PERFECT FIFTHS VERSUS AN
EQUAL TEMPERED KEYBOARD
Because a keyboard is tuned in equal-tempered intervals, where
each minor second is equal to the twelfth root of two, a so-called
perfect fifth on a keyboard is actually 2 to the (7/12) power, a bit
smaller than a perfect fifth that is a ratio of 3:2. So, if you
tune your instrument's A to a keyboard and then tune in perfect fifths,
your notes that are lower in the circle of fifths, like D, G and C,
will be too low for the corresponding notes on the keyboard.
To 'temper' your tuning, you can play a chord on the keyboard
that contains notes from various points around the circle of fifths,
and then compare each of your strings to see if they are a close enough
fit. My old violin prof liked a chord made of B, D, F and A.