source file: mills2.txt Date: Mon, 18 Nov 1996 16:22:47 -0800 Subject: Re: Reply to Gary Morrison From: alves@osiris.ac.hmc.edu (Bill Alves) Paul E wrote: > I just happened to note that theorists who derive the diatonic scale from > three triads are perpetrating a historico-geographic fallacy. > I agree whole-heartedly. I was reminded of this misunderstanding when recently rereading Mathews' and Pierce's "The Bohlen-Pierce Scale." In the introduction are the misleading statements: "The diatonic scale has provided a basis for most Western music since the seventeenth century." and: "The major triad provides the harmonic basis for the diatonic scale." In fact, the diatonic scale (at least as I define it) has been the basis for most European music since the early Middle Ages (at least that which we know through theoretical works or notation). It's impossible to know precisely when, though I have long been fascinated by this issue. Major and "natural" minor are two possible diatonic modes. I believe they were used long before Glareanus recognized them in theory as separate heptatonic entities (I presume that's who the seventeenth century reference was to). Certainly by the seventeenth century, composers were mainly interested in harmony, and "standard" 5-limit JI can be derived through interlocking 4:5:6 triads. But to phrase it as Mathews and Pierce have, it would seem that the diatonic scale was invented in order to accomodate the triad, when in fact it was "invented" centuries before the triad. I don't think this "invalidates" the Pierce-Bohlen scale -- it's absolutely a valid approach to derive a scale based on the harmonies one wants. I just don't think the diatonic scale, or even the major mode, was derived this way. >My paper is an attempt to find a set of pitches >which, like the diatonic scale, stands up on a melodic basis alone, but >leads as naturally to 7-limit harmony and 7-limit tonality, as the diatonic >scale leads to 5-limit harmony and tonality, and (if you believe Yasser was >on the right track) as the pentatonic scale leads to 3-limit harmony and >tonality. I look forward to your paper. Personally, I think Yasser had a lot of great ideas with a lot of ethno-centrist, Darwinist and ultimately unnecessary ethno-historical nonsense to try to justify them. Bill ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^ Bill Alves email: alves@hmc.edu ^ ^ Harvey Mudd College URL: http://www2.hmc.edu/~alves/ ^ ^ 301 E. Twelfth St. (909)607-4170 (office) ^ ^ Claremont CA 91711 USA (909)621-8360 (fax) ^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Tue, 19 Nov 1996 01:34 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA13540; Tue, 19 Nov 1996 01:36:13 +0100 Received: from eartha.mills.edu by ns (smtpxd); id XA16611 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id QAA09530; Mon, 18 Nov 1996 16:36:10 -0800 Date: Mon, 18 Nov 1996 16:36:10 -0800 Message-Id: <25961119002852/0005695065PK4EM@MCIMAIL.COM> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu