Comment by maybewhenthesun
3 hours ago
> Which is a strange way to teach a system that essentially comes out of physics and arithmetic. There are twelve notes for a reason.
There is of course a lot of physics involved. But there is at least as much convention at play. So imho this is a very one sided way of looking at it.
There is a physical reason the 12 notes are those 12 notes (though the exact frequencies assigned are influenced by culture as well), but lots of different cultures use less notes, or more, or extra notes inbetween.
So 'Because that is the convention.' is imho at least a good an explanation as the physics one.
It took me a while to realize that "because that is the convention" was the answer to a big chunk of my confusion about music notation. A weirdly helpful answer, but so often nobody bothers to even tell you that, so you just assume you must be missing something when you can't see where these things are coming from!
Also his physics explanation is not the best, and you can see if you just ask the next “why” question.
He talks about the harmonic series giving the basic ratios of the Pythagorean scale but why is that the case? When you solve the equations of motion of any sort of harmonic oscillator (including crucially, strings, vibrating columns of air from a wind instrument etc) you see that you can solve them using a Fourier series, so if you solve this in trigonometric form you get a_1 * cos blah_1 + 1/2 * (a_2) * cos blah_2 + 1/3 * (a_3) * cos blah_3 + … + 1/n * (a_n) * cos blah_n [1]
…so those fractions end up being the partials of the harmonic series (a_n/n) where a_n is the n_th coefficient, which you find using an integral. Now if you have a normal western musical instrument, the higher overtones (later terms of the Fourier series) are not prominent so those coefficients are small. So the terms that matter have ratios a_1, a_2/2, a_3/3, a_4/4, a_5/5 corresponding to the primary intervals that he’s talking about.
In cultures (eg Balinese and Javanese music from Indonesia) where they use a different number of tones and different scale, it’s no coincidence that they play a lot of gongs and bells, which have much more prominent higher overtones, so a different set of Fourier coefficients so different ratios are going to be “congruent”/melodious-sounding.
[1] the “blah” terms are a function of pi and the length and stiffness of the string etc. Not really relevant here.