source file: mills2.txt Date: Wed, 26 Feb 1997 02:02:46 -0800 Subject: Re: History of the Diatonic Scale - Aristoxenus and Ptolemy From: Daniel Wolf If I may second Jonathan Walker, who wrote: ''Trying to pick your way through this and other arithmetical contradictions can lead, I am convinced, to only one honest conclusion: that Aristoxenus should be understood as providing us with essentially vague, musicianly descriptions, which are distorted if we begin to squint too hard at the details, and try to endow them with more mathematical rigour than he ever countenanced --'' As John Chalmers has more than once pointed out, the classical harmonicists had the mathematical means to calculate string lengths for equal temperament, yet did not do this. Aristoxenian units - like s.rutis - can perhaps be best heard as the smallest conceptual units through which a practical musician, especially a singer, can perform. Jonathan Walker points out one notorious example where Aristoxenus's example simply does not add up, but the _idea_ of tones and limmas (semitones) can be an efficient and useful one for practical music-making. (I think that Johnny Reinhard makes an analogous claim in advocating a cent notation). I find Aristoxenus to be a poor physicist or psychophysicist but perhaps, in a broad sense, the first cognitive scientist! There is much to the perception of pitch relationships that is independent of precise tuning - the perception of serial aggregates, or the group properties that Prof. Balzano has investigated, and Aristonxenian units fall into this category. Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Thu, 27 Feb 1997 00:57 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA13341; Thu, 27 Feb 1997 00:57:13 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA13327 Received: from by ella.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) id PAA15851; Wed, 26 Feb 1997 15:55:10 -0800 Date: Wed, 26 Feb 1997 15:55:10 -0800 Message-Id: <199702262354.HAA01153@csnt1.cs.ust.hk> Errors-To: madole@mills.edu Reply-To: tuning@ella.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@ella.mills.edu