Temperaments (equal or otherwise)

Edited: January 16, 2019, 7:41 AM · On the music theory book thread someone talks of the obscurity of books on temperaments. But being new to string instruments, I am curious.
On a piano ET is achieved by the fifths being a little flat and the thirds a little sharp, yet string instruments tune in perfect (3/2) fifths. That immediately puts you out of tune with a piano accompaniment, doesn't it, unless you tune your 4 strings to the piano's notes? And then those perfect fifths make it tricky to intonate the different scales that employ those open strings. Someone asked about warming up a while back, and at the moment, I find my warming up consists of simple scales finding the correct ET intonation on those JI strings. It probably becomes second nature. Or is it possible that you have to give it thought now and then?

Replies (23)

January 16, 2019, 7:54 AM · I'm sure we've had thread on this before!

An advanced violinist needs to be able to play in tune in equal temperament, just intonation and probably Pythagorean as the situation requires.

Some people pick this up by instinct, some find it useful to think about that temperament a particular passage requires. (At the start of Bach Partita 1, for instance there is a b-flat that has to be Just for the opening chord then in quite a different place for the scale passage a few notes later).

Reading books about the historical development of temperament is doubtless fascinating for the temperament afficionado, but quite far removed from anything you need to know to actually play, unless you are playing with a harpsichordist who has set up their instrument to exactly mimic how Corelli had his on May 4th 1743 between 7pm and 9pm, in which case it's polite to pretend to share their interest.... ;)

Edited: January 16, 2019, 8:05 AM · True, equal temperament does not fall "naturally" on the ear. And it may be best to tune your A and G strings to the piano you play music with - especially if the music you will play together includes an open G string, although the difference between Gs tuned in equal and just temperaments is still quite small and undetectable by most people. For violists and cellists directly matching their lowest (C) strings to the piano is important. According to their former cellist, David Finckel, the Emerson String Quartet tuned their instruments to tuners rather than in "perfect" fifths. It avoided any related arguments.

To match the intonation of an accompanying equal-tempered instrument requires only the slightest wiggle of a finger. Vibrato will easily cover it. In most cases a 1% to 2% difference in the spacing of the fingers for half-steps is all it takes. You use your ears.
If you have an accurate smart-phone tuner you can see that it is virtually impossible to keep a note this constant.

The problem may raise it's "head's ugliest qualities" when playing double stops of more than 0.2 seconds (or so) duration with a poorly conceived equal-temperament accompaniment. Playing thirds is especially problematic, because they sound terrible in equal temperament. This problem is one the composer should have avoided!

But a little (or a "lotta") vibrato covers an amazing amount of intonation slop - including this. I hope to live long enough to find some authoritative source on how string-instrument vibrato interacts with our hearing mechanisms.

January 16, 2019, 8:16 AM · Chris, like all forums, most threads will be repeated often. I was criticised a few months back for bumping a two-week-old thread and told I should have started another, lol!
Edited: January 16, 2019, 3:00 PM · The Bach Partita example that Chris mentioned is here:

Threads are repeated often, yes. But some of these things have been very thoroughly explored in the past.

My own impression of the issue of different temperaments is as follows.

The first thing you have to do is learn to play so that the violin is in tune with itself. That's what Sassmanshaus calls the Pythagorean intonation (basic passage playing -- most of what we do) and Just intonation (adjustments for double stops, mainly for thirds and sixths).

That means being able to hear it, and being able to put your fingers in the right locations reliably all up and down the fingerboard. It's hard enough to do without worrying about whether you're in perfect tune with a piano. 99% of listeners will NEVER notice if you're playing in a different temperament system relative to the piano and even then only on long notes like the open G at the start of the Bruch Cto No. 1.

If you get to the level where you can play Solo Bach in good tune, then and only then will you have the skill to adjust to other temperaments anyway, because the adjustment between Pythagorean and Equal temperaments is even more subtle than the difference between Pythagorean and Just intonation. So in a sense, there is really no point worrying about Equal Temperament, except in the case of the occasional long note when there is the same note in the piano score. Just tune your violin in "perfect" fifths and follow the advice of Sassmanshaus which is the time-tested traditional way.

January 16, 2019, 11:03 AM · The answer to the apparent conflict between the piano and most other instruments is.....
Don't worry about it. You can't solve it.

Just think: in a piano concerto, what other instruments in the orchestra can try to match the piano? They can't, and don't try. Matching one or two strings is a fool's errand. So, sure, if you know you have to sit on an open G for two bars, try tuning it to the piano. But you won't match the piano's C because it'll be wide.
There's no way to win. If you did match the C of the piano, it won't resonate properly with the violin itself, and simply sound out of tune. Just like if you try to temper any 3rd finger note--G, D, A in first position--you may match the piano, but they will just sound out of tune.

Tune to 440, and then play in tune with yourself.

January 18, 2019, 8:41 AM · Temperaments are for accommodating the inflexibility of fixed pitch instruments (keyboards and frets, mostly). All other instruments have the ability to adjust the pitch according to context, and temperament is an irrelevant concept for them. The pitch of every note in a flexible system depends only on the context, the intent, the movement that's intended to be expressed, not a rule.
Edited: January 18, 2019, 12:37 PM · For keyboards:
Pythagorean: pure fifths and nasty thirds and sixths. Harsh. Tight semitones.
Equal: bearable fifths and slightly less nasty thirds. Useful.
Meantone: a few pure thirds, a few awful ones, and lousy fifths. Sweet and sour! Fat semitones.
Just intonation: a pipe-dream, we would need up to 5 versions of each note! (53 20-cent "average" commas per octave)

I feel we have to "build" our tuning in strong true fifths, and "indulge" in sweet pure thirds and sixths when we can.
In a long held note in a slow movement of a string quartet, I have spontaneously modified this note as the surrounding harmonies change. A comma in first position is a good 3 mm along the string, wider than my vibrato..

January 19, 2019, 11:16 AM · Adrian, you're indulging in terms and concepts that most people on this forum won't understand.

String players are simply in a state of constant adjustment to those around them, always triangulating. You listen to your stand partner, the stand in front and in back, the other string sections, the woodwinds, and trying to resolve with what your instrument needs to be in tune. You don't think in "Pythagorean" this or "Just" that or "commas,"--you just try to fit in. Each string player is like a kayak in a river, attempting to mostly stay somewhere in the middle and not get trapped in a side eddy.

January 19, 2019, 12:33 PM · Scott, of course we don't think "Pythogorean" etc. while we play, but these terms occur in discussions and documents, and I was trying to offer true, but brief, descriptions. If we are attentive to minute shifts in pitch while practicing alone, we will be better able to navigate our kayak in the presence of others!
January 19, 2019, 1:28 PM · The topic comes up frequently. The limit of pitch discernment for the trained musician is reported to be 5-6 cents. A cellist or violist that tunes to the piano A does not notice the pitch difference on the other strings until the C-string, 6 cents different, and might tune the C up a little, depending on the key. My approach to it is that there are three systems of intonation in modern western music: Equal-tempered, piano style tuning, which is good enough most of time. Horizontal/ Melodic/Pythagorian tuning, and Vertical/Chordal/Just intonation. In practice, each note is a cluster of three spots, +/- 10 cents, only 1 mm apart or less (!), high-neutral-low. You tune to the context. Just being aware of it helps. As long as you don't bend a note in the wrong direction you are OK. And - a good vibrato is wider than that. Vibrato covers a multitude of sins.
January 19, 2019, 7:15 PM · Adrian's summary on this really difficult subject of temperaments is really succinct and nicely done I think!

I would say, Andrew, I would advice you to always know which note you're in the chord and try to play in pure intervals against it unless the situation creates more complications.

How you tune your violin against piano really depends on context. You would notice that some people prefer tuning to a D minor chord from the piano — that is to give you a sense of how tight that fifth is and how you would tune strategically. If your piece is in D minor, it would be wise to have your D string in tune with the piano, sacrificing the pure fifth between D and A strings.

In reality, the difference between the fifth in EQ and JI are not terribly discernable, especially for repertoire (18th–present) most people play. Now if you're playing 16th century consort music, your choice of temperaments would have a more obvious implication...and that will be for another discussion.

January 20, 2019, 3:26 AM · I'm getting tendinitis in my right index finger from scrolling posts like that on my old screen!
January 20, 2019, 10:33 AM · For those with a great interest in the development of equal temperament, I highly recommend the book Temperament by Stuart Isaacoff: https://www.amazon.com/Temperament-Became-Battleground-Western-Civilization/dp/0375703306/ref=sr_1_1?s=books&ie=UTF8&qid=1548001874&sr=1-1&keywords=temperament+isacoff. One thing that fascinated me is that many great thinkers during the relevant period got involved in the issue, including people like Sir Isaac Newton.
January 20, 2019, 11:59 AM · "Great point about relative "perfect pitch" being more essential to quality musicianship than whatever else one might be able to muster up."

We speak of perfect pitch and relative pitch as if they were the two sole types of pitch sensitivity. But on the violin, they are not. There is a third, and (possibly) more subtle type which must be mastered to play in tune: Timbral pitch. As we advance on the violin (a select few hear it early on), we listen to timbre--the very specific mix of overtones--to tune find the pitch. The major third above the open string has a very specific mix of overtones, as does the minor 3rd. So does every other note on the violin. They are not homogeneous in timbre. Yes, you can temper F# a little up to G, but there is a timbral limit. This is why trying to match pitch with a piano is usually a waste of time: YOU will sound out of tune with yourself.

As I've pointed out in previous posts for those endeavoring to play in tune with the piano:
-who tuned the piano? Are they skilled and/or experienced? Maybe they learned to tune poorly 30 years ago and never improved, but happen to dominate the local market.
-how was the piano tuned--by ear, or by software?
-If by ear, how wide did the tuner make the octaves? What partials were used to tune?
-If by software, what settings were used? Wide, medium or narrow octaves?
-How long has it been since the piano was tuned? Pianos change differently in different seasons, sometimes with the bass going sharp and the high treble going flat. The piano may have been well-tuned in the morning, and may fall flat with the stage lights on. I tuned a piano on stage with the stage doors wide-open as equipment was loaded in. Cold or hot air was flooding in as I tuned (can't remember which). It was changing as I tuned it.
-Many pianos, in the upper range, where the violin is playing, have pretty weird pitch changes on many notes: for example, the note can be in tune on the immediate attack, and fall flat on the decay by several cents. Or go sharp after the attack, then swing flat. Try to tune with THAT...
--how big is the piano? Different size pianos may be tuned with differing octave widths. It's almost impossible, for example, to tune a 6-foot piano with a 9-foot concert instrument.

Here's my point: it's not simply playing in equal temperament. It's a clusterf#ck of factors and circumstances.

Things are not as simple as they seem. Especially equal temperament.

January 21, 2019, 12:31 PM · In that long post David M. mentioned "leading tones" My opinion is that that concept should be left in the functional harmony books and Not applied to intonation. "Leading tone intonation" aka "expressive intonation" sometimes, definitely not always, causes pitches that do not fit well into the chords; 1/2 steps too close, minor thirds too narrow, major thirds too wide. Violists and second violins in good string quartets learn to bend the notes a little in different directions. I have had some success in teaching lower level students how to play the chromatic scale (there is only one!) better in tune; alternate big and small half-steps; half-steps on the same finger wide, half-steps on adjacent fingers tight. This is partly an illusion, it compensates for the natural tendency to play out of tune. When to use neutral, tempered intonation ? : when playing with a piano, non-tonal musics, the fast chromatic scale, whole-tone scale, the two ambiguous, symetrical chords: diminished chord, augmented chord.
Edited: January 21, 2019, 8:55 PM · continued-- by "natural tendency to play out of tune" I meant physical, anatomic. If you ask a day one beginner to place four fingers on the fingerboard where they are most comfortable, those notes will be out of tune. We practice our scales, arpeggios, double-stops, to train our fingers to correctly measure the distance between the notes, the interval distances. --- Theory is not fantasy, but should be a logical, mathematical, model of what we observe in nature. The frequency of air pressure differences is real, while sound is how our brain interprets them. The analogy with light is : color is how our brain interprets small differences in wave-length.
January 21, 2019, 6:44 PM · I like to tune a bit sharper than the piano in most cases. Makes the violin brighter.

I find there are rarely any problems with intonation. Where I unison with the piano, I can adjust my intonation.

January 21, 2019, 9:31 PM · Or just...sharper.
January 21, 2019, 11:06 PM · Sometimes I get the impression that if only one can work out the difference between ET and JI, then we are 99% there : )
Edited: January 22, 2019, 3:18 AM · Practical example (from a workshop on a C major quartet):

1) Tune the quartet in pure fifths: PT
2) On a C/G drone, lower the E's for a pure third: JI.
A/E is atrocious.
3) Tune A to the new E.
D/A is atrocious. Etc.
4) Go back to 2) and try to spread the shrinking fifths equally: Meantone (since the D is halfway between C and the JI E).

If we start by tuning to the piano (ET) the result is frankly similar.

January 22, 2019, 10:37 AM · "ometimes I get the impression that if only one can work out the difference between ET and JI, then we are 99% there : )"

The differences are already known. I'm not sure what "there" is though.

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