source file: mills2.txt Date: Sun, 12 Nov 1995 12:57:29 -0800 Subject: Re: Just Tuning - definition From: Gary Morrison <71670.2576@compuserve.com> Well John, it's pretty hopeless to ask a couple hundred tuning-heads to avoid editorializing when somebody as authoritative as the Harvard guys say something as ... "distasteful" I suppose ... as that! Yeah, I've heard that Harvard definition of JI before ("any tuning that incorporates five or more acoustically pure types of intervals within the octave"). I personally doubt if it's refering to what it sounds like it's refering, and it's certainly vague whatever it's refering to. First of all, it never defined "acoustically pure". "Equal to an untempered small whole number frequency ratio" would be a reasonable guess, but of course then they'd have to define "small". Second, it doesn't define "types" of intervals. Are the fifths from scale steps 1-5 and 2-6 (regardless of their tuning) different "type"s, or is this sort of typing independent of position in the scale? If it's independent of position in the scale, is the fifth from 7-11(4) - a diminished fifth - of the same "type" as the other fifths? Are all perfect consonances one type, major another, and minor another? Third, it doesn't clarify whether "within an octave" includes an octave or not. That sounds nit-picky I know, but if you've got four other than the octave, you've got to know the answer. Here's how I suspect that definition came about: They got the number five from the number of exact 3:2 perfect fifths in the circle forming the historical Ptolemaic tuning. In that tuning, the fifths between scale-degrees 4-8(1), 1-5, 5-9(2), 6-10(3), and 3-7 are exact 3:2 fifths. 7-11(4) is not perfect, and 2-6 is where the circle breaks by inserting a comma-flat fifth. At that point, I suspect they took that number 5 and, without thoroughly understanding the question, wrapped what turned out to be deeply ambiguous words around it. I'm speculating here of course. But let me make one very important point: I suspect that it's difficult to support the idea that the definition of just intonation has been invariant over the centuries, and over the various schools of Western music. JI enthusiasts, and most others knowledgible of tuning ideas, take it to mean - essentially - the opposite of temperament. But one can probably argue fairly successfully that the definition was far more narrow in earlier times. I doubt if Ptolemy's followers would have viewed Monophony as just intonation. Considering that (according to Dave Hill) Rameau rejected 7:4 as a basic harmonic building block, I suspect that they probably would have viewed Monophony instead as more like cacophony! Fortunately for Partch fans like me, the realm of musical possibilities is far more experimental nowadays. (I'm sorry John; I accidentally deleted your message before I got a chance to answer - to you directly - the two specific questions you asked. If you'd like me to answer them specifically, please resend them to me personally.) Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Mon, 13 Nov 1995 03:26 +0100 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id RAA13689; Sun, 12 Nov 1995 17:26:12 -0800 Date: Sun, 12 Nov 1995 17:26:12 -0800 Message-Id: <951113011947_71670.2576_HHB42-1@CompuServe.COM> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu