The
amount by which a string is shortened in order to produce a sharp
is equal to its vibrating length divided by 17.8, but in practice
this factor is regarded as 18. Banjo, guitar and mandoline frets are
spaced in this way.
So
now, I am afraid, you have to do some arithmetic. If you find mathematical
division a bit tedious, you can multiply the vibrating lengths by
0.0555 which gives the same result and is a great deal faster. The
results of your calculations will give you the distances beneath the
bridge pins where tuning blades should press on the strings in order
to make them sound one semitone higher.
Do check this carefully: I haven't gone into Gildas' figures,
but, even at their fullest adjustment, the semitone levers he put
on my own harp were so sharp that I couldn't use them: they would
have needed repositioning, but I preferred instead to take them
off completely, because I found people laughed when I used them
during a sensitive piece: instead I retune between pieces, and 'suggest'
any chromatic notes which might be missing. I'll write more about
this one day and give examples, and it'll get higher priority if
you let me know you're
interested.
