# Violin tuning, equal temperament or just intonation?

I'm tuning my violin now, by making the fifths on open strings sounds most harmonious. So they are just fifths, a little wider than the equal fifth. But then would the gap between the G and E string be too big?

How do you deal with such problems?

• Too big for what? Apr 19, 2021 at 11:27
• Apr 20, 2021 at 2:32
• @phoog The accumulated difference. Three times the difference between a just fifth and an equal fifth.
– Jiu
Apr 20, 2021 at 5:00
• But that's not my question. You are clarifying the subject of your question, but that's clear: the gap between two pitches. I am asking about the purpose for which that gap might be too big. In other words: the optimum size of that gap depends on the tuning of other instruments you are playing with, on the harmonic context of the music you're playing, and on personal taste. Three just fifths have a ratio of 27:8. A just major thirteenth has a ratio of 10:3. In equal temperament, it's 2^(21/12) or 2^1.75. Any of these is the right size in some context. Apr 20, 2021 at 12:34

Violin tuning is a huge subject. If you google it you will see.

The violin sounds the very best when you tune the strings into actual perfect fifths that means just fifths not equal fifths. It gives the best resonance all over the instrument. So for that reason violinists have a tendency to tune the instrument with just tuning. But it can give problems.

Sometimes when playing chamber music like string quartet the violin players might tune the E a tad flat, either that or the violin player might avoid using an open E and play the E on the A string instead.

Other times the viola and cello players might tune the C a tad sharp, either that or place a finger at the start of the C string in order to make the open C a tad sharper.

Other times those who play an open string decides the intonation and the others need to adjust to that.

You might ask "Why not tune the instruments with equal temperament?". Well as I said the best resonance happens with just tuning. But violin players might adjust their tuning and intonation according to the music they are playing and with whoom they are playing, like small ensemble, big ensemble or playing with piano.

When tuned with just tuning the flats are often played very flat and the sharps very sharp which can be very expressive. But if you play a C sharp in a sustained A major chord you would actually intonate it slightly flat in order to get a well sounding major chord.

Anyway, some violin players might say that with the equal temperament everything is slightly out of tune. But when you play piano music you will realize that it is actually tolerable, which is why music like Chopin is beautiful.

On violin I think you play with a constant toggling between just and equal temperament.

It is common for beginners to adjust their intonation to the notes on the piano.

• I would add that early music specialists usually tune each string to the keyboard when there is a keyboard, because the keyboard's fifths are even narrower than equal temperament, and period techniques rely somewhat more on open strings. Apr 19, 2021 at 13:20
• What do you mean by "best resonance"? The notes sound louder? Or less beatings? Timbre changes? It isn't clear. Apr 19, 2021 at 22:38
• @user1079425 Best resonance means that the ratio of the frequencies is the simple fraction 3/2, instead of the seventh power of the twelveth root of two.
– Jiu
Apr 20, 2021 at 5:46

The difference between a just fifth and a perfect fifth is less than 2 cents. If you're playing solo, 99% of listeners will never notice the difference. If you're playing in an ensemble, 98% will never notice the difference, so long as you adjust your fingerings to play in tune with the other ensemble members.

If the ensemble includes an instrument in equal temperament with inflexible tuning -- like a piano -- then you will want to finger your notes in equal temperament, and you might as well tune to the 5ths on the piano.

If you are playing only with other flexible-tuning instruments -- say, in a string quartet -- this is not an issue. You simply adjust to whatever intonation is agreed upon by the ensemble. String players in thse conditions often tend towards just intonations.

• WIth a 4 string violin, there are three fifths. If you tune the first string to concert pitch, and the rest by just intonation, the last string will be 6 cents out. This can be mitigated by tuning one of the inner strings to concert pitch. Apr 20, 2021 at 0:02
• @LevelRiverSt but then the fifth in the middle would sound too flat
– Jiu
Apr 20, 2021 at 5:30
• @Jiu - as you may have seen, there's no simple solution to this tuning problem. It's ultimately the fault of mathematics: no power of two is also a power of three or five. As soon as you start stacking intervals, then you will get intervals that are not low-integer ratios (consonant). That's life. Apr 20, 2021 at 8:45
• @Jiu you misunderstood me. What I mean is, if you tune G string to concert pitch then tune in just 5ths, your D will be +2 cents, A will be +4 and E will be +6, which WILL be noticeable compared with E on a concert pitch equal tempered instrument like an electronic keyboard. But if you tune D to concert pitch then tune in just 5ths, A will be +2 and E will be +4 cents, which is less noticeable. Of course G will be -2 and (if you have a 5 string) C will be -4 but differences are spread out better. Multiple 2 cent differences add up if you start from one end, but less if you start in the middle. Apr 20, 2021 at 18:34
• @LevelRiverSt "If you tune the first string to concert pitch...": People generally don't do that. "This can be mitigated by tuning one of the inner strings to concert pitch": that's precisely how violins are typically tuned. The pitch reference is usually A. Violists and cellists have to contend with the problem, though, and, more prominently, with the interval between their open C strings and the violinists' open E strings. Apr 21, 2021 at 23:28

The fifth A-E can be tuned just, because the E string is metallic and will go down when you play!

The D string must be tuned to maximum possible height and the same for G string.

The deviations must be very small ones and your ears must accept the difference.

This was about tuning the instrument. I can also talk about how to play the intervals on the strings.

Play the octaves a little bit larger. When one octave is perfect you don't hear the upper tone clearly. After the correction you must be able to distinguish this upper tone clearly.

Major thirds must be larger and minor ones smaller, which mean that major sixths must to be larger and minor ones smaller.

The 4th must to be as large as possible.

The tritone is special interval because there we have TWO just positions. The resulting tone is different when you play C/F# like part of D7, or C/Gb like part of a Ab7 chord. Or, this tritone must be played between these two just positions!

I say all of this as a 75 years old retired violinist from Bulgaria after 27 years in OPN Nice, France.

• When I have looking into things P5 tuning is nice because pythagorean whole tones are placed on same place. The b3 I try to place ~4/9 for pythagorean or ~5/9 for just. The M3 i place 9/9 i.e. precisely on the whole tone for pythagorean and ~8/9 for just. This did not add up with what you wrote so do you have some other 'baseline' you tweak up and down than the one I use ?
– Emil
Mar 21 at 6:31
• I’ve had a go at improving the English in your post, but there are still a few words and phrases that I wasn’t sure about. Mar 24 at 11:05

Tuning is such a complex and fascinating subject yet many students of music can go many years without thinking too much about it.

I'd say there are many professional musicians who haven't thought too much about it.

There is no right tuning system for music. This is hard for many people to hear including myself a few years ago.

There is no perfect tuning system and each one has its advantages and disadvantages. There isn't even a best tuning system for each situation.

Some would suggest with ample evidence that equal temperament is the best tuning system for Western music such as Bach's Well-Tempered Clavier. Yet Well-Tempered Clavier was written for well temperament, not equal temperament.

In this example well temperament provides moments of glorious, locked-in 4th and 5th but also mandates quite out-of-tune intervals in other spots (which are pointed out in some videos).

In Well-Tempered Clavier, an equal temperament would fix these extremely out of tune intervals at the cost of the rest of the music being more out of tune. You would never find the glorious, locked-in sounds of well temperament when using equal temperament.

One tuning system has advantages while another has others. Neither is better. It comes down to preference.

One might imagine that these problems could be solved with electronic music. Each chord could be perfectly tuned in perhaps non-live setting. This, Interesting, does not fix some fundamental problems.

Yes, this situation could fix some problems with tuning such as a pianist playing the same pitches as the string section playing open strings.

If the string section has tuned using a typical just intonation, then the bottom G string will be most different the piano's G3. This could be fixed digitally either in the strings or piano.

However a huge problem arises when taking lines and phrasing into consideration. What if the violins had just played a solo open G right before. The sudden adjustment to pitch would be noticable to even non-musicians.

Some might say, "fix the piano then". But what if the piano had just been playing a descending G major scale. That sudden drop in the anticipated G would also be jarring.

There is no perfect tuning system and no best tuning system for many situations. This is just a fact that any serious musician has to accept.

Equal temperament has been widely accepted due to its versatility yet its limitations are why we will always see discussions about it.

Tuning along with many aspects of composition and performance is a subject that continues to evolve and evoke controversy.

• There's a lot of discussion here without seeming to actually answer the question. The question was "how should I tune my violin." A 428-word answer amounting to "Yeah, that's a complex question" doesn't help the original poster much. Apr 3 at 17:03