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If I have not mistaken, if I tune using a chromatic tuner or a piano, I will be tuning my violin under an equal temperament. If I tune my A to 440 and play double open strings and listen, eliminating 'flutter' or dissonance (in other words, playing perfect fifths), the D and G I believe will be sharper than that in equal temperament while the E will be flatter. What temperament am I tuning under this method, Pythagorean, Just, or some other temperament?
Also, by how many cents do the notes usually vary in this tuning system compared to those in equal temperament?
PS: I always tune my violin like this (tune the A to 440 then tune the others by playing perfect fifths and listen) but I want to know more about it.
PSS: I always see professionals tune like this but they always use small up-bows. I can only tune like this using long bow strokes (this serves as a good warm-up too, I might add). Is there any drawback to this?
Based on the ever so reliable wikipedia, the just perfect fifth is used under this system.
If I tune my A to 440 and play double open strings and listen, eliminating 'flutter' or dissonance (in other words, playing perfect fifths), the D and G I believe will be sharper than that in equal temperament while the E will be flatter.
No, the opposite is true.
Under either Just or Pythagorean tuning, the pitches in a fifth are in the ratio 3:2, that is, exactly 1.5. Under equal temperament, they are in the ratio of the twelfth root of two raised to the seventh power, approximately 1.4983071. So a Just or Pythagorean fifth is a little bigger than an equal fifth.
That means that under Just or Pythagorean tuning, the D and G strings will be tuned farther from A, therefore flatter, and the E string will be tuned farther from A and sharper, than under equal temperament.
When A strings are tuned the same, the G string will be about 4 cents flatter, the D string 2 cents flatter, and the E string 2 cents sharper than under equal temperament.
Electronic tuners are usually set up for equal temperament, but it's a matter of software to set them up for Just or Pythagorean tuning.