Tuning Curves

[Richard Brekne]

List friends

I have been dinking around with Tune Lab these past couple weeks and
found a really nice and easy way to set up a tuning based almost
exclusively on relating to the 3rd partial of reference notes. Try this
out and tell me what you think.

First you need to be able to use the numerical tuning editor, and the
<<set>> functions to set up a tuning for a given range on the piano. If
you dont know how to do that write me a private note for how to do that.
That being said.....

First, useing the numerical editor, select the 3rd partial for all notes
from D3 to E6.

Then....  tune A4 (1) and D3 (3) to 440 with Tune Labs note selector set
on A4 (1).  That gives you a perfect 3:1 octave 5th.  Then select the
note ( and partial) D3 (3) on Tune Lab and adjust the offset while
playing the note so that the phase display stops. Then use the "Add
current setting to Reference" item under the Edit menu to set this as a
reference note. Ok... then change Tune Labs note selector to A4
(3)....(third partial this time) and adjust the offset again so the
phase display is stopped while  playing A4. Then tune E6 (1) to match.
This gives you another perfect 3:1 octave 5th. Change to note E6 (3) on
the note selector, adjust the offset to stop the phase display and again
use the "Add current setting to Reference" item in the Edit menu.

Ok.. then while the numerical editor is still up,   highlight both E6
(3) and D3 (3) from the Reference points (right side of the numerical
editor) and press SET, which calculates frequencies for all notes
inbetween.

Make sure all these notes use the 3rd partial for the tuning !

This effectively calculates an even curve of 3rd partials for the range
D3 to E6. The resulting octave types are inbetween 6:3's and 4:2's which
in the lowest part of this range results in a very quiet octave, and the
high end yields around a 1.2 bps stretch for the 2:1 and  4:1 octave and
double octave types, while keeping the octave 5th dead on.

You can finish off the top by sticking with the dead on octave 5th
tempered a bit downwards so as to match your ears preferences for the
octave and double octave. This will take you all the way to the last
couple notes as you have the 3rd partial of E6 referenced and stored
from the outset.

You can similarilly handle most of the remaining bass in similar
fashion.

The resulting top end gives quite a clear sound, and appears to give the
best sustain... I got tunelab to show a clear and stable phase display
on C8 today for 6 seconds on a Yamaha C3 grand. It seems what happens is
that if the high note is close enough to the 3rd partial of the octave
5th below... then about the time the high note has lost enough of its
initial power, the 3rd partial of the octave 5th below kicks in to keep
the display from loosing it.

Anyways... give it a try and see what you think.... oh and in case you
are wondering... A4 (1) stays at 440... that is to say 440.004532 or
something like that... grin.

Cheers

RicB

--
Richard Brekne
RPT, N.P.T.F.
Bergen, Norway
mailto:rbrekne@broadpark.no
http://home.broadpark.no/~rbrekne/ricmain.html