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.

Chartres, in north-west France, is a very special version of the Gothic transcept cathedral design. Having burnt down more than once, due to wooden ceilings, its reconstruction over many building seasons and different masonic teams, as funds permitted, would have needed strong organizing ideas to inform the work (as per Master Masons of Chartres by John James).

As shown below, Chartres main towers are unequal in height and the “western” facade itself does not align to east-west, as normal Christian churches do. The left tower is also higher than the right tower and, it has been said, the left represents the Sun and the right the Moon. The height of the left tower, to its globe below its cross, is indeed the solar year of 365 days in feet. But the height of the shorter right tower, to its own globe, is not the 354.367 days of the lunar year (of 12 months); rather, it is the top of its cross, sporting a crescent moon suggesting it is a moon tower, that is 354 and a third feet high.

The cosmic time coding of the two towers as solar year->lunar year between the globe’s height (on left in red) and the top of the cross (on right in blue). But the left tower also indicates the Saturn synod of 378 days to the top of its cross. The for-square rectangle, geometrically relating the solar (diagonal) and lunar years, is shown.

That is, the height of the lunar year in feet, from the same starting point as the solar tower’s height as the solar year, the lunar year would be to the top of the lunar cross, where the crescent is attached, and not to its globe. There is then a reasonable connection between the solar and lunar years and the two towers. However, it is also interesting to see the number of days, as feet, of the left tower to its own cross. It is exactly 378 feet, the synodic period of Saturn in days. Readers of my books and this site will remember that the ratio between the lunar year and Saturn synod is exactly 16/15: a musical semitone within the ancient tuning system called Just intonation.

This arrangement suggests Chartres was built to be a time-factored monument, which may be why the cathedral was aligned to midsummer sunrise (which was a megalithic norm) rather than being aligned east-west. Built on top of a solitary promontory, horizon events would have been clear across the flat fertile plains.

This video introduces an article on a Scottish iron-age stone tower or brock which encoded the size of the Earth.

In the picture above [1] the inner profile of the thick-walled Iron-Age broch of Dun Torceill is the only elliptical example, almost every other broch having a circular inner court.

Torceill’s essential data was reported by Euan MacKie in 1977 [2]: The inner chamber of the broch is an ellipse with axes nearly 23:25 (and not 14:15 as proposed by Mackie).

The actual ratio directly generates a metrological difference, between the major and minor axis lengths, of 63/20 feet. When multiplied by the broch’s 40-foot major axis, this π-like yard creates a length of 126 feet which, multiplied again by π as 22/7, the simplest accurate approximation to the π ratio, between a diameter and circumference of a circle, as used in the ancient and prehistoric periods., generates 396 feet. If each of these feet represented ten miles, this number is an accurate approximation to the mean radius of the Earth, were it a sphere.

If we take the size of the moon in that model, as being 3/11 of 396 feet this would give a circle radius 108 feet and one can see that, using the moon, the outer perimeter of the brock was probably elliptical too.

Thank you for watching.

You can view the full article on sacred dot number sciences dot org, searching for BROCK, spelt B R O C H.

Our modern globes are based upon political boundaries and geographical topography yet they had geometrical predecessors which described the world as an image, a diagram or schemata. By some act of intuition, an original Idea for the form of the Earth had become established as a simple two-dimensional geometry, very like eastern mandalas.

Such a diagram came to be built into the Cosmati pavement of Westminster Abbey, this installed during the reign of Henry III as a gift from the Pope and one or more Cosmati master craftsmen. It was dedicated to the Saxon King (and Saint) Edward, the Confessor. This exotic pavement became the focus for the Coronations of subsequent English then British monarchs. Its presence at the heart of English then British king-making is part of what is called the Matter of Britain, one of many Mysteries as to the meaning of its design.

Square roots turn out to have a strange relationship to the fundaments of the world. The square root of 2, found as the diagonal of a unit square, and the square root of 3 of the diametric across a cube; these are the simplest expressions of two and three dimensions, in area and volume. This can be shown graphically as:

photo above of Umayyad Mosque, Damascus by Bernard Gagnon for Wikipedia CC BY-SA 3.0.

In previous articles on double squares and then St Peter’s Basilica, it became clear that squares and double squares have been embodied, within sacred buildings and art, because circles can then spawn golden rectangles from them. A golden rectangle has one dimension related to its other dimension as the golden mean {1.618034…}. Firstly, the original square plus golden rectangle is a larger golden rectangle but, secondly, the new golden rectangle (beside the square) shares its side length as one unit {1} but its other side is then the reciprocal of the golden mean (0.618034).

The golden mean is the only irrational number whose reciprocal, and square share its fractional part {0.618034 1.618034 2.618034}: there can be only one real number for which this is true. But it is in its geometrical expression, living structure and aesthetics (as in classical architecture) that lead its uniqueness to be seen as a divine ratio. Therefore, it seems, ancient human civilizations sought this golden form of harmony within the form of the Temple, especially in Dynastic Egypt and Classical Greece. The planet Venus must have reinforced this significance since its synod {584 days} is 8/5 of the solar year {365 days} and its manifestation such as evening and morning stars, move around the zodiac tracing out a pentacle or five-pointed star, the natural geometry of the golden mean.

The natural geometry of the Golden Mean is the Pentacle, traced out by planet Venus upon the Zodiac as evening and morning star. (from Sacred Number and the Origins of Civilization)

In the renaissance, the Classical tradition of Ancient Greece and Rome was reborn as neoclassicism, a famous proponent being Palladio, and further neo-classicism arose in the 19th Century and continues in the United States. From this, the previous article on St Peter’s saw its original square become rectangular in a golden way. The whole basis for this is due to the nature of squares and circles, that is: golden rectangles are easily formed geometrically through squares and circles.

The extension of St Peter’s from a square, by adding a golden rectangle, can be seen to also apply within the original square. Furthermore, there is a medium-sized square within the golden rectangle plus a small golden rectangle (see below).

The overall golden rectangle of St Paul’s of a square and golden rectangle below. Using the square within the golden rectangle, the original square above can have four such overlapping squares, to create a cruciform pattern, the upper part of which was used to lay out the Umayyad Mosque.

The medium square can be tiled four times within the large square to overlap the other medium squares, as shown above. This creates a small central square while the four regions that overlap are smaller golden rectangles. The lower golden rectangle is also repeated four times with overlapping, twice horizontally and twice vertically. It is seen that squares and golden rectangles can recede within a square, into smaller sizes, or expand around a square. It is as if all levels of scale hold a kind of fractal, based upon the golden mean.

The top six elements of the square can be seen to match the site plan of the Great (Umayyad) Mosque of Damascus, built 900 years before St Peter’s Basilica, on the site of an Orthodox Cathedral and, before that, a Roman temple to Jupiter. In other words, any golden rectangle design can contain resonances of somewhat different golden mean designs, that may express a different meaning or context; in this case the Mosque gives the notion of two squares overlapping to generate an intervening region of blending and the rectangle of overlap will then be phi squared in height (shown yellow below) relative to the width being unity – the central square’s side length.

The geometry of the Umayyad Mosque

My thanks to Dan Palmateer, for his emails and diagramming whilst on this theme of golden rectangles. One of his own pictures (below) shows the central square of the main square, by tiling the main square with the small golden rectangle.

The central square within the greater square is revealed in St Peter’s as a square within a circular area, noting that this plan (held by The Met Museum) was made after the building had been completed.

There was obviously a vernacular of golden rectangular building in Islam which was carried forth in Renaissance Europe. The potential for golden rectangular building can be all-embracing, as it is a property of space itself, due to numbers.