Another vote for the Turbo-Tuner. "Pencil and paper" gets you close,
but the calculation is for an ideal string (a cousin of the
frictionless elephant). It doesn't account for the string's stiffness
or the increase in tension when you depress it. I keep the Renaissance
lutes in sixth comma meantone and my Turbo-Tuner arrived I used it to
fine tune the position of the frets. The results were pretty
impressive - no fuss, no muss, beautiful sound.
It does take a bit of time to get used to the LED's. It will also make
you appreciate the concept of geared tuners - it's a bit difficult to
make the pattern stand *exactly* still.
As for learning to do it by ear - I think the problem (at least for
me) isn't learning to hear pure (just) intervals, it's learning to
hear slight deviations from just intervals. For most unequal
temperaments the intervals in the "good" keys aren't pure - they're
just closer to pure than ET. If you start tuning pure intervals you'll
make some things better, but other things will be worse and you can
spend an entire evening chasing yourself around the circle of fifths,
touching up things.
As for those who drag in a moral argument about how much more
righteous it is to do it by ear ("*They* didn't have fancy
electronics.") I quote an old Peanuts comic strip where Lucy tries to
take away Linus's blanket by pointing out the that his friends don't
need a security blanket. Linus takes his thumb out of his mouth long
enough to reply "My admiration for all those other well-adjusted
children is boundless."
I don't have that kind of time and I'd rather practice than tune.
Bob
---------------------------------------------------------------------------------------------------------------------------
"The square root of three is two for sufficiently large values of
three."
To get on or off this list see list information at
http://www.cs.dartmouth.edu/~wbc/lute-admin/index.html
