source file: mills2.txt Date: Thu, 22 May 1997 05:16:17 +0200 Subject: modulation From: James Kukula It might be useful to think of modulation not as selecting a different subset of notes out of a scale, but as selecting a different scale. Then we wouldn't be looking for symmetry from a scale, but rather from a set of possible scales. But just as a single piece of music usually only uses a small subset of the key signatures available in 12TET, the space of scale signatures available could really be quite abstract, because a given piece of music will only pick out a few to use. Just as the notes in a given key are not at all interchangable, but each has a unique function, so once we open up to modulation between scales, then it becomes quite acceptable for the various notes in a scale to have a unique set of available intervals. Jim Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Thu, 22 May 1997 07:59 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA07467; Thu, 22 May 1997 07:59:37 +0200 Date: Thu, 22 May 1997 07:59:37 +0200 Received: from ella.mills.edu by ns (smtpxd); id XA07464 Received: (qmail 24767 invoked from network); 22 May 1997 05:59:33 -0000 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 22 May 1997 05:59:33 -0000 Message-Id: <33b3dcac.265066577@kcbbs.gen.nz> Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu