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, ....) 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!)

> 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". Or as a thought experiment, imagine a civilization where
the epochal discovery of the small number ratios of musical
intervals led to chord construction and harmony even before melody
and counterpoint...what sort of harmony and music it would have
produced...sort of like if Bach had been a Pythagorean instead of a
Lutheran! (Listening to John Cage's organ piece 'Souvenier'
(1972), reminds me of this, too)

THanks again, Paul. -- Kelly











> --- In harmonic_entropy@yahoogroups.com, "traktus5" <kj4321@h...>
> wrote:
> >
> > hello. I heard an interesting sound today--the far off low
thud-
> > thud-thud of a helicoptor. A little bit unusually, however,
its
> > sound was distinctly pitched at the interval of a 5th (the 1st,
6th
> > and 12th harmonic?)
>
> Not unusual at all! Helicopter blades perform a periodic motion
> (around an axis, over and over again), so their spectrum must be a
> harmonic one. That follows from Fourier's theorem. A lot of
> mechanical and electronic devices emit harmonic spectra for
similar
> reasons; the infamous 60Hz hum is an example and often its
harmonics
> are a lot louder than the fundamental (in buzzy flourescent lights
> for example).
>
> > I've always wondered, and thought I would ask here, what area of
> > acoustics, or physics, or electronic music or recording
> engineering,
> > (or fluid dynamics?) might I find more information on these sort
of
> > sound phenomemon which are the by-product, not of instruments,
but
> > of natural phenomonon, and sometimes machines, where there are
some
> > pitches, but probably more inharmonic sounds and non-pitched
> > sounds.
>
> Sounds like you still have questions about what your question is!
But
> many such phenomena are well-studied, and perfectly harmonic
sounds
> are quite common in nature -- thus it's not suprising that humans
are
> hard-wired to seek out and integrate harmonically-related sounds
in
> our acoustic field of perception.
>
> > (Other good examples are the sound of water in a stream,
> > or, as mountain climbers once described it, the way far off
sound
> of
> > gale force winds howling over Denali peak in Alaska, or the
hissing
> > sound reported from inside a tornado --which all contain some
> > pitches.)
>
> Such chaotic sounds, of course, are preponderant in nature, and
> certainly all the fields you mention touch upon their mechanisms
from
> time to time. Many popular books and articles on chaos theory,
> fractals, and the like discuss how so much natural noise is "pink"
in
> its spectral charater, exhibit structure on various scales that
is,
> spookily like much human-made music, halfway between the
> memoryless "white" and meandering "brown" classical models of
> stochastic processes.
>
> Technically speaking, it makes no sense for a noise to "contain
some
> pitches". Any sound can be analysed as a fixed composite of pure
> tones and nothing else, if desired. That doesn't mean that that's
the
> way we hear, of course. (We'd be incapable of hearing the changes
in
> a sound from one second to the next if that were the way we
heard.)
> In fact, though we're perfectly capable of experiencing pitchless
> noise, our ears are seeking out harmonic series anywhere and a lot
of
> psychological experiments have evoked otherwise inaudible,
physically
> absent pitches by presenting narrow-band noise around the
frequencies
> where lower-order harmonics would be. It's kind of like how you
can
> see brief images of things moving across the screen if you look at
> TV "snow" with your peripheral vision -- we're hard-wired to
detect
> motion, and can be easily fooled into seeing it with nothing more
> than independent random noise at each point in our visual field.
>
> 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!
>
> > thanks, Kelly