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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

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.

defrost 6mo ago
> 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.
- Intermernet 6mo ago
  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.
- uwagar 6mo ago
  powers of 2 seem to work well in many things. in rhythm too. so dont be so quick to dismiss.
- codeulike 6mo ago
  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"?
  - sheiyei 6mo ago
    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.
- tshaddox 6mo ago
  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.
  - defrost 6mo ago
    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: Octave equivalence is a part of most musical cultures, but is far from universal in "primitive" and early music but gets woolly on examples. Cheers for the response, appreciated.
    - tshaddox 6mo ago
      Yeah, that sentence on Wikipedia is a bit unclear though. It might be merely claiming that, for some musical cultures, we don’t have a written record of an explicit notion of octave equivalence or tone name circularity. But I suspect there’s a clear biological mechanism which makes it easy to mistake one octave for another from any source of roughly harmonic sound. This is due to the similarity in the overtones of two harmonic sounds that differ by an octave. I would be surprised if this mechanism isn’t universal, although its on various musical systems can obviously vary a lot.
- otabdeveloper4 6mo ago
  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.)
  - defrost 6mo ago
    > 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.
    - otabdeveloper4 6mo ago
      All scales in all cultures are based on octaves and fifths. (E.g., the ancient Chinese musical scale also has 12 tones.) Also the so-called "Western music" standardized on 12 tones very late in the process, long after the Chinese figured it out. > a 12-scale with 3 bits "missing" That's all scales, even the "non-Western" ones. Microtonality is added to the standard 12 tone to add tone effects. (Synthesizers in pop music do the same trick.)
      - tolciho 6mo ago
        To confirm the claim that "all scales in all cultures are based on octaves and fifths" one might study the scales.zip scale files and find those that do not contain octaves and fifths, which should naturally be zero if the claim is true. https://www.huygens-fokker.org/scala/ https://www.huygens-fokker.org/scala/ Note also that certain musical traditions were suppressed or eradicated due to their unfortunate habit of using dissonant notes such as minor seconds, as opposed to the consonant traids favored by a particular group recently in power around the world. Happy Easter!

defrost 6mo ago

> 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.

Intermernet 6mo ago
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.
uwagar 6mo ago
powers of 2 seem to work well in many things. in rhythm too. so dont be so quick to dismiss.
codeulike 6mo ago
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"?
- sheiyei 6mo ago
  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.
tshaddox 6mo ago
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.
- defrost 6mo ago
  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: Octave equivalence is a part of most musical cultures, but is far from universal in "primitive" and early music but gets woolly on examples. Cheers for the response, appreciated.
  - tshaddox 6mo ago
    Yeah, that sentence on Wikipedia is a bit unclear though. It might be merely claiming that, for some musical cultures, we don’t have a written record of an explicit notion of octave equivalence or tone name circularity. But I suspect there’s a clear biological mechanism which makes it easy to mistake one octave for another from any source of roughly harmonic sound. This is due to the similarity in the overtones of two harmonic sounds that differ by an octave. I would be surprised if this mechanism isn’t universal, although its on various musical systems can obviously vary a lot.
otabdeveloper4 6mo ago
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.)
- defrost 6mo ago
  > 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.
  - otabdeveloper4 6mo ago
    All scales in all cultures are based on octaves and fifths. (E.g., the ancient Chinese musical scale also has 12 tones.) Also the so-called "Western music" standardized on 12 tones very late in the process, long after the Chinese figured it out. > a 12-scale with 3 bits "missing" That's all scales, even the "non-Western" ones. Microtonality is added to the standard 12 tone to add tone effects. (Synthesizers in pop music do the same trick.)
    - tolciho 6mo ago
      To confirm the claim that "all scales in all cultures are based on octaves and fifths" one might study the scales.zip scale files and find those that do not contain octaves and fifths, which should naturally be zero if the claim is true. https://www.huygens-fokker.org/scala/ https://www.huygens-fokker.org/scala/ Note also that certain musical traditions were suppressed or eradicated due to their unfortunate habit of using dissonant notes such as minor seconds, as opposed to the consonant traids favored by a particular group recently in power around the world. Happy Easter!