Author: Richard Heath

Inside Time

There are two things we can count in this world, one is the number of objects on the Earth and the other is the number of time periods between events in the Sky.

photo: The Moon, with Jupiter and Mars, on 11th January 2018. (see end for interpretation)

Objects are counted in an extensive way, from one to an almost infinite number, the count extending with each addition (or multiplication) of a population.

Time periods appear similar but in fact they emanate from measurable recurrences, such as phases of the moon, and these derive from the behaviour of celestial objects as they divide into each other.

For instance, the unit called the day is created by the rotation of the earth relative to the Sun and the lunar month by its orbit around the Earth relative to the Sun, and so on.

Thus, time originally came from the sky. Furthermore, it largely came from the zodiacal band of stars surrounding the Earth within which the planets, Sun and Moon progress eastwards. The Earth’s own orbital motion is superimposed upon those of the other planets and the inner planets (Mercury and Venus) also appear to orbit a Sun that appears to orbit the Earth once a year.

The zodiacal band is naturally divided up into a number of constellations or stars and about three thousand years ago it became popular to follow the Sun throughout the year into 12 constellations whilst the Moon tends to create 27 or 28 stars (nakshatras) where the Moon might sit on a given evening. When the moon is illuminated by the sun, the primordial month has 29 1/2 days and twelve such in less than a year hence perhaps first defining the 12-ness of our months within the year.

All celestial cycles recur and this has formed our notion of eternity, that the sky world is made up of cyclic time rather than extensive time – every year being the same cycle seen again but then numbered so that they can be referred to as to when something happened in the past. The intensive reality above our heads is the polar opposite of extensive counting of time we see in History where numbered years and days within named months provide an unbroken continuum of time and famous people are said to have made history through their actions at a given date.

Whilst on Earth we might measure feet or meters between objects, above we effectively measure angles and angular rates to arrive at a synthesis between intensive and extensive time we call a calendar, an inevitable necessity for an organised civilization. And the moon and then the sun gave rise to the early calendars that naturally led to the arising of history as a human phenomenon. The oldest myths were connected to the sky, and were less than historical because the language of the sky had not been formalized in a way we would recognize.

Myths speak of eternal patterns that repeat rather than of existential events, on earth. The sun, moon and planets were seen as gods whose generative functions were hailed as emerging from their interactions with each other.

It has been widely assumed that “primitive” thought was premature, fantasizing planetary gods out of thin air with an as yet unripened grasp on logic and reason. But a simpler explanation, for the equation of planets with super beings, was their finding of special numbers linking the planetary cycles when these were counted and compared. This quantification of celestial time evolved from knowing the days in a year and a month, into a running calendar – of various sorts. The Maya Long Count is an example where numbers could interact through week lengths of 13 and 20 days to give a sacred calendar of 260 days whilst in historical times the 7 day week emerged, tied to Saturnian time. In this way, a calendar could add weeks adapted to societal events such as having a market every Tuesday.

This is a big subject where we have all the sky data but do not spend time understanding it. In the past, the sky was our constant companion between few man-made spaces. The sky sits within the horizon and so was like a primordial cave for humans and, the sky became an early teacher through its phenomena.

Jupiter and the Lunar Year

The lunar month is like the common denominator of what happens inside time. The sun illuminates the phases of the moon during its month so that, the month combines the movements of the moon and the sun to form a synthetic (combined) period of 29 1/2 days and twelve of these months fit inside the solar year as the lunar year of 12 1/3rd months (354.367 days). Jupiter has its own relationship to the sun in that, when the sun is opposite the moon, Jupiter describes a loop amongst the stars, and strangely there are 13 1/2 lunar months between loops (Jupiter’s synodic period of 398.88 days). 13 1/2 months divided by 12 months is the ratio 9/8, a musical whole tone.

But in the image above, of Jupiter and the Moon, the moon would be full if Jupiter was going to loop (as earth “overtakes” Jupiter on the “inside lane” – the planets inspiring ancient racetracks). Mars is another “outer planet” which loops in the same way and so Mars is also not looping.

But without understanding these matters, the picture cannot be understood. The phase of moon shows where the sun is. The planets have been in conjunction. If Venus had been present, then it has a 4/3 ratio to Mars but has to remain close to the sun to appear first as an evening star, then a morning star, in a cycle 8/5 years (584 days) long compared to Mars synod (between loops) of 780 days. Less accurate than Jupiter to the Lunar year, by a day. This is what I mean by being inside time, where all the celestial bodies have relationships to one another, when these are seen by us from earth.

This is how I started, with my first book Matrix of Creation. The musical ratios and their entrance into ancient stories was explored in Harmonic Origins of the Earth. How ancient humans counted time was discussed in Lords of Time and a unified treatment made in Language of the Angels. Used alongside archaeology, more can be understood about the prehistoric and early civilizations since astronomy was the first real subject for the human race.

Sacred Geometry in Ancient Goddess Cultures (March 26th, 2024)

My new book can be pre-ordered from the publisher and other retailers.

In March next year my new book will be released (see publisher website). The book has been typeset and is out for printing, having been favorably reviewed by a peer group. (The original date was February, but printing schedules have had to be adjusted.)

figure: the punctuation of towers and western outlook. Possibly a funerial building for the king, it could be used as a living observatory and complex counting platform for studying the time periods of the sun, the moon, and even the planetary synods.

Some new material was added during production, including chapters on the design of Angkor Wat (chapter 9) and St Peter’s basilica in Rome (chapter 10), and some early articles on these can be accessed on this site, most easily through the search function.

As you can see, my books partly emerge through work presented on this website. This has been an important way of working. And whilst I am providing some ways of working that could be duplicated by others, at its heart, my purpose is to show that the celestial environment of our living planet appears to have been perfectly organized according to a numerical scheme.

My results do not rely on modern techniques yet I have had to avail myself of modern techniques and gadgets to work out what the ancient techniques arrived at over hundreds if not thousands of years.

My basic proposal is that ancient astronomers learned of the pattern of time in the sky by counting days and months between events on the horizon or amongst the fixed stars. Triangles enabled the planetary motions to be compared as ratios between synodic periods.

Continue reading “Sacred Geometry in Ancient Goddess Cultures (March 26th, 2024)”

Medieval Solfeggio within the Heptagonal Church of Rieux Minervois

This paper responds to Reichart and Ramalingam’s study of three heptagonal churches[1], particularly the 12th century church at Rieux Minervois in the Languedoc region of France (figure 1a).

image: The Church in situ

Reichart and Ramalingam discuss the close medieval association of the prime number seven[2] with the Virgin Mary, to whom this church was dedicated. The outer wall of the original building still has fourteen vertical ribs on the inside, each marking vertices of a tetraheptagon, and an inner ring of three round and four vertex-like pillars (figure 1b) forming a heptagon that supports an internal domed ceiling within an outer heptagonal tower. The outer walls, dividable by seven, could have represented an octave and in the 12th century world of hexachordal solmization (ut-re-mi-fa-sol-la [sans si & do])[3]. The singing of plainchant in churches provided a melodic context undominated by but still tied to the octave’s note classes. Needing only do-re-mi-fa-sol-la, for the three hexachordal dos of G, C and F, the note letters of the octave were prefixed in the solmization to form unique mnemonic words such as “Elami”.It is therefore possible that a heptagonal church with vertices for the octave of note letters would have been of practical use to singers or their teachers.

The official plan of Rieux Minervois

12th Century Musical Theory

In the 10th Century, the Muslim Al-Kindi was first to add two tones to the Greek diatonic tetrachord of two tones and single semitone (T-T-S) and extend four notes to the six notes of our ascending major scale, to make TTSTT. This system appeared in the Christian world (c. 1033) in the work of Guido of Arezzo, a Benedictine monk who presumably had access to Arabic translations of al-Kindi and others [Farmer. 1930]. Guido’s aim was to make Christian plainsong learnable in a much shorter period, employing a dual note and solfege notation around seven overlapping hexachords called solmization. Plainsongs extending over one, two or even three different hexachords could then be notated.

Hexachords conceptually overlapped (figure 2, left); another starting when the previous hexachord reached fa, the fifth, or when the melody again reached a given hexachord’s do of G, C or F. The Solmizations, prefixed with their note letters using Boethius’ Gamut system (Starting with our G (for Gamma ut G to e”) then A, etc., as we do today). For example, e’ would be uniquely called “Elami” since it was the note E, and the solfege la, for hexachord of G, whilst also mi, in the hexachord of C.

In contrast, the modern solfége of key signatures, without note letters, refers us to the major diatonic scale when equal tempered keyboards enable modulation of key signatures. By retaining the note letters, the hexachordal world could still reference the octave as a locational framework whilst also loosening the grip of do as tonic, as with modulation. The white notes of our keyboard were the basis of solmization with one exception: the minor hexachord starting at F had to impose the major diatonic T-t-s upon the T-t-T sequence of the diatonic scale by the solitary chromatic Bb.

Figure 2 The relations between Hexachords and the Octave of note names.
[on left, Willi Apel, 1969]

The solmization code created a namespace of unique composite words[1]. By combining note letters and hexachord positions, notes became unique words like Elami. Each note became linked to Beothius’ Gamut from G to e”, the solomised names explicitly identifying their context in the octave as well as the hexachords they belonged to (Figure 3).

Figure 3 The Solmization namespace combining Boethius’ note letters and Guido’s Solfeggio [Willi Apel, 1969]

When melodies exceeded the hexameter within which they were currently set; “In order to accommodate melodic progressions exceeding the compass of one hexachord, two (or more) hexachords were interlocked by a process of transition, called mutation”, since “in medieval theory the compass of tones was obtained not by joined octaves but by overlapping hexachords” and “tones of higher or lower octaves were not considered ‘identical’ within a Boethian scale of G to e””. [Willi Apel. 1969]

The Church as Octave within Solmization

If do of the “natural” hexachord (C) is placed on the (exactly) northern outer vertex of the fourteen vertices, then the three round pillars land, using Just intonation, in the midst of the Pythagorean tones of the major diatonic whilst the four vertex-like pillars coincide with the uniquely Just tones and semitones[1] (figure 4). The southern door marks the tritone between fa (F the minor hexachord) and sol (G, the hard hexachord). The walls of the church could therefore have usefully symbolised the intervals and note classes of the major scale[2] during the perambulation of the hexachordal plainchant, verbalized using Solmization. That is, if the church symbolized the successive octaves of the tonal world notated using hexachords, the building might have been a regional school for training singers, outside the customary cathedral and monastic schools of the 12th century. Guido’s method (staff notation and solfeggio and solmization) rapidly became famous and was widely adopted throughout north Italy and elsewhere[3]. When built, 12th century Languedoc and northern Italy was strongly populated by Cathars, so triggering the crusade from Rome and hence the subsequent confiscation of the church from its feudal owner.

[1] The practical scale of the day would have been the major diatonic since its three major thirds (between do and mi, fa and la and between sol and si) are achieved using the fifths and fourths of Pythagorean tuning in combination with the major thirds. This automatically generates the different tones and semitone found in Just intonation: T = 9/8 and t =10/9 form, in combination, the major third of T × t =5/4, short of the perfect fourth by the new Just semitone, s = 16/15.

[2] the natural scale for Just intonation when tuned using fifths, fourths and major thirds

In numerical tuning theory, the Virgin Mother would be the perfect symbol for an heptagonal church since the world of music springs from an octaval womb (whose number symbol is 2); only the male numbers (3 and 5) can reach into and divide the octave to create octaves of Pythagorean and Just intervals, then symbolic of Christ’s birth. The seven intervals and the notes of the diatonic scale provide a framework within which the magic of hexachordal singing expresses melody with a suppressed Ego or tonic. Hexachordal music strays across many tonic contexts. Numerical harmonists may have viewed tonics as titular deities of the limiting numbers required to theoretically generate Just Intonation[1], like the demiurges creating worlds but becoming an enemy of melodic freedom within them, by seeking to reference everything to their tonic. Arguably the natural tension, between static tonics of the octave and developmental movements like those found in hexachordal music, manifested the Classical traditions of sonata, concerto and symphony.

Drawing the intervals within the Church

If the two types of tone are each given a span of two or three sides of the tetradecagon, and the semitone a span of only one side, the total would be 3 + 2 + 1 + 3 + 2 + 3 + 1 equalling 15 sides rather than 14. But if one respects the natural symmetry of the tone circle about Re, as the (modern) Dorian scale, then one can make the initial tone of 9/8 symmetrical with the following tone of 10/9. In practice, nothing is lost since the church is only loosely a tone circle, with no imposition of logarithms except for those native to the ear, that hears intervals of the same size as the same size irrespective of pitch. Modes other than major could then have similarly been expressed by choosing other starting notes and vertices explicitly given within the fixed solmization words as the note letter prefix[2].

Figure 3 The encoding of intervals within the church

In the arrangement proposed, the disposition of round pillars coincides with the disposition of Pythagorean tones (of 9/8) on the outer wall, whilst the vertex-like pillars face the Just tones of t = 10/9 and s = 16/15. Pythagoras saw these now-eponymous tones of 9/8 as divinely perfect and hence a circular form is appropriate: The pure tones 9/8 are born (in numerical tuning theory) only by the divine male prime number 3 and the female octaval number 2 seen in 9/8[1]. In addition, Just tone 10/9 and semitone 16/15 require the humanly-male prime number 5 to birth them within the womb of the octave’s tone circle. The northern round pillar would also identify the necessarily shortened whole tone as Pythagorean, despite its being shortened, thanks to the association of pillar shapes with either type of whole tone.

As stated above, one can imagine that in a church, designed to represent an octave in the round, one could conduct the choir in Solfeggio.

My book on the role of musical theory in terms of both the number involved and ancient cosmological thinking is called The Harmonic Origin of the World. It came about through a virtual apprenticeship with Ernest G. McClain whose books The Myth of Invariance and The Pythagorean Plato revolutionized the subject (both books can be read in pdf at his posthumous website.)

References

Apel, Willi. Harvard Dictionary of Music. 1969.

Farmer, Henry George. Historical facts for the Arabian Musical Influence. 1930.

[1] Three Heptagonal Sacred Spaces by Sarah Reinhart and Vivian Ramalingam, pages 33-50 in Music and Deep Memory: Speculations in ancient mathematics, tuning, and tradition. in Memoriam Ernest G. McClain. ICONEA Publications 2018.

[2] which cannot join with any other number below ten or even twelve.

[3] then known as Ut–re–mi-fa-so-la-Sa-Io after the mnemonic “Ut queant laxis, resonare fibris, Mira gestorum, famuli tuorum, Solve pollute, labii reatum, Sancte Iohannes”: So that your servants may, with loosened voices, resound the wonders of your deeds, clean the guilt from our stained lips, O Saint John.

[1] Ernest G. McClain, The Pythagorean Plato 1978.

[4] a namespace arises when each name is unique whilst shared elements common to the other words, such as note letters and the solfege within hexachords.

[2] This transpositional modality is reminiscent of our later key signatures to which solfeggio is now applied.

[3] https://en.wikipedia.org/wiki/Guido_of_Arezzo.

[1] Ernest G McClain The Myth of Invariance, 1976

The Stonehenge Crop Circle of 2002

One sees most clearly how a single concrete measure such as 58 feet can take the meaning of the design into the numbers required to create it. However, metrology of feet and types of feet can hide the elegance of a design.

photo by Steve Alexander of TemporaryTemples.co.uk

I received Michael Glickman’s Crop Circles: The Bones of God at the weekend and each chapter is a nicely written and paced introduction to a given years worth of crop circles generally in the noughties. The above is the second in proximity to Stonehenge reminding keen croppers of an earlier one. This cicle preceeded the late-season (August) circle at Crooked Soley that I have an analysis of soon to be posted, drawing on Allan Brown’s small book on it.

Glickman’s chapter 10 : Stonehenge Ribbons and Crooked Soley provided a tentative analysis of the Ribbons as having the ends of the ribbons measuring 58 feet. The design was observed as making use of a single half circle building block for most of the emergent six arms emerging from the center. Michael suggested that there were 13 equal units of 58 feet across the structure.

Figure 10.4 Showing thirteen divisions of one of the three diameters of ribbons. photo: Steve Alexander.

From this I was able to observe that clearly the divisions were not equal in size and the white ones were clearly smaller as was the central circle’s diameter. Scanning the picture and placing it in my Visio program, so that a rectangle of 58mm was equal to the diameter of the right hand ribbon end, it was possible to determine that the ratio between these lengths was 5 to 4, or 5/4, from which the shorter white length must be 46.4 feet and that the diameter can be seen as 9 units across, that is 104.4 feet. The unit is 104.4 feet divided by 9 which equals 11.6 feet, which is 10 feet of 1.16 feet, the root reciprocal of the Russian foot of 7/6 feet, that is 7/6 feet divided by 175/176 (= 1.16). Going down the “Russian” root led to the diagram below.

My analysis of Michael Glickman’s figure reveals a span of 580 Russian Feet.

There are parallax errors so I have had to show the ideal designed shortened across the left-hand of the design, but the design has many numerical aspects where each arm is 27 units so that two arms are 54 which, plus the center, gives 58 times 10 equaling 580 Russian feet. But then I noted that 58 feet, divided by 5, gave the unit as 11.6 English feet while 58 feet divides into the 58 unit diameter across the crop circle.

Now we see a set of multiples of 29 are there as numbers {29 58 87 116 145 174 203 232 261 … }. The reciprocal Russian at 1.16 feet and the unit of 11.6 feet are decimal echoes of the number 29. The formula of the Proto Megalithic yard is 87/32 feet and 261/8 inches.

To be continued

One sees most clearly how a single concrete measure such as 58 feet can take the meaning of the design into the numbers required to create it.

Pauli’s Cosmic Dream

above: Wolfgang Pauli, ca. 1924. Wikipedia CC BY 4.0

Renowned psychiatrist Carl Jung had an intellectual friend in Wolfgang Pauli, a leading theoretical scientist in the development of quantum mechanics who had offered (with others) a third perspective to the deterministic physics of Newton and relativistic physics of Einstein. For example, Pauli’s Exclusion Principle explained how sub atomic particles of the same type could be connected to each other (entangled) on the level of the very small.

Dream analysis with Carl Jung opened Pauli up to the inner worlds of alchemy, archetypes, and dreams. Pauli recounted his dreams to Jung who would analyze their symbolism. One dream is of special interest here since it concerned a cosmic clock with two discs with a common center: one vertical and the other horizontal. The vertical disc was blue with a silver lining upon which were 32 divisions and the hand of a clock pointing to a division. The horizontal disc was divided into four differently colored quadrants, surrounded by a golden ring.

above: A visualization of Pauli’s report of his dream of the Cosmic Clock. The black bird would traditionally be a member of the Corvus or Crow family. In the original one sees 32 rings punctuating the outer ring. below: Jane Roberts colored it, noting it resembled Ezekiel’s vision. 

This reminded me of the 32 lunar months which take 945 days to complete so that each lunar month could be known in ancient times as 945/32 or 29.53125 days, only 57 seconds too long! The clock had three “pulses”, the first moving the hand on the scale of 32, the second pulse occurring after the hand had completed one revolution, after which, something golden and presumably the Sun, moving something on the golden ring, by 1/32 of its circumference. Pauli said the golden ring was black before the clock’s hand started moving, and it seems that Pauli experienced this goldenness as a principle of geometrical harmony. If the golden disc is the sun and, since the lunar month is the completed illumination of the moon by the sun, here the sun is lit up by the moon to become golden rather than black.

Such an apparatus would complete itself in 32 times 32 (1024) pulses, these taking 945 times 32 or 30,240 days. This long cycle is three times 10,080 which number is the diameter of the sublunary sphere (14) then 10,080 in the factorial Equal Perimeter model, a model which presents the size of the earth and moon whose diameters are in the ratio 11 to 3, the mean earth diameter of 7920 miles and moon diameter of 2160 miles. This model has been found present within many ancient monuments up to the modern era, hence expressing past cosmological knowledge. Though the vertical “face” of the clock is blue, the colors of the four horizontal quadrants were red, green, orange, and blue, each quadrant having an outward facing “monk” holding a pendulum that, by Pauli’s day, represented the counting of time as seconds, rather than as days.

The whole apparatus is held aloft by a black bird, and this can explain the 30,240 days as eighty synods of Saturn (378 days), the planet that moves (between its synodic loops each year) a similar distance on the Zodiac as the Moon moves in a single day, which is one reason why Saturn was called a god of Time. In the Greek Myths, the crow family were not black but white until the separation of the “world parents”, namely the ecliptic and equatorial planes, this separation of the parents being the cause of the long Precession of the Equinoxes in 25,920 years. More significantly, it is this separation that divides the solar year into four quadrants of the clock. The quadrants are separated by the four gates of the year: the spring and autumn equinoxes where the parents cross one another; and the summer and winter solstices where, outside of the Tropics, the sun is higher or lower in the sky, creating the four seasons.

Equating the 32 divisions in the dream with 32 lunar months has allowed what is a dream to be quantified and connected to the ancient model, in a new and factual way, where the golden ring is the Sun on the ecliptic and the bird is Saturn. Distance and Time become twin dimensions since the size of the earth and moon, in miles, are then related to the lunar month within this harmonious clock. Another boundary has also been crossed, between our conscious daytime experience, as factual, and our subconscious nighttime experience of dreaming, as imaginative. A model of time on Earth was communicated through Pauli’s dream life. Jung called it the Collective Unconscious and it is either (or both) a door to the higher intelligence responsible for the creation of time on earth or (and) to the ancient works of astronomy that had understood the world of time to be a numerical creation. For this reason, Sacred Geometry: Language of the Angels got its name.

Jung later discovered a similar dream emanating from the Christian mystic Guillaume (whose works inspired John Bunyan’s Pilgrim’s Progress). Guillaume’s “vision” was presented as a dialogue with an angel. The details are different but significantly, a small blue ball (said to represent ecclesiastical time) was floating in an golden sea of Eternity and manifesting the Trinity within the Zodiac of twelve signs (3 times 4), as 12 fishermen who together manifest the Trinity. Guillaume did not understand so the angel then talked about the three principal colors as being green, red, and gold, but abruptly stops, terminating further questioning. Jung had already found, in the number three within the Trinity a culturally dominant form of masculine thinking which came out in the dream as the color not mentioned, namely blue – the color of the “small” sphere in Guillaume’s and of the fourth blue quadrant in Pauli’s version. Blue is associated with the Goddess, portrayed in the cloak of Mary, the mother of Jesus.

The missing goddess figure is also found in Vishnu’s awakening to his creation of a new world through Prajapati, the first man. Prajapati emerges out of a lotus, a flower growing from Vishnu’s navel, a flower that had Brahma (the creator god) in its many petals. So long as Vishnu sleeps between creations, the goddess attended to him but when He awakens, she has disappeared (because she is considered the supreme reality of the creation). It was Pauli’s feminine side who had, thought Jung, like Eve revealed the cosmic clock to him.

In my forthcoming book: Sacred Geometry in Ancient Goddess Cultures (chapter 11), the harmonic model can be seen emerging from this cosmic clock of lunar month and year and the planetary synods resonating with these musically. The biblical Adam then emerges within a lunar octave of doubling from 45 (through 90, 180, 360, 720, 1440). The coordination of such stories of “first men” within scripture might not have happened through the diffusion of traditions but instead, it may subsist in something like Jung’s collective unconscious, that men dream through their feminine side (and women through their masculine side), as seen in these dreams. This makes sacred geometry in ancient matriarchal cultures significant today when masculine thinking has become so dominant. It is also interesting that the early Indian myth of Vishnu had the god sleeping at night and, as humans do , re-inventing the world during the day.

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.”