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.
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.
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.
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.
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 diabolicusin 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.”
The design of the twin towers of Chartres point to an extraordinary understanding of its designers, quite unlike pre or modern understandings of the outer planets and their harmonic ratios. We have already seen a propensity for using the ordinary English foot to indicate days-as-feet within the structure. The Façade hosts what is perhaps the most famous “rose window”, though it was only in later centuries that it would be termed thus, as the cult of the Virgin Mary became more widespread. But this cathedral was strongly dedicated to the Virgin, when built.
The two towers are separated by the same distance as the rose window is above the footings, namely 100 feet, while the façade is 150 feet wide. This has led me to rationalize the façade as being six units across of 25 feet, while the façade appears to end (and the towers begin) 200 feet above the footings.
Interpretation of the western Facade as composed as towers 4 apart, width 6 apart and height 8 units, all of 25 feet. The Rose Window is held within two 3,4,5 triangles within a wall of 2 units square.
That is the façade was therefore designed as a three by four rectangle, the rose window centrally located within a square of side length 50 feet.
In simplest units of 50 feet, 8 by 6 becomes the proportion 4 by 3, with diagonals that are 10 units (that is, 250 feet) where the rose is at the crossings of those diagonals, held between two 3,4,5 triangles.
This first Pythagorean triangle holds all of the ratios of regular musical harmony, having 4/3 (fourth), 5/4 (major third), 6/5 (minor third) between its sides, which multiplied together equal 60 and summed equal 12.
The marker stars within the circumpolar or arctic region of the sky have always included Ursa Major and Ursa Minor, the Great and Little Bear (arctic meaning “of the bears” in Greek), even though the location of the celestial North Pole circles systematically through the ages around the pole of the solar system, the ecliptic pole. In 4000 BC our pole star in Ursa Minor, called Polaris, was far away from the north pole and it reached a quite extreme azimuth to east and west each day, corresponding to the position of the sun (on the horizon in 4000 BCE at this latitude) at the midsummer solstice sunrise. This means angular alignments may be present to other important circumpolar stars in some of the stones initiating the Alignments at Le Menec, when these are viewed from the centre of the cromlech’s circle implicit in its egg-shaped perimeter.
This original “forming circle” of the cromlech could be used as an observatory circle, able to record angular alignments. Therefore the distinctive “table” stone which aligns to the cromlech’s centre at summer solstice sunrise, also marked the extreme angle (to the east) of Polaris, alpha Ursa Minor, our present northern polestar. That is, in 4000 BCE Polaris stood directly above the table stone, once per day – whether visible or not.
Such a maximum elongation of a circumpolar star is the extreme easterly or westerly movement of the star, during its anti-clockwise orbit around the north pole. Thus, if the northern horizon were raised (figure 5) until it passed through the north pole, the maximum circumpolar positions for a star to east and west would be equally spaced, either side of the north pole. If these extreme positions are brought down to the Horizon in azimuth, the angles between these extremes forms a unique range of azimuths on the ground between (a) the horizon (b) a foresight such as a menhir and (c) an observer at a backsight. Observations of these extreme elongations naturally enable the pole (true north) to be accurately established from the observing point as the point in the middle of that range. A marker stone can usefully locate a circumpolar star at one of these maximum elongations and come to symbolize that important star. A star’s location could have been brought down to the horizon using a vertical pole or plumb bob, between the elongated star and the horizon, at which point menhirs could later be placed, relative to a fixed viewing centre or backsight. This method of maximum elongations would have escaped the atmospheric effects associated with observing stars on the horizon which causes a variable angle of their visual extinction below which stars disappear before reaching the horizon.
Figure 5.The Maximum Elongation of Circumpolar Stars is a twice daily event when, looking at the horizon, the star’s circumpolar “orbit” momentarily stops moving east or west at maximum elongation in azimuth and reverses its motion.
At Le Menec the azimuths of the brightest circumpolar stars, at maximum elongation, appear to have been strongly associated with the leading stones of the western alignments (see figure 6). However, it is likely that only one of these circumpolar stars was used as a primary reference marker, for the purpose of measuring sidereal time at night when this star was visible.
Figure 6 Some of the associations between circumpolar stars and stones in the western alignments. These alignments are all to the maximum easterly elongations, perhaps established during the building of the sidereal observatory and only later formalized into leading stones at the start of different rows. Dubhe was then selected as the primary marker star for the Le Menec observatory.
To achieve continuous measurements of sidereal time from the circumpolar stars requires a simple geometrical arrangement that can draw down to earth the observed position of maximum elongation to east and west for one bright circumpolar star, the observatory’s marker star. A rectangle must then be constructed to the north of the cromlech’s east-west diameter and containing within it the observatory’s northern semicircle. The northern corners must align with, relative to the centre of the circle, the eastern and western elongations of the chosen marker star. For Le Menec the rectangle had to be extended northwards until it reached the first stone of row 6[1]. This stone is aligned, from the centre, to the maximum eastern elongation of Dubhe or alpha Ursa Major. The first stone of row 6 is therefore the menhir marking Dubhe. To the south, the initial stones of further rows all stand on the eastern edge of this rectangle, so that any point on the rectangle’s north face could be brought down, unobstructed, to the circumference of the circle.
Figure 7 shows how the form of the circumpolar region, within the “orbit” of Dubhe, is repeated by the cromlech’s forming circle. It is also true that the “northern line” then has the same length as the diameter of the forming circle, which has therefore been metrologicallyharmonized with row 6’s initial stone and the alignment to Dubhe in the east.
This arrangement has the consequence that whereverDubhe is (above the northern line and when seen on a sightline passing through the centre of the cromlech) its east-west location in the sky can be brought down, directly south, to two points on the forming circle of the observatory – all due to the star observation having been made upon a length equal to the circle’s diameter (the Northern Line of figures 7 and 8). One of these two points, on the northern or southern semicircle of the observatory, must then correspond exactly to where Dubhe is in its “orbit” around the north pole, as in figure 8.
So, what is being measured here and what would be the significance of having such a capability? Whilst the movement ofall the stars is being accurately measured, using this northern line and forming circle combination, the monument also has a reciprocal meaning. The forming circle also represents the earth’s rotation towards the east, the cause ofthe star’s apparent motion. This is because, when looking north, thefamiliar direction of rotation of the stars, when looking south, is reversed from a rightwards motion to a leftwards, anticlockwise motion. Circumpolar motion therefore directly represents the rotation of the earth. The Dubhe marker star would have represented the movement of a point on the surface of the earth, moving forever to the east. Perhaps more to the point, the eastern and western horizon are moving as two opposed points on its circular path, each moving at about the same angular speedasDubhe. This deepens the view of the forming circle as representing those ecliptic longitudes in which the fixed stars, rising or setting on the eastern and western horizons, are fixed locations on the circle through which these horizons are moving as markers on the circle’s circumference.
These two views, of a moving earth and of a moving background of stars, could be interchangeable when understood and both viewpoints are equally useful and were probably relevant to the operation of this observatory. Whilst the circumpolar stars move around the pole, the eastern and western horizon move opposite each other, running along the ecliptic, as the Earth rotates. The first view enables an act of measurement which would have given astronomers access to sidereal time and the second view provided knowledge of where the eastern and western horizons were located viz a vis the equatorialstars and therefore knowledge of whichpart of the ecliptic was currently rising or setting.
Figure 8 Recreating the circumpolar region with marker star Dubhe at the correct angle on the forming circle of the western cromlech. The star’s alignment on the northern line is dropped to the south so as to touch the two points of the circumference corresponding to that location on the circle’s diameter: one of these will be the angle of Dubhe as seen within the circumpolar sky but now accurately locatable in angle, on the observatory circle.
Dubhe had, in 4000BCE, a fortunate relationship to the circumpolar sky and equatorial constellations which would have been very useful. When Dubhe reached its maximum eastern elongation (marked by the first stone in the sixth row) the ecliptic’s summer solstice point was rising in the east. However, Dubhe’s maximum western elongation did not correspond to the winter solstice, this due to the obliquity of the ecliptic relative to north. It is the Autumn Equinoctal point of the ecliptic that is rising to the east at Dubhe’s maximum western elongation. It was when Dubhe was closest to the northern horizon, that the other, winter solstice point was found rising on the ecliptic. It is important to realize that these observational facts were true every day, even when the sun was not at one of these points within the ecliptic’s year circle.
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CONTENTS
This paper proposes that an unfamiliar type of circumpolar astronomy was practiced by the time Le Menec was built, around 4000 BCE.
