RE: [tuning] Inversion of 6:7:9

Gary Morrison wrote,

>9:7, to me at least, has a kinda freaky sound, but I like it. Or let me
>rephrase that: I should say that I like it BECAUSE of its kinda freaky
>sound. It doesn't strike me as discordant, but I have been able to use
>it as reasonably effective a dissonance, such as resolving outward to
>fourths.

>One that I'd like to experiment with is a JI version of what Ivor Darreg
>found so interesting in 17TET: Resolving 9:7, which is could be thought
>of as an unsettled version of a major third, outward to 7:5, which is a
>very consonant tritone. That would then be more or less the reverse of
>the traditional tritone resolution. One could then resolve that outward
>to 5:3.

The "7:5" is not very consonant in 17TET, where the best approximation of a
7:5 is 18¢ flat of a just 7:5.

But along similar lines, in my 22-tET paper
(http://www-math.cudenver.edu/~jstarret/22ALL.pdf), 9:7 is the
"characteristic dissonance" of the symmetrical decatonic scale (whose odd
limit is 7), much as the tritone is the "characteristic dissonance" of the
traditional diatonic scale (whose odd limit is 5). The term "characteristic
dissonance" refers to an interval's occurence in the scale as a "diminished"
version of an interval that is usually a consonance (4:3 and 3:2,
respectively), allowing one to easily find one's position within the scale
(hence the strong cadential quality).