9/24/00

This paper will attempt to describe the mechanisms that order the solar system to keep it in place and functioning as it does. It will also attempt to relate the solar systems mechanism to either musical harmonics or the Mayan Tzolkin.

Let's arrange the Sun and planets in sequence, arbitrarily assigning musical notes to all, as a first test, just to see what it may infer:

Sun- Note A
Mercury- Note B
Venus- Note C
Earth- Note D
Mars- Note E
Jupiter- Note F
Saturn- Note G
Uranus- Note A
Neptune- Note B
Pluto- Note C, 39.5 au., (mean)
Planet X- Note D, 43.7 au., (mean)

This just gives us some kind of order to the concentrics and eccentrics of the planets, that we know is there.

Next, we'll number all as follows, representing a Prime note Sun (1) and its musical sinewave nodal harmonics of 7 notes of an octave plus the repeated partial octave to the 11th note which is again, the 4th (Hypothetical Planet X). We'll ignore the asteroid belts (I call them egressing lunoids as planetary remnants moving outward, opposite of the planets ingressions toward the Sun). Later on we will find that the asteroids, as science calls them, are in a harmonic position, musically, that can be called note F#, which is known as a "register shift" position in music.

Let's assume that Sun and planets have the characteristics of their respective notes: 1, 2, 3, 4, 5, 6, 7, 1, 2, 3, 4 based upon harmonics, resonance and universal order. Extending to the right of this series (Sequential leftmost vertical column) we see a pattern emerging in sequential order, Table 1, below. This pattern will reveal the note of Planet X no matter what the Prime Sun note is. Any appropriate note can be substituted (1-7), relating to its planet, according to the linked information on this page and number 1 will always be the first note. There are as many different beginning notes as there are notes in a scale. Which one is correct has yet to be discovered.

Table 1

 Sun- A 1 5 2 6 3 7 4 Mercury- B 2 6 3 7 4 1 5 Venus- C 3 7 4 1 5 2 6 Earth- D 4 1 5 2 6 3 7 Mars- E 5 2 6 3 7 4 1 Jupiter- F 6 3 7 4 1 5 2 Saturn- G 7 4 1 5 2 6 3 Uranus- A" 1 5 2 6 3 7 4 Neptune- B" 2 6 3 7 4 1 5 Pluto- C" 3 7 4 1 5 2 6 Planet X- D" 4 1 5 2 6 3 7 Unknown- E" . . . . . . .

Notice, if you will, that the number series for the Sun (1, 5, 2, 6, 3, 7, 4) is the same as the number series for any other planet except for the displacements of the series. Uranus is the repeat of the Suns number series in this Table of 8 notes (1Sun to 1Uranus). Other extended (8-13 notes) or contracted (7 notes) Tables may show a Saturn or Jupiter octave resonance with the Sun. We can keep adding "Unknown" planets and displace the above number sequences (go beyond 7 to, perhaps a double octave of 14 or 26) to see what resonant numbers show up. At this point the numbering of planets is arbitrary until we find a whole system based upon the dynamics of physics.

Historical Trans-Neptune Planet Sightings and Distance Measurements

At this point we have to include a list of planet researchers, the planets they discovered and the astronomical distances they recorded at the time of discovery:

(52 au., Todd, 1877)
(45 au., Flammarion, 1879)
(100 au. / 300 au., Forbes, 1880)
(45 au. / 60 au., Gaillot, 1880-1885)
(41.25 au., "Oceanus", 56 au., "trans-Oceanus", 72 au., "unknown", Jackson, 1880-1885)
(50 au., Grigull, 1880-1885)
(46.6 au., 70.7 au., Hans-Emil Lau, 1900)
(47 au., Dallet, 1901)
(50.6 au., Grigull, 1901)
(42.25 au., 56 au., 72 au., Jefferson, 1904)
(51.9 au., Planet "O", Pickering, 1909)
(44 au., 66 au., Gaillot, 1909)
(51.9 au., Planet "O", Pickering)
(75 au., Planet "P". Pickering)
(Planets O, P, Q, R, S, T, Pickering, 1908-1932)
(123 to 67.7 au., Planet "P", Pickering, 1928)
(75.5 au., Planet "P", Pickering, 1931)
(48.2 au., Planet "S", Pickering, 1928)
(47.5 au., Planet X, Lowell)
(5.79 au., Planet "U", Pickering, 1929)
(32.8, au., Planet "T", Pickering, 1931)
(39.82 au., Stewart, 1930)
(75 au., trans-Neptunian, Pickering)
(78 au., trans-Plutonian, Sevin, 1946)
(77.8 au., trans-Pluto, Sevin)
(77 au., trans-Plutonian, Schutte, 1950)
(65 au., trans-Plutonian, Kitzinger, 1954)
(*** au., Van Flandern, 1970-Present)
(80 au., Whitmire / Matese, 1987)
(60.8 au., Powell (JPL)) Data suggested this planet was "approximately twice the orbit of Pluto and three times the orbit of Neptune period, suggesting that it....had a orbit "stabilized" by mutual resonance with its nearest neighbors..."

This list may be useful later in determining how they fit within the various whole systems of planet position. We will soon discover there are at least 4 whole systems of measurement that seem to be conclusive.

Information on Planets and Respective Notes:

"Saturn dramatically demonstrates the pervasiveness of the Golden Proportion in our solar system. Known as Phi, 1.618122977 or .618, the Golden Proportion is the framework origin of all Nature. Though only an abstraction, it is through comparison with this mean, that we establish the individuality of any natural event or living geometry".

"Actually organic life is created in the form of a lateral octave, where the Do is our sun, Si the planets and La, Sol, Fa the organic life on Earth. Then Mi in this additional octave enters into the Earth and Re into the Moon. "Ray of Creation" in the Gurdjiff-Ouspensky system. Just Intonation...connects to...phenomena in Nature and our Solar System".

Upon drawing Tables for 7-13 notes we can insert Ray Tomes scale of ..."Galilei, the Father of Galileo Galilei. Included is his quoted discourse:

do (1), re (9 / 8), mi (5 / 4), fa (4 / 3), so (3 / 2), la (5 / 3), ti (15 / 8), do (2),

which may be represented a whole number proportions, called Just Intonation:

24, 27, 30, 32, 36, 40, 45, 48

"do-mi-so are 24-30-36 which can cancel to 4 : 5 : 6.
fa-la-do which are 32-40-48 cancelling to 4 : 5 : 6
so-ti-re (re from the next octave) gives 36-45-54 which cancels to 4 : 5 : 6 again. So every note is linked to "do" by three major chords which have ratios of 4 : 5 : 6".

Ray Tomes, after studying economic cycles for some years, realized that these (longer) cycle periods were very near exact fractions of 35.6 years with short cycles of proportion 2 and 3 involved.

He was struck by a realization, in his words: "These fractions of 35.6 years were in fact frequencies of 4 : 5 : 6 : 8 which is exactly a major chord in music. Also, the shorter cycles turned out to be exactly in the proportions of the just intonation musical scale plus a couple of black notes (E flat and B flat if we are in the key of C)".

(Note: Thereby establishing a correspondence between year-periods and musical ratio).

A harmonic system, each note generating respective harmonics, was found by Ray, to produce, most often the 4, 6, 8 and especially the 12th harmonic, much more than the 11th or 13th harmonic.

He then extends the ratio from 48-96 as follows:

48, 54, 60, 64, 72, 80, 90, 96. White keys
......56..................84.............Black keys
C.....D.Eb.F....G.......A.Bb...B.....C. Scale of C.

"...the strongest expected harmonics in the range 48 to 96 are 48 : 60 : 72 : 96 which is our old friend the major chord 4 : 5 : 6 : 8"

He later discovers the long-cycle harmonic of 34,560 years, the 3 : 4 : 5 : 6 : 0 ratio again!

He notes the minor chords as "transition zones" between the major chords...show(ing) the harmonics from 20 to 360 and shows some of the strong harmonics 240, 288, 360, 480 which makes a minor chord (ratios 10 :12 :15 : 20)".

He then relates these long-cycle ratios to the strong shorter harmonics of stellar body placement, predicting distance.

Related Study Material:

"The revolution period of Mars divided by the revolution period of Earth equals an interval in music called a major 7th".

"These equations are analogous to the trademark of the ancient pyramid builders who incorporated such astronomical numbers as 25920 (years in the great cycle or precession of the equinoxes) in their monuments. Notice their trademark which is to have the half step represented as half 1.059 and to show this interval in multiple ways. It's very simple if you follow their logic; a half step in music IS the major 7th! Starting on any root note, going down one half step is the root note's major 7th. Example: Root note "C". Down one half step is "B". Up a major 7th is also "B"

"Mars / Earth and Earth / Mars, show us the same interval with their diameters and rotation/revolution periods".

"The Mars diameter divided by the Earth's diameter = exactly one half of 1.059(one half step in music)".

The Sumerian Pantheon in base 60 McClain

Wiccan Correspondence Warnings Whole Systems

"THINKING IN WHOLE SYSTEMS seems to be not only the habit of mind that the theory of correspondences encourages, but also the most effective way to practice it:

Correspondences work best when drawn between systems, rather than applied arbitrarily between individual things. Individual things fall into categories, e.g. "colors", "alphabets", "numbers", etc., and each of these has its system, which you should try to understand. Then you can see how underlying principles correlate.

(Example: The notes of the musical scale are often correlated with the astrological planets or signs of the zodiac solely on the basis of the order in which they occur, not because they share common attributes).

Be careful about violating integrity of systems being correlated.
It is easy to be misled by superficial correspondence of number. E.g. not all groups of seven fit comfortably with the seven visible planets -- just try making the seven chakras fit!

Yet if numbers don't correspond, integrity is again often compromised. E.g. if you hold your circles in a five-sided building..., how will you call the four quarters? Do the four elements really fit all that well with the points of the pentacle"?

The Quadrivial Compass(Circle Diagram) Dee Finney

A Correspondence between the Pythagorean Tetraktys and Musical Notes of Planets.

The Torus Generator, Dee Finney

"All of matter is generated from transformations of ONE flow form. This spinning donut "engine" (the torus) Ęburning white in the center, bounces off your visual screen, in each of the seven possible spins of the tetrahedron. The percent of motion straight forward versus aside, of the vortex (photon) as a whole, makes a simple visual vector ratio from 440 to 880 angstroms, and each color of the rainbow is created in sequence by pure geometry (Ron Oldchurch, San Diego). The seven spins which make the tetrahedra are described in "Fields of Form" by Lawrence Edwards. These seven spin angles nest the photons simplicial flow form onto the cones of the eye. Thus these cones measure the tilt of the photon on geometry's simplest form, the origins of color from pure geometry".

"What this shows is that everything that exists in the universe is a harmonic of a single universal wave and that there is only one law that governs the entire cosmos".

"Because harmonics divide both space and time in the same proportions it is not surprising that they also divide other derivatives of these. Velocity is just distance/time and it is also the case that the velocity of various waves follows the same pattern. The speed of light in different substances tend to be musical proportions from the speed of light in vacuum, e.g. in water it is almost exactly 3/4 of in vacuum. Also, the speed of sound makes a similar pattern but at about 1/34560 of the speed of light and the speed of heat is correspondingly slower again".

"The density of different states of matter follows 34560^3 ratios because volume is the cube of linear dimension. We find that neutron stars are about 34560^3 or 10^13 more dense than ordinary matter and that the universe as a whole is about (34560^3)^2 less dense".

"The three sets of speeds of waves and the various densities began to make me think that perhaps mind and spirit are the more rarified waves that the theory predicts. There would also be many sublevels, because the 34560 ratio is only the strongest ratio but many others of 2, 3, 4, 12 and the musical ratios 3/2, 4/3, 9/8 etc occur. This seems like it might well fit to the theosophical ideas concerning the planes of existence and the divisions of these into matter-mind-spirit and further subdivisions to subtle body and sublevels of mind and so on".

The Greek Esoteric Music Theory McLennen

The Music Scale of Newton's light Experiment 60 Color and Music

Solar System Data The Nine Planets and Moons

Solar Overview Solar and Planet Geometry Based Upon Phi and Roots

Kepler's Musical Spheres Kepler relates Planet Orbital Period to Music

Catastrophic Theory of Mountain Uplifts
(A Crustal Deformation Theory) by Donald W. Patten and Samuel R. Winsor (Have not studied as of 12/10/00)

Exerpts concerning ratios, only:

5." Resonance slot. In the Catastrophic Era, the Earth had a 92.25-million mile orbit radius, not today's 93.0 million miles. (This "slot" in space puts the Earth's orbit in a 12:1 orbit timing resonance with Jupiter and a 30:1 resonance with Saturn, also 85:1 with Uranus. This explains the 360 day (not 365 day) ancient year and ancient calendar; 360 day calendars were the norm in ancient societies".

"In this ancient orbit the Earth circled the Sun in 12: 1 resonance with Jupiter, in 30:1 resonance with Saturn, and in 85:1 resonance with Uranus. Mars had an orbit of 720 days, in 1:2 resonance with Earth's orbit. It was a symphony of motion. These ratios also mean the orbit of Mars was in 6:1 resonance with Jupiter and 15:1 resonance with Saturn".

"Saturn, if in a 30: 1 resonance with Earth's orbit, would have been found in one or the other of only five zodiacal zones during ancient flyby years. Those zones would have been Scorpio, Pisces, Leo, Gemini, and Capricorn, and no others. We know also that in the October flybys the giant Jupiter, in 12:1 resonance, was always in Cancer. When Saturn was 180 degrees opposite from Jupiter, in Capricorn, the two giants caused the maximum warping of Mars' orbit".

"Bohr found electrons moved, for the first 4 shells of hydrogen, 2160 kps, 1080 kps, 720 kps and 540 kps related exactly to proportions: 12 : 6 : 4 : 3, and follows the inverse square as precisely as the planets".

Antikythera Mechanism   Calculating the position of Sun and Moon; Greecian (includes ratio numbers).

This theory probably describes a compressed grid matrix that, when expanded, is the Mayan Tzolkin, I hypothesize, being the structure of space.

1) Pythagorean Scale
2) Newtonian Scale
3) Golden Pyramid
4) Newtonian Harmonic Pyramid
5) Pythagorean Harmonic Pyramid
6) Dodecaphonic Harmonic Pyramid

Planetary Voices  (Frequencies and Notes)

Crystal Keys Of Earth  (Personal and Earth Notes)

PART IV. SPIRA SOLARIS ARCHYTAS-MIRABILIS A Phi Based Solar System

B. GROWTH FUNCTIONS AND EQUIANGULAR SPIRALS

As noted in the previous section, there seems little doubt that the exponential planetary functions based on the phi-series are better understood in terms of exponential growth most suitably represented by equiangular logarithmic spirals. (background information and details concerning this complex topic and its relationship to the Fibonacci series may be found in Fibonacci Numbers and the Golden Section).

With respect to the present astronomical application and the exponential planetary framework it may be noted that all mean periods (planet-synodic-planet) increase by phi while all planetary periods per se increase by phi squared. Therefore the required period function should increase by the square root of phi per 90-degree segment and by phi squared per revolution. Thus for explanatory purposes, commencing with unity, the first 90-degree segment would have the value 1.27201965, the second (the half-cycle, or 180 degrees) 1.618033989 (phi itself), the third 2.058171027, and at the full cycle, phi squared = 2.618033989. Or, in keeping with the present astronomical application as determined in the previous section, commencing with the phi-series sidereal period of Venus of 0.618033989 years, unity is obtained at the half-cycle (the Venus-Mars synodic period and also the sidereal period of Earth) with the phi-series sidereal period of Mars obtained at the full cycle, etc.

We therefore require an equiangular rectangle in polar coordinates6 such that the phi-series planetary periods may be obtained by applying the same exponents as before (x = 0 to 7, etc.). However, because pi in effect "cancels out" in relation [9] we remain with an exponent that can be partitioned into whatever subdivision desired, e.g., and in particular, into 1/360ths or one degree per step, i.e., 360 degrees per successive revolution. It is at this juncture that it becomes apparent that although corresponding equiangular spirals for the mean planetary distances and the mean velocities could be determined in a like manner, it would be entirely redundant to do so, since the distances and the velocities are already integral elements of the equiangular period spiral. Moreover, commencing with a base period provided by Mercury (Mt, phi-based, as before) plotted per degree, the sidereal periods occur at 360 degrees, the synodic periods at 180 degrees, the distances (Mercury and Earth excepted) at 60 degrees and 300 degrees, and the velocities at 120 degrees and 240 degrees respectively. In fact all that we require for this particular equiangular spiral are three basic figures, i.e., an equiangular square, an equiangular triangle and an equiangular hexagon, as shown below in Figure 6 from Mercury to Mars:

Fig 6 omitted, PHI Solar System

For the outer planets the latter parameters pertain to the inner regions of the spiral while the reverse holds for the inner planets. The situation encountered with Earth is explained by its synodic location between Venus and Mars; the position for the distance of Mercury is complicated by the fact that the mean heliocentric distance is also identical to that of the Mercury-Venus mean synodic period. We can also apply subdivisions of one sixth of a revolution to derive parameters for the sixty degree intervals, i.e., derive what is essentially an equiangular hexagon. Although the spiral continually increases per degree, for simplicity Table 4 below shows the sixty-degree points for each revolution; colored entries indicate the same values in the columns for the periods, distances and velocities. These are the more obvious correlations; there are also others, especially with the inclusion of the inverse velocities.

The next matrix I worked on starting in 1989 was the Solar System matrix. I was moving from a static grid to a a circular or cycle matrix. It is based on the idea of the planet-scale, connecting the different planets with certain scales - taking the musical scale as an direct expression of the universal order. At the root of this idea is the work of Pythagoras, which established a parallel between the spatial relationships and the intervals contained in the scale.

"The Pythagorean scale is not a mode, for a mode is the product of special conditions belonging to the realm of culture and myth. The Pythagorean scale is an unconditioned, archetypal manifestation of cosmic principles. Number and proportions, as Pythagoras understood them, belong to the realm of archetype. In order to effectively operate in that realm man needs to develop a mind that has basically freed itself from bondage to biological energies and mythic-cultural specialization and exclusivism. When conceived by the archetypal mind, music can become, at least potentially, a universal, supercultural language."

Gordon Limbrick, 'The Hidden Significance of Sound'. Music Physician for Times to Come, an anthology by Don Campbell. p. 308.

There are a number of different planet-scale schemes. One common element I found between them is the desire to find a true relation between music and our perception of outer space, whether the schemes seemed arbitrary, intuitive or actually scientific. For the purpose of ordering a piece with this type of hierarchy, I came up with a scheme. I used the pitches of a minor scale to start (G minor natural) for respectively Earth (G), Moon (A), Venus (Bb), Mars (C), Mercury (D), Jupiter (Eb), Saturn (F). For the the more remote planets, Uranus, Neptune and Pluto, I used a series of pitches that were not included in the original G minor natural scale - therefore opening a door to chromaticity and dissonance. The initial inclusive scale ("Basic Scale" on the example) was transposed in all the keys contained in the scale to establish a continuity - there is a progression in the succession of pieces, the first in the key of G, the second in the key of A, etc. That is how the internal logic was devised. To that original scale, I superimposed a "harmonic scale" a minor third above. At that point, I had enough of a structure to work with and enough freedom to develop material uninhibited. This is how Existence was developed. (See examples 3a,b,c,d) Since 1991, I have been working with the Earth Tone in both of its aspects: the correspondence with the 24-hour cycle and the correspondence with the yearly cycle. According to the method devised by the Swiss Scholar Hans Cousto, planetary frequencies can be made audible by octave transposition.

Planetary frequencies are based on orbiting times: 24 hours for the Earth, 224 days for Venus, 4,332 days for Jupiter, etc. Rotations entail vibrations. In order to move from the planetary vibrations to those of our earthly music one must 'octavise' between 26 and 50 times - depending on the planet's distance from the sun. Our solar system thus covers a range of exactly ten octaves, exactly paralleling - in another of those miraculous suprises - our ear. (...) The ratio between time (still with reference to the Cousto method) and frequency is:

Frequency = 1/Time

The frequency produced by the Earth's orbit around the sun (365 1/4 days) is thus calculated by dividing 1 by 365 1/4. To make that frequency audible I must double it - i.e. octavise it - until I reach the sphere of tonal vibrations perceptible to our ears. (...) This is the most precise and most plausible of the many procedures discovered since Pythagoras for making audible the sounds made by the planets - the 'harmony of the spheres'."

The Third Ear, by Joachim-Ernst Berendt, Element Books, 1988, p. 88. Two works emerged from this hypothetical connection. The first one is Variations on the Orange Cycle and the second one is the Gaia Cycle matrix, from which I created Tronik Involutions. (See example 4) Created in1993, The Gaia Cycle Matrix is a mandala which parallels a succession of twelve I Ching hexagrams, a twelve zodiac signs sequence and a twelve key signature sequence. This is how the connection between I Ching hexagrams and the key signatures works: the first piece, Earth, corresponds to the 11th month and to the I Ching hexagram which contains six Yin lines. The key used, based on the Earth Tone (C# = 136) is a modified C# minor (with the addition of an occasional A#). C# minor has four sharps (F, C, G, D). In the next piece, Return, the hexagram contains one Yang line under six Yin lines. In this Yin/Yang logic, evolution is created by the replacement of a Yin by a Yang. One more Yang, one less sharp: only three sharps now, (F,C,G) and have F# minor. Next piece - can you guess - is represented by an I Ching hexagram with two Yangs under four Yins - and one less sharp again (F, C) - B minor. Heaven, which is all Yang, is the only major key used (B flat). From here on the process reverses to one less Yang/one more flat. The subsequent hexagram, Encounter, proceeds with one Yin under six Yang lines. So there is a dynamic between each part, a certain logic is established.

These various matrices represent the macro-structure of a work which could be one to two hours long. Within this framework, each section is usually 5 to 10 minutes long. This is all I want determined before hand. Once the basic structure of the entire piece is set up it functions as a guideline, a grounding, an orientation. Within the macro framework I use a number of microstructures, and I allow myself the freedom to sometimes break out of them. Whereas all my macros are somewhat similar in their style the micros are varied and inclusive. At the micro level, freedom of form is my main concern. I draw upon a number of methods including instrument design, universal mode improvisation, aleatory series, and texturing, and using texts.

(Under Construction).

(Note: After we collect enough hints concerning the ratio of planet distance and their implications, and study this for a time, we will formulate the best conclusion).

Impossible Correspondence Index