Gibson's modes

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