Ten equal tunings

}PS...where is everybody? I miss the action..

I've been thinking hard about which tunings I would have if I had
unlimited resources for guitars and generalized keyboards. As I mention
in my paper, I don't like equal temperaments with more than 34 notes per
octave, since it becomes possible to approximate the same interval in
more than one way (assuming the ear has a 1% tolerance), which is more
confusion than I want to deal with. So I came up with the following
symmetrical scheme:

7, 10, 12, 15, 19, 22, 26, 29, 31, 34

Notice that subtracting any of the numbers above from 41 gives another
one of these numbers.

A brief summary:

7: The Thai tuning.
10: Fun with neutral triads and 5tET subsets (there was an article in
Ear Magazine East on 10tET).
12: For all those paid gigs.
15: Read Blackwood, "Modes and Chord Progressions in Equal Tunings",
Perspectives of New Music Vol. 29 No. 2 (1991) pp. 166-200.
19: Read Mandelbaum, Haverstick, Yasser, Yunik & Swift, etc.
22: Read my paper (a slightly messed up version is at
http://www-math.cudenver.edu/~jstarret/microtone.html under "Notes on
Microtonality"). It describes 10-note scales that are 7-limit analogues
to the 5-limit diatonic scale. Also the first ET consistent through the
11-limit.
26: A meantone tuning that commits all the errors of 12 in the opposite
direction. Amazingly, two diatonic scales a half-octave apart contain
all the septimal completions of each other's consonant triads. Also the
first ET consistent through the 13-limit.
29: The purest 3-limit intervals of any ET below 53. Also the first ET
consistent through the 15-limit.
31: Read Fokker, etc. Approximates 7-limit JI and 1/4-comma meantone
very well.
34: Approximates 5-limit JI very well, perhaps the best of these tunings
for Indian music. Also contains 17tET which contains Arabic scales.


SMTPOriginator: tuning@eartha.mills.edu
From: Aline Surman
Subject: 34 in the news
PostedDate: 27-02-98 00:15:29
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: 27-02-98 00:14:08-27-02-98 00:14:09,27-02-98 00:14:10-27-02-98 00:14:10
DeliveredDate: 27-02-98 00:14:10
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 C12565B7.007FA200; Fri, 27 Feb 1998 00:14:19 +0100
Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA12744; Fri, 27 Feb 1998 00:15:29 +0100
Date: Fri, 27 Feb 1998 00:15:29 +0100
Received: from ella.mills.edu by ns (smtpxd); id XA12748
Received: (qmail 22983 invoked from network); 26 Feb 1998 15:14:22 -0800
Received: from localhost (HELO ella.mills.edu) (127.0.0.1)
by localhost with SMTP; 26 Feb 1998 15:14:22 -0800
Message-Id: <34F5FD57.37EE@dnvr.uswest.net>
Errors-To: madole@mills.edu
Reply-To: tuning@eartha.mills.edu
Originator: tuning@eartha.mills.edu
Sender: tuning@eartha.mills.edu