Comment by codeulike
15 hours ago
Maths and physics are a terrible way to learn the artistic side of music, but if you are interested in "why does a fifth chord sound nice" or "why are the black and white keys on a piano in that particular pattern" you can get interesting (partial) answers by looking into the maths of frequency ratios and the physics of overtones and how they affect the cilia of the inner ear. Music differs between cultures but there are some universals such as the Octave (edit: by which I mean doubling of frequency, not how its divided up) and nearly all cultures have some form of music ... There is something universally human about it, and so its a doorway to studying how our minds work.
> but there are some universals such as the Octave
Universal in the sense that a number of rocks or a number of sheep can be doubled just as a frequency can?
The notion that there are 8 sub divisions to a doubled frequency interval isn't universal. Balinese Gamelan doesn't even neccessarily have an agreed number of "notes" in an "Octave" from one village to the next.
There aren't 8 subdivisions in an octave in western music either. Well, there are in any given scale, but there are also many scales. "Octave" is a misleading term. Given that it's just a doubling of frequency, the term is sort of as good as any other, and that douibling exists in pretty much all cultures that have developed string, pipe or other resonant body based music (including hitting hollow logs and plucking vibrating reeds / sticks / tines).
It's pretty much the foundational idea of any modality. No matter how you divide it up, the purest harmony is doubling or halving.
The commenter presumably was talking about octave equivalence, which is reportedly present across all or nearly all historical musical cultures that we know about. It’s also supposedly present in some other mammals.
reportedly present, yes .. but the debate is still hot on universal.
I was asking to tease out some PoV perspective, again Gamelan doesn't neccessarily have powers of two, or 12, etc divisions of a doubling (or Octave, if we're using that term); it's a non western style of percussion that has a suprising number of local variations (it's essentially near unique to Balinese culture) in divisions and tunings.
The Octave wikipedia entry includes:
but gets woolly on examples.
Cheers for the response, appreciated.
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Universal in the sense that a number of rocks or a number of sheep can be doubled just as a frequency can?
Yes thats what I meant, the doubling of frequency. It might seem trivial but the fact that doubling frequency sounds "right" to humans is actually quite interesting. Why does it sound "right"?
Interference is most of the answer. With frequencies f and 2f you get the smoothest interference patterns, even if the tones have a lot of harmonics. This applies reducingly to increasingly fractional ratios.
1.5**12 is about 129.74, which is as close as you can reasonably get to a power of two.
So yes, the 12-tone scale is a universal thing - you want both octaves and fifths in your scale.
(12 is actually too much, so usually that's pared down to something like 4 or 5 or 7 tones, this is where you get cultural variation.)
> 1.5*12 is about 129.74,
Math checks out.
> So yes, the 12-tone scale is a universal thing -
I don't follow the logic here though. It's certainly true that a 12-tone / Chromatic scale is ubiquitous within the Western Music tradition .. but the universe is reportedly a little larger.
Even Western Music includes exceptions like the 9-note augmented scale, though the argument can be made that it's a 12-scale with 3 bits "missing" - not a case that can be made about a non-western 7 note percussive scale.
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129.74 is not really close to a power of two. 31-tet scales have a better approximation of a 5th (and an impressively better approximation of a minor 7th).
The obvious exception in the western system would be the blues scale, which arguably has 9 tones (7 equal tempered notes, plus a just tempered 3rd and 7th).
And Indian ragas break all of these rules. They have scales that don't have 8 notes, scales that don't use equal temperament, and even a few scales that don't repeat on octaves.
powers of 2 seem to work well in many things. in rhythm too. so dont be so quick to dismiss.