An interesting scale in 19-tet

Dear nineteeneers,

Thought some of you might be interested in this scale in 19-tet:

0 3 6 7 8 9 11 13 18 or 3-3-1-1-1-2-2-5-1

You can think of it as a major scale with a flat sixth and a high
leading-tone, i.e.
0 3 6 8 11 13 18 or 3-3-2-3-2-5-1,
*plus* an extra note on either side of the fourth (notes 7 and 9)

It's not particularly attractive played just as a scale, but it (plus its
modes) is completely unique in 19-tet, in that every possible interval
(considering inversions equivalent, so an interval of 1 is equivalent to
18; an interval of 5 equivalent to 14, etc) is present an equal number of
times--namely, four times each.

Actually the ten-note scale formed by the notes _left_out_ of the
nine-tone scale above also shares the same property (each interval-class
appears five times instead of four though).

So this scale, and its complement, are the only subsets of 19-tet that
share the same uniform spread of intervals that you find in the whole 19
(namely, 19 of each interval-class).

It's the complete opposite of the 7-out-of-12 diatonic, which has a
different number of each kind of interval (2 semitones/M7ths, 5
tones/m7ths, 4 m3rds/M6ths, 3 M3rds/m6ths, 6 P4/5ths, 1 tritone).

I thought it was cool anyway!

best --jon