Why would anyone bother with strict JI beyond the 5-limit? For the cost of only
a 2.7 c error in any 11-limit interval you can have a LOT more consonances.

Thanks to Paul Erlich for pointing out the unevenness of my earlier 22 tone
11-limit tuning and asking why I stopped at 22 tones. For no good reason as it
turns out. You can trash that 22 tone tuning in favour of the strictly proper 31
tone tunings below.

The lattice below is really two lattices. One must choose between Gbb and Ex
(they are only 13 cents apart). I think it is obvious to choose Gbb since this
gives 5 otonal hexads and 4 utonal. When this choice is made we are left with 31
tones in 4 step sizes, 30.4 c, 36.2 c, 49.2 c and one step of 55.0 c (between Cb
and B#). It may be considered as a detempered 31-tET.

Sorry about the width (85 characters). I hope I managed to avoid word-wrapping
it outgoing. If it looks like a mess, it might come good if you widen your
window. Otherwise you're going to have to paste it somewhere else and delete
some returns. When it is right it looks like a diagonal stack of 6 hexagons
(with flies buzzing around them).

(Ex)-----Bx
/ \ / \
G#/ \ D#/ \
A#
Bb F C / G \ / D \

Fx------Cx------Gx------Dx
/ \ / \ / \ /
(Ex) A / Bx\ E / \ B / \ F#/
C#
Cb Gb Db / Ab \ / Eb \ / \ /
5 G#------D#------A#------E#------B#
/ \ / \ / \ / \ /
/ 7 \ Fx Bb/ Cx\ F / Gx\ C / Dx\ G / D
/ 11 \ Abb Ebb / Bbb \ / Fb \ / \ /
4-------6-------9 A-------E-------B-------F#------C#
otonal hexad / \ / \ (Ex)/ \ Bx /
legend G# Cb/ D#\ Gb/ A#\ Db/ E#\ Ab/ B# Eb utonal hexad
/ Cbb \ /(Gbb)\ / \ / legend
Bb------F-------C-------G-------D
1/9-----1/6-----1/4
/ \ / \ Fx / \ Cx / Gx Dx \ 1/11/
A / E \Abb/ B \Ebb/ F#\Bbb/ C# Fb \1/7/
/ \ / \ / \ / \ /
Cb------Gb------Db------Ab------Eb 1/5
/ \ / \ G# / \ D# / A# E# B#
Bb / F \ / C \ / G \Cbb/ D (Gbb)
/ \ / \ / \ /
Abb-----Ebb-----Bbb------Fb
\ A / \ E / B F# C#
Db\ / Ab\ / Eb
\ / \ /
Cbb----(Gbb)

!
! keenan5.scl
!
11-limit, 31 tones, 9 hexads within 2.7c of just, Dave Keenan 27-Dec-99
31
!
36.19153216 ! Bx
85.39311378 ! C#
115.8026469 ! Db
151.994179 ! Cx
201.1957607 ! D
231.6052938 ! Ebb
267.7968259 ! D#
316.9984075 ! Eb
353.1899397 ! Dx
383.5994728 ! E
432.8010544 ! Fb
468.9925866 ! E#
499.4021197 ! F
548.6037013 ! Gbb
584.7952335 ! F#
615.2047665 ! Gb
651.3962987 ! Fx
700.5978803 ! G
731.0074134 ! Abb
767.1989456 ! G#
816.4005272 ! Ab
18/11 ! Gx
883.0015925 ! A
932.2031741 ! Bbb
968.3947062 ! A#
998.8042393 ! Bb
1048.005821 ! Cbb
1084.197353 ! B
1114.606886 ! Cb
1169.590467 ! B#
2/1 ! C

The lattice below is a near miss. 8 complete 11-limit hexads. At least it only
has 3 step sizes, 30.4 c, 36.2 c, 49.2 c. It may be useful when fewer than 31
tones are to be made available.

We can't put B# here because it clashes with Cb ( ) Fx------Cx------Gx
/ \ / \ / \
A / \ E / \ B / \
F#
Gb Db / Ab \ / Eb \ /
\
5
C#------G#------D#------A#------E#------B#
/ \ / \ / \ / \ /
/ 7 \ / Fx\ Bb/ Cx\ F / Gx\ C / G D
/ 11 \ Dbb Abb / Ebb \ / Bbb \ / Fb \ / Cb
4-------6-------9 A-------E-------B-------F#
otonal hexad / \ / \ / \ /
legend C# G# / D#\ Gb/ A#\ Db/ E#\ Ab/ B# Eb utonal
hexad
Fb / Cbb \ / Gbb \ / \ /
legend
Bb------F-------C-------G-------D
1/9-----1/6-----1/4
/ \ / \ Fx / \ Cx / Gx \
1/11/
A Dbb/ E \Abb/ B \Ebb/ F#\Bbb/ Fb Cb
\1/7/
/ \ / \ / \ / \ /
Gb------Db------Ab------Eb 1/5
C# / \ G# / \ D# / \ A# / E# B#
Bb F / C \ Fb/ G \Cbb/ D \Gbb/
/ \ / \ / \ /
Dbb-----Abb-----Ebb-----Bbb------Fb------Cb
\ / \ A / \ E / B F#
Gb\ / Db\ / Ab\ / Eb
\ / \ / \ /
Fbb-----Cbb-----Gbb ( ) Can't put Dbb here because it clashes with C#

Regards,

-- Dave Keenan
http://uq.net.au/~zzdkeena