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Some people seem to make the case that having some keys beat more than others (as is in the case in the older well-tempered tuning systems) is a feature not a bug. But on the other hand, the equal tempered tuning system seems completely dominant and rarely even questioned at this point. Historically, why was the change made to equal temperament given that the various keys would lose some of their unique character?

  • 8
    In 2000, Howard Goodall wrote “Big Bangs” to accompany a TV series that covered “the story of five discoveries that changed musical history”. Episode 2 covered Equal Temperance. I do not know if the book is still available, but the episode is available on U-Tube. Search for “Howard Goodall Big Bangs 2 Equal Temperament”. I have not watched the series recently, but I found it fascinating. – Tony Dallimore Feb 17 at 0:11
  • @TonyDallimore I found that episode and watched it. It was great thanks for sharing. Its really nice to know that there is a full TV episode dedicated to this topic. – J. Lenthe Feb 17 at 21:28
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    I've heard that Mozart threatened to kill anyone who played his music in equal temperament! I can't find any serious references, though. If true, it would indicate that equal temperament was known in his time, but was not seen as a clear improvement… – gidds Feb 18 at 10:41
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    Now that you can create instruments in software that can play arbitrary frequencies, it would be nice if people experimented with alternate tunings. – Paul Reiners Feb 19 at 21:29
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Partly to allow the same, diatonic, piece to be played at different pitches as @Tim suggests. But also, I think, because music started getting more tonally adventurous within the SAME piece. When you start wanting to visit (say) the mediant key as well as just the dominant and subdominant, equal temperament is a must.

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Some people seem to make the case that having some keys beat more than others (as is in the case in the older well-tempered tuning systems) is a feature not a bug.

Yes, but I don't think that was ever a major consideration. Originally, all tuning systems just tried to give good approximation to just intonation (JI). At first just for a few neighbouring diatonic keys, which can be done quite easily. But then composers wanted ever more freedom for modulating anywhere, and thus we came to well temperament. That did allow playing in any key with acceptable error to 5-limit JI, but how exactly this error played out was of secondary concern.

Of course...sure enough, Bach, being the grand master of meticulous multiscale[pun intended] thinking, made an art (or science?) out of this effect itself with his Well-Tempered Clavier pieces. But, Bach is Bach, nobody else is. Maybe if he had written a detailed explicit treatise on how to use each of the keys in well temperament, that would have stayed longer. But most composers just took WT as, well, basically an approximation of the approximation that is 12-edo: they jumped to the opportunity of using any key they wanted and still getting an approximation to JI. And then it was the obvious next step to make that approximation literally the same regardless of key.

  • Those clavier pieces are easily my favorites. The f-minor one is delicious. – Stian Yttervik Feb 19 at 7:40
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Simply so that any music could be played in any key and it would sound the same. Problem with tuning to another temperament means that pieces sounded particularly good in some keys, and particularly bad in others. And re-tuning often isn't a quick answer - especially on instruments such as piano!

Non-fretted stringed instruments, such as violins, trombones and voices are not really affected by 12tet, and will have a tendency to re-tune certain notes out of 12tet, so they sound 'more in tune'.

So it was more of a 'one size fits all' approach that won over - yes, always a compromise, a slight dumbing down if you like, but far more practical overall.

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As a temperament junkie, I'd just like to humbly add to all the answers above that one way of looking at it is in terms of thirds and fifths: temperaments in Western music tend to be thirdier or fifthier. 12TET is almost as fifthy as it gets, two cents short of just is pretty good and a lucky coincidence of mathematics- but the thirds are pretty far off. 1/4 tone meantone is thirdier but hairier in distant keys. Just intonation further increases quality at the expense of quantity (of nice keys to use). All have their place.

  • Comments are not for extended discussion; this conversation has been moved to chat. – Dom Feb 20 at 4:54
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I thought I didn’t understand your question before I’ve found the other answers voted up.

It seems that you know the different tuning systems and their problems and advantages.

So I thought answering this kind won’t be sufficiently.

Historically, why was the change made to equal temperament given that the various keys would lose some of their unique character.

The old tuning systems have been only useful for some keys on all those instruments that can’t be adjusted/ tuned while playing. So they sounded simply wrong in certain keys.

The unique character was described already by Plato and sustained even after the introduction of the well-tempered tuning system. But I could‘t find a consensus in all ths theories.

0

Well, no one knows for sure, but one of the most important features of equal temperament is that it supports "semitone counting". For example, if I play one note (say D), and then go up 3 semitones and play that note (in this case F), the simple fact that these are 3 semitones apart tells me that this interval will like a JI minor third to within a reasonable error tolerance.

Without equal-temperament, this kind of "semitone counting" doesn't work so well. For example, if I tune my white keys to JI C Major, the interval between D and F turns out not to be a JI minor third (which has a frequency ratio of 6/5). Instead, the interval between D and F ends up being a Pythagorean minor third (which has a frequency ratio of 32/27), and consequently a mild clashing sound will be heard if you play both these notes together.

In some contexts, this clashing sound might actually be desirable, since it will make the resolution of the phrase even more satisfying. But in other contexts, the interval will just seem mistuned, and then the musician is faced with the difficult question of whether to retune the D or the F. Avoiding these kinds of complexities is one of the main factors that slowly led people towards equal temperament.

For what it's worth, my opinion is that now that we have computers that can automate the more technical aspects of microtonal music theory, we really should start exploring non 12-TET music more systematically and ambitiously. And of course, we have electronic keyboards, that can be retuned on the fly virtually instantaneously. It would be a mistake not to exploit these new technologies to escape the limitations of 12-TET.

  • 27:16 is a Pythagorean major sixth. – phoog Feb 18 at 5:20
  • Also, the thirds and sixths of 12-tone equal temperament are closer to Pythagorean than to 5-limit just. – phoog Feb 18 at 6:38
  • @phoog, good catch, I fixed the ratio. – goblin Feb 18 at 7:18
  • @phoog, in regards to your second comment, I'll try to summarize my thoughts with the following observation: there's probably something psychological going on here with the way music is perceived. If you're playing in 5-limit JI C major and you suddenly throw the listener a Pythogorean minor third by playing D and F simultaneously, the listener will probably notice that this is interval sounds a bit strange. But if you're playing in equal temperament C major, the listener is already accustomed to the dissonance level you're using, and they're probably not going to find the interval between... – goblin Feb 18 at 7:26
  • ... D and F problematic, because it's at the same dissonance level as what they're already getting. I think this lends credence to my point that "semitone counting" only really works in equal temperament (or something close to it). So that added simplicity is still there. On a related note, it would be interesting to try to find out if people find the extra 6 cents difference between the 12TET minor and the Pythagorean minor third large enough to have a meaningful preference for the 12TET minor third. A potential confounding factor is that the 12TET minor third will sound better simply... – goblin Feb 18 at 7:29

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