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Vocal chords share similar qualities to musical instruments in that pitch rises as string length diminishes. The vibration of vocal chords varies inversely as the square root of the linear dimensions of an organism. The larger animal tends to have a deeper bass, whereas the smaller animal tends to have a higher pitch.
From On Growth and Form (52-53):
The vibration of vocal chords and auditory drums has this in common with the pendulum-like motion of a limb that its rate also tends to vary inversely as the square root of the linear dimensions. We know by common experience of fiddle, drum or organ, that pitch rises, or the frequency of vibration increases, as the dimensions of pipe or membrane or string diminish; and in like manner we expect to hear a bass note from the great beasts and a piping treble from the small. The rate of vibration (N) of a stretched string depends on its tension and its density; these being equal, it varies inversely as its own length and as its diameter. For similar strings, N α 1/r², and for a circular membrane, of radius r and thickness e, N α 1/(r²√e).
But the delicate drums or tympana of various animals seem to vary much less in thickness than in diameter, and we may be content to write, once more, N α 1/r².
Suppose one animal to be fifty times less than another, vocal chords and all: the one’s voice will be pitched 2500 times as many beats, or some ten or eleven octaves, above the other’s; and the same comparison, or the same contrast, will apply to the tympanic membranes by which the vibrations are received. But our own perception of musical notes only reaches to 4000 vibrations per second, or thereby; a squeaking mouse or bat is heard by few, and to vibrations of 10,000 per second we are all of us stone-deaf. Structure apart, mere size is enough to give the lesser birds and beasts a music quite different to our own: the humming-bird, for aught we know, may be singing all day long. A minute insect may utter and receive vibrations of prodigious rapidity; even its little wings may beat hundreds of times a second. Far more things happen to it in a second than to us ; a thousandth part of a second is no longer negligible, and time itself seems to run a different course to ours.
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