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Why 12 notes in Western music?

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Re: Why 12 notes in Western music?

#11

Post by InCityDreams »

locusofself wrote: post #3

I'm not a music theory expert, just a guy who has played guitar by ear for 28 years. Equal temperament is definitely a compromise .. I find myself constantly trying to "sweeten" the tuning of my guitar strings relative to the song/key I am playing. You can tune your guitar with the most accurate guitar tuner in the world (I have strobe tuners by Sonic Research and Peterson), and some things still just sound out of tu…

Apart from ensuring my intonation was spot on, and my frets nicely shaped, scalloping my frets allowed me a lot of what may be the 'sweetness' you are after - a slightly harder pressure, without finger gymnastics, allows minor pitch corrections (but you can't go flatter). Regular guitars just seem dead to me. I also shaved parts of my neck - significantly - along different parts of it ie it's not 'smooth', it's shaped only for me, and how i want to play in the different registers.

Re: Why 12 notes in Western music?

#12

Post by locusofself »

criddell wrote: post #9
locusofself wrote: post #3

I'm not a music theory expert, just a guy who has played guitar by ear for 28 years. Equal temperament is definitely a compromise .. I find myself constantly trying to "sweeten" the tuning of my guitar strings relative to the song/key I am playing. You can tune your guitar with the most accurate guitar tuner in the world (I have strobe tuners by Sonic Research and Peterson), and some things still just sound out of tu…

There are guitars with frets that aren't straight lines that try to address some of the problems: https://guitargearfinder.com/faq/true-temperament-frets/

I've seen those! Pretty cool. I've also seen people put intermediate frets on certain notes.

Re: Why 12 notes in Western music?

#13

Post by lioeters »

jbverschoor wrote: post #8

12 notes, 12 hours, 12 months., even 12 monkeys.

> The duodecimal system, which is the use of 12 as a division factor for many ancient and medieval weights and measures, including hours, probably originates from Mesopotamia.

https://en.wikipedia.org/wiki/Duodecimal#Advocacy_and_%22doz...

Re: Why 12 notes in Western music?

#15

Post by abetusk »

This comes up every so often and in my mind, there is an answer and it has to do with how well the notes in the "temperament" combine to produce near-enough approximations to simple fractions.

That is, take a temperament, combine each pairs of notes together. For each pairs of notes, find a close-enough fraction to it and give it a score depending on how many of these pairs produce simple fractions.

The 12 note equal temperament produces one of the best scores, assuming some (perhaps arbitrary) constraints.

There are some papers getting at this idea [0].

I even wrote a small program to try and do this [1]. Farey sequences are used for best rational approximation [2] [3].

I think this even gets at why some chords sound "sour/sad" while others sound "happy/full", because they have less or more constructive interference between the notes in the range of where we can hear.

Obviously this has a lot to do with culture, so it's not as clear cut but at least this approach is better than just thinking it's completely arbitrary.

[0] https://www.researchgate.net/publication/267806865_Measures_...

[1] https://github.com/abetusk/scratch/blob/release/src/music/be...

[2] https://www.johndcook.com/blog/2010/10/20/best-rational-appr...

[3] https://en.wikipedia.org/wiki/Farey_sequence

Re: Why 12 notes in Western music?

#16

Post by [deleted] »

SeanLuke wrote: post #4

We've seen this before: and it's likely wrong. He ended his experiment too soon at 24 divisions, but even a little googling should have told him to go to 31, which is more accurate than 12. The 12-note scale long predates the notion of just or equal temperament.

[deleted]

Re: Why 12 notes in Western music?

#17

Post by dmarchand90 »

TheOtherHobbes wrote: post #7

12 notes tuned in equal temperament is a workable compromise between musical expressiveness, harmonic ratio accuracy, readability, and finger precision. It's also an established standard, which is a huge deal because it means you have access to a huge established repertoire. A 31-TET acoustic piano would be huge, extremely complicated, and probably unplayable. Smaller instruments mostly just aren't practical. In theo…

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....

Re: Why 12 notes in Western music?

#18

Post by khitchdee »

criddell wrote: post #9
locusofself wrote: post #3

I'm not a music theory expert, just a guy who has played guitar by ear for 28 years. Equal temperament is definitely a compromise .. I find myself constantly trying to "sweeten" the tuning of my guitar strings relative to the song/key I am playing. You can tune your guitar with the most accurate guitar tuner in the world (I have strobe tuners by Sonic Research and Peterson), and some things still just sound out of tu…

There are guitars with frets that aren't straight lines that try to address some of the problems: https://guitargearfinder.com/faq/true-temperament-frets/

FWIW, A sitar also has a 12 note scale, but the frets are moveable so you can tune by ear. The drawback is, you only play melodies on the top string and there are no chords. It's possible to design a guitar where the frets are spaced at harmonic intervals and not equal tempered, but then, you can only play in one key, the key of E and you can't capo or play barre chords. However, if you do play such a redesigned guitar in the key of E, it will sound sweeter because all your notes will be harmonic and you could play chords.

Re: Why 12 notes in Western music?

#19

Post by tshaddox »

criddell wrote: post #9
locusofself wrote: post #3

I'm not a music theory expert, just a guy who has played guitar by ear for 28 years. Equal temperament is definitely a compromise .. I find myself constantly trying to "sweeten" the tuning of my guitar strings relative to the song/key I am playing. You can tune your guitar with the most accurate guitar tuner in the world (I have strobe tuners by Sonic Research and Peterson), and some things still just sound out of tu…

There are guitars with frets that aren't straight lines that try to address some of the problems: https://guitargearfinder.com/faq/true-temperament-frets/

I'm a bit confused by that article. It says things like "the problem is that equal temperament isn’t perfect" and "because guitars are imperfect instruments, they can never be completely in-tune" and "if you tune your open strings perfectly to pitch, you may still notice that some chords sound slightly out-of-tune."

That doesn't sound like a description of a problem with equal temperament. In fact, the whole point of equal temperament is that any given chord has precisely the same tuning in every key. Isn't the purpose of these staggered frets to tune the guitar to more accurately match equal temperament? In other words, a guitar string played on the 7th fret is supposed to be tuned exactly 7 12-TET semitones above that string played open, but with completely straight frets (in lines exactly perpendicular to the strings) it's difficult to get every fret on every string to be accurately tunes.

I believe this is what's referred to as intonation. Many guitars have some form of manual adjustment, like a movable bridge saddle for each string, and it's common to use that to slightly adjust the length of each string so that e.g. the 12th fret is accurately in tune with the open string. These "true temperament" guitars seem to have done a similar thing but with small adjustments to each fret on each string. Presumably the fret arrangements are designed to match that exact guitar fretboard with some specific guitar strings?

The article says "with a normal guitar, if you play an A Major chord, then play a D Major chord, those chords will be slightly out-of-tune with each other." Again, this doesn't sound like a description of a problem with equal temperament. From what I can tell, these "true temperament" frets would help specifically with playing the same chord/interval in different positions.

Re: Why 12 notes in Western music?

#20

Post by WalterSear »

dmarchand90 wrote: post #17
TheOtherHobbes wrote: post #7

12 notes tuned in equal temperament is a workable compromise between musical expressiveness, harmonic ratio accuracy, readability, and finger precision. It's also an established standard, which is a huge deal because it means you have access to a huge established repertoire. A 31-TET acoustic piano would be huge, extremely complicated, and probably unplayable. Smaller instruments mostly just aren't practical. In theo…

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... .

It's still twelve notes.
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