source file: mills3.txt Date: Thu, 28 Aug 1997 18:35:22 +0200 Subject: Re: Matrices (digest 1166 topic 2) From: Mark Nowitzky Hi Graham (and tuning list at large), Thanks for your exposition on the use of matrices to represent intervals and scales (Digest 1166 Topic 2, Subject: Matrices for beginners). Tuning systems are sometimes hard to visualize, so I always appreciate various ways of representing them. (I've even resorted to gluing toothpicks together to help conceptualize 5-limit just intonation. People now think I'm a "psycho"!) At 04:15 PM 8/27/97 -0700, you wrote >... >A C major scale (not the only one) can be defined using t, s and p >as follows: > > C D E F G A B C > t+p t s t+p t p+t s > >This can be written using matrices: Okay, just to prove I was following you, here's a correction: You wrote You meant ---------------- ---------------- (C) (5 3 2) (C) (5 2 3) (B) (5 3 1) (B) (5 1 3) (A) (4 2 1) (A) (4 1 2) (G) (3 2 1)(t) (G) (3 1 2)(t) (F) = (2 1 1)(s) (F) = (2 1 1)(s) (E) (2 0 1)(p) (E) (2 0 1)(p) (D) (1 0 1) (D) (1 0 1) (C) (0 0 0) (C) (0 0 0) The s and p got confused on the second (top) half of the scale (G,A,B,C). You wanted to end up with 5 minor tones (t=10/9), 2 diatonic semitones (s=16/15), and 3 syntonic commas (p=81/80). By the way, do you know a good way to visualize 4 dimensions, for things like limit-7 just intonation? (My glued toothpicks only work for 3 dimensions.) Thanks again, --Mark +------------------------------------------------------+ | Mark Nowitzky | | email: nowitzky@pacificnet.net | | www: http://www.pacificnet.net/~nowitzky | | "If you haven't visited Mark Nowitzky's home | | page recently, you haven't missed much..." | +------------------------------------------------------+ SMTPOriginator: tuning@eartha.mills.edu From: PErlich@Acadian-Asset.com Subject: RE: Srutis PostedDate: 28-08-97 19:23:47 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 19:23:56-28-08-97 19:23:56,28-08-97 19:23:45-28-08-97 19:23:45 DeliveredDate: 28-08-97 19:23:45 Categories: $Revisions: Received: from ns.ezh.nl by notesrv2.ezh.nl (Lotus SMTP MTA v1.1 (385.6 5-6-1997)) with SMTP id C1256501.005F9069; Thu, 28 Aug 1997 19:23:48 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA04285; Thu, 28 Aug 1997 19:23:47 +0200 Date: Thu, 28 Aug 1997 19:23:47 +0200 Received: from ella.mills.edu by ns (smtpxd); id XA04283 Received: (qmail 27644 invoked from network); 28 Aug 1997 17:23:44 -0000 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 28 Aug 1997 17:23:44 -0000 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu