RE: [tuning] Re: Trines, triads, octave-affinity and "rootedness" (Erlich)

Margo wrote,

>From another angle, using "smooth" in a way which may not necessarily
>be synonymous with your "smoothness," I'm tempted to guess that 2:3:4
>may be more "smooth" than 3:4:6 because the fourth above the lowest
>note of the latter sonority may be in tension with the third partial
>of the lowest note. Likewise, might this tension come into play with
>the lower fourth of a 3:4:5 sonority vis-a-vis a 4:5:6 sonority?

Well, compared with the definition of "smoothness" as the opposite of Plomp
"roughness", your usage clearly attaches added importance to the lowest
sounding note. Which is what I was getting at with the idea of "rootedness".

>You're evidently coming
>from a perspective in part of 18th-century inversion theory

I don't think I'm too influenced by that. However, since Partch was largely
concerned with intervals between pitch classes regardless of octave
transpositions, and he coined the terms otonal and utonal, it seems better
to use other terms to describe the distinction between the two trines, which
as you note, can be regarded either as analogous to major and minor, or
instead, as analogous to the different inversions of the major chord.