The Tetraktys as plan of planetary harmony and the four Elements

In "Planetary Resonances with the Moon" I explored the astronomical matrix presented in The Harmonic Origins of the World with a view to reducing the harmonic between outer planets and the lunar year to a single harmonic register of Pythagorean fifths. This became possible when the 32 lunar month period was realized to be exactly 945 days but then that this, by the nature of Ernest McClain’s harmonic mountains (figure 1) must be 5/4 of two Saturn synods.


Figure 1 The elimination of 5 as a factor in the harmonic mountain for 36 lunar years, resolved using matrix units of one tenth of a month and the limit 360 units.

Using the lowest limit of 18 lunar months, the commensurability of the lunar year (12) with Saturn (12.8) and Jupiter (13.5) was “cleared” using tenths of a month, revealing Plato’s World Soul register of 6:8::9:12 but shifted just a fifth to 9:12::13.5:18, perhaps revealing why the Olmec and later Maya employed an 18 month “supplementary” calendar after some of their long counts.

By doubling the limit from 18 to three lunar years (36) the 13.5 is cleared to the 27 lunar months of two Jupiter synods, the lunar year must be doubled (24) and the 32 lunar month period is naturally within the register of figure 1 whilst 5/2 Saturn synods (2.5) must also complete in that period of 32 lunar months.

Continue reading “The Tetraktys as plan of planetary harmony and the four Elements”

Distribution of Prime Numbers in the Tone Circle

first published 13 February 2018

The ancient notion of tuning matrices, intuited by Ernest G. McClain in the 1970s, was based on the cross-multiples of the powers of prime numbers three and five, placed in an table where the two primes define two dimensions, where the powers are ordinal (0,1,2,3,4, etc…) and the dimension for prime number 5, an upward diagonal over a horizontal extent of the powers of prime number 3. Whilst harmonic numbers have been found in the ancient world as cuneiform lists (e.g. the Nippur List circa 2,200 BCE), these “regular” numbers would have been known to only have factors of the first three prime numbers 2, 3 and 5 (amenable to their base-60 arithmetic). Furthermore, the prime number two would have been seen as not instrumental in placing where, on such harmonic matrices, each harmonic number can be seen on a harmonic matrix (in religious terms perhaps a holy mountain), as

  • “right” according to its powers of 3.
  • “above” according to its powers of 5.

The role of odd primes within octaves

An inherent duality of perspective was established, between seeing each regular number as a whole integer number and seeing it as made up of powers of the two odd two prime numbers, their harmonic composition of the powers of 3 and 5 (see figure 1). It was obvious then as now that regular numbers were the product of three different prime numbers, each raised to different powers of itself, and that the primes 3 and 5 had the special power of both (a) creating musical intervals within octaves between numerical tones and (b) uniquely locating each numerical tone upon a mountain of numerical powers of 3 and 5.


Figure 1 Viewing the harmonic primes 3 and 5 as a mountain of their products, seen as integer numers or as to these harmonic primes
Continue reading “Distribution of Prime Numbers in the Tone Circle”

Autonomous Nature of Ancient Numerical Mysteries

The numerical foundations of the “earth mysteries” were nominally present in the medieval doctrine of the four numerical arts, the Quadrivium of sacred numbers, geometry, musical harmony and astronomy. However, these foundations need to be applied to something real which is: the numerical nature of the world seen from being alive upon it. This application gives a completely different set of results to modern science where, instead, numbers are being employed for measurements and calculations (using the physical laws discovered after the medieval period came to an end.)

The ancient mysteries treated numbers as having characteristics
seen to be active within the world.

In applying these numerical arts, one comes into contact with mysteries in the form of ancient monuments, art and literary works, these containing the clues required for developing, in oneself, a kind of skill. This skill can mature into being able to recover information in the most unlikely circumstances because something apparently other to oneself is active within you: a developed sense. This I call the autonomous nature of the mysteries, which is essential when going beyond what is simply data in books, monuments, etc. I believe it is mistaken to call such mystery work historical since it is actually happening in the present moment to create something new, whilst appearing to reference data from the past. Historical data provides the necessary starting points for a new work of reconstructing the mysteries within oneself.

Continue reading “Autonomous Nature of Ancient Numerical Mysteries”