Re: The augmented triad

[Paul H. Erlich wrote:]
>But the most consonant tuning for the augmented triad is something near
equal temperament.

I think it was John DeLaubenfels who used a phrase in one of his post
something along the lines of 'creatures of equal temperament...'* I've
always really, REALLY liked the augmented triad family of chords... I also
feel that the 1-3#5 serves as a good (i.e., positive) example of the
potential possibilities that can rise outside the compass of just
intonational organizing, thinking, and referencing. Of course this is not
to say that there's anything 'wrong' with JI organizing, thinking, and
referencing...** Only that I believe there are indeed other fundamentally
valid (structural) possibilities to at least be considered (and hopefully
mined).

Dan

*This ['creatures of temperament...'] is also mentioned (in the context of
the augmented triad) by Ellis in Helmholtz' "On the Sensation of Tone."
"From what follows it is evident that the transformation could only take
place in tempered intonation. The tones confounded are all 42 cents apart,
and could not possibly have been confounded in just intonation." [Alexander
J. Ellis, footnote pg. 339, _On the Sensation of Tone_]

**I've posted about recasting the augmented chord in interval ratios of 19
a couple of times... TD 74: "One of my very favorite 12-tET [single octave]
chords is the 1-3-#5-7 (@3+3+b3), which to my ear[s] 'needs' a >15/8 (or
13/7) major seventh to retain its (personally desirable) 12-tET
character... So I personally prefer a +19/15 + 5/4 for the augmented triad
with a +6/5 on top (+19/15 + 5/4 + 6/5 @ 1/1, 19/15, 19/12, 19/10)." And TD
75 pertaining to a 1-3-#5-7 + 1-3-5-7 set @ 240 : 304 : 380 : 456 : 570 :
684 : 855 : 912, where +19/15, +5/4, +6/5, +5/4, +6/5, +5/4, +16/15 = 1:1,
19:15, 19:12, 19:10, 19:8, 19:6&2/3rds (57/20), 19:5&1/3rd (57/16), 19:5.