Sacred Geometry and Construction Module of San Galgano Abbey

He who wants to design a figure cannot do so unless he is capable of becoming that figure himself. Therefore, only the Composer of a sacred construction knows completely the project and the physical and metaphysical characteristics of his work: he is the one who has written the visible and invisible score in order to then execute it in form. This completed architectural form we can only analyze and study and we must do so with respect and reverence, trying to move with the same spirit that nourished the mind and heart of these wise architects. Following are the studies and logical reasoning that led to highlighting the construction module of the Abbey of San Galgano. As already explained in the article on the musical geometries of the Gothic temple (see Mathesis, Numbers 1 and 2), the Master Builders, in order to graft a precise mystical idea into the proportions of the plan and the rhythm of the elevation, instead of using subjective measures and relationships, used a precise relationship defined by the interaction between numbers of symbolic value. This relationship, called the construction module, represents the physical and metaphysical DNA of the entire building, as it regulates the immanent aspect, that is, technical-aesthetic and, at the same time, conveys and expresses the transcendent aspect, or rather symbolic-theological that is at the origin of the project, giving the entire construction a plastic harmony to which is added an even more mysterious harmony of a spiritual nature. Therefore, in the process that leads to defining the construction layouts of a temple we have three indispensable elements: the mystical Idea from which the project originates, the primitive circle theurgically qualified into sacred space and the construction module which has the purpose of polarizing in the purified form the mystical idea inspiring the Temple. We said that the construction module was actually translated into a numerical relationship, but this was not calculated but rather applied through particular geometric-symbolic processes that led to generating the Square of the Earth. This is a quadrilateral inscribed in the director circle that manifests and establishes on the concrete plane the mystical Idea, that is, an aspect of the Celestial Will polarized by the module. The four vertices of the Square of the Earth determine the ground points where the four columns of the Transept Crossing will be erected. All the nodal points of the construction then originate from this epicenter whose symbolic essence is propagated both in plan and in elevation through geometric-musical principles proper to the mathematical structure of the Cosmos. To analyze a symbolic project of a sacred building it would be necessary to have the drawings, possibly with dimensions. In the absence of these we can reconstruct them by measuring as precisely as possible the main parts that compose the Work to be analyzed. In this case, the surveys and drawings made by Architect Antonio Canestrelli were of great help, which report the dimensions of the nodal points of the plan and elevation of the monument, many of these confirmed in loco by our measurements. The missing dimensions we then deduced from the drawings so they are not free from errors, which, if there were any, are nevertheless of small constructive entity and practically irrelevant in the symbolic process of geometric crystallization of a mystical/theological idea in the complex form of an Abbey or a Cathedral. Let us concentrate on the measurements of the transept crossing. The rectangle in question has one side of $11.15$ meters: the width of the central nave taken on the axis of the large columns. The other side is $8.75$ meters: the length of the transept. The ratio of these two measurements equals perfectly (considering a tolerance of a few millimeters) the square root of the golden number, i.e. $\sqrt{\phi} = 1.2720$: We therefore have that the Transept Crossing evidences a particular right triangle in which the sides are in geometric succession of ratio square root of the golden number. This means that the major cathetus $BC$ is equal to the minor cathetus $AB$ multiplied by $\sqrt{\phi}$, i.e. $BC = AB \cdot \sqrt{\phi} = 1.272 \cdot 8.75$ m. At the same time, the hypotenuse $AC$ is equal to the major cathetus multiplied by square root of $\phi$, i.e. $AC = BC \cdot \sqrt{\phi} = 1.272 \cdot 11.15$ m. Finally, we have that the diagonal of the transept crossing is in golden ratio with the length of the transept (Fig. 5). $AC = AB \cdot \phi = 1.618 \cdot 8.75$ m. For our investigation of the presumed module of this Abbey, it was fundamental to discover that this particular rectangle can be derived through the intersection of two circles having radii of 8 and 7 units. In particular, the circle of value 8 units is the foundation circle (defined C1 in the drawing) oriented to the East and on whose circumference is located the center of the second