What frequencies should the violin and viola be tuned to?

Question

I'm using this app to tune my violin, it supports many temperament options.

What I want to do is tune the A string to 440Hz first, then comparing the other strings sympathetically to the adjacent string, E by A, D by A and G by D.

Here are some of the temperaments:

• Equal tempered perfect octave
• Equal tempered perfect fifth
• Just tempered Schugk
• Just tempered Barbour
• Pythagorean
• Pythagorean perfect

Among many others I didn't think are relevant.

Is there any temperament that you can point out and tune perfectly by that so the violin is tuned by perfect fifths to A as explained in the beginning of my question?

What's the standard for tuning a violin in classical music? What's the standard for tuning it when playing it rock/jazz at gigs with piano/keyboard etc.?

Update

I just bought a 5 string violin.
How do I tune the C string, is it relative to the G string (C = 130.37Hz)?
What's the common tuning of the C string among violists and 5-string violinists?

Answer 1

As per the app you were asking, Pythagorean is the temperament you're looking for.

The perfect fifth is the 2:3 frequency ratio (and small rational number frequency ratios are required for the sympathetic vibrations to work). So if your A string is 440Hz, the tuning is as follows:

• E - 660 Hz
• A - 440 Hz
• D - 293.33 Hz
• G - 195.56 Hz
• C - 130.37 Hz

If you tune by ear from A, your tuner app should be able to verify that these are indeed the frequencies you have (to the nearest 0.1Hz or so).

In the Waves tuner for Android, and in its earlier variant called Gstrings, one can select the "Pythagorean" or "Pythagorean A" temperament to match these frequencies precisely.

You may find other numbers on the internet, like 659.26Hz for the E string. Do not trust these numbers. 2:3 is your friend.
These frequencies correspond to equal temperament, which is only sometimes used for the violin.
One may use equal temperament when playing with the piano for example, and even then only if one wants to play lots of open strings.

Disclaimer: I play guitar :)

Answer 2

Standard tuning for solo violin in classical music is just intonation.

Tune the A string and, from there, tune the other strings with just-intonated perfect fifths. Some times, as a compromise you may need to tune the violin temperate, for example when you need to play many open strings in duo/ensemble with a instrument not capable of just-intonation. Otherwise the standard way is just intonation.

The violin is very responsive to sympathetic resonance. If you play a just-intonated open string G-D it will cause sympathetic resonance in other strings and you will hear a more rich spectrum of sound/overtones. If you tune temperate you don't hear overtones and the sound color of the instrument, as result of overtones, is not so rich.

Note that while the guitar and other modern stringed instruments with fixed frets are tuned in equal temperament, string instruments without frets, such as those of the violin family, are not. The violin, viola, and cello are tuned to beatless just perfect fifths... from this article.

If I tune my open strings temperate the overtones I would get by pressing the string softly (flageolet) will be out of tune! This has to do with how the violin is built. So actually, if I do not tune the open strings with just intonation fifths, I will be creating wrong vibrations, conflict with the natural harmonics that the strings would sympathetic resonate with.

About your question of which to use, I think when tuning open strings in fifths they are actually the same. This example is for the C key and refers the deviation in cents from the temperate system):

Answer 3

You are working with a violin. It has four strings tuned in perfect fifths. Intonation on a violin, which has no frets, is something that you produce with your fingers, not with an electronic measuring device like your tuner. You can produce any kind of intonation or temperament on a violin that you can train your ears and fingers to recognize. You are not limited to twelve exact pitches in an octave. You can slur up or down by any amount, to produce vibrato, or any kind of microtonality.

Various different systems of intonation or temperament, like those found on your electronic tuner, chiefly apply to tuning keyboard instruments like the piano or harpsichord.

Electronic tuners that provide various schemes of intonation are used for "early music", "historically-informed performance" and the like, to tune replicas of "historical" instruments to play music that was composed in the years before the modern system of 12-tone equal temperament came into popularity. Basically that's anything before the beginning of the 20th century, but it applies particularly to any music written before the beginning of the 19th century.

Bach, Handel and Vivaldi did not use modern 12-tone equal temperament like on the modern piano. Today, many people play music written by these composers on modern instruments in 12-tone equal temperament. However, there are some musicians who practice "early music" and "historically-informed performance", and they perform these pieces by these composers using the earlier tuning systems that these composers actually used when they composed the music.

I work for a Baroque chamber orchestra that plays replicas of instruments from circa 1640 to 1790, and they tune to A=415, a half-step lower than the modern system of A=440. They tune their harpsichord and organ to a fractional-comma mean-tone temperament system that only works well in certain keys, and all the other instruments (such as the Baroque violin, viola, cello, viola da gamba, and bass violone) play in tune with the harpsichord or organ. An electronic tuner with alternate historical temperaments is something that this group might conceivably use, although our harpsichordist is so experienced that he can tune his harpsichord to any of the commonly-used historical temperaments entirely by ear, without using any electronics. He starts with a single pitch from one tuning fork and listens carefully and counts the beats of slightly out-of-phase intervals as he tunes the harpsichord.

Answer 4

You want A=440hz if playing modern (post baroque) music; usually A=435 hz if playing baroque or earlier in or close to its original period intonations.

Whether to use the 2/3 relationship also depends upon which intonation system is being used and which key. Pythagorean tuning at 2:3 resonance is "equal temperment" - which should NOT be used if doing original period intonations; only the octaves were perfect doubles and the "perfect 5th" isn't always the pythagorean system's 2/3 relationship.

That said, the 2/3 relationship is particularly well suited for the viol family, due to the 5th/octave pairing harmonics, and the use of harmonics in tuning is, in many cases, closer than the audience can hear, even if it's not perfect on the oscilliscope or tuner...