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Middle C is 261.63 Hz. The next half-step up (C#) is 277.183 Hz.

Why are these notes, while a tone at, say, 265 Hz, is not? Or what about 269.1488 Hz -- nearly absolute middle of the two?

Why do we recognize certain frequencies as notes?

Middle C is 261.63 Hz. The next half-step up (C#) is 277.183 Hz. Why are these notes, while a tone at, say, 265 Hz, is not? Or what about 269.1488 Hz -- nearly absolute middle of the two? Why do we recognize certain frequencies as notes?

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[–] 0 pt

Because European-based assholes decided 440Hz was "center A". I prefer a 432Hz tuning, myself. It feels richer and fuller and deeper.

The numerical ratios between the notes stay fixed: 1:2 is an octave, 1:1.5 is harmonic. When you iterate harmonics within an octave you get approximately twelve notes.

So that's why. It's not limited to 440Hz or 432Hz, you can choose any frequency, call that your center note, and build the frequency ratios out from there. I promise they'll sound good. Harmonics sound nice in any tuning. The aesthetic difference produced by different tunings is hard to explain, you just have to experience it.

You can just skip the rest of this comment.

The ancient Greeks took two strings, one at twice the length of the other. This defines the octave. Take the smaller string, multiply it by 1.5, is it longer then the longer string? No. Multiply that string by 1.5, yielding 2.25. is it longer than the longer string? Yes, so cut it in half (1.125). Multiply that string by 1.5, you get 1.6875. On the 12th iteration, it's 1:1.0136, just over 1% different... but when actually tuning say, a piano, you can't ignore it. You have to favor the ivories or distribute the sonic irregularity evenly. The next time the harmonics iterate to such a nice octave, it's at 41, with a 1:0.9886. Some instruments have been built for that scale, but few.