Another great 12-tone subset of 22-tET

In preparing for the Microthon, I tuned my keyboard to a "normal"
(i.e., octaves are still octaves) 12-tone mapping that includes the 7-
out-of-22 scale that we discussed recently, the quasi-equal
heptatonic (numbers indicate interval sizes in 22nds of an octave):

'D'(4)'E'(3)'F'(3)'G'(4)'A'(3)'B'(3)'C'(3)'D'

Again, this scale reminded Ara Sarkissian of the music of some Arabic
land (I forget which), and, as Dave Keenan pointed out, also happens
to have four excellent triads: 'D minor', 'E minor', 'F major',
and 'G major' (thus 'D minor 7' and 'E minor 7' are also excellent).
It's a great scale to play around with since it combines a very non-
Western melodic structure with some familiar, near-5-limit-JI
harmonies.

When I tuned this, I rather arbitrarily tuned the black keys to other
22-tET pitches.

I woke up today thinking it would be nice if there were some way to
use the black keys to allow a modulation to a hyper-Pythagorean
diatonic scale, whose Aeolian mode has nearly just 6:7:9 triads as
its i, iv, and v. Well, I figured out how to do this and, lo and
behold, my keyboard was already tuned that way! And, furthermore, not
one but _three_ hypermeantone diatonic scales were lurking there!
Behold:

D(2)D#(1)E(3)E#(1)F#(2)'G'(2)G#(2)'A'(2)A#(1)B(3)B#(1)C#(2)D

The hyper-Pythagorean Aeolian scales available are

G# A# B C# D# E F# G#
D# E# F# G# A# B C# D#

and

A# B# C# D# E# F# G# A#

One could play with this mapping forever (though I like to be able to
switch to the other two I've suggested here and programmed on my
keyboard, which are the hexachordal dodecatonic scale and the 12-tone
hyper-Pythagorean scale -- each multi-trick ponies as well)!

I wrote:
> In preparing for the Microthon, I tuned my keyboard to a "normal"
> (i.e., octaves are still octaves) 12-tone mapping that includes the
7-
> out-of-22 scale that we discussed recently, the quasi-equal
> heptatonic (numbers indicate interval sizes in 22nds of an octave):
>
> 'D'(4)'E'(3)'F'(3)'G'(4)'A'(3)'B'(3)'C'(3)'D'

Oops -- the interval between 'D' and 'E' is 3, not 4, 22nds of an
octave. Sorry!

That's neat Paul!

-- Dave Keenan
http://dkeenan.com