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Why 12 notes in Western music?

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Re: Why 12 notes in Western music?

#131

Post by dmarchand90 »

analog31 wrote: post #34
dmarchand90 wrote: post #17

Earlier quoted context omitted.

There used to be a lot of tempers floating around. For example a lot bach's music is not really supposed to be played in modern equal temper https://www.ethanhein.com/wp/2020/what-does-the-well-tempere... .

I consider the 12 tone scale to be a technology. The historical temperaments were compromise solutions to the problem of getting a useable scale within the skills and patience of the musician. A harpsichord had to be tuned before every performance, by the musician.

I can't find a public source, but in "the great courses " series on bach they mention that he had written notes on the 'feeling' each of the many different tempers could give and in a sense we have lost some flexibility in our ability to compose music

Re: Why 12 notes in Western music?

#132

Post by drBonkers »

smlacy wrote: post #27

Another possible explanation, which I'm surprised the author didn't go through is the "Circle of Fifths" which basically says: Since Fifths sound so great, why not just keep doing that? When we get to the next octave, then come back down. If we get to a place that's "pretty darn close" to another note, then stop. The Python explanation looks like: f = 440 for i in range(13): print(i,f) f = f * 3/2 if f > 880: f=f/2.0…

I love math explanations in Python, thank you.

Re: Why 12 notes in Western music?

#133

Post by euroderf »

elihu wrote: post #125
euroderf wrote: post #24

A long-winded way of saying that if you want to hit the 3:2 and 4:3 sweet spots "closely enough", dividing the octave into 12 logarithmically equidistant bins works very well, and better than any other number of bins less than 50 (or maybe 30).

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 :)

Re: Why 12 notes in Western music?

#135

Post by posterboy »

dwringer wrote: post #53
smlacy wrote: post #36

Earlier quoted context omitted.

Its the use of the musical concept of Fifths that's the key here: We just derive the notes from what sounds good, not what makes sense mathematically? I'm just using Python to mirror the author's analysis -- you can derive "12 notes" pretty much just by using your ear and listening to the Fifths.

A perfect fifth is just 150% (3/2) the frequency of the root, just as an octave is 200% (2/1). "What sounds good" is in a certain sense based on the harmonic series, and in that sense it is equivalent to what makes sense mathematically. A problem is that if you stack perfect fifths to get 12 notes then they won't sound in tune with each other across different keys. It's this issue which forms the crux of the linked p…

I think it's integral to the theorie seeing the fifth as 3 times, the octave as 4 times and the prime as 2 times an arbitrarily low root key. Trivially, the 2^n multiples form octave intervals but between C12 and C24 there's your twelve tones on a logarithmic scale. Naturally, it doesn't transpose in integer intervals if stepping down.

Re: Why 12 notes in Western music?

#136

Post by anon291 »

smlacy wrote: post #27

Another possible explanation, which I'm surprised the author didn't go through is the "Circle of Fifths" which basically says: Since Fifths sound so great, why not just keep doing that? When we get to the next octave, then come back down. If we get to a place that's "pretty darn close" to another note, then stop. The Python explanation looks like: f = 440 for i in range(13): print(i,f) f = f * 3/2 if f > 880: f=f/2.0…

This is the reason. You can keep going but it's just pointless. Things sound good enough at this point

Re: Why 12 notes in Western music?

#137

Post by anon291 »

thomasqbrady wrote: post #49

This piece is a good example of circular reasoning, isn’t it? The question “Why are there 12 notes in Western scales?” Is answered first by presuming that 4ths and 5ths sound pleasant (to whom? a Westerner?), the “4th” and “5th” being intervals ON a Western scale, which the author then reverse-engineers back to the 12-note scale which they assumed from the start. There are other scales you could start from, in which…

4ths and fifths are used in most standard systems of music.

Actually it's just fifths because fourths are just fifths.

And fifths sound good because of physics.

For example the pentatonic scale used in a lot of eastern music is subsumed by the western scale.

Re: Why 12 notes in Western music?

#138

Post by unrealp »

kazinator wrote: post #62

When we divide the octave into various equal steps using equal temperament, we find that there is a local maximum at 12, which yields a good approximations for important intervals. But the "why" cannot be explained just using arithmetic. There is a history behind it. Twelve note instruments didn't begin with equal temperament. There are twelve notes in western music because the diatonic scale has 7 notes, and alterat…

"'only' at 22 points given by nature" >> this isnt true. The sa and pa are non movable and dont have upper and lower shruti is for a practical reason. Tanpura, which is a drone instrument has typical tuning of sa and pa notes. Singers typically sing with tanpura, to get reference pitch. If singer sings variation (shrutis) around sa and pa, it causes acoustic beats (https://en.wikipedia.org/wiki/Beat_(acoustics)) where the volume appears to vary slowly. For example, tanpura sa drone string is tuned to 139 hz and singer sings 140 hz then audience hears beat of 1 hz. The beats are unpleasant so these shrutis are avoided. There is no 'natural' reason here.

Re: Why 12 notes in Western music?

#139

Post by flobosg »

buildsjets wrote: post #32

"Flying Microtonal Banana" - because why not fret a whole bunch of guitars for 24-Tet and record an album? https://guitar.com/news/music-news/king-gizzard-stu-mackenzi...

Also Syzygys[1], a duo using a 43-tone scale[2].

[1]: https://www.youtube.com/watch?v=HkYWccNb0-4

[2]: https://en.wikipedia.org/wiki/Harry_Partch%27s_43-tone_scale

Re: Why 12 notes in Western music?

#140

Post by joshka »

jacquesm wrote: post #120
joshka wrote: post #117

Earlier quoted context omitted.

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…

There are some assumptions about phase in there.

Yeah, you're right.
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