source file: mills2.txt Date: Thu, 15 Aug 1996 11:58:36 -0700 Subject: RE: octave equivalence From: PAULE >The Bohlen-Pierce tritave unarguably exhibits one kind of >"tritave equivalence" that is analogous to (one kind of) octave >equivalence. This is: for a harmonic sound with partials at f, >2f, 3f, 4f, 5f, 6f, ... and its octave with partials at 2f, 4f, 6f, 8f, >.. playing the two together adds no new frequency >information. Similarly, when a sound with only odd partials f, >3f, 5f, 7f, 9f, ... and its tritave with partials at 3f, 9f, 12f, ... >playing the two together adds no new frequency information. >In fact, if you program up the scale, you can hear this kind of >equivalence. Western music has always had a very good "tritave" (perfect tweltfth). Even with a complete harmonic spectrum, the tritave adds no new frequency information. Why was this never perceived as an equivalence before? The naive answer is that all our timbres with even partials suggest octaves as the most direct kind of equivalence. But the fact of the matter is that we don't hear partials; all we hear is virtual pitches and timbres. Inharmonic partials are easy to hear and can form the basis of equivalence judgments. But octave equivalence appears to be a diffent kind of phenomenon entirely. >Perhaps this is a >result of our 12-tet octavocentric brainwashing (i.e., cultural >conditioning). I doubt it. It seems to be universal, and widespread in the animal kingdom. People sing, and even speak, in octaves everywhere. I'm going to keep playing with the P-B and triple P-B scales, but I've failed to make myself hear tritave equivalence, not for want of trying. I've heard 7-limit intervals and chords as consonant, though, which motivates most of my microtonal exploration. Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Fri, 16 Aug 1996 01:20 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA15063; Fri, 16 Aug 1996 01:21:00 +0200 Received: from eartha.mills.edu by ns (smtpxd); id XA15022 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id QAA11755; Thu, 15 Aug 1996 16:20:58 -0700 Date: Thu, 15 Aug 1996 16:20:58 -0700 Message-Id: <34960815231943/0005695065PK3EM@MCIMAIL.COM> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu