Appendices: Part D – Musical Concepts (excerpt 4)
The concept of the interconnectedness is a result of the narrow frequency range of 4 – 14 cps and the periodic nature of spherical harmonic waveforms, of which all earthly forms are composed, which find forms of expression in music, whose structure represents our lapse of consciousness, the ratio of 1.5, 2:5 or π/2, language and DNA, and was the life’s work of Johannes Kepler. Even though he was the author of three of the planetary laws, a scientist and mathematician, these accomplishments were a result of a lifelong obsession with “seeking evidence for a harmony of the world such as was handed down as a legend from antiquity”³⁶ from the Egyptians to the Pythagoreans. He found his world harmony in the form of musical laws, for example, the ratio or interval of one frequency to another, and demonstrated it in his H͟a͟r͟m͟o͟n͟i͟c͟s͟ ͟M͟u͟n͟d͟i͟ ͟L͟i͟b͟r͟i͟ ͟V͟ ͟(͟F͟i͟v͟e͟ ͟B͟o͟o͟k͟s͟ ͟o͟n͟ ͟W͟o͟r͟l͟d͟ ͟H͟a͟r͟m͟o͟n͟y͟)͟ in 1619.
Kepler discovered that the angles of the planets of our solar system, as measured from the Sun at their closest (aphelion) and furthest (perihelion) points within twenty-four hours, paralleled the musical intervals and in most cases represented chords (three notes or more). As Rudolf Haase in C͟o͟s͟m͟i͟c͟ ͟M͟u͟s͟i͟c͟ pointed out, “Kepler’s planetary harmonics, therefore, hold true to this day; they are a reality that belongs as much to the eternal state of the cosmos as do his famous planetary laws.”³⁷ Posthumously, Kepler’s view of the interconnectedness of reality was borne out in 1953 by Heinrich Husmann in his Husmann Theory of Consonance, which was the result “of very careful experiments and their mathematical interpretation. At the core of these is the discovery that, as a result of the nonlinearity of human hearing [as a result of logarithmic relationships of our senses], there are sounds that arise in the ear besides those that reach the eardrum.”³⁸
Haase continues, “These inner sounds are of two different kinds. First, there are s͟u͟b͟j͟e͟c͟t͟i͟v͟e͟ ͟o͟v͟e͟r͟t͟o͟n͟e͟s͟: every incoming tone acquires an additional overtone row in the ear with the same construction as that occurring objectively in nature, so that these subjective (or auricular) overtones considerably amplify those already entering [in other words, as the wave’s amplitude is squared, it actualizes or manifests as an object/image/event in a three-dimensional reality]. Secondly, there arise in the ear whenever two or more notes are sounded [hence with every interval which is 12√2, or 1.05, if it is a note and encompasses the symbolic representation of √2 as the Principle of Alternation, i.e., duality or Yin & Yang] so-called combination tones [for example, the triadic and quadratic structure of DNA and RNA would represent chords, as would their hexagonal/crystalline structures].”³⁹ These either add or subtract the frequencies of the given tones, hence we also speak of “summation” or “difference tones”. This concept of a differential response also correlates to the process of our three-dimensional color channel visual system.
The combination tones in the ear are formed from the incoming frequencies (which would be in the 20 – 20,000 cps range) and result in seventy-two overtones per interval. Haase further states, “First of all, it appears that the coincidence of overtones and combination tones will only be possible if the interval in question is made from a ratio of whole numbers.”⁴⁰ [harmonics or octaves is based on this concept]
Then, in summation, he adds, “In other words, the interval proportions on which our musical system has been founded since antiquity have arisen neither by accident nor from speculation, but correspond exactly to a physiologically explicable disposition of our ear.”⁴¹ Finally, he says, “This means, however, that traditional Western music is finalistically oriented, directed toward a goal, and that this goal has always been man himself.”⁴² [because it is based on our 0.8 – 1.2s lapse of consciousness, which is the result of the periodic nature of a confined sinewave, or spherical harmonic waveform].
The cosmologies of the world’s great religions (as they try to express the intangible) of the Sumerians, Egyptians, Hindus, Hebrews, Greeks and Christians are shown to be based on the primacy of number (Jung’s archetype of order) via tone-mandalas and tuning systems in Dr. Ernest McClain’s book, T͟h͟e͟ ͟M͟y͟t͟h͟ ͟o͟f͟ ͟I͟n͟v͟a͟r͟i͟a͟n͟c͟e͟:͟ ͟T͟h͟e͟ ͟O͟r͟i͟g͟i͟n͟ ͟o͟f͟ ͟t͟h͟e͟ ͟G͟o͟d͟s͟,͟ ͟M͟a͟t͟h͟e͟m͟a͟t͟i͟c͟s͟ ͟a͟n͟d͟ ͟M͟u͟s͟i͟c͟ ͟f͟r͟o͟m͟ ͟t͟h͟e͟ ͟R͟g͟ ͟V͟e͟d͟a͟ ͟t͟o͟ ͟P͟l͟a͟t͟o͟. In the book, he demonstrates that music is one avenue capable of developing and projecting a philosophical framework. By citing extensive passages from the E͟g͟y͟p͟t͟i͟a͟n͟ ͟B͟o͟o͟k͟ ͟o͟f͟ ͟t͟h͟e͟ ͟D͟e͟a͟d͟, the R͟g͟ ͟V͟e͟d͟a͟, the B͟i͟b͟l͟e͟, and P͟l͟a͟t͟o͟’͟s͟ ͟R͟e͟p͟u͟b͟l͟i͟c͟, he demonstrates the recurrence of similar number ratios and mathematical logic as it is expressed in the sacred hymns, as they appear in the ancient cultures of Babylon (Sumeria), Egypt, Greece and Israel.
End Notes:
36 Cosmic Music, Schneider, Haase,& Lauer, p. 111
37 Ibid., p. 121
38 Ibid.
39 Ibid.
40 Ibid., p. 122
41 Ibid.
42 Ibid., p. 123
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