source file: mills3.txt Date: Thu, 25 Sep 1997 19:02:04 +0200 Subject: Re: et fretting question From: Paul Hahn On Thu, 25 Sep 1997 Peter.Blasser@oberlin.edu wrote: > Why does everyone use 22tet instead of 24tet frets on their instruments? > It seems to me, after testing it out on a spreadsheet program, that 22tet > does not imitate 4/3, 16/9, even 9/8 well enough. I do see a better > imitation or ability to play 7/4, 5/4 and quarter tone tetrachords. has > anyone heard a 22tet compared to a 24tet? Is there a noticeable > difference? I guess what it all boils down to, is, what sounds best? The reasons for this are based in a concept for which Paul Erlich coined the term "consistency". Paul E. and I had a lengthy discussion on this some time back in which some variations and extensions of the concept also came up, but in brief an ET is consistent within a given harmonic limit if the ET's approximation of harmonic intervals within that limit is distributive. Example: 12TET is consistent within the 5-limit because 5/4 is approximated by 4 steps, 6/5 is approximated by 3 steps, and their product 3/2 is approximated by 7 steps. To get back to the question, 22TET is consistent up to the 11-limit, while 24TET is only consistent to the 5-limit. (In this respect it is actually worse than its subset 12TET, which is consistent to the 9-limit.) Peter, if you are interested I could dredge up some of the messages from the last time we discussed this. (Hey, is the list archived anywhere?) --pH http://library.wustl.edu/~manynote <*> O /\ "Well, so far, every time I break he runs out. -\-\-- o But he's gotta slip up sometime . . . " SMTPOriginator: tuning@eartha.mills.edu From: flynn@mills.edu Subject: w.a. mathieu's _harmonic experience_ PostedDate: 25-09-97 19:46:14 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 19:45:54-25-09-97 19:45:55,25-09-97 19:44:58-25-09-97 19:44:58 DeliveredDate: 25-09-97 19:44:58 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.00619437; Thu, 25 Sep 1997 19:45:49 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA31033; Thu, 25 Sep 1997 19:46:14 +0200 Date: Thu, 25 Sep 1997 19:46:14 +0200 Received: from ella.mills.edu by ns (smtpxd); id XA31041 Received: (qmail 2966 invoked from network); 25 Sep 1997 17:39:52 -0000 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 25 Sep 1997 17:39:52 -0000 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu