RE: 7:4 versus...

Harold wrote:

>--create a pure 4:5:6:7 chord on your synth
>--create a 4:5:6 triad, but add a 9/5 on top (9/5 * 4/4)
>--create a 10:12:15:18 chord on the same root as each of the previous
chords

>After you are convinced thatchord #1 is smoother than chord #2[...]

Harold, the "classical" dominant seventh chord is a 4:5:6 triad with a 16/9,
not a 9/5, on top. While the 4:5:6:7 is unquestionally smoother and more
consonant, it is unfamiliar sounding, and Western musicians trained in tonal
triadic diatonic practice will initially prefer a 4:5:6 triad with a 16/9.

In 41-tet, the three "dominant seventh" chords would be
0 13 24 33 (7/4 on top)
0 13 24 34 (16/9 on top)
0 13 24 35 (9/5 on top)
In 12, they are all the same. In 19 and 31, the last two are the same. In 22
and 27, the first two are the same. That's why I went to 41.

>Another ear-shock: 22 also has a very good 11/8. Try playing a
>4:5:6:7:9:11 chord in 22, and you'll see what I mean. We all know that
>in 12, we must omit the major third of this chord (5/4), but notice
>how smooth this chord is with good 7/4 and 11/8 approximations!

In 12, the closest approximation to this chord, both mathematically and
aurally, is
C E G Bb D F#. I never heard of omitting the major third of this chord.


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