source file: mills3.txt Date: Thu, 25 Sep 1997 22:13:30 +0200 Subject: Symmetry (was Re: Barbershop and Equal-Step Tuning) From: Paul Hahn On Thu, 25 Sep 1997, Carl Lumma wrote: > There was also another term that Ivor used, "symmetry". He never defined it > too well, but he complained that 12-tone was too symmetric, and that when > one first began Xenharmonic exploration, it was crucial to "knock the ear > out" with a non-symmetric tuning like 19-tone. Could this be the same > thing, Ivor's term for consistency? It seems to me what Ivor was getting at was probably the fact that 12 has many factors, which allows one to create what theorists call "scales of limited transposition". E.g. 3 1 3 1 3 1 has only four different transpositions, because transposed by 4 steps it's unchanged. (You can create such a scale because 4 is a divisor of 12.) OTOH, in 19TET it's impossible to create such scales, because 19 is prime. --pH http://library.wustl.edu/~manynote <*> O /\ "Well, so far, every time I break he runs out. -\-\-- o But he's gotta slip up sometime . . . " SMTPOriginator: tuning@eartha.mills.edu From: PErlich@Acadian-Asset.com Subject: Reply to Peter Blasser and Carl Lumma PostedDate: 25-09-97 22:20:24 SendTo: CN=coul1358/OU=AT/O=EZH ReplyTo: tuning@eartha.mills.edu $UpdatedBy: CN=notesrv2/OU=Server/O=EZH,CN=coul1358/OU=AT/O=EZH,CN=Manuel op de Coul/OU=AT/O=EZH RouteServers: CN=notesrv2/OU=Server/O=EZH,CN=notesrv1/OU=Server/O=EZH RouteTimes: 25-09-97 22:20:10-25-09-97 22:20:11,25-09-97 22:19:14-25-09-97 22:19:15 DeliveredDate: 25-09-97 22:19:15 Categories: $Revisions: Received: from ns.ezh.nl by notesrv2.ezh.nl (Lotus SMTP MTA v1.1 (385.6 5-6-1997)) with SMTP id C125651D.006FB186; Thu, 25 Sep 1997 22:19:59 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA31143; Thu, 25 Sep 1997 22:20:24 +0200 Date: Thu, 25 Sep 1997 22:20:24 +0200 Received: from ella.mills.edu by ns (smtpxd); id XA31137 Received: (qmail 29997 invoked from network); 25 Sep 1997 13:20:21 -0700 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 25 Sep 1997 13:20:21 -0700 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu