Musical Elevations and Sacred Geometry in Gothic Cathedrals and Christian Iconography

The Musical Elevations of the building designated the 2:3 ratio between length and width of the construction, and finally the plan of the building itself was often obtained simply by unfolding a cube on a plane, thus referring to the geometric harmony of this solid expressed by Boethius in De Arithmetica. On these musical aesthetic canons established by Pythagoras, highlighted by Saint Augustine and Boethius, and taken up by the School of Chartres and Saint Bernard of Clairvaux, the elevations of Gothic cathedrals are generally founded. These proportions were in fact generally used to determine the heights of some fundamental guidelines such as the column line, the upper line of the arches, the base line of the triforium and that of the clerestory. A typical example is that in which the height of the columns is in a 3 to 4 proportion with respect to the height of the arch line, 2 to 3 with respect to the beginning of the triforium and 1 to 2 with respect to the end of the triforium, respected in numerous cathedrals of the mature period of French Gothic. These three fundamental heights define what could be called the rhythm of the cathedral's elevation, which provides a guide to all other architectural elements. In design practice, however, this rhythm of elevation, formed by musical consonance ratios, was realized through the use of various geometric forms and symbols that indicated to the designer the center and compass opening necessary to close the arch or draw the vault. In numerous cases, in fact, the arch of the nave, or the vault of the cathedral are realized thanks to the use of a five or seven-pointed star. Generally, to close a pointed sixth arch, a center and radius were necessary which were suggested to the builder by stellate geometric figures. Such is the case - for example - of the side naves of Amiens cathedral obtained thanks to the use of the seven-pointed star. In this case, the center where to point the compass is found simply by reporting half the height of the column from the center of the central nave, while the radius to close the arch is obtained thanks to a second circle derived from a seven-pointed star inscribed in the first. A similar procedure is found episodically in the structuring of the cathedral vault itself. In figure 13.13, for example, the closure of the vault of a cathedral whose interior corresponds to the interior of Amiens cathedral is represented. In this case the elevation of the cathedral is given by the triple repetition of the square delimited by the width of the central nave and the height of the columns. By reporting this square 3 times, in fact, the external height of the cathedral is obtained. Now to find the closure of the cathedral it is sufficient to inscribe a five-pointed star inside the circle of the third square. The lower vertex of the pentagon internal to the five-pointed star will determine the height at which to point the compass to draw the arc. The exact position of the center and radius of the arc is obtained simply by drawing another circle in the upper part of the star having as radius the height of the pentagon internal to the star. This circle intersects two points along the horizontal line of the star which provide, once reported to the right heights, the center and radius of the arc thus allowing to complete the design. Christian iconography, like a cathedral, is a true temple. This is the first point that must be considered whenever approaching the study of traditional Christian iconography, especially that of the Eastern church and especially that relating to the golden period of the Novgorod school. In this historical context, iconography was endowed with a rich and substantial theology of Light, mainly due to the work of Saint Gregory Palamas. The icon, in fact, is a theophanic place, a center of transparency on which divine presence is poured thanks to the work of the theurgic artist who has been able to tune, through appropriate science, the sensible icon to the archetypal or intelligible icon. The artist, in a state of holiness, models and shapes his work conforming it to his state of interior communion with God One and Triune and His Divine Uncreated Energies, thus vitalizing the substances created by him and transforming them into a radiating center. In Christian iconography, therefore, the painter, before anything else, is a saint who, with his painting, performs a sacred act binding a material and sensible visual support to a spiritual and intelligible reality. The archetypal icon formed by the Initiate, who has painted and registered it in the world of eternal archives, is in connection with the wooden icon painted with appropriate spiritual colors, vitalized by the divine "presence". The archeosophical icon concentrates, defends against distractions and temptations, and homologates consciousness and biological energies of the body to the "presence" itself. The icon, says Pavel Florensky in his Royal Doors, "lifts the mind from images to archetypes", evoking a spiritual vision in the consciousness of the faithful. The icon evokes an archetype, that is, it awakens a spiritual vision in consciousness: for those who have contemplated this vision clearly and consciously, this new, secondary vision through the icon is also clear and conscious. But for another, the icon will respond to a spiritual perception profoundly dormant below awareness. The true Christian icon is not just a simple symbol, nor a simple religious representation, but is the fruit of a sacred act with its own liturgy that makes it something special: a center of radiation, a vehicle of divine presence. The consecration of an icon involves the penetration of the icon by the divine uncreated energies. In other words, God's love and the celebrant's love resolve in enveloping the icon with an energy operating on the faithful who contemplates and loves it. In this theurgic-artistic process, geometry plays a fundamental role. Geometry in fact turns out to be an essential and indispensable part of traditional Christian iconography, especially of the Eastern tradition that we will examine. In this chapter, therefore, we will first analyze the meaning of this painting and the reason why these artists resorted to geometric figures as a base on which to substantiate their figures, then we will see some traditional geometric rules with their relative practical applications.