This is a study of Beats and the Fine-Structure Constant 137. Converting the Fine-Structure Constant into musical interval.

Ray Tomes Defines the Fine-Structure Constant as a Beat Frequency.

"The fine structure constant is perhaps the most prevalent
dimensionless constant, turning up in the ratio of many different
things at the atomic scale. There are two occurrences of the fine
structure constant in the periods of Jupiter's satellites, and the two
values are identical and very similar to the atomic values. Given
the many other similarities of forces and structures between the
atomic and solar system scales it is suggested that this is more
than coincidence. Rather, it is evidence for the **underlying common
law** that leads to similar processes on all scales".

(**Note**: That law should be musical / geometric harmonics. I
noted that 2^18th power = 242**144**, is a gematric number. Squaring 2^37th power = **137**438953472, a possible indication of the harmonics of both numbers being slightly more than an octave apart in a 19 note scale).

Jupiter Satellite

Period (days)

Frequency (nHz)

Beat frequency (nHz)

**Ratio II/beat **

"The relationship among the frequencies of I, II and III has long been known and is usually expressed as I - 3xII + 2xII = 0. However the presence of alpha (or 1/alpha) has not been reported previously to my knowledge. The fine structure constant from atomic phenomena on earth is 1/137.0360. The difference is 0.033%, but the differences in the periods of I, II and III must be only 0.00026% to get such an agreement. It is stretching coincidence that a less than 1 in 100,000 chance should come up twice at such close quarters".

"It is known that alpha varies depending on the energy intensity at which observations are made, with 1/alpha reducing at higher energies. Therefore it is perhaps to be expected that 1/alpha would be slightly higher at a location which is further from the sun and from the surface of the nearest planet".

"Although Saturn also has two pairs of satellites with nearly 1 to 2 ratios in their periods, the beat frequencies of these do not yield the fine structure constant when divided by satellite frequencies". Ray Tomes

File 58 Beats Taking Ray Tomes data of the Fine-Structure Constant being a beat frequency of 2 higher frequencies and comparing it to musical beat ratio:

(**Note**: If a beat frequency (137, fine structure constant) is the result of period ratios divided by their satellite frequencies, then, logically, we can conclude, according to the rules of musical beats of Professor Tyndall who debated Helmholtz, that):

"to determine the consonances of the octave, fifth, fifth, and major third for two simple tones, without employing combination-tones- He writes as follows- "bearing in mind the beats and the dissonance vanish when the difference of the two rates of vibration is 0; that the dissonance is at its maximum when the beats number 33 per second; that it lessens gradually afterwards and entirely disappears when the beats amount to 132 per second- we will analyze the sound of our forks, begi nning with the octave. Here our rates of vibration are":

(**Note**: I add a formula to bridge musical ratio and **137**).

"512 - 256; difference = 256 ** or x^(octave) - x = 137**. It is plain that in this case we can have no beats, the difference being too high to admit of them".

"Let us now take the fifth. Here the rates of vibration are- 384 - 256;
difference = 128 **or x^(1.5) + x = 137**. This difference is barely under the number 132, at which the beats vanish; consequently the roughness must be very slight indeed".

"Taking the fourths, the numbers are- 384 - 288; difference = 96 **or x^(1.33333333) - x = 137**.

Here we are clearly within the limit where the beats vanish, the consequent roughness being quite sensible".

"Taking the major-third, the numbers are- 320 - 256; difference = 64", **or x^(1.25) - x = 137**).

(**Note**: Understanding that 137 is a beat frequency and assigning a ratio (example: x^ =1.3333333) to a higher frequency, then subtracting (x), a lower frequency which equals 137, gives a formula for finding the 2 higher frequencies if we understand that 137 + x = higher frequency).

"Here we are still further within the limit, and accordingly the roughness is more perceptible. Thus we see the deportment of our four tuning-forks is entirely in accordance with the explanations which assigns the dissonance to beats.

"It will not be difficult to test the value of the above reasoning. Starting from the rate of 256 vibrations selected by Prof. Tyndall, all that can be deduced from his definition of beats and dissonance at the head of the extract is that the maximum of dissonance will fall on the interval 256 : 256 + 33. i.e. 256 : 289; and all intervals larger than 256 : 256 +132, i.e. 256 : 388, will be free from dissonance".

"These numbers indicate almost exactly a whole-tone and a fifth respectively. Each of these results is contrary to experience: the dissonance of a whole-tone is less harsh than that of a half- tone; and intervals greater than a fifth are by no means equally free from dissonance. Moreover, it follows that the determination of the octave by this reasoning is delusive, for the process would bring out, as perfect consonances, a seventh or a flat ninth, which are extreme discords, just as readily as an octave. If we apply the same method to other parts of the scale than that to which Prof. Tyndall has restricted himself, the results are even more remarkable".

"Thus, starting from the higher octave of 256, viz. 512, the maximum roughness falls on 545, a half-tone, and dissonance ceases after 644, which lies between a major third and a forth. For the next octave, i.e. starting from 1,024, dissonance ceases before we reach the interval of a whole-tone. If we take the lower positions on the scale we obtain opposite results. With 128 as our fundamental note, the maximum dissonances falls on 161, slightly above a major third, while roughness extends to 260, just beyond and octave. With 64 the worst dissonance is 97, just above the fifth, and roughness reaches 196, another octave higher. Starting from 32 the worst dissonance 65 is just above the octave, and roughness is not got rid of until 164, two octaves and a major third from the fundamental note"....

Helmholtz, Sensations of Tone

© Copyright. Robert Grace. 2001