Sacred Geometry and Golden Proportion in Cistercian Abbeys

He spoke and had as measure a golden reed, to measure the city, its gates and its walls. The city is square-shaped, its length is equal to its width. The angel measured the city with the reed: it measures twelve thousand stadia; the length, width and height are equal. From the Apocalypse itself we thus obtain geometric indications relative to the City of God that refer to the figure of the Square ("The city is square-shaped") and the Cube ("length, width and height are equal") and all the numbers associated with these figures such as $4$, $12$, etc., which, consistently with the mathematical conception of the time, were conceived exclusively in geometric form. In particular, the Cube was considered as a figure particularly suitable for developing in Cistercian abbeys the symbolic analogy with the Heavenly Jerusalem. In the medieval context, indeed, the cube had been the fruit of numerous speculations initiated first by the Pythagorean school, but then developed by St. Augustine, Boethius, etc. Such speculations wanted the cube as the principal harmonic figure from which all fundamental musical ratios flowed. The cube as symbol of the Celestial Jerusalem thus communicated two main fundamental ideas: the idea of immutability, fixity and perfection given by the equal measure in height, width and depth; the perfect harmonicity deriving from the proportions that govern it. If we indeed consider the geometric figure of the cube, this results formed by $8$ vertices, $12$ edges and $6$ faces. The ratios between these $3$ numbers give rise to the $4$ fundamental musical ratios for ancient music: - $\frac{1}{2} = \frac{6}{12}$ unison ratio or diapason - $\frac{2}{3} = \frac{8}{12}$ octave ratio or diapason - $\frac{3}{4} = \frac{6}{8}$ fifth ratio or diapente - $\frac{3}{4} = \frac{6}{8}$ fourth ratio or diatesseron The ratios of fourth, fifth and octave indeed constituted the base of most of the melodic framework of antiquity, as in the case of Philolaus' tetrachord DO-FA-SOL-DO. For the reasons exposed above, the main geometric figure of Cistercian Abbeys became the square (or cube if thought in perspective sense) which used as fundamental module was reported according to the fundamental proportions derived from the cube going to construct what were the fundamental guidelines of the abbey. A significant example for our analysis is represented by the plan of Clairvaux abbey, built by St. Bernard's brother under the direction of St. Bernard himself. In the construction of the abbey one proceeded first by determining the central square of the cloister according to traditional procedures codified since the time of the ancient Romans by Vitruvius, but with every probability dating back even to earlier Egyptian epochs. Once obtained and realized the fundamental module of the abbey, such module was reported according to the previously mentioned proportions and derived from numerical ratios derived from the cube. In particular, the repetition of the central module four times went to form the central cloister in the center of which was placed a tree, as symbol of the tree of life described in the center of the Heavenly Jerusalem and beside which was placed a well or fountain as symbol of Christ. To these proportions dictated by the cube must be added a proportion that for its importance and for its symbolism has always been used in architectural geometric symbolism so much as to deserve the name of Golden Proportion. This ratio is a ratio known since antiquity that has as its particularity that of being perceived by man as beautiful and harmonic so much that its use has been promoted from ancient Egypt to our days. In Pythagorean times this number was associated with the mystery of Light being it derived from the five-pointed Star. In Plato's time instead such number was associated with the Mystery of Unity.