source file: mills2.txt Date: Tue, 23 Jul 1996 07:33:04 -0700 Subject: RE: VFX tuning From: PAULE 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