RE: [tuning] beta dominance [12-22 scale]

Hi Joseph...

The subject line ("beta dominance") refers to what?

>Sorry, I mis-typed. Or more accurately, I mis-"thought." It is, of
>course, the DOMINANT 7th chord I was talking about... Eb-G-Bb-Db, which
>was what you wanted me to try, with root, fifth and seventh on the black
>keys and the third, "G," on the white key...

>This was the one where there was virtually NO beating in your 12-22
>scale, compared to clearly audible beating in the 12t-ET version.

Well, unfortunately the tritone is still exactly the same as in 12-tET, and
the fifth is much worse (being already nearly perfect in 12-tET). But the
other four intervals in the chord, 5:4, 6:5, 7:6, and 7:4, are all better
than in 12-tET.

>So the experiment was really a striking success.

>I also, just now, tried what, I believe, you are considering the
>"mirror"... E-G#-B-D, with the root, fifth and seventh on "white" keys
>and the third on a black...

That's not the mirror -- that one of the original dominant seventh chords I
was talking about. The mirror is the half-diminished seventh, with the root,
third, and seventh on one color, and the diminished fifth on another color.
There are five possible roots for these, just as there are five possible
roots for the really smooth "dominant seventh" chords including the two you
found above.

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