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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?

Thanks in advance!

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    Too big for what?
    – phoog
    Apr 19 at 11:27
  • @phoog The accumulated difference. Three times the difference between a just fifth and an equal fifth.
    – Jiu
    Apr 20 at 5:00
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    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.
    – phoog
    Apr 20 at 12:34
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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.

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    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.
    – phoog
    Apr 19 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 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 at 5:46
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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.

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    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 at 0:02
  • @LevelRiverSt but then the fifth in the middle would sound too flat
    – Jiu
    Apr 20 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 at 8:45
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    @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 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.
    – phoog
    Apr 21 at 23:28

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