source file: mills2.txt Date: Mon, 24 Feb 1997 18:01:10 -0800 Subject: Re: Reply to Matt Nathan From: alves@Orion.AC.HMC.Edu (Bill Alves) While there are a lot of interesting issues that have been raised in this exchange, I would specifically like to respond to the one about historical precedence of tuning models for the diatonic scale. PAULE wrote: >I think the diatonic scale long predated the discovery of 5-limit harmony in >most cultures (India is a possible exception, though only 3-limit >consonances are mentioned in the original texts). It was constructed from >melodic considerations only, which means that ratios beyond the 3-limit are >of negligible importance. Ascribing 5-limit ratios to the diatonic scale is >in most cases, as I have said before, a historico-geographic fallacy, and a >very Eurocentric one at that. > >It must be said, though it partially supports Matt's viewpoint, that many >cultures (the West, India, Arabia) seem to have discovered the 5-limit >relations through their SCHISMATIC, not SYNTONIC, approximations. It seems >that Pythagorean tuning was extremely well developed long before any >theoretical understanding of the 5-limit came about. > Dan Wolf talked some about the distinction between theory and practice, and I think it's a crucial distinction. First, when does a culture NEED a precisely defined, standardized tuning system? Several possible answers occur to me (though there may be others): 1) when it is desirable for several fixed-pitch instruments to play together (the definition of "fixed-pitch" may be a gray area, I know), 2) when there are instruments with frets or a single sounding body per pitch (even then they don't necessarily have to be standardized), 3) when there is an important numerological justification. Many cultures don't meet any of these criteria. Even those for whom #3 is important, such as India, China, Persia, and (sometimes) ancient Greece, there's often no evidence that these mathematical constructs had any relationship to practice. Lacking that evidence, the possibility arises that so-called Pythagorean tuning was invented as a way of describing musical systems already in practice. While it's possible to derive scales purely mathematically, I am skeptical that most scales, including the diatonic, were initiated this way. Perhaps scales evolve intuitively, though that intuition may be based on mathematical models that may not be verbalized by the musician. (Thus the octave is virtually universal, but musicians may not be aware that its significance derives from its closeness to 2:1). Overblown fifths, small number ratios, Pythagorean cycles, tendency towards equal step sizes, these are all possible models for an (originally) unspoken basis for the diatonic scale. If that's the case, I don't think it's possible to say for sure which is correct from a historical point of view. When dealing with non-fixed-pitch instruments, we are in even more trouble. The deviations from a theoretical standard tuning system of a melodic line sung by a voice alone or played on a bamboo flute alone can easily approach the syntonic comma. Oh, I know, some of this may just be bad musicianship, but I still think it's very problematic to derive a precise tuning system from such music. Indian sources, it's true, give elaborate tuning instructions for the vina, but nearly all of them, back to the vedas, ascribe primacy to the human voice. 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, 25 Feb 1997 18:26 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA16881; Tue, 25 Feb 1997 18:26:20 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA16882 Received: from by ella.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) id JAA10721; Tue, 25 Feb 1997 09:13:56 -0800 Date: Tue, 25 Feb 1997 09:13:56 -0800 Message-Id: <009B06CFCD89BA6A.638D@vbv40.ezh.nl> Errors-To: madole@mills.edu Reply-To: tuning@ella.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@ella.mills.edu