Figure 1 The Cathedral at Night by Robert Breuer, CCSA, Wikipedia Commons

Koelner Dom bei Nacht 1 RB 1It seems worthwhile to look at the geometry and metrology of this cathedral, to the extent that I can. It has the greatest ratio of height to width, over three times as high. As usual the building plan is in the shape of a cross (figure 2), with a thin upper roof describing a Roman cross in the proportions of 5 across and 8 down. The ratio has meaning as two early Fibonacci numbers, hence approximating the Golden Mean (phi). Eight also generates an octagon - an arena of completedness whilst Five generates the pentagon and is a humanly divine number - four limbs and a head of the "human fiver", a geometry filled with the phi ratio. Astronomically, the practical solar year of 365 days divides into five 73 day units, which unit then divides into the synod of Venus, 584 days equalling 8 x 73 days.

Cologne Roof

Figure 2 The crucifix of the roof seen from the air.

A link was made by medieval symbolists between the Virgin Mary and Venus, not least through the astrological connotation of Virgo (the Virgin constellation) diametrically opposite to Pisces (the Fish), the latter embematic of Jesus as Pantocrator and master of an Age of Pisces, into which the spring equinox had entered (dispelling Pan as Aries). I have previously noted how the mother-and child-motif could symbolise the inner solar system of Venus and the Moon, the two being strongly present in the star and crescent and brightest reflective objects of our skies. The moon dies for three days only to be resurrected and so on, whilst Venus, due to orbital resonance, has a highly structured set of Fibonacci relationships to those living on earth. 

The analysis in Figure 2 is using pure ratios (or relative proportions) to see the building as a whole. Exact measures are not important as one can see that the ratios, in providing a simpler view, directly reveal an intentionality to the building's design. I would also like to invoke another view of the building; as it having precedents in ancient Greek temple design, occupying a rectangular plot normal for land use, explored in previous articles Megalithic Origins of Greek Temples and Fields, Racetracks and Temples in Ancient Greece. That is that the Gothic cathedral is not far different to the traditions of the Greek temple prior to Rome and the Romanesque which preceeded the Gothic style.

 

We have seen, in analysing Chartres, that the floor plan and main facade (with twin towers) can reveal interesting metrological and rationic insights. Having only the web to provide plans, I conducted a measuring exercise using an already busily interpreted German image which ACTUALLY HAD SCALE MARKED. This is a common problem, especially now data clouds are replacing reliance on technical drawing; clouds are often hard to access as to actual measurements within what they record.

 Cologne Dimensions facade

Figure 3 Measurements on the Facade of Cologne Cathedral.
The use of root geographic Roman feet (0.971 ft) allowed the lunar year in English feet to secretly become the 365 day year because the two periods are of the ratio 1/ 0.971. This foot then gives the height of the towers as equal to 18 lunar months, a time period associated with Adam (see Harmonic Origins of the World).

The design seems to have involved at least two types of foot and fortunately the English foot encodes the syndodic period of the lunar year as (an apparent) 354.4 feet above the pediment. This would place the monument as having some harmonic content since the two outer planet synods are then definable as two of the three intervals important to the Church modes. The bounding geometry of the facade at Cologne can be seen rationically as having been a double square, thence demanding its extreme height to width. One can usefully return to the geometrical approach with which we started, on the roof:

Cologne Dimensions facade structuralmethod

Figure 4 The Facade seen as formed within a vertical double square

Having super-imposed the double square, the crossed lines of the lower square are both √2 of the sides "worth" 9 lunar months. The central pinnacle of the lunar year is 12 lunar months and the half side or the unit squares are 4.5 lunar months. This allows by Pythagoras' method 122 x 4.52 =  √657/4 = 12.816 months. Saturn's synod is 12.8 months, a geometrical coincidence accurate to one part in 1000 or 42 minutes.

This presentation of octaves within monuments is presented with other examples in my forthcoming book The Harmonic Origins of the World, including the Parthenon and Olmec city of Teotihuacan. An octave 720:1440, based upon biblical character Adam, was quite ubiquitous in the ancient world as being the least limiting number capable of generating the Greek modes which became Church modes. For this reason, I have added the menu item HARMONICS extending the scope of and techniques for harmonic interpretation within monuments, especially those called post-megalithic whose form is inexplicable and whose builders remain an enigma. It seems that the harmonic doctrine, along with the megalithic toolset of metrology and geometry went underground in order to preserve this knowledge of the harmonic nature of the world. With every example, the Gothic design methods become clearer and the case for a hidden school, responsible for the Gothic cathedral design, more substantial.