source file: mills2.txt Date: Tue, 16 Jan 1996 18:08:34 -0800 Subject: Re: Manuel Op de Coul's list From: Gary <71670.2576@compuserve.com> Bruce Gilson asked: > my question is how precisely the given ET scale had to match the interval. The pretty much accepted definition of precise just intonation - at least by the readers of this list (more on that in the last paragraph) - is that all notes must exactly match simple whole-number ratios. Simplicity of the ratio, and accuracy of the match are the ideals, not any particular limit, as with 5-limit Ptolemaic historical tunings. To me, it seems likely that in the 13th century (if memory serves, that's roughly when 5-based harmony began to be accepted as harmonious rather than dissonant) anything but those specific ratios recognized at the time, would have been considered inaccurate renditions of the accepted ones. So, for example, I'd almost bet money that even an exactly precise 9:7 third would have been considered an off 5:4. Time have changed though. Every modern Just Intonationalist I know of views 9:7 as an ideal in its own right. Now an absolute, 100% exactly perfect match is almost always impossible, but therein lies the distinction between inidealities in the performance, and an accurate rendition of a tempered (nonjust) tuning. So to present a degenerate example, consider a performance by instruments tuned to equal-temperament and intended to produce 400-cent thirds, but wherein the performers consistently produced exactly precise 5:4 thirds. In my book that would be failed performance in equal-temperament more than a successful performance in just intonation, although by default, it would be that as well. My caveat to the "pretty much accepted definition", stems from the rather puzzling definition presented in the otherwise quite authoritative Harvard Dictionary of Music. Best I recall, none of us on the list could make head nor tail of that definition. Feel free to check the archives for more on that. And a kind ambassador from the list sent (or at least attempted to send) a message to the Harvard folks. The message read, to summarize down to a single a word, "huh?!". Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Wed, 17 Jan 1996 10:02 +0100 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id BAA18126; Wed, 17 Jan 1996 01:02:13 -0800 Date: Wed, 17 Jan 1996 01:02:13 -0800 Message-Id: <960117020359_71670.2576_HHB41-7@CompuServe.COM> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu