--- In harmonic_entropy@yahoogroups.com, "traktus5" <kj4321@h...>
wrote:
>
> Hello Paul! (I didn't know you were around...) Thanks as usual for
> your thought-provoking, wide-ranging, and encouraging comments!
>
> >...humans are hard-wired to seek out and integrate harmonically-
> related sounds in our acoustic field of perception>
>
> Practially speaking, does 'harmonically-related' mainly mean
> the 'root tracking' primary difference tones, or does it also
> include the secondary, tertiary and higher combination and
summation
> tones (eg, 2F, 3F, ....)

Neither. None of the difference tones do any "root tracking" on
general stimuli. Rather, it's *virtual pitches* that are the audible
manifestation of our brain's 'root tracking' ability. Virtual pitches
do not, in general, agree in pitch with any of the combinational
tones. And it's a good thing if you've ever used 12-tone equal
temperament (though you've never revealed whether or not you do). The
difference tone of a C-E major third in 12-equal is a low C#! Yet we
hear the root pretty much as a C . . .

> I get the impression the latter are only
> releted to extreme sound events --(which reminds me how John Cage
> said he liked all sounds, except those which cause pain!)

On the contrary: the cubic combinational tone 2*f1 - f2 is, under
normal, not-too-loud circumstances, *louder* than the quadratic
or "primary" difference tone f2 - f1. It is thought that the brain
may contribute to this sensation, while most other combinational
tones are purely a result of nonlinearities in the ear's response.

> > Anyway, I'd love to help you in your quest as much as I can --
you
> > should feel free to e-mail me as you progress!>
>
> You are very generous. Your comments have been helpful to me, as I
> love chords (Bach) and numbers, and I'm glad you're available for
> future comment on my project, which is tyring to figure out
> what's 'functional' in the "octatonic" (non-dominant) harmony I
fool
> around with, and whether it has has anything to do with "the
> numbers".

OK, please post the specifics of this to the tuning list, or wherever
you feel it's appropriate, and I'll take a look.