Sacred Geometry and Musical Proportions in Reims Cathedral Construction
was the first harmonic consonant, but qualitatively distinct from C. Figure 15: Geometric passages to obtain the transept of Reims Cathedral from the square of the earth. from Saint Augustine and still from the school of Chartres and from Saint Bernard of Clairvaux. The two circles of Fig. 15.2, connected to each other according to the musical ratio of fifth, are then amplified in a golden manner through the use of the five-pointed star. To obtain this amplification, we simply draw a regular pentagon inside the circle inscribed in the square of the earth. By extending the lines of the pentagon, we obtain a five-pointed star, whose circumscribed circle corresponds to the golden amplification of the starting circle (see Fig. 15.3). From the lines of the square of the earth, extending them and intersecting them with the found circle, we will obtain the central points of the eight columns that surround the base square. The corresponding connecting lines of the columns determine the width of the transept and side naves. If we now execute the same procedure on the circle circumscribed to the square of the earth, we obtain the limits of the transept itself (see Fig. 15.5) obtaining a rectangle with sides in golden ratio. Through the five-pointed star, we have obtained a harmonic-golden amplification of the two central circles, allowing us to draw the entire transept and to find the fundamental points that will give origin to the choir, apse, and naves (see Fig. 16 and Fig. 17). The following drawings highlight the successive geometric steps that develop and conclude the construction of the plan of Reims Cathedral (see Fig. 18). In a few, simple and logical steps, it is possible to derive all the essential lines of the cathedral plan of Reims, starting from the square of the earth, expanded according to a harmonic-musical amplification associated with two fundamental ratios: $\frac{3}{2}$, musical ratio of fifth, and $\varphi$, the golden ratio. Identical operations, involving the same numbers $\frac{3}{2}$ and $\varphi$, will then be used for the construction of the elevation of the cathedral which we will discuss in the next issue of Mathesis. The two circles found are in a relative ratio derived from the golden proportion. In particular the two circles are in ratio $1:\varphi^2$. This property derives from the use of the five-pointed star which is an infinite generator of golden proportion. Figure 16: Geometric passages generating the choir of the Cathedral. Figure 17: Geometric passages generating the apse and nave of the Cathedral. Figure 18: Plan of Reims Cathedral with measurements taken in meters; on the right the representation of the plan taken from Viollet le Duc.