source file: mills2.txt Date: Mon, 25 Nov 1996 09:34:24 -0800 Subject: RE: non-octave scales and octave equival From: PAULE Brian wrote- >Paul Erlich goes on to write that "In the case >of inharmonic partials, octave equivalence may >play less of a role, but still exists, and is less >demanding as to intonation." Both [...] experiments >[...] strongly contradict this >statement. In particular William Sethares has >a set of instrument timbres resynthesized with >all harmonics stretched so that the octave is a >ratio of 2.1 instead of 2.0, etc. >Playing a vertical octave dyad with such timbres >produces unbearable dissonance; but playing a >vertical octave whose ratio is 2.1 rather than 2.0 >produces the familiar sensation of octave >equivalence. So the evidence *strongly* indicates >that 2:1 octave equivalence goes away when the >timbre becomes inharmonic, and this is confirmed >by William Sethares' mathematical procedure for >finding scale pitches from an inharmonic timbre. What's contradictory? >2, 3, 4, 5, 6 are highly consonant. >7 is less so, intermediate in fact between consonance >and dissonance; 8, 9, 10 are highly consonant, 11 >is much less consonant... Whatever that means, I don't think 10:9 is more consonant than 8:7! Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Mon, 25 Nov 1996 18:51 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA07388; Mon, 25 Nov 1996 18:53:19 +0100 Received: from eartha.mills.edu by ns (smtpxd); id XA07345 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id JAA04087; Mon, 25 Nov 1996 09:53:16 -0800 Date: Mon, 25 Nov 1996 09:53:16 -0800 Message-Id: <9611251749.AA21172@tcm.mit.edu> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu