Re: MUSIC OF THE SPHERES: Wavelength vs. Frequency , Part III

Message 40447
From: "wallyesterpaulrus" <wallyesterpaulrus@y...>
Date: Thu Oct 31, 2002 9:19 pm
Subject: Re: MUSIC OF THE SPHERES: Wavelength vs. Frequency , Part II(Correction)

--- In tuning@y..., Bill Arnold <billarnoldfla@y...> wrote:

> wouldn't it show a concentric pattern in terms of viewed on an
> oscilloscope or properly designated device,

only if the device could measure the vibration at every point in the
surrounding three-dimensional space.

> with the FIRST HALF WAVE OUT of INCREASED
> PRESSURE, and the SECOND HALF WAVE OUT of DECREASED PRESSURE?

and so on, alternating for as long as the sound continues . . .

> Thus, if successive FULL WAVES were viewed, it would look similar
> to the Rutherford/Bohr DIFFRACTION PATTERNS for certain, simple atoms?

this is a superficial similarity. for one thing, the diffraction
patterns do not have spherical symmetry, but only circular symmetry.

> And, if all NOTES were so VIEWED, a VISUAL INDEX OF PATTERNS OF
> NOTES would be created, and I wonder if such has already been done;
> if so, IS the data, WAVELENGTH included, and VISUAL PATTERNS online,
in books?

this seems so trivial i don't know why you'd expect to find it in a
book. concentric spherical wavefronts, separated by the given
wavelength. that's all there is to it!

> Maybe it might be useful for TWO or MORE notes intereacting? Has
> that been done?

see the websites on interference that i posted (was it last week)?
some of them show the pattern of vibration caused by *two* sources
playing the same pitch. this of course applies to any wave
phenomenon, not just sound.

> Would you deem it useful for musicologists, building note
> systems?

not particularly.

kindest regards,
paul
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Thank you very kindly, Paul, for your thoughtful answers, and assisting
me in visualizing concentric SOUND in circular symmetry.

I am going to quote below what I would guess is a CHORD (?) with 10
specific NOTES: and now, based on the above, I would like to be able
to visualize the combined SOUND so produced: would the resultant
pattern of vibration of the 10 specific NOTES all sounded at once
from a single point source as specified in our hypothetical and
controlled experiment create a harmonious pattern?

Wouldn't that pattern result in a series of distinct waves of
circular symmetry?

And wouldn't that pattern be unique to that chord, and that chord
alone [assuming I am correct in calling it a chord]?

Wouldn't an Index of all chords (?) in a visual representation form
be useful to musicologists, and assist tuning as an artform?

If so, wouldn't they be akin to diffraction patterns, only in
SOUND?

And lastly, if the answer is yes, then would different instruments
creating the same SOUND chords (?) create the same patterns, or
would there be variants per each instrument? And wouldn't that
be useful for the same, and other reasons?

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Message 40207
From: Charles Lucy <lucy@h...>
Date: Sat Oct 26, 2002 10:45 pm
Subject: Music of The Spheres and Bill Arnold's numbers

I have read the papers that Bill Arnold sent me.
My initial reaction is that the 0,3,6,9,12,24,48.96,192, 288, 384
sequence is similar to the traditional harmonics series.
In the following respective musical pattern related to frequency (e.g.
in Hz.):
(using integer ratio "old" traditional logic that harmonics don't beat
i.e. Pythagorean)

3 = first Octave (3*1) e.g. C1
6 = second octave (3*2) e.g. C2
9 = second octave + fifth (3*3) or (6*(3/2)) e.g. G2
12 = third octave (3*(2^2)) e.g. C3
24 = fourth octave (3*8) e.g.C4
48 = fifth octave (3*16) e.g. C5
96 = sixth octave (3*32) e.g. C6
192 = seventh octave (3*64) e.g. C7
288 = seventh octave + fifth (3*76) or 192*(3/2)) e.g. G7
384 = eighth octave (3*132) e.g. C8

This is simplistic, yet could suggest an octaving sequence.

Charles Lucy - lucy@h... (LucyScaleDevelopments)
------------ Promoting global harmony through LucyTuning -------
for information on LucyTuning go to:
http://www.harmonics.com/lucy/
for Lucytuned Lullabies go to http://www.lucytune.com
or http://www.lucytune.co.uk or http://www.lullabies.co.uk

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Thanks in advance,
meant kindly,

Bill Arnold
billarnoldfla@yahoo.com
http://www.cwru.edu/affil/edis/scholars/arnold.htm
Independent Scholar
Independent Scholar, Modern Language Association
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-------------------------------------------------------------------

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--- In tuning@y..., Bill Arnold <billarnoldfla@y...> wrote:

> would the resultant
> pattern of vibration of the 10 specific NOTES all sounded at once
> from a single point source as specified in our hypothetical and
> controlled experiment create a harmonious pattern?

it would sound like a single note, with a very pure and boring
timbre, since all the higher pitches are harmonic overtones of the
lower, and not very interesting ones at that.

> Wouldn't that pattern result in a series of distinct waves of
> circular symmetry?

spherical symmetry. you could express it all as a single waveform, if
you knew the relative amplitudes and phases of the components. and
you'd depict this waveform with a two-dimensional graph, with the
radial direction along one axis, and amplitude along the other.

> And wouldn't that pattern be unique to that chord, and that chord
> alone [assuming I am correct in calling it a chord]?

yes, although "timbre" might be a better term, since it sounds more
like a single note than like a bunch of notes.

> Wouldn't an Index of all chords (?) in a visual representation form
> be useful to musicologists, and assist tuning as an artform?

not really, since the visual representation would be different for
different phase-relationships between the components, but these phase-
relationships have virtually no audible effect.

> If so, wouldn't they be akin to diffraction patterns, only in
> SOUND?

sound itself can experience diffraction, but here we are merely
talking about depicting waveforms.

> And lastly, if the answer is yes, then would different instruments
> creating the same SOUND chords (?) create the same patterns, or
> would there be variants per each instrument?

every instrument has different amplitudes in its harmonic partials,
among other variations.

Message 40463
From: "wallyesterpaulrus" <wallyesterpaulrus@y...>
Date: Fri Nov 1, 2002 7:41 pm
Subject: Re: MUSIC OF THE SPHERES: Wavelength vs. Frequency , Part III

--- In tuning@y..., Bill Arnold <billarnoldfla@y...> wrote:

> would the resultant
> pattern of vibration of the 10 specific NOTES all sounded at once
> from a single point source as specified in our hypothetical and
> controlled experiment create a harmonious pattern?

it would sound like a single note, with a very pure and boring
timbre, since all the higher pitches are harmonic overtones of the
lower, and not very interesting ones at that.

> Wouldn't that pattern result in a series of distinct waves of
> circular symmetry?

spherical symmetry. you could express it all as a single waveform, if
you knew the relative amplitudes and phases of the components. and
you'd depict this waveform with a two-dimensional graph, with the
radial direction along one axis, and amplitude along the other.

> And wouldn't that pattern be unique to that chord, and that chord
> alone [assuming I am correct in calling it a chord]?

yes, although "timbre" might be a better term, since it sounds more
like a single note than like a bunch of notes.

> Wouldn't an Index of all chords (?) in a visual representation form
> be useful to musicologists, and assist tuning as an artform?

not really, since the visual representation would be different for
different phase-relationships between the components, but these phase-
relationships have virtually no audible effect.

> If so, wouldn't they be akin to diffraction patterns, only in
> SOUND?

sound itself can experience diffraction, but here we are merely
talking about depicting waveforms.

> And lastly, if the answer is yes, then would different instruments
> creating the same SOUND chords (?) create the same patterns, or
> would there be variants per each instrument?

every instrument has different amplitudes in its harmonic partials,
among other variations.
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Thanks again, Paul, for that thoughtful and full response, and I must
say it does confirm a lot of what I suspected about the entire question
raised by Pythagoras comparing the humming of the strings with the spacings
of the planets. I appreciate you bringing me up to speed :) with the terms
used by musicologists to talk about some of the same things talked about in
astrophysics.

By the way, are you aware of the Sound Waves Generated and Trapped Inside
the Sun? See clickable URL below, report from the website:
===========================================================================
http://science.msfc.nasa.gov/ssl/pad/solar/p_modes.htm

Surface Waves and Helioseismology
THE SUN

5-minute Oscillations
Patches of the surface of the sun oscillate up and down with a typical period of about 5
minutes. The nature and source of these "5-minute oscillations" was a mystery for many
years after their discovery in 1962. These oscillations are shown in the image on the
left as areas of blue and red where the blue areas are moving toward us (blue-shifted)
and the red areas are moving away from us (red-shifted). The fact that this signal is
strongest near the center of the imaged disk of the sun and weakest near the edge
indicates that the motions are primarily radial - inward and outward. A movie (3.7Mb
MPEG) constructed from a series of these images (taken at the rate of one per minute for
150 minutes with the GONG network instruments) shows how individual patches are
blue-shifted and then red-shifted through several cycles. The result is an apparent
chaotic vibration of the sun.

Click on image for larger version.

p-Modes
The mysterious source of these oscillations was identified by way of theoretical
arguments in 1970 and confirmed by observations in 1975. The oscillations we see on the
surface are due to sound waves generated and trapped inside the sun. Sound waves are
produced by pressure fluctuations in the turbulent convective motions of the sun's
interior. As the waves move outward they reflect off of the sun's surface (the
photosphere) where the density and pressure decrease rapidly. Inward moving waves are
refracted (their direction of motion bent) by the increase in the speed of sound as the
temperature increases and eventually return to the surface. These trapped sound waves set
the sun vibrating in millions of different patterns or modes (3.7 Mb MPEG movie). Since
sound is produced by pressure, these modes of vibration are called p-modes. One mode of
vibration is shown in the image above as a pattern of surface displacements exaggerated
by over 1000 times. A movie (1Mb MPEG without audio, 6.5 Mb MPEG version with audio)
shows how this mode of oscillation consists of two oppositely moving waves.

Click on image for larger version.

Helioseismology
These sound waves, and the modes of vibration they produce, can be used to probe the
interior of the sun the same way that geologists uses seismic waves from earthquakes to
probe the inside of the earth. Some of these waves travel right through the center of the
sun. Others are bent back toward the surface at shallow depths. Helioseismologists can
use the properties of these waves to determine the temperature, density, composition, and
motion of the interior of the sun. A number of fascinating discoveries have been made in
the last few years using the science of helioseismology. The image above (from M. J.
Thompson) shows the internal rotation rate of the sun with red for fast and blue for
slow. The variation we see at the surface between the equator and the poles extends
inward and then rapidly disappears at the base of the convection zone (shown by the
dashed line).
==========================================================================================
Thanks in advance,
meant kindly,

Bill Arnold
billarnoldfla@yahoo.com
http://www.cwru.edu/affil/edis/scholars/arnold.htm
Independent Scholar
Independent Scholar, Modern Language Association
-------------------------------------------------------------------
"There is magic in the web" Shakespeare (Othello, Act 3, Scene 4)
-------------------------------------------------------------------

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Do you Yahoo!?
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--- In tuning@y..., Bill Arnold <billarnoldfla@y...> wrote:
> Message 40463
> From: "wallyesterpaulrus" <wallyesterpaulrus@y...>

> it would sound like a single note, with a very pure and boring
> timbre, since all the higher pitches are harmonic overtones of the
> lower, and not very interesting ones at that.

We now know of a number of planetary systems, but we don't have very good knowledge of any of them. We *do*, however, have good knowledge of the extensive systems of moons of the gas giants. Tune 'em up as chords and rock on!

----- Original Message -----
From: "Gene Ward Smith" <genewardsmith@juno.com>
To: <tuning@yahoogroups.com>
Sent: Friday, November 01, 2002 5:33 PM
Subject: [tuning] Re: MUSIC OF THE SPHERES: Wavelength vs. Frequency , Part
III

> --- In tuning@y..., Bill Arnold <billarnoldfla@y...> wrote:
> > Message 40463
> > From: "wallyesterpaulrus" <wallyesterpaulrus@y...>
>
> > it would sound like a single note, with a very pure and boring
> > timbre, since all the higher pitches are harmonic overtones of the
> > lower, and not very interesting ones at that.
>
> We now know of a number of planetary systems, but we don't have very good
knowledge of any of them. We *do*, however, have good knowledge of the
extensive systems of moons of the gas giants. Tune 'em up as chords and rock
on!

actually, my existing _Solar System Chord_ audio-files
(some in collaboration with Robert Walker) are only the
beginning of what i hope will be a long series of experiments
in creating a "sonic orrery" of our solar system.

i hope to eventually map all kinds of data to sonic events,
such as the eccentricity of the orbits, the tilt of the
planets's orbits from the ecliptic, the orbits of the moons,
the rotations and tilt of the planets and their moons, etc.

the goal is to finally have as complete as possible
a sonic mapping of solar system data -- something which
would enable one to hear at once (analogous to "seeing
at a glance") a vast arry of *periodic* planetary data.

-monz
"all roads lead to n^0"