source file: mills2.txt Date: Mon, 24 Feb 1997 12:06:04 -0800 Subject: Reply to Matt Nathan From: Daniel Wolf PAULE wrote the following: '' 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.'' and: '' Ptolemy's scales (much like his astronomical models) seem to have been derived from geometrical and mystical, not scientific (the appropriate science for music is psychoacoustics), considerations, so they don't count. '' Response: You can't have it both ways. There are alternative readings of the historical materials, but the most convincing rationale for the use of schismatic approximations of intervals with five as a factor would be a doctrinal or mystical commitment to a three limit. (And, in practice, most Saz players correct their schisma-off thirds to 5-limit ratios). That Ptolemy would go beyond the three limit in his tunings was contrary to the prevailing neo-pythagoreanism, and, among the classical harmonicists, Ptolemy is probably farthest from any such mystical tradition. In fact, his _Harmonics_ is virtually the only classical source to clearly discern between theoretical and actual tunings. The remainder of the remark, criticising Ptolemy on the basis of the superior propriety of a discipline (Psychoacoustics) which would wait until the late 19th century to be established (in Leipzig), and whose scope and dimensions were well ouside of the scientific discourse of Ptolemy's time is, simply, ridiculous. As to the historical priority of a three-limit in music theory (given Assyrian and Chinese evidence), I assume this is true, but the advent of work with a monochord (and the entire discipline of harmonics) is not characterised by an innocence towards higher prime numbers. I would suggest that the prior three-limit theories were not constructed with such innocence but in full comprehension of the fact that additional primes were not going to create any systemic closure, and that factors of three were sufficiently complex to generate a large supply of useable tones, thus the ''mystical'' attributes of the number three were a - for us - comprehensible recogition of real mathematical and musical properties, while not explicitly condemning the introduction of higher primes - which may very well have been part and parcel of the actual musical practice. Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Mon, 24 Feb 1997 22:30 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA18840; Mon, 24 Feb 1997 22:30:44 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA18846 Received: from by ella.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) id NAA00081; Mon, 24 Feb 1997 13:28:23 -0800 Date: Mon, 24 Feb 1997 13:28:23 -0800 Message-Id: <009B062A3ED25FFE.398B@vbv40.ezh.nl> Errors-To: madole@mills.edu Reply-To: tuning@ella.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@ella.mills.edu