Helicoptor harmonics

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?)

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. (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.)

thanks, 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

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

--- 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.

--- 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,

Whoops -- just noticed this. No. By 'Harmonically-related', I mean
having frequencies which approximate small integer multiples of a
fundamental frequency. This fundamental frequency may not be
physically present but will be supplied to the consciousness by the
brain's "virtual pitch" mechanism. As I mentioned, this in general
will differ from the pitches that may arise as combinational tones.
But virtual pitches and combinational tones are both "subjective" in
that they are not physically present in the sound in the air or when
it arrives at the eardrum. Here, I was referring to relationships
within the sounds that *are* physically present around the listener.

Hope this is getting clearer,
Paul