4:5:6:7 and Dominant 7th

In response to Andrew Milne and others:

My ears & experience tell me that the 12-ET dominant 7th (major-minor 7th)
chord
is a representation of 4:5:6:7. In my tonal compositions in 19, 22, and
31-ET, I have deliberately made use of the best match to 4:5:6:7 as a
dominant 7th,
and contrast it with other 7th chords, such as 10:12:15:18 (minor-minor 7th)
and 8:10:12:15 (major-major 7th).

The resulting voice-leading of 10:12:15:18 followed by 4:5:6:7, with both
built on the same tonic, is naturally microtonal, and very acceptable to my
ears. I also find the voice-leading of 4:3 to 7:4 of V to 5:4 perfectly valid.

My evolving theory of >12-ET tonality treats 7:4 built on scale degree 5 as
a necessary "chromatic" inflection of scale degree 4, comparable to the
raising of the 3rd of the V7 chord in minor keys in standard 12-ET
practice. I do not
consider 9:5 or 16:9 to be proper 7ths for 4:5:6 in >12-ET practice--they
should be treated as passing tones, and not be fused onto 4:5:6 when a
better 7:4 match is available.

Those of you who write in >12-Ets simply for purer 3 and 5 limit intervals
will naturally object--but understand that my rationale for using >12-ETs
is to extend
traditional harmonic practice through the additional simple 7 and 11-limit
intervals
available in >12-ETs.

Those of you that have a cassette of my music might wish to add their
evaluation
of this practice.



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