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There are several other temperaments like 19-TET and 31-TET, but almost all modern music uses 12-TET. Why aren't the two former used more often?

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    12-tone equal temperament isn't as common as you think. It's fairly easy to find examples of major thirds tuned to a ratio of 5:4, which is basically 10/31 of an octave. Of course these people aren't using 31-tone equal temperament either; they're just not using any equal temperament.
    – phoog
    Dec 10, 2023 at 23:42
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    12-TET is more common only in Western music, and only when "forced" to use fixed tuning. Even in Western classical music (but not only), musicians fix tuning of individual notes based on many aspects, and sometimes they also do it for fixed pitch instruments. Still, most of Western music is based on the "simpler" 12-TET, which may not be always "fully consonant", but is also easier and simpler to play and to listen to: our brains are quite adaptable, and tend to simplicity, unless educated to do otherwise. That's one reason for which pentatonic scales are more common in popular/folk music. Dec 11, 2023 at 3:21
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    Instruments such as clarinets also use out-of-tune (read: not 12TET) notes as more convenient notes to use in trills (note that the alternate fingerings for the same note on a clarinet often produce notes several cents away from each other).
    – Dekkadeci
    Dec 11, 2023 at 8:11
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    @Dekkadeci That has nothing to do with temperament. Those alternate and trill fingerings are usually only used when the notes are too fast for standard fingerings and fast enough that the bad intonation is not noticeable. There are only as few cases where an alternative might be used to for example bring a major third down to just intonation. Mostly the compensation is done by embouchure.
    – PiedPiper
    Dec 11, 2023 at 11:11
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    Non-autotuned vocalists, what temperament do they use? Neurotic, impulsive, phlegmatic? Dec 11, 2023 at 13:48

5 Answers 5

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What would the motivation be? Either you have an instrument with fixed pitches like a piano, and then it is not practical to play in anything other than 12-TET. Or you don't, and then it is more compelling to play in locally converging pure intervals.

19-TET or 31-TET make mainly sense with synthesized music, and even then many synthesizers use the 12-TET based MIDI or a piano keyboard as their language of talking about pitch.

That makes for quite an entry threshold that will mainly be crossed by people obsessed with tunings, and that's at best a comparatively small fraction of composers, and not really a major interest for most of the audience.

The good enough is the enemy of the better, and 12-TET is good enough for most. And those not satisfied with it will more often than not rather lean towards well-tempered tunings than equally tempered ones.

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    It's possible to tune a fixed-pitch instrument to something other than 12-TET, but you need a keyboard layout that supports, e.g., C# and D♭ having separate keys.
    – dan04
    Dec 11, 2023 at 16:45
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    I think the reason why so many people are like "what's the point?" when asked about alternative tunings is because they haven't actually heard what music, or even basic chords and scales, sound like. The more people are shown the possibilities beyond 12-TET, the more accepting they will be of them. I should also mention that there are isomorphic keyboards that support a whole bunch of different tunings despite being fixed-pitch instruments, although a lot of them right now are only controllers as opposed to something that has everything built in.
    – 000
    Dec 11, 2023 at 18:28
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    @ElEctric I agree, but it's important not to expect people to just fall in love with 31-edo on first contact. Although many will appreciate that a major chord sounds somewhat more pure in it than in 12-edo, this does come at a cost of more complexity (even when using something like the Lumatone), and while this is itself also an opportunity it's not a tradeoff everybody is willing to make. Dec 11, 2023 at 21:18
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    @ElEctric I’ve heard a lot of non-12TET music, and currently I’m borrowing a Bohlen-Pierce clarinet, and I still don’t see (or hear) the point. 31 EDO and others just sound weird. And it’s a big pain and kinda expensive to make using any other system practical. So it seems like going through a lot of trouble for no benefit to me. Dec 31, 2023 at 13:51
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    @leftaroundabout To my ears the improvement of the sonority of a major chord played in 31 EDO on a lumatone is very subtle, while the difference between a melody I like in 12 TET versus a melody I don’t like is huge. So it makes a lot more sense to me to spend the most time and effort making better music in 12 TET over spending a lot of time and effort figuring out how to effectively use a microtonal instrument and/or work with or create a microtonal ensemble for a difference that is barely audible even to my well-trained ears. Dec 31, 2023 at 13:58
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Using an equal temperament makes it practical to transpose music into arbitrary keys without affecting which intervals are consonant and dissonant. When using non-equal termperaments, transposing most pieces of music into at least some keys would result in consonant intervals becoming dissonant, dissonant intervals becoming consonant, or both.

An advantage of 12-TET is that it includes pitches that have perfect 2:1, 4:1, and 8:1 ratios, and almost perfect 3:1 ratios and 6:1 ratios, without needing an excessive number of pitches. The only ratios below 8:1 that are not accurately represented are 5:1 and 7:1. While a 29-tone or 41-tone equal temperament could offer even more accurate 3:1 and 6:1 ratios, subdividing each octave into 29 or 41 pitches would be much more awkward than subdividing into 12.

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    In 29-TET and 41-TET, the major thirds are approximately an 81/64 in ratio while minor thirds are 32/27, making both somewhat dissonant and tense-sounding. 19, 31, and even 43 and 50 are a lot less awkward in comparison since their major and minor thirds are much closer to their just ratios.
    – 000
    Dec 12, 2023 at 3:57
  • @ElEctric: Some temperaments come closer than 12-TET to having a 5:1 ratio available but sacrifice the accuracy of the best available 3:1. Given that the function of the perfect fifth in a chord is usually to sonically blend with the root, while the function of the third is usually to add "color", pushing the perfect fifth from being 0.113% flat to being 0.416% flat would work against that function. Consider an E chord, with a root at 164.81Hz and a fifth at 987.77. A 6x harmonic would be 988.86Hz, yielding a beat of about 1Hz--only noticeable on long notes.
    – supercat
    Dec 12, 2023 at 16:30
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    @ElEctric: I've heard music samples at 19-TET, and to my ear they don't really work, and I think the perfect fifth is the problem. The 12-TET perfect fifth beat frequencies are slow relative to the tempo of most music, and fits with the way that most instruments' sound undulates with time. The 19-TET beat frequencies are much faster.
    – supercat
    Dec 12, 2023 at 16:36
  • Yeah, 19-TET can sound very strange to a lot of people since its intervals are wildly different from what we are used to. I personally think 31-TET would be the optimal alternative tuning for much non-classical music, since the differences between its sound and 12-TET's sound are enough to be noticeable but they aren't so much that it sounds jarring, unlike 19-TET, and the number of notes is still manageable on instruments like guitars.
    – 000
    Dec 12, 2023 at 17:42
  • @ElEctric: The only way I could see 31-TET as being manageable would be if there were a way of easily notating what pitches the staff positions would represent, and how far a note should be displaced from its "staff-position" note. Trying to almost triple the number of frets on a guitar doesn't seem practical to me, though.
    – supercat
    Dec 12, 2023 at 17:44
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  • The harmonic and melodic language is more familiar, and change is difficult to introduce.
  • Instruments are generally designed for 12-TET.
  • There is an enormous body of music that uses microtonality — almost all non-Western music does — but it remains less known in the west, and it doesn't use systems like 19- or 31-TET.
  • For Western music, not much is actually gained by using other temperaments. The music that does use it tends to focus on musical elements other than melody and harmony: timbre, rhythm, individual intervallic sounds.
  • Popular music, in particular, relies on a common musical language to appeal to the largest possible audience. For rock'n'roll and its descendants, that's 12-TET. It's conceivable this could change eventually with the rise of electronic music, but it will be a long time coming.
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    "Instruments are generally designed for 12-TET." This is very much a chicken-and-egg situation, where instruments are generally designed for 12-TET since 12-TET is so popular but 12-TET is so popular since instruments are generally designed for it. I think, in the future, once alternative tunings become more widely known in Western music then we'll see an increasing amount of (some) non-12-TET versions of instruments, like guitars, that used to be mostly 12-TET.
    – 000
    Dec 11, 2023 at 14:37
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It depends on what you listen to. In recent years I discovered how fun it is to play fretless instruments and then I actively searched out music in other temperaments. I am doubtful I would have even heard about them if I hadn't begun playing these instruments myself. So I wouldn't be surprised if it is simply because people do not know about it.

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  • It's very likely that people not knowing about other tunings is the real reason, and this is in turn a result of music education failing to mention them. I'm quite appalled that you and I are almost the only people here who even thought that this was a possibility.
    – 000
    Jan 1 at 3:19
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We have a 12-tone system because no one can find a better number.

If we lost all music, it would return in the same form with the same musical key structure.

In the same way, if we lost standard tuning on guitar, it would come back again because no one can find a better tuning.

There won't be any new tunings on guitar that are more successful.

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  • What is meant by "better"?
    – 000
    Dec 12, 2023 at 2:31
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    This is insulting to most of the world's music, which does not use the 12-TET system, was formed before it, and has lasted for millennia.
    – Aaron
    Dec 12, 2023 at 2:46
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    I would actually concede that there is a good chance that 12-edo would be re-developed anew if all music was lost. But it's also perfectly plausible that for example ¼-comma meantone would hold on for longer and then be gradually replaced by 31-edo (which is better compatible with ¼-comma than 12-edo). - As for guitar tuning, I completely disagree: if standard tuning were forgotten (and all songs written in it) and guitarists had to come up with something from scratch, it would almost certainly be at least slightly different. Dec 12, 2023 at 13:54

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