source file: mills2.txt Date: Fri, 17 Nov 1995 17:55:00 -0800 Subject: Re: TUNING digest 561 From: MORGAN ELLINGTON SMITH I'm not sure what everybody says about this, but according to Harry Partch the 12-tone scale is derived from both the partials themselves and their relations to each other. For instance, the perfect fourth is derived from the fourth partial's relation to the third partial, transposed to be in relation to the fundamental. The seconds and sevenths must be derived by partials of partials, for instance the minor sixth is derived from the fifth partial's relationship to the eighth partial (which is found as the fourth partial of the second partial's overtone series, thus staying within the five-partial limit). If your fundamental is C, then, you get an "A flat" in your scale because it is a minor sixth up from the fundamental, even though that tone does not occur in the harmonic series. I assume that Partch's thinking is in line with other theorists, but with Partch you never know. The information above I got from _Interval_, when they published an early draft of an intro to _Genesis_ called "Exposition of Monophony." I hope this is some of what you were looking to find out, and I realize this may be stuff you already knew. Morgan Smith Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Sat, 18 Nov 1995 08:55 +0100 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id WAA14229; Fri, 17 Nov 1995 22:55:46 -0800 Date: Fri, 17 Nov 1995 22:55:46 -0800 Message-Id: <951118015447_109856415@mail02.mail.aol.com> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu