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by devnonymous 1884 days ago
Ah alright, I finally understand you. What you meant to say is the reason why Western classical music is built on the 12 note chromatic scale is because the musicians used the math! It has nothing to do with history. Sound about right?
2 comments
kaoD 1884 days ago
Although I agree with you... didn't Pythagoras derive the pythagorean tuning of diatonic doing the math with the 3:2 ratio?

I know near zero music history, but I was under the impression that that's the evolution from diatonic scales and eventually into our western music system.

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goto11 1883 days ago
Yes, intervals are just ratios of numbers, corresponding to frequency ratios. 2:1 is an octave, 3:2 is a fifth, 4:3 a fourth and so on. I didn't even know this was controversial.

Of course a lot of other stuff in music and music theory is due to history and tradition. For example the names of the intervals (octave, fourth, fifth etc.) presumes a 7-note scale. Using 7 as reference is tradition, e.g. the pentatonic scale has 5 notes.

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kaoD 1883 days ago
> Using 7 as reference is tradition, e.g. the pentatonic scale has 5.

That's our point.

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goto11 1883 days ago
Ok, but that is kind of orthogonal to the point I was making. I was just stating that it follows from the math that the notes in a 7-note scale are not evenly spaced. The same is true for a pentatonic scale, for the same reason: The intervals corresponds to the simplest ratios (2:3, 3:4 etc.) but these do not in turn correspond to divide the octave evenly.
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goto11 1884 days ago
Not exactly, although I think I understand what you are getting at.

What I meant was that the interval between a major third and fourth in a 12-tone chromatic scale has to be a semitone due to math, not due to some historical accident or decision.

It might be an accident of history that we use a 12-step scale in the first place though, since you can have arbitrary many intervals in an octave - but you can't just divide the octave in arbitrarily places and get music out of it. The intervals still have to be ratios.

(Well I'm sure some avant-garde composer have tried making music with intervals that are not ratios just to be clever, but I hope you get my point!)

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