Cologne Cathedral Facade as Double Square

image: The Gothic cathedral of Cologne by night, by Robert Breuer CC-SA 3.0

On the matter of facades of Gothic cathedrals, I hark back to previous work (February 2018) on Cologne cathedral. This was published in a past website that was destroyed by its RAID backup system!

As we have seen with Chartres, some excellent lithographs with scales can often exist online from which one can interpret their sacred geometrical form and even the possible measures used to build that form. The Gothic norm for a facade seem more closely followed at Cologne facade which has two towers of (nearly) equal height.

We saw at Chartres that an underlying geometry using multiple squares may have been used to define a facade and bend it towards a suitable presentation of astronomical time, in a hidden world view that God’s heaven for the Earth is actually to be found in the sky as a pattern of time. This knowledge emerged with the megaliths and, in the medieval, it appeared again in monumental religious buildings built by masons who had inherited a passed-down but secret tradition.

A Prologue to Cathedral Music

In my book Matrix of Creation I observed that the Lunar Year of 12 months appear to be like Plato’s World Soul, of 6:8::9:12 only raised by a fifth (3/2) to be (9:12::13.5:18). The number 12 is then the 12 lunar months of the lunar year and the 13.5 are the 13.5 lunations which are the synodic period of Jupiter (398.88 days). The synod of Saturn (378 days) is then caught between the 12 and 13.5, near the geometric mean of the octave 9::18, as a location known to tuning theory as the upper Just tritone of 64/45 (= 1.422), a prime example of the diabolicus in music. That is the Moon appears to be a central part and factor of an astronomical instrumentality relating Jupiter and Saturn, the two outer gas giants of the solar system.

Without knowledge of geocentric astronomy, megalithic metrology, sacred geometry, and the study of numbers (the four higher parts or Quadrivium of the Traditional Arts), it is impossible to read such monuments, and the truths placed within them.

The Double Square

The properties of the double square, here proposed as a vertical 2 by 1 rectangle embracing the whole facade, are to be seen in many other posts you might want to reference (this link opens a new search tab). It seemed to me that the key orientation was the crossing of the lower square’s diagonals, a location where Chartres has its Rose Window and in this case, the domed top of a major rectangular window.

Referring to the diagram below, the bottom square is the cosmic octave’s “ballast” of 9 lunar months and the top square the “active portion” of an octave in which 12 lunar months (or lunar year) is the fourth note of the octave uplifted numerically by 3/2. Saturn’s synod of 12.8 months is 12.8/9 = 64/45, musically √2 which is the length of the lower square’s diagonals which cross the arch of the main window. The red arrow thus signifies by its arc the location of Saturn as the tritone (geometric mean) of the octave.

The Façade of Cologne as the double octave of Plato’s World Soul elevated by 3/2.

The left tower is slightly lower that the right, indicating that the Saturn synod (378) is less than the Jupiter synod (399). Musically, Jupiter is 3/2 is the fifth in the octave 9::18, numerically 13.5 lunar months. If one halves the right side of the upper square into two, this is where the fifth belongs and this point is also a whole tone (9/8) above the lunar year, whilst Saturn is 16/15 above the lunar year as 12.8 lunar months.

Plato’s World Soul, transformed

In a single figure, the transformation of Plato’s World Soul of 6:8::9:12, as simplest solution, then masked the hidden doctrine that, in lunar months, the very same is implemented in the relationship of the outer giant planets to the Moon as lunar year but trasformed by a musical fifth. The dominant and subdominant are the lunar year and Jupiter synod, with the Saturn synod providing the “satanic” tritone which acts in denial of the octave “god”. This octave of 19::18 has only survived in the Supplemental Glyphs of the Olmec (additional to long counts), who appear to have received it from the collapsing Bronze Age of the Eastern Mediterranean around 1500 BC (see my Sacred Number and the Lords of Time).

Abandoning the geocentric perspective of the planets for the heliocentric “washed away [this] baby with the bathwater”, that the moon was the intermediary in simple numbers of months of the principle of cosmic harmony in the higher worlds. Holding us back from seeing the old perspective is our fond belief that cosmic design was part of religious fantasies in which God, gods or angels had made the sky of the earth. Whilst we know so much about space, time has been neglected for its astronomical action upon the present moment within which change is the prime phenomena, as the Buddha said “change is the only thing that does not change.”

Astronomy 4: The Planetary Matrix

The re-discovery of the ancient planetary matrix, seen through three my three books: Matrix of Creation, Harmonic Origins of the World and Sacred Geometry: Language of the Angels.

Harmonic Origins of the World inserted the astronomical observations of my previous books into an ancient harmonic matrix, alluded to using the sacred numbers found in many religious stories and the works of Plato, who might have been the savior of what Pythagoras had garnered from ancient mystery centers circa. 600 BC. According to the late Ernest G. McClain*, Plato’s harmonic technology had been widely practiced in the Ancient Near East so that, to the initiated, the stories were technical whilst, to the general population, they were entertaining and uplifting stories, set within eternity. Ancient prose narratives and poetic allusions conserved the ancient knowledge. Before the invention of phonetic writing in Classical Greece, spoken (oral) stories were performed in public venues. Archaic stories such as those attributed to Homer and Hesiod, gave rise to the Greek theatres and stepped agoras of towns. Special people called rhapsodes animated epic stories of all sorts and some have survived through their being written down. At the same time, alongside this transition to genuine literacy, new types of sacred buildings and spaces emerged, these also carrying the sacred numbers and measures of the megalithic to Classical Greece, Rome, Byzantium and elsewhere, including India and China.

* American musicologist and writer, in the 1970s, of The Pythagorean Plato and The Myth of Invariance. website

Work towards a full harmonic matrix for the planets

In my first book (Matrix of Creation,) I had not yet assimilated McClain’s books, but had identified the musical intervals between the lunar year and the geocentric periodicities of the outer planets. To understand what was behind the multiple numerical relationships within the geocentric world, I started to draw out networks of those periods (matrix diagrams) looking at all the relationships (or interval ratios) between them. This revealed common denominators and multiples which linked the time periods through small whole numbers. For example, the 9/8 relationship of Jupiter’s synod to the lunar year could be more easily grasped in a diagram to reveal a structural picture, visualized as a “matrix diagram” (see figure 1).

Figure 1 Matrix Diagram of Jupiter and the Moon. figure 9.5 of Matrix of Creation, p117.

One can see the common unit of 1.5 lunar months, at the base of the diagram, and a symmetrical period at the apex lasting 108 lunar months (9 lunar years referencing the Maya supplemental glyphs). I re-discovered the Lambda diagram of Plato (figure 8.7), and even stumbled upon the higher register (figure 2) of the Mexican Quetzalcoatl (figure 8.1) made up of {Mercury, the eclipse year, Tzolkin, Mars, Venus}, Venus also being called the feathered serpent. These periodicities are of adjacent musical fifths (ratio 3/2), which would eventually be shown as connected to that of the outer planets, using McClain’s harmonic technology, in my 5th book, Harmonic Origins of the World (see figure 3).

Figure 2 Incomplete discovery of the Maya Quetzalcoatl, in fig. 8.1 of Matrix of Creation. I had not noticed that 390 days, times 2, is 780 which is the synod of Mars! This is in fact 41.8949 Node Days, which might be significant.

Also called the flying serpent in Pharaonic Egypt, this set of musical fifths, apparently undocumented in the near east, was part of the Mexican mysteries of the Olmec and Maya civilizations (1500 BC to 800 AD). The serpent is flying harmonically, 125/128 above the inner planets – for example, the eclipse season is 125/128 above the lunar year: 354.367 days × 125/128 = 346 days, requiring McClain’s harmonic matrices to integrate these two serpents, in Harmonic Origins of the World (figure 9.3).

Figure 3 The two harmonic serpents of “Heaven” and “Earth”

By my 6th book, Sacred Geometry: Language of the Angels, I had realized that the numerical design surrounding our “living planet” sits, is a secondary creation – created after the solar system, yet it was discovered first, before the heliocentric, exactly because the megalithic observed the planets from the Earth. I therefore propose an alternative timeline for the ancient mysteries. Instead of proposing a progenitor civilization such as Atlantis, as per Plato’s Timaeus: of an island destroyed by vulcanism.

My working hypothesis is that Atlantis and similar precursor solutions, simply “kick the can down the road” into an as-yet-poorly-charted prehistory for which there is no strong evidence. In contrast, the sky astronomy and earth measures found in use by the megalithic can only be the product of that singular megalithic culture. There is clear evidence of megalithic monuments recording an understanding of the cosmos then found in the ancient mysteries. Megalithic evidence can show the geocentric world view as being their achievement, based upon the numbers they found using geocentric observations, counting lengths of time, using horizon events and the mathematical properties of simple geometries.

Geocentrism was the current world view until it was superceded, by the Copernican heliocentric view. The new solar system, held soon found to be held together by naturals gravitational forces between the large masses, forces discovered by Isaac Newton. The subsequent primacy of heliocentrism, which started 500 years ago, caused humanity to lose contact with the geocentric model of the world, which had the planets in the same order relating the two serpents of outer and inner planets. All references to an older and original form of astronomy, based upon numerical time and forged by the megalithic, was dislocated and obscured by the heliocentric physical science and astronomy of the modern day – which still knows nothing of the geocentrically order that surrounds us.

Figure 4 The Geocentric Model by 1660

The geocentric model entered Greek astronomy and philosophy at an early point; it can be found in pre-Socratic philosophy … In the 4th century BC, two influential Greek philosophers, Plato and his student Aristotle, wrote works based on the geocentric model. According to Plato, the Earth was a sphere, stationary at the center of the universe.

Wikipedia: “Geocentric model”

Saturn’s “Measuring” of the Lunar Month


How the Moon was seen to be like Saturn in expressing the Sacred Number 28.

illustrated SCRIPT

To measure the length of a lunar orbit, one needs to see any prominent stars that the moon is passing by in her orbit.

This sort of procedure is implied in Indian astronomy, and other traditions, where the sky was first divided into 28 or 27 equal parts, called lunar mansions (nakshatras).

The lunar mansion on a given day was identified by the name of the lunar mansion seen behind it.  In B.C. 2350, the system started with the spring equinox which stood on the seven sisters or Krittikas.

This was in the Zodiac constellation Taurus the Bull, but the mansion, one of 28, was called Ashwini – the Horse’s Head. In this way Indians still speak of “the moon in Ashwini”.

The division into 28 probably came from the observation of Saturn’s loops which resembled the twenty seven and a third days for a lunar orbit, though the first is a frequency of synods while the latter is a frequency of earth rotations, both relative to the ecliptic / Signs / Mansions.

Hounds & Jackals as Venus Counter

The Petrie Museum has a game called Hounds & Jackals or 58 holes, from Egypt’s Middle Kingdom and widely found elsewhere, in the ancient world. Two players had a set of sharp ended sticks with animal heads, which sat in each of the 29 + 29 = 58 holes. The top hole is larger (as with the Cretan 34-hole circular kernos, at Malia in Crete).

Cretan 34-hole Kernos

One can see the possibilities in such artifacts stored objective numerical information while being kept, within the cultural life of the people, through having a valuable everyday purpose (rather like the 52 playing cards do). This was exactly how Gurdjieff saw it that, he proposed a meeting of wise men in Babylon, it was seen that ancient knowledge would be forgotten were it not that art, games, buildings, dances, music and so on were designed to incorporate the knowledge until such time that human would be able, once again, to understand what they meant. In his book Beelzebub’s Tales he termed such artifacts as being logominisms, loosely translating to “meaning objects”.

Continue reading “Hounds & Jackals as Venus Counter”

Book: Matrix of Creation

Sacred numbers arose from ancient man’s observation of the heavens, and represent the secrets of cosmic proportion and alignment. The ancients understood that the ripeness of the natural world is the perfection of ratio and that the planetary system–and time itself–is a creation of number. We have forgotten what our ancestors once knew: that numbers and their properties create the forms of the world.

Introduction to my first book, Matrix of Creation

My first book interprets the planetary system through pure number. The numbers involved in this interpretation are surprisingly simple and will be accessible to anyone holding a basic arithmetic education. From this approach we have gained substantial new insights into the realm of mythology, religious thought and what have become known as the Traditional Arts. We show that the solar system evolved from pure number and can no longer be thought of as an accident of nature.

It is also no coincidence that this work lies poised between the realm of mathematics and the world before numeracy. In the ancient world, numbers assumed god-like powers that were continually creating the world through stable numerical relationships. The core of this ancient science developed such a view naturally through simple astronomical observations, by counting events and regular movements in the night sky. This science was then artic­ulated as mythological stories, calendars, sacred geometry, musical theory and monumental architecture, such as the Great Pyramid and Stonehenge.

These artefacts, found in all ancient cultures, have remained obscure to the modern world because modern science has become too sophisticated to see the simple celestial relationships which demonstrate that the planetary system, including the Sun and Moon, hold to a particular design.

Continue reading “Introduction to my first book, Matrix of Creation”