Yahoo Tuning Groups Ultimate Backup tuning Re: MUSIC OF THE SPHERES: Wavelength vs. Frequency

I, Bill Arnold, have my remarks below,
after wallyesterpaulrus and Charles Lucy
responses to my MUSIC OF THE SPHERES:

But we begin with Guy Murchie, author of the book
MUSIC OF THE SPHERES, and a quote from the
Old Farmer's Almanac, 1981:

"For the past 2500 years, man has searched unsuccessfully
for a simple harmonic or mathematical law to explain the
relationship of the planets. And yet the possibility of
a universal harmony, encompassing everything from atomic
particles to celestial bodies, seems more real than ever...
Is there order among the planets? Or, as Pythagoras once
put it, is there Music in the spheres?

Pythagoras is believed to have been the first person ever
to demonstrate a connection between music and geometry.
In the sixth century B.C. he discovered that using a finger
to divide a harp string precisely in half produces a tone
exactly an octave higher. This in turn led him to theorize
that, because of this obvious geometry in the humming of
the strings, there must conversely be music in the spacing
of the spheres."

==========================================================
From: Bill Arnold <billarnoldfla@yahoo.com>
Message 40186
Date: Sat Oct 26, 2002 3:52 pm
Subject: Re: MUSIC OF THE SPHERES

/tuning/topicId_39746.html#40137

What I am suggesting IS that perhaps musicologists ought to
INVESTIGATE the MATH and PHYSICS of NOTES, their FREQUENCY,
their PERIOD, their PERIODICITY, and yes, in my way of SEEING it,
whether or not...in their DISTANCES or RADIANS from their respective
CENTERS and their respective VIBRATION ORBITALS. It is my firm belief,
based on MATH and PHYSICS that the reason Pythagoras SAW what he did
IS because there IS such a SIMILARITY between the DISTANCES between
the planets as there are between the NOTES in the C Octave as I have
suggested on this message board. We will get to that understanding,
of verification or denial of it, only by investigation.

I, Bill Arnold, write: I believe that perhaps this is worthy of some
discussion. By calculations, atoms are shown to have SIZE: they have
a CENTER or NUCLEUS and ORBITALS or PARTICLES moving round in an
ENCLOSED SPACE. I SEE the SAME in the solar-planetary system and I SEE
the SAME in DIFFRACTION PATTERNS of atoms as put forth years ago by
Rutherford. It seems reasonable to me, because the MATH and PHYSICS
of music is quantified, termed and defined, that a similarity probably
EXISTS, theoretically, in music and awaits amplification.

I do NOT conclude that NOTES have NECESSARILY a CENTER and ORIBTALS,
but WHY NOT? Why should they defy the LAWS OF MATH and the LAWS OF
PHYSICS and not have SIZE?
====================================================================
/tuning/topicId_39746.html#40137

wallyesterpaulrus wrote, "sounds imaginative. like a dream."
=====================================================================================
Message 40207 From: Charles Lucy <lucy@harmonics.com>
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
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

===================================================================================
My, Bill Arnold's, remarks:

So: are musicologists and astrophysicists speaking the same language?

If we compare mathematically, as Pythagoras suggested, and Murchie
summarized: "the obvious geometry in the humming of the strings, there
must conversely be music in the spacing of the spheres."

WHAT precisely are we seeking to compare mathematically? Is the
"humming of the strings" the FREQUENCY of NOTES as suggested by me
and quantified most accurately by Charles Lucy, on Tuning, above?

Or: Is the "humming of the strings" the WAVELENGTH, as outlined
below?

That is the QUESTION for musicologists.

I would begin, with the following citations and URLs:

=========================================================================

http://hyperphysics.phy-astr.gsu.edu/hbase/sound/diffrac.html#c1

Scroll down to:
"Loudspeaker Sound Contours

One consequence of diffraction is that sound from a loudspeaker will spread
out rather than just going straight ahead. Since the bass frequencies have
longer wavelengths compared to the size of the loudspeaker, they will spread
out more than the high frequencies. The curves at left represent equal
intensity contours at 90 decibels for sound produced by a small enclosed
loudspeaker. It is evident that the high frequency sound spreads out less
than the low frequency sound.

These equal intensity curves were measured in an undergraduate sound
laboratory experiment.

Note that the wavelength of the 100 Hz sound is about 3.45 meters, much
larger than the speaker, while that of the 2000 Hz sound is about 18 cm,
about the size of the speaker."
=========================================================================
Frequency: the number of cycles per second, f in 1/seconds or Hertz (Hz)

Wavelength: repeat distance of wave
Traveling Wave Relationship
Wave Calculation

http://hyperphysics.phy-astr.gsu.edu/hbase/wavrel.html#c2

Wave Calculation
This is a general exploration calculation using the wave relationship.

Wave velocity = frequency x wavelength
Wavelength = m = x10^m = x10^ft.
Frequency = Hz = x10^Hz
Wave velocity = m/s =x10^m/s = x10^ft/s.

A single frequency traveling wave will take the form of a sine wave. A
snapshot of the wave in space at an instant of time can be used to show
the relationship of the wave properties frequency, wavelength and
propagation velocity.

The long wavelength sounds of the bass drum will diffract around the corner
more efficiently than the more directional, short wavelength sounds of the
higher pitched instruments.

The motion relationship "distance = velocity x time" is the key to the
basic wave relationship. With the wavelength as distance, this relationship
becomes l=vT. Then using f=1/T gives the standard wave relationship:
This is a general wave relationship which applies to sound and light waves,
other electromagnetic waves, and waves in mechanical media.
===========================================================================

My remarks: Should the DISTANCE or Pythagorean "spacings of the spheres/planets"
be compared to FREQUENCY or the WAVELENGTH of NOTES, and which of the latter
truly represents the Pythagorean "humming of the strings"?

Whereas WAVELENGTH of a sound or note of 100 Hz is circa 3.45 meters,
and a sound or note of 2000 Hz is circa 18 cm: thus, the lower NOTES are
LARGER IN SIZE. Is that not what is meant by WAVELENGTH: SIZE?

Thus, Pluto, the outer planet, which has a WAVELENGTH LARGER IN SIZE, maybe
should be equated with lower NOTES, perhaps just the opposite of what is done
if FREQUENCY is used? The WAVELENGTH is proportional to DISTANCE and is
related to the SIZE of the NOTE by a PROPORTION of PI times DIAMETER or 2
RADIANS [from the formula PERIMETER = PI DIAMETER or PI 2 RADIANS: what is
traditionally referred to as the DISTANCE of the planet from the Sun]. And
conversely, Mercury as the first planet would be equated with higher NOTES,
the SHORTEST WAVELENGTH?

So: musicologists, which IS it: FREQUENCY or WAVELENGTH of the NOTES which
is equated
with DISTANCES of the planets?

Thanks in advance,
meant kindly,

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

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

> I would begin, with the following citations and URLs:
>
>
======================================================================
===
>
> http://hyperphysics.phy-astr.gsu.edu/hbase/sound/diffrac.html#c1
>
> Scroll down to:
> "Loudspeaker Sound Contours
>
> One consequence of diffraction is that sound from a loudspeaker
will spread
> out rather than just going straight ahead. Since the bass
frequencies have
> longer wavelengths compared to the size of the loudspeaker, they
will spread
> out more than the high frequencies. The curves at left represent
equal
> intensity contours at 90 decibels for sound produced by a small
enclosed
> loudspeaker. It is evident that the high frequency sound spreads
out less
> than the low frequency sound.
>
> These equal intensity curves were measured in an undergraduate sound
> laboratory experiment.
>
> Note that the wavelength of the 100 Hz sound is about 3.45 meters,
much
> larger than the speaker, while that of the 2000 Hz sound is about
18 cm,
> about the size of the speaker."

yup, these satisfy the relationships with the speed of sound that i
posted earlier.
>
> My remarks: Should the DISTANCE or Pythagorean "spacings of the
spheres/planets"
> be compared to FREQUENCY or the WAVELENGTH of NOTES, and which of
the latter
> truly represents the Pythagorean "humming of the strings"?

that's certainly a possibility, but again, the wavelength
corresponding to a given frequency will depend on the properties of
the MEDIUM in which the wave travels. air at 27 degrees C, 800mmHg?
air at 30 degrees C, 750mmHg? water? earth? all have different speeds
of sound.

> Whereas WAVELENGTH of a sound or note of 100 Hz is circa 3.45
meters,
> and a sound or note of 2000 Hz is circa 18 cm: thus, the lower
NOTES are
> LARGER IN SIZE. Is that not what is meant by WAVELENGTH: SIZE?

geez -- haven't you been reading my posts? this is exactly what i've
been talking about. and *what* size corresponds to a particular
frequency depends on the medium through which the wave travels.

> Thus, Pluto, the outer planet, which has a WAVELENGTH LARGER IN
SIZE, maybe
> should be equated with lower NOTES, perhaps just the opposite of
what is done
> if FREQUENCY is used?

bill, if frequency is used, pluto *is* the lowest note, since pluto
has the lowest frequency!

> The WAVELENGTH is proportional to DISTANCE and is
> related to the SIZE of the NOTE by a PROPORTION of PI times
DIAMETER or 2
> RADIANS [from the formula PERIMETER = PI DIAMETER or PI 2 RADIANS:
what is
> traditionally referred to as the DISTANCE of the planet from the
Sun].

i don't agree. this is the circumference of the circle. it's not the
wavelength of any wave!

> And
> conversely, Mercury as the first planet would be equated with
higher NOTES,
> the SHORTEST WAVELENGTH?

if you use frequency, mercury is still the highest note, since it has
the most rapid frequency.

> So: musicologists, which IS it: FREQUENCY or WAVELENGTH of the
NOTES which
> is equated
> with DISTANCES of the planets?

monz used frequency. it's really up to you. musicologists don't deal
with planets! :)

🔗monz <monz@attglobal.net>

> From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
> To: <tuning@yahoogroups.com>
> Sent: Monday, October 28, 2002 4:57 PM
> Subject: [tuning] Re: MUSIC OF THE SPHERES: Wavelength vs. Frequency
>
>
> --- In tuning@y..., Bill Arnold <billarnoldfla@y...> wrote:
>
> > I would begin, with the following citations and URLs:
> >
> >
> ======================================================================
>
> > So: musicologists, which IS it: FREQUENCY
> > or WAVELENGTH of the NOTES which is equated
> > with DISTANCES of the planets?
>
> monz used frequency. it's really up to you.
> musicologists don't deal with planets! :)

to be specific: i equated the ratios of the set
of orbital periods of 7 of the planets (from
Venus to Neptune) with the frequency-ratios of a
7-note chord.

"Solar System Chord"
/tuning/files/monz/solarsystem/Solar2.mid

i left Mercury and Pluto out of the actual audio
file because their ratios were outside the audible
range, being respectively too high and too low.

(changing the overall "tonic" of the chord could
have included either one of them, but that would
shorten the "coverage" at the other end probably
make a second planet at that end -- i.e., either
Venus or Neptune -- also inaudible.]

and here's a logarithmic (i.e., Semitones)
"8ve"-equivalent graph of the pitches in the chord:

/tuning/files/monz/solarsystem/solar.gif

it's interesting to me:

- how the whole sonic structure vaguely approximates
a major triad with 4:5:6 proportions;

- how Mercury and Pluto, anchoring either end of
the chord, both have almost the same ratio, several
"8ves" apart, of course.

(sheesh ... when am i ever going to get around to
making webpages about this for my website? ...)

for the benefit of those who are interested, here's
the data for this "more accurate" mapping, a
second attempt at the piece, quoted from an old
tuning list post:

--------------- begin quoted post -------------

Egged on by some of Kraig's criticisms and given a boost by the
astronomy links Paul posted, I decided to hunt down more precise
info on the planets's orbital periods, and to make a more accurate
version of 'Solar System'. Here it is:

http://www.egroups.com/files/tuning/monz/solarsystem/Solar2.mid

There's not a lot of difference, but to my ears, this version is
a bit more strident, and brings out the 'major chord' quality
of the orbital-period ratios even more strongly.

Thru my speakers, I can't hear Pluto or Neptune at all, and
can just barely discern Uranus at the bottom and Mercury at
the top when I turn off all the other planets. I'll leave
these four planets out of my analysis.

The 'major chord' effect is due mainly to Saturn, Jupiter, and
Venus, with Mars reinforcing Saturn 4 '8ves' higher. Earth
adds most of the piquancy with a pseudo-'major 7th'.

So the aural effect (at least as I hear it; 'your mileage may
vary') causes Saturn to sound as the 1/1 - it is actually almost
exactly 3 '8ves' and a 135/128 5-limit 'semitone', or what Ellis
called the 'larger limma' (92 cents), above the inaudible Pluto.

Jupiter is 1 '8ve' and 375 cents higher than Saturn - pretty
darn close to an '8ve' + 5/4.

Mars is about 37 cents below the 4th '8ve' above Saturn. It's
also 2 '8ves' and 788 cents above Jupiter.

Earth is 4 '8ves' and 1057 cents above Saturn - pretty close
to one of my favorite intervals, an 11/6 'neutral 7th' (= 1049
cents). To my ears, the more important audible relationship is
that between Mars and Earth: 1094 cents, only 6 cents wider than
a 15/8 'major 7th'. I think this stands out quite strongly in
the chord. Earth is also 3 '8ves' + 682 cents above Jupiter.

Venus is very high and bright, almost exactly a 13/8 above Earth
(altho to my ears it really sounds a lot like an 8/5 'minor 6th'),
an '8ve' + 735 cents above Mars, 4 '8ves' + 323 cents above
Jupiter (pretty close to a 6/5 'minor 3rd'), and 5 '8ves' +
698 cents (a nice meantone '5th'!) above Saturn.

Here's the more accurate data, which supercedes the tables in
my original post:

Orbital period
days years

Mercury 87.969 0.24084
Venus 224.701 0.615187
Earth 365.256363 1.0
Mars 686.98 1.8808
Jupiter 4332.71 11.8621
Saturn 29.458
Uranus 84.01
Neptune 164.79
Pluto 248.54

The figure given for the Earth's orbital period is known as
the 'sidereal year': the time it takes for the Earth to make
a complete revolution with respect to the stars. It can also
be expressed as 365 days 6 hours 9 minutes 9.76 seconds.
All 'year' values are given in terms of sidereal years.
I really had to hunt for an accurate value for this, and
finally found it at
http://www.treasure-troves.com/astro/SiderealYear.html

This is different from the 'solar' or 'tropical year', which is
the one we're normally familiar with. This is the time it
takes for the Earth to make a complete revolution with respect
to the Sun's position in our sky. The solar year is 365.2421988
days, or 365 days 5 hours 48 minutes 45.9747 seconds. It is
20 minutes 23.5 seconds shorter than the sidereal year.

(Our standard system of leap-years gives a solar year 365.2425
days long, as described at the link above. This means that
after 3,319 years 10 months, we will lose a day.)

Again, these are also mean values, because they change slightly
over time.

Here is a table of the semitone values of the orbital ratios:

SEMITONES

Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune Pluto

Mercury 0.00 16.24 24.65 35.58 67.47 83.21 101.36 113.02 120.13
Venus 0.00 8.41 19.35 51.23 66.98 85.12 96.78 103.90
Earth 0.00 10.94 42.82 58.57 76.71 88.37 95.49
Mars 0.00 31.88 47.63 65.77 77.44 84.55
Jupiter 0.00 15.75 33.89 45.55 52.67
Saturn 0.00 18.14 29.81 36.92
Uranus 0.00 11.66 18.78
Neptune 0.00 7.11
Pluto 0.00

Note that this time I accepted the period of 248.54 years for Pluto,
because the majority (and most recent) of the webpages I've found
use that figure. Can anyone verify the correct value for Pluto?

In any case, the pitch I chose for Pluto's 1/1 is so low that I
can't hear it on my system, and most likely neither can anyone else.
Such is the fate of our cold little faraway planetoid...

-------- end quote post -------

-monz
"all roads lead to n^0"

🔗Joseph Pehrson <jpehrson@rcn.com>

🔗Bill Arnold <billarnoldfla@yahoo.com>

Message 40326 From: "Joseph Pehrson" <jpehrson@r...>
Date: Tue Oct 29, 2002 3:06 pm
Subject: Re: MUSIC OF THE SPHERES: Wavelength vs. Frequency

***Besides, hasn't Pluto been "dissed" of late? Don't they think
it's just one of the Kuiper belt asteroids??:

http://www.nineplanets.org/kboc.html

Besides, I just read in the Times that yet *another* planet candidate
has been discovered. Anybody remember the name??

I, J. Pehrson

Hi, Joe, and others. I have sent my papers over the years round the
world, and recently to a few members on these message boards. One member
who has them plans to put them online. I will let him identify himself if
he wishes. I hope and anticipate he will put them on a site that is
accessible in public archives.

In the interim, I would say that my papers discuss all that. The fact that
those who do not know better continue to "dis" Pluto does not take away from
the math, nor the physics that I suggested explains the relatables in my
published papers.

Briefly: aside from members reading my papers, I would say, others can "dis"
all they want. Pythagoras was right in the main. I just changed the base
of the arithmetic system from measuring using the astronomical unit,
Sun 0, Earth 1, to an ORDINAL system of Sun 0, Mercury 1, calling my
system: the solar unit system. Given that, and some of the physics, I
offered the thesis originally given by Pythagoras: the Sun is only part of
the solar-planetary system, and therefore it is a misnomer to call it a
solar system.

By including the planets in the name of the system, solar-planetary system,
it leaves room to explain that the system is in accordance [in a chord
dance :)] with a hull of the system. Now that word hull is up for grabs.
I am not going to go further than to say that the solar influence at some
point ends in its dance with the planets. Pluto might be on the edge.
It might be inside the edge. It might be outside the edge. The math
tells me what I surmised and published back in 1979 and I predicted that
what they call the asteroid belt and I call Ceres* might be akin to what
IS out on the edge of the system as we describe it: another Pluto* belt;
and they, the astronomers, have a name for it: the K. belt, named after
someone or something. The point for me is that astronomers [star namers]
seem to rule the roost and the astrophysicists [star physicists] seem to
let the astronomers describe the solar system in astronomical units and
make other statements, generally, that are back in the dark ages, by my
way of thinking. They have ignored my papers for two decades, so what:
me worry?

I had a nice correspondence, years ago, with Clyde Tombaugh, the astronomer
who found the planet Pluto in his telescope, years ago, and he was not
happy with the "dissing" of his planet, and I agreed with him. I still agree
with him. But then, he understood my point, that Cere* is a planet in the
same way; inasumch as I was emphasizing the ORBITALS of the planets in a
harmonic sequence and NOT the individual orbits.

This is so Key: it's beyond the comprehension of some. Again, this is back
to H.'s Uncertainty Principle: in the former, we search for the mean data,
statistically, over long periods of times, and statistically project ORBITALS,

and in the latter, we search for the particle in one orbit and project the
singular PARTICLE or planet and its location at a particular place and time.

[I hope I am understood, but do not panic
if I am not: I, admittedly, am a theorist.]

I stand by my papers: BODE'S LAW EXPLAINED and ON THE SPECIAL THEORY OF ORDER.

Thanks in advance,
meant kindly,

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🔗Joseph Pehrson <jpehrson@rcn.com>

🔗gdsecor <gdsecor@yahoo.com>

🔗Bill Arnold <billarnoldfla@yahoo.com>

Message 40318From: Bill Arnold <billarnoldfla@y...>
Date: Tue Oct 29, 2002 12:37 am
Subject: Re: MUSIC OF THE SPHERES: Wavelength vs. Frequency
=========================================================================

http://hyperphysics.phy-astr.gsu.edu/hbase/sound/diffrac.html#c1

Scroll down to:
"Loudspeaker Sound Contours
These equal intensity curves were measured in an undergraduate sound
laboratory experiment.

Note that the wavelength of the 100 Hz sound is about 3.45 meters, much
larger than the speaker, while that of the 2000 Hz sound is about 18 cm,
about the size of the speaker."
=========================================================================
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Message 40319 From: "wallyesterpaulrus" <wallyesterpaulrus@y...>
Date: Tue Oct 29, 2002 12:57 am
Subject: Re: MUSIC OF THE SPHERES: Wavelength vs. Frequency

yup, these satisfy the relationships with the speed of sound that i
posted earlier.
>
> Whereas WAVELENGTH of a sound or note of 100 Hz is circa 3.45
meters,
> and a sound or note of 2000 Hz is circa 18 cm: thus, the lower
NOTES are
> LARGER IN SIZE. Is that not what is meant by WAVELENGTH: SIZE?

geez -- haven't you been reading my posts? this is exactly what i've
been talking about. and *what* size corresponds to a particular
frequency depends on the medium through which the wave travels.

>
> The WAVELENGTH is proportional to DISTANCE and is
> related to the SIZE of the NOTE by a PROPORTION of PI times
DIAMETER or 2
> RADIANS [from the formula PERIMETER = PI DIAMETER or PI 2 RADIANS:
what is
> traditionally referred to as the DISTANCE of the planet from the
Sun].

i don't agree. this is the circumference of the circle. it's not the
wavelength of any wave!
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
According to the HyperPhysics website: the WAVELENGTH of a sound or note of
100 Hz is circa 3.45 meters, and a sound or note of 2000 Hz is circa 18 cm."

My question is: is the WAVELENGTH which is referred to as 3.45 meters or 18 cm,
is that the DIAMETER or the RADIAN?

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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