12 note Orwell scale

To further the debate about the best keyboard layout for
microtonal music, I've recently pumped for a Halberstadt.
This has the advantage of being cheap and easily available,
but isn't ideal for every tuning system, partly because of
a bias towards 12 note periods.

Well, here's a scale with 12 notes from an Orwell
temperament. It's chosen so that the missing note from the
13 note Orwell MOS is between E and F, and C major is in
tune to the approximation of 4:5:6. In addition, C-Bb
approximates 7:4 and C-Db approximates both 16:15 and 15:14.

The mapping of Orwell generators to keys is:

0 -4 5 1 -3 2 -2 7 3 -1 8 4 0

C D E F G A B C

(Adopt a fixed width font for optimal satisfaction.)

It sounds out of tune but with smooth harmony. It has pure
fifths, but not so many of them. Regular correspondents may
be concerned at the limitation of 12 notes to the octave.
However, I fully believe that this provides sufficient
material for creative music making.

The following fifths are in tune as approximations to 3:2:

Eb-Bb
C-G
Gb-D (sic)
E-B
C#-G#

C-E-G and Eb-Gb-Bb are (approximate) 4:5:6 triads.
C-Eb-G, E-Gb-B and Gb-A-D are 6:7:9 triads. E-G-B and
Gb-Bb-D are 10:12:15 triads. C-E-G-Bb-C-F is a 4:5:6:7:8:11
chord and Eb-F-Bb-Db is a 6:7:9:11 chord. With some of
these chords, the notes are not what you'd expect, as a
result of this being a subset of a 13 note scale instead of
having consistent fingering with 12 notes.

Here's a Scala file:

! orwell12_po.scl
!
12 note Orwell scale, pure octaves
! Unstretched TOP-RMS
114.295
157.131
271.426
385.722
! note from Orwell13 omitted 428.557
542.852
657.148
699.983
814.278
928.574
971.409
1085.705
1200.000

For those with keyboards that have retunable 12 note
octave scales, here are the offsets in cents for notes other
than C:

14.3 -42.9 -28.6 -14.3 42.9 57.1 -0.0 14.3 28.6 -28.6 -14.3

And for purists who want a mathematically optimal tuning
with no compromises:

! orwell12_rms.scl
!
12 note Orwell scale, TOP-RMS tuning
12
114.353
157.210
271.563
385.916
! note from Orwell13 omitted 428.773
543.126
657.479
700.335
814.689
929.042
971.898
1086.251
1200.604

Graham