--- In harmonic_entropy@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:
> --- In harmonic_entropy@yahoogroups.com, "traktus5" <kj4321@h...>
> wrote:
> > Hello group. I read the statement below, and was wondering if
you
> > scholars would be kind enough to say whether it is true, and if
so,
> > where I could learn more about it?
> >
> > "When different frequency waves meeet, they add and multiply.
>
> It depends in what sense you mean "add" and "multiply". It can't
be
> in one and the same sense.


I see what you mean. I'm mindful of your earlier comments
on 'multiplication tones'. I saw the comment in a 'sacred
geometry' text (indulge me for a moment), where, I believe in the
pre-Hellenic style of algebra [eg, Egyptian], there is a permutation
of phi where there is addition on one side and multiplication on the
other, which caught my attention, since, being the musician and
number mystic I am (numbers are archetypes -- didn't Plato believe
so too? -- so intervals are for me too), I've always been struck by
three beautiful chords which have that same feature of simutaneous
addition and multiplication:
5/4 x 3/2 = 15/8; 5/3 x 4/3 = 20/9; and 7/5 x 3/2 = 21/10 -- where
the numerators add up to, and the denominators multiply up to ( in
the first case) 8...and, in the next two chords, give 9, and 10, in
the same manner. That's all! And they're such beautiful sounding
chords to boot, so far removed from that detestable (in my opinion)
sound of the dominant seventh chord (alone), or even the triad!

(I know my numbers are somewhat arbitrary, there being alternative
numberings for the intervals, but I am comfortable with Occam's
razor approach of lowest number, and have some other
considerations...and see my comments below about temporarily setting
aside tuning issues during this stage of my research.)


>
> > Phi
> > permits waves to intersect in orderly, harmonic patterns...
>
> This seems to be *least* true for phi and *most* true for simple-
> integer ratios, doesn't it?

Yes!

>
> >thus waves
> > of a different length form a stable nest.
>
> Ditto.

Continuting from above, that's what I'm trying to get my hands on...
reading about the mixing of light waves...that, for instance, the
dominant seventh chord and triad have practially no 'nest'; it's
strait out of one harmonic series, just one vibration pattern, or
expanding circle of sound, so to speak, whereas the mixture of
harmonic patterns in other chords is clearly more interesting....
(I'm still working this out)...and am trying to figure out how it's
related to presumed basic forces in music, such as the tritone,
minor-ness, and the self similarity, or energy gradient, of I is to
V as IV is to I.


>
> > In electronics, this
> > is 'heterodyne', and is used to modulate radio and tv signals..."
>
> We can discuss heterodyning, and we can heterodyne using Phi as
the
> frequency ratio, but nothing about heterodyning assumes or
> necessarily has to do with Phi.
>
> > Also (---going out on limb here!) could it be possible that
there
> is
> > some sort of interaction of harmonics, almost like the
interference
> > pattern referred to above,
>
> I don't know what interference pattern was referred to above,
> exactly. Could you give more from this source? I'm sure there was
> more to it than these unclear, seemingly erroneous statements
about
> Phi.


It's a fairly, I realize, mushy 'geometrical philosophy' essay.
I'm reading up on heterodyning, to clarify.



> > but at the level of harmonics, which is
> > involved with the perception of 'chord color'? I guess I'm sort
of
> > thinking of that older theory of dissonance pertaining to
> coinciding
> > partials....
>
> Well, then a chord would seem to have a different color if it were
> tuned slightly differently, yes?

Absolutely. You've been very patient with my bias. I just haven't
had the exposure to microtonal music yet, (Bach, Stravinsky,
Schoenberg, Part, Cage, etc, yes) and just work on my piano, which
I don't tune myself, but share, with the tuning group, an intense
interest in the math of music, and a desire to expand beyond
conventional harmony (my speciality being alternate, 'functional'
[non-dominant] harmony). Can you suggest an easily obtainable CD
of alternate tuned music? (I have no speakers on my computer.)

Thanks for your comments. -Kelly