An odd number is an integer which cannot be divided by 2; the set of odd numbers is 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, creates 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.
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