## How the West Lost Alchemy

#### Clipped from Mind-Energy.net:

Happy holidays. I’m presenting another article by drew hempel. I’ve asked drew to write in more detail on the subject of the connection between math and music and how it connects to the paranormal. I felt that his article The Secret of Psychic Music Healing was assuming too much of the reader and so asked him to write a more explanatory article, which I now present.

**Against Archytas: How the West Lost Alchemy or Paranormal Complimentary Opposite Harmonics**

(anti-copyright, free distribution)

Philolaus, one of the early Pythagorean writers, detailed that this “subcontrary mean” or complimentary opposite harmonic caused any attempt at subdividing the scale into symmetry as a failure. In contrast Archytas changed the “subcontrary” complimentary opposite mean into the “harmonic mean” using “divide and average” mathematics. The outcome has precisely opposite the meaning of “harmony” which for Pythagoreans referred to the paranormal source of sound as the Goddess Harmonia or what I call female formless awareness. For Philolaus the perfect fifth as 2:3 could be inverted to 3:2 and then extended another fifth to 9:4 and then divided back into the octave, below 2, for the major second interval of 9:8 or C to D. Yet 9:8 cubed or three major second music intervals equaled the 3:2 perfect fifth music interval, plus a tiny ratio called “the comma of Pythagoras.”

This “comma of Pythagoras” is the difference between the “divide and average” octave system adopted by Archytas and the complimentary opposite fifths inverting into fourths, used by the orthodox Pythagoreans. The “comma of Pythagoras” is the key to harmonic alchemy whereby 2:3, the perfect fifth, is yang in Taoism and 3:4, the perfect fourth, is yin. As Gurdjieff desribes the “shock” of the diatonic scale, whereby the “inverse ratios” do not line up with the octaves, is intensified as the octaves expand. In contrast Archytas argued that 9/8 cubed or three major second intervals equals the square root of two as the Greek Miracle, the axiomatic algebra of the precise incommensurable irrational number. What Archtyas essentially did, as I’ll describe, is equate the perfect 5th or 2:3 with the perfect 4th or 3:4 as equally-divided or symmetric ratios through a “divide and average” mathematics.

Archytas took the Babylonian geometric mean of 6:8::9:12 used for harmonics and then applied the Pythagorean Tetrad 1:2:3:4 so that the 2:3 ratio of complimetary opposite frequency was converted to 3:2 as a materialistic vibrating string length. This became known as the Law of Pythagoras even though it goes against the true meaning of the complimentary opposites when this “inverse ratio” is combined with the “divide and average” commutative property. Gurdjieff, for example, still relies on the “inverse ratio” of density or string length versus frequency or consciousness. But Gurdjieff does not use Archytas’ “divide and average” symmetric-based mathematics, instead Gurdjieff relies on the Law of Three aka the Tetrad, or octave-fifth-fourth, to resonate through the comma of Pythagoras as the “shocks” of alchemy. In Taoism this system of alchemical shocks is taught as the 12 harmonic nodes along the outside of the body, enabling healing and paranormal energy, an exercise called “the small universe.”

Philolaus, one of the early Pythagorean writers, detailed that this “subcontrary mean” or complimentary opposite harmonic caused any attempt at subdividing the scale into symmetry as a failure. In contrast Archytas changed the “subcontrary” complimentary opposite mean into the “harmonic mean” using “divide and average” mathematics. The outcome has precisely opposite the meaning of “harmony” which for Pythagoreans referred to the paranormal source of sound as the Goddess Harmonia or what I call female formless awareness. For Philolaus the perfect fifth as 2:3 could be inverted to 3:2 and then extended another fifth to 9:4 and then divided back into the octave, below 2, for the major second interval of 9:8 or C to D. Yet 9:8 cubed or three major second music intervals equaled the 3:2 perfect fifth music interval, plus a tiny ratio called “the comma of Pythagoras.”

This “comma of Pythagoras” is the difference between the “divide and average” octave system adopted by Archytas and the complimentary opposite fifths inverting into fourths, used by the orthodox Pythagoreans. The “comma of Pythagoras” is the key to harmonic alchemy whereby 2:3, the perfect fifth, is yang in Taoism and 3:4, the perfect fourth, is yin. As Gurdjieff desribes the “shock” of the diatonic scale, whereby the “inverse ratios” do not line up with the octaves, is intensified as the octaves expand. In contrast Archytas argued that 9/8 cubed or three major second intervals equals the square root of two as the Greek Miracle, the axiomatic algebra of the precise incommensurable irrational number. What Archtyas essentially did, as I’ll describe, is equate the perfect 5th or 2:3 with the perfect 4th or 3:4 as equally-divided or symmetric ratios through a “divide and average” mathematics.

Archytas took the Babylonian geometric mean of 6:8::9:12 used for harmonics and then applied the Pythagorean Tetrad 1:2:3:4 so that the 2:3 ratio of complimetary opposite frequency was converted to 3:2 as a materialistic vibrating string length. This became known as the Law of Pythagoras even though it goes against the true meaning of the complimentary opposites when this “inverse ratio” is combined with the “divide and average” commutative property. Gurdjieff, for example, still relies on the “inverse ratio” of density or string length versus frequency or consciousness. But Gurdjieff does not use Archytas’ “divide and average” symmetric-based mathematics, instead Gurdjieff relies on the Law of Three aka the Tetrad, or octave-fifth-fourth, to resonate through the comma of Pythagoras as the “shocks” of alchemy. In Taoism this system of alchemical shocks is taught as the 12 harmonic nodes along the outside of the body, enabling healing and paranormal energy, an exercise called “the small universe.”

## Leave a Reply