4 ms·

Eh, I think you'd need a new universe, as it's a pretty basic principle of math: 3^12 ~= 2^19 You can take two long strings of equal length (A & B), and plu

Eh, I think you'd need a new universe, as it's a pretty basic principle of math: 3^12 ~= 2^19 You can take two long strings of equal length (A & B), and pluck them, and they'll make the same sound. Then you can take scissors cut string A in half, and it'll sound different. (This is an octave.) Then you can cut string B into thirds, and it too will sound different. If you pluck both of your new strings at the same time, you'll find they sound quite nice together (the difference between these two is called a "fifth"). And after 12 rounds of cutting string B into thirds, and 19 rounds of cutting string A in half, you'll happen to have a string from each group that are almost identical in length and pitch. But it won't line up exactly! They'll be about 1.4% different in length, which roughly works out to a quarter-semitone difference in pitch (i.e. 1/4th the distance from one piano key to the next).

tshaddox 4y ago
But who says the creatures need to perceive sound in such a way that the harmonic series has sensory significance? To be honest I’ve never seen a compelling evolutionary explanation for why “hearing the harmonic series” developed in the first place. It obviously seems useful to be able to perceive sounds generated by (roughly) harmonic oscillators, since those occur naturally for various reasons, but why octave equivalence?
- rrrrrrrrrrrryan 4y ago
  I don't think you need to imagine "creatures" - there are humans on earth whose culture's music doesn't have the concept of octaves, let alone fifths. All the real action in their music is in its rhythmic complexity. But my comment was in reply to this statement specifically: > Somewhere there is a perfect universe where 12 fifths form an octave. For this to be true, I think you'd indeed need a new universe where 3^12 = 2^x, where X is a whole integer.
  - tshaddox 4y ago
    I'm not talking about explicit notions of octaves and octave equivalence, although those do exist in very many musical traditions and appear to be extremely widespread in musical traditions where tones have names (if not ubiquitous—I'm not aware of any exceptions). I was referring to the claims that octave equivalence is in some sense hard-wired in the human brain, or sometimes claimed to be all or many mammalian brains. I'm not qualified to evaluate these claims or even whether how well-accepted they are among experts, but such claims do seem to pop up all over the place when discussing music perception.
    - rrrrrrrrrrrryan 4y ago
      I'm much less qualified: I took a "World Music 101" class in college that described some Native American tribes whose songs had drums, and cries that fell in pitch from high to low to call down the spirits from above, but their music had no concept of octaves. And I agree with you. While I can imagine a culture that hadn't "discovered" the octave, it's difficult to imagine people who can't even perceive octaves when presented with them, and quite easy to imagine other creatures that cannot perceive them.
    - maxdamantus 4y ago
      The basic reason for octave equivalence is not from human subjectivity. It's from the fact that something that repeats "x" times is also something that repeats "x/2" times, eg a sequence such as: ABCABCABCABCABCABC Can be thought of as "ABC" repeated 6 times or "ABCABC" repeated 3 times. If you replace the letters with numbers, you can treat the numbers as samples of a sound wave. Just to be clear: the magical number here is 2 (not 12 or 8 or 7) since "octave equivalence" refers to the fact that you can multiply a frequency by 2 and get the same note. Unless the sound is a perfect sine wave, there isn't a particular frequency associated with it due to these alternative interpretations.
- joshka 4y ago
  Look at it from a frequency perspective instead of genetic. When you overlay two waveforms that are related x:1, the zero points of the waveforms align. The wave resets at the same instant. If instead the waveforms are related not exactly, then you get a change in where the reset point is that drifts and causes the wave to exhibit beating (changes in volume). If you have a 2:1 (octave) relationship between 2 waveforms, then you won't hear the beating as the beat frequency exactly overlaps the frequency of the lower frequency. If you have say two notes that are not quite in the octave ratio, then you hear beating at the difference in frequency. E.g. say 440Hz and 888Hz (instead of 880Hz), you have beating occurring at 448Hz, which you'll hear as an 8Hz (448Hz-440Hz) wobble in the sound volume of the combined wave.
  - jacquesm 4y ago
    There are some assumptions about phase in there.
    - joshka 4y ago
      Yeah, you're right.
  - ordu 4y ago
    > If you have a 2:1 (octave) relationship between 2 waveforms, then you won't hear the beating as the beat frequency exactly overlaps the frequency of the lower frequency. If we take a look into a human ear we'll see there an apparatus which physically splits sound into a spectrum of frequencies (a long narrowing tube, sound comes from one end and it creates resonances at different places) and a lot of receptors which placed in such a way that allows them to specialize on different frequencies. I know nothing that would point to an innate ability of this apparatus to feel octave as something special compared with a mix of two random frequencies. So the peculiarity we hear pops up on later stages of sound processing. But why it pops up? Moreover there is an evidence (I have no link, sorry) that the peculiarity of an octave is a cultural thing, not a genetic one. European music teaches us to feel octave as something special. There are tribes not exposed to European music who doesn't feel consonance and dissonance like we do. My hypothesis that a mind picks correlation between a frequency and a double frequency. I mean it is not because of some funny math comparing two sine waves, it is because sounds essentially are not single sines. Two sounds forming an octave are both sums of many sine waves, and there is a huge overlap between sets of frequencies, so they sound similar. And then, when mind trains on this data, it becomes conditioned on a similarity of double frequencies, so it starts think of two sines with frequency ratio of 2:1 as of similar. The similarity is just a correlation. And people who didn't tried to make a music with strings cannot grasp the idea, because natural sounds mostly much more complex than just sum of a several sines with frequencies that are multiples of some base frequency.

tshaddox 4y ago

But who says the creatures need to perceive sound in such a way that the harmonic series has sensory significance? To be honest I’ve never seen a compelling evolutionary explanation for why “hearing the harmonic series” developed in the first place. It obviously seems useful to be able to perceive sounds generated by (roughly) harmonic oscillators, since those occur naturally for various reasons, but why octave equivalence?

rrrrrrrrrrrryan 4y ago
I don't think you need to imagine "creatures" - there are humans on earth whose culture's music doesn't have the concept of octaves, let alone fifths. All the real action in their music is in its rhythmic complexity. But my comment was in reply to this statement specifically: > Somewhere there is a perfect universe where 12 fifths form an octave. For this to be true, I think you'd indeed need a new universe where 3^12 = 2^x, where X is a whole integer.
- tshaddox 4y ago
  I'm not talking about explicit notions of octaves and octave equivalence, although those do exist in very many musical traditions and appear to be extremely widespread in musical traditions where tones have names (if not ubiquitous—I'm not aware of any exceptions). I was referring to the claims that octave equivalence is in some sense hard-wired in the human brain, or sometimes claimed to be all or many mammalian brains. I'm not qualified to evaluate these claims or even whether how well-accepted they are among experts, but such claims do seem to pop up all over the place when discussing music perception.
  - rrrrrrrrrrrryan 4y ago
    I'm much less qualified: I took a "World Music 101" class in college that described some Native American tribes whose songs had drums, and cries that fell in pitch from high to low to call down the spirits from above, but their music had no concept of octaves. And I agree with you. While I can imagine a culture that hadn't "discovered" the octave, it's difficult to imagine people who can't even perceive octaves when presented with them, and quite easy to imagine other creatures that cannot perceive them.
  - maxdamantus 4y ago
    The basic reason for octave equivalence is not from human subjectivity. It's from the fact that something that repeats "x" times is also something that repeats "x/2" times, eg a sequence such as: ABCABCABCABCABCABC Can be thought of as "ABC" repeated 6 times or "ABCABC" repeated 3 times. If you replace the letters with numbers, you can treat the numbers as samples of a sound wave. Just to be clear: the magical number here is 2 (not 12 or 8 or 7) since "octave equivalence" refers to the fact that you can multiply a frequency by 2 and get the same note. Unless the sound is a perfect sine wave, there isn't a particular frequency associated with it due to these alternative interpretations.
joshka 4y ago
Look at it from a frequency perspective instead of genetic. When you overlay two waveforms that are related x:1, the zero points of the waveforms align. The wave resets at the same instant. If instead the waveforms are related not exactly, then you get a change in where the reset point is that drifts and causes the wave to exhibit beating (changes in volume). If you have a 2:1 (octave) relationship between 2 waveforms, then you won't hear the beating as the beat frequency exactly overlaps the frequency of the lower frequency. If you have say two notes that are not quite in the octave ratio, then you hear beating at the difference in frequency. E.g. say 440Hz and 888Hz (instead of 880Hz), you have beating occurring at 448Hz, which you'll hear as an 8Hz (448Hz-440Hz) wobble in the sound volume of the combined wave.
- jacquesm 4y ago
  There are some assumptions about phase in there.
  - joshka 4y ago
    Yeah, you're right.
- ordu 4y ago
  > If you have a 2:1 (octave) relationship between 2 waveforms, then you won't hear the beating as the beat frequency exactly overlaps the frequency of the lower frequency. If we take a look into a human ear we'll see there an apparatus which physically splits sound into a spectrum of frequencies (a long narrowing tube, sound comes from one end and it creates resonances at different places) and a lot of receptors which placed in such a way that allows them to specialize on different frequencies. I know nothing that would point to an innate ability of this apparatus to feel octave as something special compared with a mix of two random frequencies. So the peculiarity we hear pops up on later stages of sound processing. But why it pops up? Moreover there is an evidence (I have no link, sorry) that the peculiarity of an octave is a cultural thing, not a genetic one. European music teaches us to feel octave as something special. There are tribes not exposed to European music who doesn't feel consonance and dissonance like we do. My hypothesis that a mind picks correlation between a frequency and a double frequency. I mean it is not because of some funny math comparing two sine waves, it is because sounds essentially are not single sines. Two sounds forming an octave are both sums of many sine waves, and there is a huge overlap between sets of frequencies, so they sound similar. And then, when mind trains on this data, it becomes conditioned on a similarity of double frequencies, so it starts think of two sines with frequency ratio of 2:1 as of similar. The similarity is just a correlation. And people who didn't tried to make a music with strings cannot grasp the idea, because natural sounds mostly much more complex than just sum of a several sines with frequencies that are multiples of some base frequency.