source file: mills3.txt Date: Sat, 23 Aug 1997 09:55:35 +0200 Subject: Re: reply to me From: gbreed@cix.compulink.co.uk (Graham Breed) Paul Erlich wrote: > I regret that our previous discussions were interrupted due to problems > with the list server. I'd be happy to continue discussing those issues > if you are so inclined. But I'd like to understand this question: I'd be happy to continue the discussion. I remember some stuff about 9 being a coordinate direction, a recipe for saturated chords, and an argument about octave invariance that did reach some kind of conclusion. Anyway, to my question: > Now, does anyone know of a 2-D approximation (linear > temperament) that covers 22tet? Approximating the > enharmonic diesis (7 0 -3)H and syntonic comma (-4 4 -1)H > to be equal doesn't work. If it did, it would cover 12, 22, > 34 and 46tet. It is, incidentally, significant that these > are all even numbers. Looking back through the archive, I see you (Paul) covered these in March: >> Doubly postive systems resembling 22-tet are also possible. I >> will post some such tunings at a later date. > > What is the definition of "doubly positive?" Do you mean, two positive > systems separated by exactly one-half octave? If so, I hope you don't give > away any more of my secrets, at least until XH 17 comes out, which is, when? > Or did someone else come up with the idea of two positive systems separated > by exactly one-half octave before I did? Whatever "doubly positive" means, the scales you mentioned are the ones I thought didn't work. I wanted a 0-comma scale to be just, preferably Pythagorean, but I can see now that there's no problem with having tritones in there. I've had a good look at them, but I haven't worked out the 7-limit approximation yet. Can you help here? Getting back to Paul's message: > In the ancient Hindu > sruti system, the syntonic comma (-4 4 -1) is reckoned as one sruti, > while the interval 2048/2025 (is that a diaskhisma?) is zero srutis. > That last interval is (11 -4 -2)H, I believe. Thanks for using my notation. Setting (11 -4 -2)H to zero using the method I outlined on the list before gives this temperament. The defining matrix has a determinant of -2, which is where the tritones come from. As regards srutis, are these ancient or medieval in origin? The document defining Sa- and Ma-grama on a 22 note scale seems to me to be the earliest clearest record of 5-limit diatonic outside of Europe. I welcome corrections on this. SMTPOriginator: tuning@eartha.mills.edu From: gbreed@cix.compulink.co.uk Subject: Re: Nomenclature PostedDate: 23-08-97 17:20:10 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: 23-08-97 17:20:15-23-08-97 17:20:16,23-08-97 17:18:07-23-08-97 17:18:08 DeliveredDate: 23-08-97 17:18:08 Categories: $Revisions: Received: from ns.ezh.nl by notesrv2.ezh.nl (Lotus SMTP MTA v1.1 (385.6 5-6-1997)) with SMTP id C12564FC.00543C88; Sat, 23 Aug 1997 17:20:05 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA20124; Sat, 23 Aug 1997 17:20:10 +0200 Date: Sat, 23 Aug 1997 17:20:10 +0200 Received: from ella.mills.edu by ns (smtpxd); id XA20130 Received: (qmail 13347 invoked from network); 23 Aug 1997 15:20:06 -0000 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 23 Aug 1997 15:20:06 -0000 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu