Just Temperament tuning systems

Edited: July 17, 2017, 6:34 AM · What is the difference between just temperament Schugk or Barbour? Under which circumstances would either be used? Also, if you want to calculate just tuning for the E major scale, for example, at what frequency do you put E4? Or should you start with concert A?

Replies (12)

July 17, 2017, 12:17 PM · You're asking something so esoteric and limited in a practical sense that I doubt you'll get many answers, at least on this forum.

You don't "calculate" tunings or frequencies other than A=440 or whatever general reference pitch you want. We often temper notes a little this way or that depending on the context or moment, but who plays a string instrument by "calculating" specific pitches? And even if you calculated the tuning for an E scale, no music stays in one key very long. How would that affect playing in related keys, like B or A? Or E-flat?
(This is why equal temperament won out...)

I could see this question being relevant to a keyboard instrument, but not for the violin. Maybe you could explain your question in a little more detail as to what you're trying to do?

July 17, 2017, 5:05 PM · "What is the difference between just temperament Schugk or Barbour?"



July 17, 2017, 6:57 PM ·
If you wanted your piano or harpsichord tuned according to one of these temperaments, fine. I take the numbers, punch them into my tuning program and voila, you have Schugk or whatever. But I don't see how this applies to string players in the real world.
July 18, 2017, 2:15 AM · Just temperament doesn't really work for more than one measure!
We can make beautiful triads : CEG, GBD, FAC, even ACE, but the A will be comma too low for DFA, which is a pity.

For those who accuse us of self congratulatory nit-picking, a comma is about 1/5 of an equal-tempered semitone, and is about 4mm wide in 1st position: wider than my usual vibrato!

Edited: July 18, 2017, 5:52 AM · A good violin player rarely sticks to equal temperament. Equal temperament just doesn't sound that good, a good violinist uses the intonation that sounds the best to their ear and that is going to be closer to just temperament than equal. The violinist plays the note so it sounds in tune, equal temperament does not sound it tune, just temperament sounds the best, but it depends on the context and sometimes, like with open string, there is no adjustment of intonation possible.

Scott Cole may think he's playing in equal temperament, but I'd bet if you put a tuner on all his notes you'd find he is tempering his scale more just than equal in temperament.

July 18, 2017, 6:44 AM · In practice, we accept what the keyboard or ensemble is doing, but make small ajustments "on the fly" to make certain chords more euphonious.
I have found myself adjusting a long held note as the surrounding harmonies change.
July 18, 2017, 7:35 AM · "Scott Cole may think he's playing in equal temperament, but I'd bet if you put a tuner on all his notes you'd find he is tempering his scale more just than equal in temperament."

Did you read my post? I never claimed to be playing in equal temperament. I'd never advocate a string player try to play in equal temperament. In fact, I'm always correcting students that play wide 6ths, which sound ok on the piano but ugly on the violin.

I just tried to make the point that playing a string instrument by some chart of tuning numbers is impractical.

July 18, 2017, 10:31 AM · Modern practice is to start with A440 and then to temper notes away from the Equal Temperament frequencies depending on context.

In general, melodic lines tend towards wider major thirds, sixths and sevenths than Equal Temperament, a characteristic of Pythagorean tuning. Half steps can be played quite narrow.

Just Temperament has narrower major thirds, sixths and sevenths than Equal Temperament and sounds good for double stops, but rather odd for melodic lines.

For a practical guide to temperaments for the string player, try the following link:


July 18, 2017, 10:46 AM · Just temperament would have perfect thirds which are much wider, not narrower than equal.
July 18, 2017, 12:28 PM · Hi everyone, there is no "just temperament". By definition a temperament tempers with just intonation ratios.

Fixed pitch instruments (keyboards, guitars, etc) use temperaments. You won't come across an accapella choir discussing what temperament they should use. Even though we string players have fixed open strings, we're less "stuck" then keyboard instruments and have much larger degree to adjust. We tune strings in some kind of temperament, but after that it's up to the fingers to get us as close to perfection as we can.

Just Tempered (Schugk) and Just Tempered (Barbour) are names of temperaments. I would love it if someone can explain how the numbers are derived...

I think we can all use some clarification because intonation is such a complicated topic already, we don't need additional incorrect information.

July 18, 2017, 12:31 PM · "Just temperament would have perfect thirds which are much wider, not narrower than equal."

You have to be specific.

In equal temperament, minor 3rds are narrow and major 3rds are wider.

Edited: July 18, 2017, 1:34 PM · Sorry, I had it backwards. A perfect third is 386 cents, and equal one 400 cents that would make an equal third wider than perfect.

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