source file: mills2.txt Date: Thu, 22 May 1997 19:27:47 +0200 Subject: RE: Equal Divisions -- of What? From: gbreed@cix.compulink.co.uk (Graham Breed) As I started this off, I may as well explain myself. By the "harmonic series" I meant the set of harmonic overtones. I forgot that there was a quite different harmonic series in maths. It's one of those confusing things like 13 being a lucky number. My point is that the overtone series exploits the same symmetry as ETs, but in a different scale. JI can be derived from this series, and so exploits the symmetry. Where subsets of an ET are used, the analogy is even better, as we are dealing with small integer ratios in both cases. Paul Erlich wrote: >However, pitch space is not the same as frequency space. In fact, pitch >space most closely resembles log-frequency space. If I routinely use "pitch" to mean the logarithm of frequency, will people understand what I mean? Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Thu, 22 May 1997 19:29 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA07873; Thu, 22 May 1997 19:29:04 +0200 Date: Thu, 22 May 1997 19:29:04 +0200 Received: from ella.mills.edu by ns (smtpxd); id XA07869 Received: (qmail 12224 invoked from network); 22 May 1997 17:28:59 -0000 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 22 May 1997 17:28:59 -0000 Message-Id: <97052217264143/0005695065PK2EM@mcimail.com> Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu