141–150 of 164 posts
Yes, but why is that? Why did we evolve to like these particular combination of notes? Or, why do they remind us of some other natural sound?
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Is it not true that the shape of the waveform (sinusoidal, saw-like etc) is created by the relative weights of each harmonic? E.g. if you take any random sound wave, Fourier-transform it, you'll find the weight of each harmonic. Or are you saying there is a separate quality to sound waves that can cause their shape to be different even if each harmonic has the same relative weight with respect to the fundamental?
Yes, this quantity is the relative phase of the harmonics, although the human ear is generally considered to be insensitive to phase.
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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 equiv…
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 waveform…
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.
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Actually, 41 has a better 4th and 5th, only being off by about half a cent, as opposed to being off by about 2 cents. It also has thirds and sixths that are quite a bit better (though still not great), and it has very good 7-limit intervals, which is something 12-EDO has nothing even remotely close to. 31 is generally decent all around, but it has worse 4ths and 5ths than 12-EDO. 53 EDO is even better than 41, having…
I guess I could imagine a piano that is 53/12 times the size of a current piano, but I wouldn't want to have to play it :)
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The numbers 12 (2x2x3), 24 (2x2x2x3), 30 (2x3x5), 60 (2x2x3x5) and 360 (2x2x2x3x3x5) crop up in a lot of older counting systems because they're so conveniently divisible.
One twelfth the atomic weight of one carbon-12 atom is the atomic mass constant. What does string theory sound like? https://periodic.lanl.gov/79.shtml http://en.wikipedia.org/wiki/Atomic_weight
> pairs of notes whose frequencies are multiples of 4/3 or 3/2 sound very pleasing when played together. Yes, but why is that? Why did we evolve to like these particular combination of notes? Or, why do they remind us of some other natural sound?
In general anything more complex than "birds like blue feathers because it shows a strong immune system" is unlikely to have a simple satisfying evolutionary reason to exist that is less than 80% wrong.
If we look at the groups next door, Z11 and Z13, they are of prime order, so every element generates the group => there is a cycle of “fifths” for each interval. Beautifully symmetric, perhaps, but less structure to enjoy.
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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 waveform…
> 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 whic…
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> Viewing sound waves that don't synchronize with each other as being better matched than sound waves that do synchronize is less plausible than violating the fundamental theorem of arithmetic Actually it's perfectly plausible. People couldn't imagine others enjoying hearing a tritone -- and nobody in 1800 would imagine we'd enjoy listening to punk, hip hop, or Death Metal, and yet, millions do. We can surely conside…
> Actually it's perfectly plausible. No, for this to be plausible, you would need to have some theory of why the two notes matched with each other. There is no such theory; they have been chosen to be as unmatched as possible. > nobody in 1800 would imagine we'd enjoy listening to punk, hip hop, or Death Metal This is false. >> That hypothetical species wouldn't recognize two notes an octave apart as being similar >…
This is both pedantic, condescending, and unwilling to entertain an idea.
In any case, just for anybody interested:
>No, for this to be plausible, you would need to have some theory of why the two notes matched with each other. There is no such theory; they have been chosen to be as unmatched as possible.
Nothing has in 12-tet has been "chosen to be as unmatched as possible". Instead, we've chosen it to match the ratios as close as we can, given the compromises we had (simpler instruments, larger range, etc.).
The 12-tet values still has strict mathematical properties, it's not just some random off collection of pitches - and it could be that, which is perceived as "perfection" by the imaginary alien race (that it is equally spaced values on a logarithmic scale).
Earlier quoted context omitted.
> 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 whic…
What? No, you said it, the ear splits the sound into frequencies and physically puts sensors into places where they resonate. Octave resonates in the same place. (but higher octave resonates in one additional place)