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Comment by jagthebeetle | Hacker News Reader

Isn't this just by definition of equal temperament? If you want a pitch to double after 12 steps (multiplicatively), you choose 12-TET. Other musical systems exist (e.g. quarter-tone scales), and have existed.

So the musical notes thing is by human fiat, which at least pi^2 isn't. Perhaps I'm missing your meaning though?

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Before the current "equal temperament" system there was a "just temperament system" that basically harks back to Pythagoras. The main intervals in the C scale are very close to whole fractions of low numerator and denominator. The problem is that this doesn't work very well in every key. So the emergence of modern music came with a few tries at averaging these things out until equal temperament in the log scale arose.

Some of the character of older music is actually lost because of this. But hey, now all keys work the same.

>which at least pi^2 isn't

pi^2 is 9.87. If that counts as close to 10, then half of all numbers are close to some integer. And the significance of 10 is entirely cultural. Nothing in math favours base 10, we use it because the right civilisations were dominant at the right time. Other civilisations counted using base 4, base 5, base 6 or base 12 (e.g. using the five fingers and a closed fist to count up to 6 for each hand).

The reason that powers of the 12th root of 2 are used is that these numbers are close to simple rational numbers, which the human auditory system can pick up.

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