source file: mills3.txt Date: Sat, 10 Jan 1998 20:27:39 +0100 Subject: Re: 22TET From: gbreed@cix.compulink.co.uk (Graham Breed) I would be very surprised if any temperament significantly different to 22 equal supported decatonic scales. Vanishing septimal commas is a difficult trick to pull off. The octave is the best interval to define a harmonic scale around. Once you've done that, the octave should be very accurate. Although you should think about the octaves, it would be annoying if "the same" chords in different registers were out of tune with each other. I tend to think that low primes should be tuned best. The more complex harmony you use, though, the more accuracy is required for _all_ intervals. Carl Lumma wrote: > It just stands to reason that there are all kinds > of effects, probably most of them un-discovered, based on the "anomalies" > of JI. Remember that there are a lot of temperaments out there! Most of what you can do in JI should work schismically, as all the commas are there. > 1) Conventional theory is full of holes. The tritone is spelled as an > augmented forth in certain contexts, and as a diminished fifth in others, > but it's the same pitch. All the enharmonics should be thrown out in 12. No, the tritone is not always the same pitch. It can be 7/5, 10/7, 25/18 or 36/25. The first two do not arise in a diatonic context. So, 25/18 is an augmented fourth and 36/25 a diminished fifth. The difference between them, 63 cents, is not negligible. 12-equal enharmonies are irrelevant as diatonic scales work in all meantones, and the notation reflects this. When Paul Erlich says "scale steps" he obviously means the 7 note diatonic scale. I didn't have any trouble with this when I read the paper first. SMTPOriginator: tuning@eartha.mills.edu From: mr88cet@texas.net (Gary Morrison) Subject: Re: TUNING digest 1293 jloffink PostedDate: 10-01-98 22:22:22 SendTo: CN=coul1358/OU=AT/O=EZH ReplyTo: tuning@eartha.mills.edu $MessageStorage: 0 $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: 10-01-98 22:21:49-10-01-98 22:21:50,10-01-98 22:21:41-10-01-98 22:21:42 DeliveredDate: 10-01-98 22:21:42 Categories: $Revisions: Received: from ns.ezh.nl ([137.174.112.59]) by notesrv2.ezh.nl (Lotus SMTP MTA SMTP v4.6 (462.2 9-3-1997)) with SMTP id C1256588.0075595F; Sat, 10 Jan 1998 22:22:14 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA12128; Sat, 10 Jan 1998 22:22:22 +0100 Date: Sat, 10 Jan 1998 22:22:22 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA12117 Received: (qmail 18571 invoked from network); 10 Jan 1998 13:22:19 -0800 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 10 Jan 1998 13:22:19 -0800 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu