematical basis of both musical time and
musical tone. The two times, in this view, might be said to be
“in harmony,”
the simplest possible.
Henry Cowell
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