.."the harmonic intervals of the 7 notes of the scale explored by Pythagoras, which have certain correspondences to the intervals of the 7 planets of antiquity, and perhaps to the 7 shells of the modern atom, not to mention the 7 octaves of the piano keyboard and the 7 octaves of the Periodic Table of Elements",

9.2

"or, in lesser degree, Bodes Law and Balmers Ladder, the table of particles, the moon ratios of Jupiter (Io + 2 Ganymede = 3), the rings of Saturn",

See An explanation

"and the node of the Trojan asteroids. Next, there are the wave ratios that shape and govern sea waves (groups vs. single waves), dunes, snowdrifts, tides, molecules, atoms and other forms of flowing energy- the harmonics and oscillation in pendulums, springs, and all manner of elastic, chemical, electromagnetic and living bodies. Then the radii of atomic shells, proportioned to the rule of single squares 1, 4, 9, 16, 25 (Addition of odd integers- 1+3=4, 1+3+5=9, 1+3+5+7=16, 1+3+5+7+9=25",

..."and the numbers of electrons in atomic shells to the rule of doubled squares 2, 8, 8, 32, 50......, the 32 symmetry groupings of crystals (1+1=2, 1+1+6=8, 1+1+6+10=18, 1+1+6+10+16=32)".

"the 230 distributions of objects in space, the various progressions and means, arithmetic, geometric, harmonic- and so on...and on...

The meaning of this seemingly endless music, to me, is that not only does the atom sing, but it sings in tune with the stars and with the whole surround in space-time, resonating its significant harmonies with other atoms and with all sorts of other energies known and unknown, In truth, reality seems to be a kind of blossoming limit imposed upon budding possibilities by the harmonics of energy motion- and that limit gives form and value to all things, gives concreteness to abstraction and actuality to potentiality".

...Speaking of the spectral fingerprints of the atom, he adds...."J.J Balmer, became so fascinated with the riddle of their music like intervals...he succeeded in working out a "ladder" or climbing",

(Note: Could it be descending sequence only?),

"sequence of the frequencies of all the known hydrogen lines, each frequency being a definite fraction of the ladders limiting frequency (3,287,870,000 mega cyc/sec) beyond which the sequence does not go. And these fractions, in turn, formed a beautiful harmonic series, each denominator a cardinal square in natural succession, each numerator 4 less",

9.5.1

"than its denominator- 5/9, 12/16, 21/25, 32/36, 45/49, 77/81.... a kind of Bodes Law for hydrogen",

9.6.1

"smallest of the inner spheres, since, if one recalls the mysterious number 4 that Bode added",

9.7.1

"to each planetary distance, one may well wonder, could Bode's 4 be in any sense related to the 4 that Balmer subtracted from his denominator?"

9.7.3

9.8 Diagram. Balmers Spectral Frequency 6564.7

..."As the dynamics of atoms further unfolded, it became evident that the series of spectral lines Balmer studied is not only quantized (unit like) but comes specifically from the light emitted by the hydrogen electron in dropping from the 3rd, 4th, 5th and higher levels to it's 2nd shell near the atoms nucleus. And this led to the realization that the wave lengths of all radiation producing visible light are functions of the distances between the atoms shells down to shell 2, the drop from shell 3 to shell 2 radiating red light, from shell 4 to 2 (the first overtone) as blue, from shell 5 (the second overtone) as violet, and so on".

9.8.2

"Yet visible light is such a tiny part of the spectrum that other kinds of light normally invisible.....which is how it happened with the so called

Lyman series of ultra-violet light emanating from from the narrow limits of shell 1, with the

Paschen series of short infrared from the not-so-narrow shell 3, the Brackett series of longer infrared from wider shell 4, and

Pfund series of still longer waved radiation from the still wider shell 5....

Each of these invisible rainbows of spectral music, you see, is a world unto itself that took legions of scientists on several continents many years to develop. Special towers and observatories were built for spectroscopy of the sun and stars, modern counterparts of Stonehenge, Cusco and the great pyramids of Egypt and Mexico, and their powerful series of prisms, lenses and reflectors magnified and widened the spectrum into literally a hundred thousand lines and bands that now reach a total linear spread of more than a mile. Even the very simple Balmer series on

visible hydrogen has become an extension ladder of 31 rungs",

"some of them traceable to hydrogens extra shells called 'virtual" orbits because the hydrogen electron never attains them under earthly atmospheric conditions but only when the atom is vastly expanded in vacuous space. And some of them originate not with the single H atom but with the H^2 molecule and its added frequency of rotation about an axis perpendicular to the line connecting its 2 H nuclei, not to mention the interference beats from their combinational vibrations".

..."In trying to understand why the structure of the atom prevented it from emitting quanta of all energies, Bohr investigated ....JJ Balmer....by 1885 several separate lines had been observed...Their wave lengths had been measured....and found to be 6563 Angstroms, 4861 A, 4340 A, 4102 A, 3970 A 3889 A and 3835 A. Balmer...saw it was possible to relate the frequencies (v) of these lines by an equation which he wrote as:

v = K(1/2^2 - 1/b^2) ,

where K was a constant, and b had an integral value between 3 and 11. The term (in parentheses) is not an actual frequency but proportional to one.

This Balmer formula may be derived by squaring each of the integers 1, 2, 3, 4 and 5 by itself, thus obtaining the series

1, 4, 9, 16 and 25.

Using these new numbers as denominators of fractions, still another set of numbers is obtained: 1/1, 1/4, 1/9,1/16, 1/25.

Subtracting each fraction from the first result in the series 1/1 - 1/4, 1/1 - 1/9, 1/1 - 1/16, 1/1 - 1/25, and

subtracting each fraction from the second results in another series of 1/4 - 1/9, 1/4 - 1/16, and 1/4 - 1/25.

This ladder-like set of numbers represents numerically the 4 frequencies of the visible hydrogen spectrum then known..... (later) new frequencies were found by J.R. Rydberg, in 1890, to be in agreement with the frequencies calculated by the following generalized equation:

v = K(1/a^2 - 1/b^2),

where a and b are integers.....the enigma remained. No explanation for this simple equation, too , could be found".

(Note: Even though I feel these ratios and equations are very interesting the intuitive inductive reason I have about these, is that they can be used to calculate musical ratio and interval to match natures ratio and interval. Musically tuned machines will be the machines that mimic the harmonic Universe of the future, until, of course, humans internally become the ultimate harmonic integrated, Phi based consciousness and machines are no longer needed.)

9.9 Hydrogens 4 Shells and Kilometers per Second .

"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".

Music of the Spheres

By Guy Murchie

523. M938 (1967)

9.10 Quantum Numbers

..."in 1961 Murry Gell-Mann..of C.I.T. ...found a striking pattern of classical physics, now called the "eightfold way' (after a Buddhist religious phrase)...involving assigning 8 quantum numbers to each particle for 8 different quantities conserved".

9.10.1

The Ambidextrous Universe

By Martin Gardner

501. G175, pg. 210

"All atoms and all matter can be assembled from these 8 particles".

Scientific American

1981, pg. 51

9.11 A Better Number System

"I assert that the fundamental atoms of reality are cycles, and that all physical properties can be defined in terms of simple cycles, and cycle ratios".

Tom Potter

© Copyright. Robert Grace. 1999