source file: mills2.txt Date: Mon, 23 Dec 1996 09:45:15 -0800 Subject: Re: Systematizing Tuning Again From: Gary Morrison <71670.2576@compuserve.com> I suspect that Matt Nathan and I are saying the same thing in two different ways. Matt is concentrating in particular on tuning systems that have an indefinite number of pitches, like JI or meantone tunings. Those are systems though. In meantone, you always choose notes on a circle of a fixed-sized fifth, and similarly in 5-limit JI you always make major triads take the form of 4:5:6 (or with one or more notes octave-displaced). (I'm calling the 81:64-based major triad a 3-limit JI.) But if we're not saying the same thing, then let me suggest that the analogy I posed between particle physics and tunings is based on a similarity between laws of harmony and counterpoint, and the laws of physics. Picking pitches chaotically makes it more difficult to create a sensation of inevitability and thus logical resolution in a cadence. The traditional form of tritone resolution (leading tone upward, and seventh down) is based largely upon the hindsight-obviousness of resolution by half-steps to a quintessentially less discordant interval. A lot of what makes that so much sense, is simply that 12-toned systematics convinces us that half steps are the smallest possible pitch difference. The fact that the tritone is so dissonant and yet so close a consonant, makes us hear that resolution and say "ah yes, how could we ever imagine it otherwise". That's a lot of what makes that resolution satisfying. Similarly, in science, the best-accepted ideas are ones that have a sense of hindsight-obviousness. Scientists, and to a fair degree musical audiences, like hindsight-obvious relationships between pre-known elements. It's much harder to deal with something that requires you to accept an all-new axiomatic idea. Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Mon, 23 Dec 1996 18:48 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA01542; Mon, 23 Dec 1996 18:51:24 +0100 Received: from eartha.mills.edu by ns (smtpxd); id XA01535 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id JAA25422; Mon, 23 Dec 1996 09:51:21 -0800 Date: Mon, 23 Dec 1996 09:51:21 -0800 Message-Id: <199612231228_MC1-DC3-5B92@compuserve.com> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu