When playing a fretless instrument (like violin), what frequency should be used to tune beginning of each key?
I believe that for A major and A minor, 440Hz is the tonic. What will be the frequency of the C in C Major?
How about Bb major? What frequency should be the Bb tonic? Is it like the m2 of the A major scale? Maybe like the 7th of the C Major scale?
Is it tuned according by Just Intonation? Equal Temperament?
I'm rather looking for the formula that enables calculating the tonic of each key, rather than a list which could also be handy.
I'm afraid I wasn't so clear, so let me try to explain again.
In general I'm talking about fretless instruments in standard tuning (A=440Hz). The standard playing on these instruments would be Pythagorean. However, what if you want to play in Bb major. Do you use the Bb of Equal Temperament or what?
UPDATE on Caleb Hines' and leftaroundabout's answers.
This is almost obvious that the low Bb (
465.12Hz) of the Pythagorean C Major (
C=261.63Hz), and even the high A# (
471.47Hz), both make no sense to use as the tonic of Bb major.
So you're right that the open-string A is anyway going to be a bit low for a Pythagorean-expecting ear. Anyway the question is what compromise do we take, is it the Bb of ET (
466.16Hz) or the JI's (
I'm curious what's the standard among orchestral string players (fiddlers should obviously tune to ET).
P.S. I picked Bb as an example, but the question applies to other keys like A# (question solved if answer is ET).