RE: [tuning] through the looking glass [12-22 scales]

I wrote (discussing near-5:6:7:9 half-diminished seventh chords in my
12-out-of-22 keyboard mapping),

>> I meant the root is one color and all the other notes
>> are the other color.

Joseph Pehrson wrote,

>For these chords I hear a STRIKING difference between the 12-22 scale
>and the 12t-ET. Virtually NO beating the in 12-22. For me, these
>chords had as pronounced a difference as the dominant sevenths... Is
>this the way it "should" be??

Well, sort of -- in this 5:6:7:9, just as in the 4:5:6:7 we looked at
before, the 3:2 (aka 9:6) is worse in 22-tET than in 12-tET, and the 5:7 is
the same, while the 5:6 and 6:7 are better. This chord also contains a 5:9,
which is 19¢ off in 22-tET and 18¢ off in 12-tET. The interval that really
makes the difference is the 7:9 -- it's only 1¢ off in 22-tET, but 35¢ off
in 12-tET.

So, one of the things that's really neat about 22-tET is that it gives you
two _different_ versions of a half-diminished seventh chord, _both_ of which
you've found to be smoother than the 12-tET half-diminished seventh. If you
were to use the full 22-tET mapping (with the skipped Es), you could play
some microtonal shifts between one type of half-diminished seventh and the
other (two tones remain fixed while the other two move by 1/22 octave),
thereby giving "quartertones" a harmonic logic that is very rarely
associated with them.

I enjoy a similar effect with minor seventh chords, though you've said you
weren't too fond of the 12:14:18:21-approximating chord such as the one
found at Eb-Gb-Bb-Db in the 12-out-of-22 mapping (the other one is
10:12:15:18-approximation such as found at C-Eb-G-Bb).

The great thing about this 12-out-of-22 mapping, besides representing many
of the important resources of 22-tET, is that all chords that "look" the
same, in terms of both the pattern of colors and the interval-sizes looking
the same, sound the same; and you can even reverse the colors (black ->
white, white -> black) and the chord will still sound the same. So once
you're familiar with the different chords you want to use, you can navigate
around the tuning fairly easily (with the caveat, of course, that's you'll
be restricted to just 12 out of the 22 tones).

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