4 ms·

> 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

> 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.

seanhunter 1mo ago
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.
- pierrec 1mo ago
  For metallophones used in Gamelan music, I don't think the key difference is emphasis on higher vs. lower overtones. Rather, their overtones don't follow the harmonic series but are still well-defined. Their tuning goes along with that, and it works given that particular non-harmonic timbre, but wouldn't work with western classical instruments, which tend to approximate the harmonic series in their overtones. In all cases the lower overtones remain the most audible and the most important ones for tuning and finding consonance.
seba_dos1 1mo ago
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!
- ludston 1mo ago
  It's a bit more circular than that. The music you were raised with sounds good to you, which means you want to understand how to make music like that hence the dominance of 12 tones and major and minor scales in Western music. But also, nobody bothers to talk about this because for beginners without sufficient focus on mastery by copying other people, they're generally not going to be able to do anything notable with music anyway, so this kind of meta-theory is an unnecessary distraction. (And by the time you are actually decent with music literally years have passed and you've probably stumbled upon this idea by then)
  - dyzone 1mo ago
    > The music you were raised with sounds good to you Speaking for myself, the music I was raised with doesn't sound that good to me.
    - PaulDavisThe1st 1mo ago
      What is meant here is that there are different musical cultures around the world, and if you grew up in one that, for example, prominently uses quarter-tones/microtones (e.g. a lot of music from Arabic and Indian cultures) then we know that you will have a different reaction to, say, Bach, than someone who grew up in a culture that uses strict equal temperament. It does not mean "my parents played a lot of <X> and that doesn't sound good to me".
      - hn993302 1mo ago
        I grew up with Western music, and now Arabic music is one of my favorites. I really don't think Westerners hear semitones differently. Also, a lot of Arabic music is 12-tone, and even if it weren't, they probably appreciate Bach the same way.
nprateem 1mo ago
And even saying the 12 notes must have specific frequencies is wrong. It's very common when creating synths for example to detune them to create richer sounds, or play on dissonance to some extent.
- maybewhenthesun 28d ago
  That's what I meant when stating 'the exact frequencies are culturally defined'. There are lots of tuning systems. Equal temperament is just 12 (logarithmic) equal steps. But other tuning systems use different priorities. The basis is physical, though. It's always about trying to get the frequency ratios as simple as possible (or as close as possible to a simple ratio). Based on the fact that natural overtones are always (more or less) integer multiples of the base frequency so that's what sounds pleasing to us. Using only integer ratios is impossible though, so we have to deviate from those. And on top of that we want to deviate because people get bored ;-)
hn993302 1mo ago
I tried making things like a 7-TET keyboard in JS at some point and concluded that they probably picked 12 because there are a lot of factors and it's a manageable number. Almost no two notes sounded harmonious on my 7-TET. I know plenty of cultures use other scales too.

seanhunter 1mo ago

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.

pierrec 1mo ago
For metallophones used in Gamelan music, I don't think the key difference is emphasis on higher vs. lower overtones. Rather, their overtones don't follow the harmonic series but are still well-defined. Their tuning goes along with that, and it works given that particular non-harmonic timbre, but wouldn't work with western classical instruments, which tend to approximate the harmonic series in their overtones. In all cases the lower overtones remain the most audible and the most important ones for tuning and finding consonance.

seba_dos1 1mo ago

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!

ludston 1mo ago
It's a bit more circular than that. The music you were raised with sounds good to you, which means you want to understand how to make music like that hence the dominance of 12 tones and major and minor scales in Western music. But also, nobody bothers to talk about this because for beginners without sufficient focus on mastery by copying other people, they're generally not going to be able to do anything notable with music anyway, so this kind of meta-theory is an unnecessary distraction. (And by the time you are actually decent with music literally years have passed and you've probably stumbled upon this idea by then)
- dyzone 1mo ago
  > The music you were raised with sounds good to you Speaking for myself, the music I was raised with doesn't sound that good to me.
  - PaulDavisThe1st 1mo ago
    What is meant here is that there are different musical cultures around the world, and if you grew up in one that, for example, prominently uses quarter-tones/microtones (e.g. a lot of music from Arabic and Indian cultures) then we know that you will have a different reaction to, say, Bach, than someone who grew up in a culture that uses strict equal temperament. It does not mean "my parents played a lot of <X> and that doesn't sound good to me".
    - hn993302 1mo ago
      I grew up with Western music, and now Arabic music is one of my favorites. I really don't think Westerners hear semitones differently. Also, a lot of Arabic music is 12-tone, and even if it weren't, they probably appreciate Bach the same way.

nprateem 1mo ago

And even saying the 12 notes must have specific frequencies is wrong. It's very common when creating synths for example to detune them to create richer sounds, or play on dissonance to some extent.

maybewhenthesun 28d ago
That's what I meant when stating 'the exact frequencies are culturally defined'. There are lots of tuning systems. Equal temperament is just 12 (logarithmic) equal steps. But other tuning systems use different priorities. The basis is physical, though. It's always about trying to get the frequency ratios as simple as possible (or as close as possible to a simple ratio). Based on the fact that natural overtones are always (more or less) integer multiples of the base frequency so that's what sounds pleasing to us. Using only integer ratios is impossible though, so we have to deviate from those. And on top of that we want to deviate because people get bored ;-)

hn993302 1mo ago

I tried making things like a 7-TET keyboard in JS at some point and concluded that they probably picked 12 because there are a lot of factors and it's a manageable number. Almost no two notes sounded harmonious on my 7-TET. I know plenty of cultures use other scales too.