RE: [tuning] Reply to William Annis

I wrote,

>>(b) one should remember that it fails to allow even some of the simplest
of
>>Western triadic music to be performed.

William Annis wrote,

> That's fine. I'm not trying to do western triadic music,
>though of course that will be an influence in my music, since I've
>steeped myself in it for 15 years or so now. :)

Everyone seems to have misunderstood this. I wasn't talking about _your_
scale, William; I was talking about the regular duodene on the 3-5 plane. My
point was simply that one should be aware of its limitations with regard to
Western triadic music, so that one can be aware of the potential limitations
of an analogous construct (i.e., your scale) with regard to any new style
using harmonies based on 3 and 7.

With regard to your V-IV-I progression, it seems like you're proposing a
"diatonic" scale of

1/1 9/8 7/6 4/3 3/2 14/9 7/4 (2/1)

In this scale you'll find a "wolf" interval of 21:16 between 4/3 and 7/4.
One way to eliminate this is to temper out the scale; i.e., in 22-equal:

0 4 5 9 13 14 18 (22)

I call this scale "sub-minor" in my paper on 22-tone equal temperament. If
you're looking for a 12-tone superset, an excellent one is

0 2 4 5 7 9 11 13 14 16 18 20 (22),

which falls naturally on a standard keyboard starting on A, and contains not
only awesome 3-7 resources but full 3-5-7 ones as well.