odd number

an integer which cannot be divided by 2; the series of every other integer beginning with 1.

The ancient Greeks are purported to have created the distinction between even and odd numbers because of their musical studies:

Because the 2:1 frequency ratio, or "octave", gives a sound which so strongly resembles the 1:1 or starting pitch, the Greeks characterized this 2:1 relationship as female and even.

3:1, on the other hand, created an entirely new pitch, and so (along with 1:1) was considered to be male and odd.

4:1 again produces another 'octave' of the original pitch, and so is again female and even.

5:1 again produces another new pitch, and so is male and odd.

6:1 produces a pitch an 'octave' higher than 3:1, and so is again female and even.

...and so on.

[from Joe Monzo, JustMusic: A New Harmony]

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