Just intonation vs Equal temperament

[PaRaDoXu]

If you recorded a part in Just Intonation would you ever try to mix it with other elements that are in Equal temperament?
Is it even possible? Personally I'd just try to use the same fondamental note for everything and see what happens but I'm not sure...

[BertKoor]

Is it even possible?

Sure that is "possible" !

This is a real thing in any orchestra. Bowed string instruments are using just intonation (if they were taught right). Modern Arab orchestras including equal temperament keyboards.

Does that bother you? Do you even notice?

[jamcat]

Just intonation is really only for harmonization. You're going to play the melodic line in Pythagorean or Expressive intonation (with non-fixed pitch instruments.)

Think of it like Pythagorean horizontally, and Just intonation vertically. And the vertical intonation from chord to chord will change dynamically, based on the horizontal intonation of the melodic note that is being harmonized. It's pretty complicated stuff to work out in a MIDI sequencer, but real players with good intonation will do it naturally.

And yes, there may be some fixed pitch equal temperament instrument like piano accompanying as well. Which the other players may compensate for to some degree.

[mjolnir]

how many cents difference are we talking about? isn't it only in quantities of light chorusing/ensemble?

[Ah_Dziz]

I like equal temperament over just intonation. If I want to get very precise with frequencies I get into 24 tone scales with MTS ESP.

[jamcat]

how many cents difference are we talking about? isn't it only in quantities of light chorusing/ensemble?

I assume you’re talking about playing (for example) the 5th scale degree in Equal temperament and Just intonation together in unison?

In that case, yes, there would be just some slight chorusing between these unison notes. In Equal temperament, the E above A440 (root) is 659.255 Hz. In Just intonation it is exactly 660 (3:2 ratio).

But the slightly imperfect ratio in Equal temperament is enough to cause beating between the root and 5th, while there is no beat in Just intonation, just an anodyne placidity.

The difference gets greater as you get away from perfect intervals. For example, in they key of A(440) the major 3rd (C♯) is 554.365 in Equal temperament and 550 (5:4 ratio) in Just intonation, a difference of over 4 cents.

The purpose of Just intonation is to have these perfect and consonant ratios (which are derived from the natural overtone series) in your harmonic structures. But the distance between melodic intervals is going to use Pythagorean tuning, which is based on the circle of (pure) 5ths. It is that relationship—with its large major 3rds and narrow leading tones—that makes melodies their most musical and expressive, while stacking natural overtone ratios makes chords their most sonorous and consonant.

And it is this dynamic intonation, where pitches deviate in frequency based on their function and context, that makes real music sound fluid, organic, and complex. It’s something we’ve lost due to the compromise of fixed, uniform frequencies in Equal temperament.