source file: mills2.txt Date: Sat, 5 Oct 1996 11:25:53 -0700 Subject: Re: To Gary, Paul E, Re: non-octave scales From: Gary Morrison <71670.2576@CompuServe.COM> > under certain strict conditions (in > which the partial structure of the tones is more or less irrelevant), > powers of 3 (and possibly of 5) do replicate the smilarity condition > eliceted by powers of 2 in tonal or modal polyphony. Aha! I'm working my way through Bill Sethares' manuscript at the moment, but I would definitely be interested in reading that later. Thanks for the offer/suggestion. I can vouch for the meaningfulness of that suggestion in two regards: First, I have briefly worked with ... "squashing" for lack of a better word ... traditional music (melodies alone mostly, but not entirely) to a tuning of 12 equal steps per 3:2 instead of 12 equal steps 2:1. After listening to that for a while, I found that 3:2 started to have a mild duplicating effect much like the octave. This of course harkens back to the debate not long ago about whether or not you can hear primes or not. After he did his first rendition of his taped lecture-demo "Introduction to Nontraditional Harmony", Dave Hill changed his belief from the idea that each prime provides a new harmonic feeling, to his belief that each ODD number provides a new feeling. As I think I mentioned, he concluded that that was probably true because powers of two give a feeling of duplication, thus ruling out multiples of 2 from having truly fundamental effects upon harmony. Everything left though, he concluded, should have truly fundamental effects. My immediate response to that was, "why do you conclude that there are no other fundamental effects associated with other primes other than 2's duplication effect? Why should we rule out the possibility that powers of three or of five have a distinctive effects of their own?" The second regard in which I can relate to your conclusion that other intervals can have moderate duplicating effects, is with regard to my search in 88CET for pitch relationships that can function for note-doubling. I described my conclusions in my series on 88CET, but the short version is that that is - to a large extent anyway - a matter of the doubling interval needing only to be more "bland" than the other intervals. For example in a comparatively harmonically simple chord like a major triad, you can't get a doubling effect from fifths. Our ears perceive the result as a basically different harmony, like a seventh or ninth chord. But if you start with a more complex and intense harmony, like a 7:9:11 chord, doubling a note by a much more easy-going, simpler-sounding harmony like a fifth (or even a major tenth, perhaps surprisingly) doesn't seem to have much effect on the overall character of the chord. Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Sat, 5 Oct 1996 20:25 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA14430; Sat, 5 Oct 1996 19:27:14 +0100 Received: from eartha.mills.edu by ns (smtpxd); id XA14426 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id LAA17123; Sat, 5 Oct 1996 11:27:12 -0700 Date: Sat, 5 Oct 1996 11:27:12 -0700 Message-Id: <961005182241_71670.2576_HHB44-6@CompuServe.COM> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu