source file: mills3.txt Date: Fri, 12 Dec 1997 14:41:37 +0100 Subject: Gibson's modes From: "Paul H. Erlich" Ironically, all 28 of Gibson's modes "work" in 22! In other words, each of his four basic scales can be expressed in 22TET with all four of its consonant triads sounding quite pure. I found this out while noodling on a 12-out-of-22 keyboard tuning last night. The usual diatonic scale can, of course, only have five out of its six consonant triads "in tune" in 22, which is presumably what Gibson has in mind when he talks about the circle of fifths not closing. The other problem with diatonic scales in 22 is that they contain 3, instead of 2, step sizes. Three out of Gibson's four basic scales also have one more step size in 22 than in 12 or 19. But one, the non-western one, has 3 step sizes in all of these tunings, in addition to having four consonant triads in all of these tunings. Perhaps it is not surprising that I found myself gravitating to such non-western modes on my 22-tone guitar some time ago. SMTPOriginator: tuning@eartha.mills.edu From: "Paul H. Erlich" Subject: RE: Oops... back to school for me PostedDate: 12-12-97 14:44:44 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: 12-12-97 14:42:50-12-12-97 14:42:51,12-12-97 14:42:35-12-12-97 14:42:35 DeliveredDate: 12-12-97 14:42:35 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 C125656B.004B52B3; Fri, 12 Dec 1997 14:44:40 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA12635; Fri, 12 Dec 1997 14:44:44 +0100 Date: Fri, 12 Dec 1997 14:44:44 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA13692 Received: (qmail 9848 invoked from network); 12 Dec 1997 05:43:04 -0800 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 12 Dec 1997 05:43:04 -0800 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu