Question about Just Intonation

May 21, 2011 at 06:22 PM ·

My understanding of just intonation is that it requires one to practice a sort of situational intonation, making each pitch fit within its harmonic context.  Now, if I am playing F sharp in the context of a major third with D, it will need to be low.  But if I add another third under the D and have a B minor chord, then the F sharp will need to be slightly higher in order to make a better fifth with the B.  What do I do when a single pitch changes harmonic context while it is being held or reiterated?  Say, for instance, the F sharp started out as the third of D major and then suddenly became the fifth of B minor? Do I change the pitch as I am playing the note? What if I am called upon to play a (high) E flat harmonized with a G below in a minor sixth, and then the E flat becomes the seventh of a diminished seventh chord built on F sharp? The E flat will then be too high, will it not?

Replies (46)

May 21, 2011 at 10:42 PM ·

the last thing you want in d major is a low f sharp

May 22, 2011 at 02:34 AM ·


In general, you can't really change the pitch of enharmonic notes if they occur closely together. A good example would be in the Scherzo from MIdsummer Night's Dream: 7 after B, there is an F#, but it changes harmonically to a G-flat. I don't thing the pitch of this note should change. It would be pretty obvious.

Notes that are related to open strings are generally not open to negotiation--either they're in tune or they're not, regardless of what the harmony is.

May 22, 2011 at 09:22 PM ·

On the contrary, Ausar, in just intonation the F# in D major should be low, in order to be pure with the D.

May 22, 2011 at 09:53 PM ·

Ausar, the reason for the low F# in D in just intonation is that it is matching one of the important harmonics (the 4th) of the D, which is a low F#.  

Here is a  simple example of this phenomenon using the G string.

First, make sure all the strings are tuned in exact 5ths.  Play the open G, but not too strongly – you don't want to go sharp.  Let it resonate and then play the B on the E-string.  If you adjust that B until it is slightly flat then you will get a pleasing resonance  with the 4th harmonic of the G-string. The resonant "flat" B is in fact slightly flatter than the perfect 5th B on the E-string, which will not resonate with the G harmonic.  

Similarly, if you're playing a G-major chord including the open G and D strings and the B on the A string, you'll get a better resonance if the B is flat enough to resonate with the 4th harmonic of the open G.

I have been told by an orchestral colleague who went on a quartet workshop that it can sometimes be a good idea in a quartet for the cello and viola to tune their C strings a few cents sharp so that the 4th harmonic (an E) resonates with the open Es of the violins. I would guess that the use of this specialized tuning might depend on the key of the work being played. 

Of course, if you're playing in a non-just intonation environment (orchestra etc) an F# that is sharper than the just intonation F# will usually be expected.  

May 22, 2011 at 10:07 PM ·

Another thought ... good intonation is of course very important, but I feel if one delves too deeply into the minute detail of intonation it will be found that its mathematics becomes exceedingly complex, and trying to take this into account could cause other aspects of playing to suffer. Humans aren't digitally programmed intonation devices.

May 22, 2011 at 10:36 PM ·

 i dont know about this 'just' intonation. none of any of the great violinists ex. heifetz, milstein ever used this type of intonation. perfect example is milstein playing the beginning of 3rd movement to brahms concerto. the third d and f sharp are not intune with it self but in tune melodically. The f sharp is really close to the g and the d is perfect with the open d. If milstein were to play the f sharp intune with the d it would sound really flat. 

In g major  b thats intune to the open g would be terribly flat... it should be intune with the b harmonic on the e string. (the harmonic on b when you play it with 2nd finger in third position)

May 23, 2011 at 12:11 AM ·

May 23, 2011 at 01:20 AM ·

 ha maybe i was a bit to superlative with my last post :)... a better example is hefietz's brahms third movement!. hehe... of course they knew about just or 'perfect' intonation. I'm only saying that intonation should be relative based upon were you are coming from and where you are going. To my ears, in that gershwin recording, hefietz did not only use perfect intonation with his double stops ex. 1:18 the thirds are played melodically. The g and b are not in tune with each other. The b is perfect with the harmonic and the g is perfect with the open string. At 1:07 the major 7th is exactly what it suposed to be.. a major interval. The c and b, a major 7th up, are far apart. 

Another example is in the Loure of the e major partita.... you wouldnt want to play the first double stop with a low g sharp or a high e for that matter 

May 23, 2011 at 02:15 AM ·

yes you would :) 14 cents lower than equal tempered :P

i think there is a lot of gray area once the level of artistry becomes higher in soloists... 

but for quartet playing for example, its absolutely paramount

May 23, 2011 at 02:26 AM ·

 :) it may just be my ears but when i hear heifetz play the loure this is what i understand. The first octave b - b is perfect and in tune with harmonic on e string. The next g sharp is close to the b as it is a MINOR third. Then a perfect f sharp going to a g sharp that is bright but not as bright as the first one. Then the double stop- the e seems to me as perfect with the g-sharp a bit bright. however the next one, the d and f sharp are in tune with each other... it seems the same with milstein


but i totally agree with you on the toscha seidel thing.. thats just incredible what he does!

May 23, 2011 at 03:57 AM ·

May 23, 2011 at 09:10 PM ·

Back to your original question, Michael: I suppose the answer has to be, "It depends."  If you're playing with a piano, you really can't, as the piano's unalterable equal temperament trumps your ability to modify the pitch.  If you are playing with string players, yeah, the pitch should change.  With winds or brass, depends on how good they are!

May 24, 2011 at 06:51 PM ·

There is excellent information (with demonstration) about this online at

May 25, 2011 at 01:03 AM ·

Did Heifetz and the other old-school violinists really understand just intonation? I have my doubts.  I just listened to the Bach G minor sonata which Heifetz recorded in 1934.  Not a single chord is in tune.  On the other hand, Joseph Joachim in 1903 shows a keen understanding of just intonation (listen to how his G minor chord rings!) So what happened in the space of 30 years? Did violinists gradually lose the ability to hear harmonies properly?

May 25, 2011 at 01:42 AM ·

i would recommend you use these ear buds that my guardian buys - they are called Q-Tips (go to

May 25, 2011 at 01:43 AM ·

 otherwise known as cotton swabs

May 25, 2011 at 02:09 PM ·

Thanks, you can keep the cotton swabs for yourself.  I stand by my statement.  I challenge anyone to listen to the Heifetz and tell me his chords are justly tuned.  His G minor chord is too narrow. 

May 25, 2011 at 03:24 PM ·

I have wondered about part of the OP's OP as well, regarding orchestral playing.  If I'm holding a note, and the chord changes underneath it, my dilemma is (a) if I hold to my original pitch, I may sound out of tune with the new chord, but (b) if I change, it will sound like the flute player can't hold a pitch.  If they are separated chords (e.g. the opening of "Scheherazade" or the Midsummer Night's Dream overture), it's easy to play the new E at a slightly different pitch to fit the new chord; but it gets touchier with, for example, the 25-second-long B-flat at the beginning of Beethoven's 4th symphony.  (Also there are I think 3 people holding that B-flat in different octaves, so if we shifted, we would have to do it all at the same time and to the same degree.) Or the moving notes would have to adjust their pitches to the [hopefully] steady drone.  I've played Beethoven #4 a bunch of times but never had a conductor address it.  The answer seems to be "hold the pitch and put up with the discomforts."

May 25, 2011 at 09:24 PM ·

My understanding, Bruce, is that symphony orchestras by and large play in equal temperament rather than just intonation.  So if everyone in the orchestra plays the correct pitches of the equal temperament scale, there shouldn't be any need to make adjustments such as you would make in just intonation. 

May 25, 2011 at 11:21 PM ·

 in the heifetz recording: The first chord is perfect! perfect G on E string and low B flat! the interval B flat to G is a MAJOR sixth! I uphold to my first statement, that hefietz rarely used this 'just' intonation! one does not want to tune sixths and thrids 'justly' or 'perfectly' all the time. It depends where you are going to and where you are comping from. What makes G minor- the b flat, eflat, and f-sharp. Therefore the b flat should be tuned as it is melodically!

May 26, 2011 at 02:13 AM ·

Sassmanschuss has a pretty good take on it, in my opinion.

May 26, 2011 at 02:53 PM ·

Ausar, I think both of us agree that Heifetz did not use just intonation.  Where we disagree is whether he ought to have used just intonation.  Let's look at that opening chord of the Bach.  It is a G minor chord, the key of the piece.  The purpose of the chord is to establish the tonal universe of the sonata, to call the listener to attention with a clear, ringing affirmation of the tonic chord.  The best way to get a chord to ring is to tune it acoustically pure (i.e., "just").  In just intonation, major thirds are narrow and minor thirds wide.  This dictates a fairly wide minor third between G and B flat, and thus a fairly high B flat.  Heifetz does not do this; his B flat is too low, it's either an equal tempered third or even narrower - I'm not sure.  Listen to Joachim in 1903 and the effect is markedly different: he tunes his B flat higher than Heifetz does, and the result is a justly tuned (or close to it), ringing G minor chord. 

Today's historically informed violinists understand this concept, as do many mainstream violinists I've heard; Joachim in 1903 understood it.  Violinists of Heifetz' generation apparently did not understand it (or at any rate Heifetz did not, on the evidence of this one recording).  Why this is, I don't know; it would make an interesting historical study.  Probably the ubiquity of equal temperament in training by the early 20th century had something to do with it, maybe also the increasing use of vibrato.

May 27, 2011 at 01:07 AM ·

 oh 'tis true what you say! sorry if i was arrogant, I just dont like it when people call the intonation of heifetz or milstein under question. You are precisely right! you think he should use just intonation. I think he shouldnt. However, in my opinion, heifetz, milstein etc knew exactly what just intonation was but used it sparingly. When i hear major thirds tune justly, i hate it becuase it does fit melodically with the key. for example, g major deserves a really bright B, therefore when playing the third in that key, the b should be in tune with the scale. If the b is tune justly, it sounds terribly flat and not even in the key of g major, but just an isolated third. one may use jsut intonation probably when playing schoenberg or bartok where the aspects of keys come into quesiton

May 27, 2011 at 01:42 AM ·



Have you ever listened closely to harpsichord playing, tuned in the older meantones?

How do you feel about the chords?


May 27, 2011 at 02:46 AM ·

 the violin is not a harpsichord or a piano for that matter! never should one play the violin with piano intonation

May 27, 2011 at 03:15 AM ·

Hey Ausar, I didn't say or imply any such thing. Please answer the question.

May 27, 2011 at 03:57 PM ·

 The whole question of temperament is of limited utility to non-fixed pitch players, i.e. all orchestral instruments except harp and percussion. In reality, we are neither obliged to nor, in 99% of cases, able to produce unvarying fixed representations of each pitch class within a piece. While grasping the basic options available-- ET, just, various meantones, expressive, etc-- is necessary and helpful, it is my opinion that clinging slavishly to ET or expressive concepts of intervals at the expense of vertical intonation with other players is a grave error. 

Bruce, they ought to be tuning to you-- you were there first! But if they don't, and it really is a long note, seems to me like you should adjust. Just my two cents.  

May 29, 2011 at 06:58 PM ·

I want to say that I'm gratified to have been able to start an extensive discussion about subtleties of tuning, a subject not very widely discussed or taught, and often seemingly ignored.  As anyone who reads this thread can see, there are different schools of thought about this topic, but it I think it's important that we violinists at least get every side of the issue on the table for discussion.  We can't afford to ignore an issue that is connected to the very heart of our instrument and its resonance. 

May 30, 2011 at 10:57 AM ·


Congratulations, you have basically claimed that you know more about intonation than possibly the greatest musician of all time. Very realistic claim! The discussion reaches a low point.


harpsichord sounds wonderful, because it uses the mean-tone intonation (its basically just intonation, but meant to play just in only certain keys, sacrificing others that were not really used at that time).  after listening to harpsichord, piano just sounds really out of tune... :) I think it was Boulez who dramatically said he hates listening to piano because it's just so out of tune naturally.

May 30, 2011 at 05:41 PM ·

1) I think the pertinent question is do you think Heifetz understood intonation, based on the empirical evidence of his playing? Simply sweeping the question under the rug because of preconceived notions of his expertise won't do.  

2) I don't know if Heifetz was the greatest musician of all time (nor do I know how one could possibly make such a judgement, given that the vast majority of musicians who have ever lived are not preserved on record).  But more relevant than whether I know more than Heifetz is whether Joachim knew more than Heifetz, which was one major theme of my posts. 

3) I agree with your statements about harpsichord tuning.  Most old harpsichord temperaments preserve elements of just intonation in the simpler keys, while the "out of tuneness" that occurs in the more remote keys can have an expressive appeal of its own. 

May 30, 2011 at 09:16 PM ·

For a violin duet written in 31 tones equal temperament (by Dutch composer Henk Badings) you could go here. Track 5. I got used to it immediately. Track 7 is interesting too.

May 30, 2011 at 09:18 PM ·

 you're right michael, heifetz did not understand intonation.

May 30, 2011 at 09:25 PM ·

DK, I don't know if Heifetz understood intonation, but he certainly practiced it. Have you heard his Vitali Chaconne, with organ accompaniment, on Youtube? If you haven't, do give it a listen: it's priceless. I don't care which system of intonation he uses.

May 30, 2011 at 11:01 PM ·

 i never claimed any such

May 30, 2011 at 11:07 PM ·

 how can you guys say heifetz does not understand inotnation!!!!

May 31, 2011 at 01:03 AM ·

Ausar, how old are you?

Michael: The greatest musician of all time might be Keith Richards :-)

May 31, 2011 at 01:27 AM ·


May 31, 2011 at 08:37 AM ·

i was being sarcastic. of course heifetz understands intonation. ridiculous to even discuss what heifetz understands and doesn't understand. his playing is beyond intonation systems.

bill, keith richards might not only be the greatest musician, but the last musician. that guy is invulnerable.  When the world ends, its going to be him and 3 cockroaches left, and he'll say to one of them "you know, i smoked your uncle"

May 31, 2011 at 10:52 AM ·

Your discussion about intonation interested me, so I listened to the Vitali Chaconne of three violinist for 2 minutes each due to time constraint.

I listened first to Heifitz and because to my ears (a hook for abuse) he sounds out of tune, I put the electronic tuner next to the loudspeaker. He was all all over the place on most of the notes and it confirmed my suspicion. The man probably plays on gut feeling (no pun intended).

Oistrakh was better but it seems that his violin was tuned slightly lower than 440, but he also was not always consistant.

Then I listened to Sarah Chang, and  in the intonation game she  leaves them for dead. She has incredible intonation on almost all her notes.

So my conclusion is, start to listen to the modern players. As in the sporting field the old records has long ago been surpassed. 

May 31, 2011 at 01:52 PM ·

(-: Keith Richards--Rocks! :-)


...and so once again, I come back to what I said before: there are not 12 fixed frequencies to the octave. If you use a chromatic tuner to check the intonation of players, you are merely checking them against 12TET. Violin is an infinity instrument and there is absolutely NO LAW requiring music to fall into a strict intonation system. Intonation is RELATIVE. Intonation is part of musical EXPRESSION.

If we look at classical music as if it were akin to sports records, we lose everything that is worthwhile. If the performance of perfection is all that matters, then use a computer and samples--that is surely better than Heifetz. Or Oistrakh (either of them).

As for the Harpsichord, I brought it up precisely because of Ausar's claim that the chord must have a high third to "sound right." Well, that ain't the case if you are playing violin with a harpsichord. If the harpsichord is playing in its home key, the major third will be closer to Just than is the case wit ha piano--and considerably closer than a Pythagorean 3rd. Remember that Equal temperament puts a major third in a compromise position--in between the high third of Pythagorean, and the low third of Just.  Depending on the period of the music, the harpsichord might be tuned to 1/6 mean tone, or qtr-comma meantone, or to some other mean tone or a well temperament etc--not to Just. Meantone has a pure third, but the 5ths are messed with (1/4 or 1/6th of the diatonic comma at a time, per key....I am simplifying here). If you play the harpsichord in a distant key, it will sound wildly out of tune.

I think it is worth noting that violinists find themselves playing along with many different sorts of fixed-pitch instruments as well as with purely fretless ensembles. You cannot position yourself didactically in one "correct" way of doing things, because these situations call for different ways of doing things.

May 31, 2011 at 11:01 PM ·

someone should tune a piano like a harpsichord, and then play some baroque/classical sonatas. theres a new best selling recording, no? imagine how nice it would sound if the chords are so much more in tune...

May 31, 2011 at 11:21 PM ·

Listening to old recordings of the Vitali chaconne is an absurd way to try to judge different players' intonation, as the organ accompanying the violin is a fixed pitch instrument and the violinist must accomodate its temperament.  Depending on the age of the organ, it may be tuned in any of a number of temperaments.

Even Keith plays a fixed-pitch instrument, so he is probably a little out of the loop on intonation..

June 1, 2011 at 02:46 AM ·

Haha. guitars aren't fixed pitch, but they ain't infinity either-they have string bend and string push :-)

On the idea of pianos being tuned to a meantone: I was once lucky enough to have the chance to ask Dr. Rephann about that--he said that pianos do not respond well to meantone. I didn't discuss long enough to learn why, but he knows his harpsichords and his pianos.

June 1, 2011 at 05:48 PM ·

Fortepianos are rather frequently tuned variously unequally, including in meantone; it works great. 

June 1, 2011 at 09:29 PM ·

A long time ago I read about the reason why a piano does not sound too much out of tune, even though it is. According to the book, a physics textbook, the harmonics one hears depend on the spot where the hammer hits the string. If that spot corresponds with a node in a certain harmonic vibration of the string, that harmonic will be (nearly) absent from the sound. In 12TET, thirds are not pretty, so it would make sense to hit the string at 1/5 of its length, to eliminate the fifth harmonic. In 1/4 comma meantone, thirds are sweet and beautiful, but fifths are not, so the problems of that tuning method become more noticeable on a piano optimized for 12TET.

If you know more about this, please comment.

June 4, 2011 at 09:29 PM ·

One of the things you learn if you study baroque violin is that you absolutely must tune to just intervals in order to maximize the resonance of the instrument, as a baroque violin doesn't have as much power of projection as a modern violin.  Nevertheless, I believe the basic principle should be the same when playing a modern violin: one has to make the instrument ring.  Heifetz lived at a time when the older ideal of violin sound based on pure resonance was giving way to an ideal based on powerfully projected sound (aided by vibrato), and it seems to me that the loss of just intonation (obvious when you compare Joachim's playing with Heifetz') is tied in with this change.   

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