Tune Lab

[Richard Brekne]

List..

Recently bought myself a laptop, and Cyber-Ear just came in the mail a
week ago. Have been having loads of fun with Pianalyser, and in general
getting to know more about Electronic Tuning aids. I had downloaded a
copy of Robert Scotts Tune Lab some time ago, and I have wanted to try
it out. Last night after work I got home and started thinking ... uh
oh... grin.

Any ways, I got to thinking about the twelfth root of two, partials, and
temperament. After a bit of thought, and dinking around with my
calculator (just to make sure I wasn't out in left field with shoulder
pads on), I decided to try the following experiment with Tunelab today.

First, tune A4 to 440, then set the partial to 2 and adjust the offset
till the tuning display stands still, and lock on that. Then tune the
4th partial of A3 to match that. (this much has been suggested before by
another tuner who has a nice tuning procedure for Tune Lab on the net).
After doing this I read and noted frequencies in Hz. of the 4th partials
of both A3 and A4. Dividing the upper by the lower gave me the ratio
between the actual 4th partial of each of these. Taking the 12th root of
this ratio gave me the "rate of growth" for the 4th partials for all
notes between A3 and A4 which would guarantee that they would be equally
distant (as in cents) from one another, given the actual stretch of the
octave.

Starting at the frequency for the 4th partial of A3, I multiplied that
frequency by this "rate of growth" number, to obtain the frequency for
the next notes frequency value for its 4th partial, and repeated this
process for each successive note. Once done, it was easy to set Tune
Labs reference frequency for each note to these resulting values and
then tune each note (partial set at 4 for each note as well.. grin).

The resulting temperament was really really nice. Thirds were very even
indeed. I repeated the whole process for the 5th partial thinking that
if these then were already at the resulting values, then I was
guaranteed that the major thirds were going progressively beat faster
exactly as in a "theoretical" temperament. I had to very slightly adjust
two notes. (less then 0.30 cents). All fourths, fifths, sixths sounded
also very fine indeed.

Shouldn't be to difficult to automate this process for say the first 8
partials really. The user would have to of course decide the octave
stretch first and then both A's would have to be sampled to get the
frequencies for the partials. But its a way of very precisely spacing
the notes (tempering) taking direct regard to the real inharmonicity of
any given piano, for any given stretch, for any set of partials one
decides is best to evenly space.

Perhaps this is kinda like a "well, of course dummy" to some of you out
there.. but I had a good time carrying out the process, from thinking
through the idea to the resulting temperament. And it seems like it
works really well. Took about 40 minutes (long time to temper a piano,
but this was the first time and I fumbled around a bit).

Any ways, thought I'd just throw this one into the mash. Would welcome
any comments. (grin... even ones about football bats... )

Richard Brekne
I.C.P.T.G.  N.P.T.F.
Bergen, Norway