source file: mills2.txt Date: Tue, 31 Dec 1996 07:04:14 -0800 Subject: Re: pure or just From: Daniel Wolf <106232.3266@compuserve.com> J. Reinhard wrote: ''I believe the use of "just" is reference to honest as being explicit to nature's overtone series. It is first used by Thomas Morley in his treatise on music _A Plaine and Easie Introduction to Practicall Musicke_ (1597), the first of its kind.'' ''Just'' could not have been defined by anyone in the sixteenth century with reference to an overtone series, as that concept had yet to be developed. One of the now obsolete meanings for ''Just'' is ''exact'', and it used in this sense to distinguish Just intervals from tempered, which were used as approximations. I find it not very useful to define Just with any appeal to nature, as real, existing nature is frustratingly free of exact overtone series as anyone who has ever tuned a stretched string or a metal bar or played a brass instrument (I'm a trombonist by training) has experienced. It is safer to define Just intonation in terms of whole number ratios, and then to distinguish between varieties of JI on the basis of the genus (a la Euler) or limit (a la Partch). So Pythagorean tuning is a type of (3^n) or three limit JI; much tonal music can be performed in (3^n,5^n) or five limit JI; the Partchian Diamond is a species of (3^4,5^2,7^2,11^2) or eleven limit JI etc. The Morley text (1596) - excellent for rhythmic modes and diminution but decidedly deficient for intonation - is the first of what kind? An earlier (if inferior) treastise was published in English in 1584, and Morley's debt to previous non-English publications is everywhere in evidence (e.g. the monumental _Dodecachordon_ of Glareanus (1547) and Trigini's _Compendium_ of 1588 - from which Morley plagiarized his examples of cadential treatment). Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Tue, 31 Dec 1996 17:05 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA05802; Tue, 31 Dec 1996 17:08:13 +0100 Received: from eartha.mills.edu by ns (smtpxd); id XA05796 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id IAA13555; Tue, 31 Dec 1996 08:08:10 -0800 Date: Tue, 31 Dec 1996 08:08:10 -0800 Message-Id: <32C8C869.44B1@ix.netcom.com> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu