source file: mills3.txt Date: Thu, 25 Sep 1997 22:20:24 +0200 Subject: Reply to Peter Blasser and Carl Lumma From: "Paul H. Erlich" Peter Blasser wrote, >Why does everyone use 22tet instead of 24tet frets on their instruments? Everyone? Wow, I thought I was the only one! (I did see a few in Experimental Musical Instruments once). Considering the amount of electric Arabic pop music I hear these days, I suspect there are a lot more 24-tet guitars than 22-tet. Actually, I did inspire a guy (Steven Rezsutek) on this list to refret his guitar to 22-tet, after he independently came up with a lot of the same ideas as I did. Let's say you're trying to play a 4:5:6:7 chord. In cents this is 0 386 702 969. In 24-tet, you'd start with 0 400 700. If you used 1000 (as in 12-tet) for the top note, your 7:6 would be 33 cents out-of-tune. If you used 950, your 7:5 would be 33 cents out-of-tune. Both are pretty bad. In 22-tet, using 0 382 709 982 has a maximum error of 17 cents (in the 7:5). That's about the same as the maximum error of a triad in 12-tet (16 cents). Not too bad! (The same goes for 1/7:1/6:1/5:1/4). Another reason I like 22-tet is certain scales it contains. The pentatonic scale is a nice source for 3-limit harmony and is OK in 7-tet but almost perfect in 12-tet. The meantone diatonic scale is a nice source for 5-limit harmony and is OK in 12-tet but better in 19, 31, or 50-tet. I discovered/invented some nice scales for 7-limit harmony and their optimal tuning is very close to a subset of 22-tet. Carl Lumma wrote, >If we can agree that there is a difference between re-tuning music made for >100 cent equal, as powerful a model and good-sounding a tuning as it is, and >playing music made for 7+ limit Just Intonation, however embellished, I agree! That's why I'm more interested in 22-tet than 19, 31, or 50-tet. >then >maybe we can be free to appreciate the excellent musicianship that thrives >in every idiom the world over. Whoops! I lost your train of thought. SMTPOriginator: tuning@eartha.mills.edu From: Peter.Blasser@oberlin.edu Subject: Re: 22tet and 24tet PostedDate: 25-09-97 23:14:29 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 23:14:16-25-09-97 23:14:17,25-09-97 23:13:20-25-09-97 23:13:20 DeliveredDate: 25-09-97 23:13:20 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.0074A551; Thu, 25 Sep 1997 23:14:04 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA31195; Thu, 25 Sep 1997 23:14:29 +0200 Date: Thu, 25 Sep 1997 23:14:29 +0200 Received: from ella.mills.edu by ns (smtpxd); id XA31185 Received: (qmail 6974 invoked from network); 25 Sep 1997 14:14:27 -0700 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 25 Sep 1997 14:14:27 -0700 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu