source file: mills3.txt Date: Sat, 23 Aug 1997 17:20:10 +0200 Subject: Re: Nomenclature From: gbreed@cix.compulink.co.uk (Graham Breed) James Kukula wrote: > For the phonemic analogy - well, phonemes are really language specific. There > is no universal set of phonemes. For an overarching theory of the musical > analogue of phonemes, probably some kind of mathematical system might > work. Group theory would work if every interval could be combined with every > other interval to form another legal interval. But this strong a rule drives > one to equal temperament. Category theory is like group theory, but it > restricts what elements can be combined with what other elements. But it > probably wouldn't work for music. I don't know the specifics of either group or category theory, but this is definitely something like what I do with matrices. You can define scale "families" by a basis (primitive group?) and define a practical scale as a finite subset, usually octave repeating. This works for ETs, linear temperaments and JIs. Beyond that, you just have to specify all the intervals in cents. The matrices are used to convert between bases. Beyond that, scales really aren't complicated enough to justify bringing in standard mathematical theory. SMTPOriginator: tuning@eartha.mills.edu From: rapoport@mcmail.CIS.McMaster.CA Subject: Re: TUNING digest 1162 PostedDate: 24-08-97 03:44:53 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: 28-08-97 09:57:27-28-08-97 09:57:28,28-08-97 09:55:01-28-08-97 09:55:01 DeliveredDate: 28-08-97 09:55:01 Categories: $Revisions: Received: from ns.ezh.nl by notesrv2.ezh.nl (Lotus SMTP MTA v1.1 (385.6 5-6-1997)) with SMTP id C12564FD.000997BA; Sun, 24 Aug 1997 03:44:46 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA20311; Sun, 24 Aug 1997 03:44:53 +0200 Date: Sun, 24 Aug 1997 03:44:53 +0200 Received: from ella.mills.edu by ns (smtpxd); id XA20323 Received: (qmail 7963 invoked from network); 24 Aug 1997 01:44:49 -0000 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 24 Aug 1997 01:44:49 -0000 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu