source file: mills2.txt Date: Sat, 2 Nov 1996 02:04:43 -0800 Subject: Re: Intervals list From: Gary Morrison <71670.2576@CompuServe.COM> Bill Sethares, in the manuscript for his up-coming book, describes a detailed study of levels of discord. I think the study was conducted by Plomp and Levelt (or something like that - I don't have the reference in front of me). But anyway, two factors strike me as especially significant about Bill's approach: 1. It builds from experimental results that strike me as hard to believe, but I'm 90% confident are due to the fact that the experimenters used sinewaves (their "dissonance" curve looked somewhat like the integral of a typical bell-curve if you can imagine that), and 2. Bill uses this seemingly unrealistic set of experimental results with sinewaves, to form what is almost certainly the most complete, accurate, and practical approach to the meaning of "consonance" and "dissonance" (the latter more accurately being called "discord"). Along the first lines - surprising conclusions of the indepth experimental study - it concluded that minor ninths and major sevenths are about as consonant as octaves. I find that difficult to swallow even with sinewaves. I have a preconceived notion that major sevenths and minor ninths have to be comparatively discordant in ANY timbre. I have to confess that, based upon his accompanying tape, it could well be that my preconceived notion in that regard is at least partly false. But anyway, I'm about 98% certain that what I'll find as I read further, is that he'll attribute the discord of major sevenths and minor ninths absolutely 100% to a "rough" (fast) beat between the second harmonic of the lower tone with the fundamental of the higher tone. That suggests that half-wave symmetrical tones (no even harmonics) will not produce discordant M7s and m9s, which again strikes me as counterintuitive. But the undeniable fact of the matter is that Bill's techniques and ideas absolutely DO work. That in turn seems to make it hard to deny that what I described above is indeed a case of preconceived notions. Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Mon, 4 Nov 1996 21:16 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA16536; Sat, 2 Nov 1996 20:26:05 +0100 Received: from eartha.mills.edu by ns (smtpxd); id XA01566 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id LAA01387; Sat, 2 Nov 1996 11:26:02 -0800 Date: Sat, 2 Nov 1996 11:26:02 -0800 Message-Id: <009AAC840564E580.8B7F@vbv40.ezh.nl> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu