Nonatonic Tryhill 11-limit scale in 22-tET & reply to Dan Stearns

I wrote,

>and the harmonic lattice is
>
> 10
> /|\`.
> / | \ 5--------18
> . . .21 \ | `. ,' `. 10
>. /,' `.\| 0--------13 /|\`.
> 3--------16 `. / | \ 5--------18
> 8--------21 \ | `. ,'
> `. /,' `.\| 0--. . .
> 3--------16

Actually, the note 3 would form a very stable tonic for this scale, since
the chord 3 21 13 16 10 approximates an otonal 1:3:5:7:11 chord! So the
scale should be written as

0 2 5 7 10 13 15 18 19 (22)

Manuel, this may be a good addition to the scale archive, plus its Tryhill
pentatonic "generator"

10
`.
5--------18
`. ,' `.
0--------13

0 5 10 13 18
(which generates the nontatonic above through duplication at 3/22 octave)

We can go even further -- this scale itself can be generated from the
Tryhill 3-tone

5
`.
0--------13

which generates the pentatonic above through duplication at 5/22 octave (and
is also known as the subminor triad).

All in all, these scales are probably the best hint so far at what hyper-MOS
may have to offer (any others?)

Dan Stearns wrote,

>What's missing from the three-term series is the built-in ordering
>rule supplied by the single generator of the two-term series

Perhaps the fact that the interval of duplication is different at the
different stages of construction is what's making this problem rather
difficult?