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I have recently learnt about different tuning methods, and 12-tone equal temperament is a very well-designed compromise. However, are there usage scenarios where it's better to use just intonation compared to 12-tone equal temperament? How can I attempt to do so? (My primary instrument is piano, if that's relevant.)

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    You would need an instrument that did not explicitly have discrete tuning, like a piano or fretted guitar. So anything from the violin family is possible. Some would say Just is always appropriate and 12TET is meh. – user50691 Nov 28 '20 at 3:19
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    A cappella singing is one example – Todd Wilcox Nov 28 '20 at 8:34
  • My electric piano will do let you play with a variety of temperaments (and it isn't an especially up-market one) so looking into an electric piano that can do it is probably the easiest way of trying then out. If you own one then read the manual - maybe it can? – DavidW Nov 28 '20 at 20:42
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    @DavidW a keyboard can't really be used in just intonation, though, unless you limit yourself to a small number of chords (like three or four). True just intonation requires constant adjustment of the tuning of certain notes, which is not possible with a keyboard. Lots of people say that "just intonation makes the keyboard sound best in one key," but even in only one key you either have some chords that are out of tune or you have to make compromises in the tuning, at which point you no longer have just intonation but some temperament. – phoog Nov 28 '20 at 23:17
  • If you are using a MIDI instrument you can use Scala, Mutabor or zynaddsubfx for various tuning experiments. Scala provides high-end tools for tuning constructions, Mutabor is focused on dynamic tunings and zynaddsubfx is a synthesizer with tuning support. – Tobias Schlemmer Nov 30 '20 at 13:57
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Just about any time instruments are in use which can (and do) play using JI. So, if instruments such as guitar, piano, organ are part of the ensemble, it's going to be 12tet as the order of the day.

Using instruments such as those from the violin family, trombones and obviously voices, all of which can play those notes which sound more in tune using JI will produce a more harmonious sound particularly together, compared with 12tet.

It seems that they will naturally stray to JI in their playing anyway, which isn't possible for those tuned to 12tet.

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  • For what kind of works are 12TET not appropriate? – Joy Jin Nov 28 '20 at 12:18
  • @JoyJin - 12TET kills some of the joy in listening to those luscious barbershop sevenths in barbershop music. Strict 12TET also ruins electric guitar pitch bends and whammy bar use along with trombone glissandos. – Dekkadeci Nov 28 '20 at 14:08
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    @JoyJin "appropriate" is subjective. I find equal temperament inappropriate for renaissance and baroque music. Some would presumably disagree. – phoog Nov 28 '20 at 15:11
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Actually all amateur bands with instruments that allow some degree of freedom in the tuning, as well as choirs, should use Just Intonation for harmonies.

It is relatively easy to learn to recognise a just tuned chord and to adapt towards just tuning. But its nearly impossible to adapt towards 12-TET. One problem in 12-TET is that the third is somewhat dissonant. Even worse: consonance increases in both directions from a third, on the one side there is the just third, on the other the pythagorean, which both are more consonant than 400ct. So in a larger ensemble, the major third should always be intonated a little bit narrower than in 12-TET. This allows adaption towards one pitch. Otherwise the players may be locked in their consonance optimum and have no easy way to meet in one exact pitch.

There are surprisingly many instruments that allow some realtime tuning. Guitars can bend up, brass instrument are easier to bend down, while bending up is possible to a certain extent. Even woodwind instruments such as recorders allow some flexibilty.

On the other hand: You should always consider playing a piece in the tuning it was composed for. Tuning is nothing about pitch or transposition, it defines the tone colour. For example there exist so called Hamiltonian cycles in the Tonnetz of thirds and fifth, which can be used to visualise major and minor triads. When you play them in the proper well-tempered tuning, the tension rises and drops according to the mistuning of the chords. This gives the phrase an overarching tension dynamics, that is lost in 12-TET (Yes, 12-TET is not really well-tempered).

Tuning clashes can easily produced if the melodies of different voices tell another JI-story than the final harmony. Most choirs find them, when they first come to the corresponding position in the piece. As far as I know there is nobody really knows, how a choir really intonates. It is somehow related to JI, but there are melodic compromises. The latter can be trained to a certain extend, so that pianists tend more towards 12-TET than other instrumentalists that are more dependent on just intonation such as strings (open strings on violins and guitars have an important impact on the sound).

You can try it out yourself: Record a piece in different tunings and listen to them later. The question is always which one has more life and which one has a more sterile atmosphere. So, analytical hearing is not very helpful in this question. And it depends always on the composition which tuning is the best. Some pieces that are made for 12-tet sound mistuned in any other temperament, while others start can give you exciting new insights with another special tuning. It is said (I don't have the reference at hand) that Bach used the wolf as a feature of the tuning in certain compositions.

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    The equal-tempered major third is 400 cents, not 300. – phoog Nov 30 '20 at 23:25
  • thanks @leftaroundabout for the correction. Actually, dissonant has been intentionally preferred over consonant. – Tobias Schlemmer Dec 2 '20 at 14:36

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