source file: mills2.txt Date: Thu, 8 Aug 1996 12:50:11 -0700 Subject: RE: Non-octave scales; monkeys banging o From: PAULE Well, I set up my keyboard to play the Pierce-Bohlen scale with a harmonic tone having no even partials (i.e., no octaves in the harmonic series). When I improvised a melody over a drone bass, trying to emphasize the notes that would theoretically be consonant, I found that 33 steps above the bass sounded like a resolution while 39 steps above the bass did not. So much for the theory of tritave equivalence! Clearly there is a lot more equivalence in 16:1 than in 17:1 or 15:1 or 27:1 -- octave equivalence is a real and unavoidable phenomenon. My hypothesis is that our virtual pitch sensations are quite indistinct as to octave register, even though our pure tone sensations (e.g., formant perception, vowel recognition) may be quite specific in this regard. The best approximations of the 88CET scale to the octave are only slightly farther out than those normally used in gamelan music, so perhaps even your generic inharmonic timbre would allow you to hear some octave equivalence there. But certainly the tolerability of out-of-tune, especially of stretched, multiple octaves increases with the size of the interval -- Yasser showed that a rapid atonal passage played in a lower register of the piano and doubled in a high register sounded the same to his subjects when the upper part was played a semitone higher. Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Fri, 9 Aug 1996 15:09 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA09875; Fri, 9 Aug 1996 15:09:11 +0200 Received: from eartha.mills.edu by ns (smtpxd); id XA09873 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id GAA24396; Fri, 9 Aug 1996 06:09:08 -0700 Date: Fri, 9 Aug 1996 06:09:08 -0700 Message-Id: <199608091306.JAA01605@cerberus2.Ensoniq.Com> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu