source file: mills2.txt Date: Thu, 5 Dec 1996 14:12:30 -0800 Subject: CPS From: "Adam B. Silverman" GenevaI have been fooling around with some scale and would like to ask you if I am correct; I don't quite unerstand the concept of CPS scales as explained in the Warren Burt articles in 1/1. However, I have been looking at the scales described by Johnny Reinhard recently on the tuning forum, as used by his wife under the name "Harmonic 13." This scale in its non-abbreviated form (Mayumi R. leaves out several notes and adds a couple of others, if I recall correctly) includes only pitches with a numerary nexus of 13. This scale might be better described as the 13-Plane Scale, since all of its tones are found on the "13-plane" of a multi-dimensional lattice containing ratios of all primes less than 13, inclusive. The 13-Plane Scale is easily divided into two subsets. The first always has 13 in its numerator, and its pitches are: ratio 1/1 (13/13) 13/12 13/11 13/10 13/9 13/8 13/7 cents 0 139 289 454 637 841 1072 The second always contains 13 in its denominator, and is the inversion of the previous subset. ratio 1/1 (13/13) 14/13 16/13 18/13 20/13 22/13 24/13 cents 0 128 359 563 746 811 1061 My question: is this simply another way to find CPS pitches? Am I completely misguided about these two concepts? Yours, Adam _________________ Adam B. Silverman 153 Cold Spring Street; A3 New Haven, CT 06511 (203) 782-1765 abs22@pantheon.yale.edu Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Thu, 5 Dec 1996 23:15 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA16684; Wed, 4 Dec 1996 07:31:37 +0100 Received: from eartha.mills.edu by ns (smtpxd); id XA20741 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id WAA20846; Tue, 3 Dec 1996 22:31:34 -0800 Date: Tue, 3 Dec 1996 22:31:34 -0800 Message-Id: Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu