RE: VFX tuning

I wrote:

>>3. Interpolating often produces strange results. It appears to insist that

>>all steps be exactly the same number of cents, and takes the liberty of
>>changing one of your endpoint pitches to make this possible. Often, the
>>resulting interpolation is backwards, decreasing in pitch rather than
>>increasing as you go up the keyboard, with one huge step from an extremely

>>low note to an extremely high note in the middle. The order in which you
>>specify the endpoints does not seem to matter.

Steve Curtin wrote:

>I hadn't looked at interpolation that closely but I had tried it out with
>many of the standard ETs such as 19 etc. Can you give a specific case for
>the backwards interpolation?

I tried mapping the Bohlen-Pierce scale, where a minor ninth on the keyboard
becomes a perfect twelfth (and 2 cents) acoustically. It took many attempts
on different parts of the keyboard before I could get a "forwards"
interpolation, and then extrapolate.

768 tones/octave is good enough for my purposes. I tried a circulating
temperament, where the circle of fifths was nominally adjusted by -3, -2,
-1, 0, +1, +2, +3, +2, +1, 0, -1, -2 cents. F# was the most dissonant major
chord, as expected, but B-flat, rather than C, was the most consonant. I
don't think there would be much of an audible difference for music that goes
by at a reasonable pace, so I'm not going to complain. But if there is a
systematic way of getting better results, I'd like to know about it.


Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl
with SMTP-OpenVMS via TCP/IP; Tue, 23 Jul 1996 17:09 +0100
Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI)
for id IAA08425; Tue, 23 Jul 1996 08:09:18 -0700
Date: Tue, 23 Jul 1996 08:09:18 -0700
Message-Id: <90960723150509/0005695065PK3EM@MCIMAIL.COM>
Errors-To: madole@ella.mills.edu
Reply-To: tuning@eartha.mills.edu
Originator: tuning@eartha.mills.edu
Sender: tuning@eartha.mills.edu