The Geometry of Gothic Architecture and the Proportions of the Music of the Spheres

The heptagonal shape and its geometric layout have been the subject of a great deal of speculation. Because some apses in Gothic cathedrals are heptagonal, there must be a methodology implicit in the layout of the geometric shape. Two particularly important sources help us arrive at an understanding: the exceptional of the Capitular archive of the Cathedral of Tortosa, which contains the main neo-Platonic sources among its codices dating from thirteenth and fourteenth centuries, and the parchment known as la traça de Guarc (c.1345-1380), which shows the layout of the non-constructed cathedral. These sources show a heptagonal apse with an arithmetical and geometric dimension, based on a metrological and tonal musical proportion of 9/8, which is perfectly compatible with the bases of the quadrivium. The lateral and radial chapel, as the basic unit and feature element in fourteenth-century Gothic cathedral design, can be used as a pattern, and its measurement establish the basic unit for the overall proportions of the cathedral. This is the Music of Spheres that also appears at the Harmonices Mundi, Livri V (1619), by Johannes Kepler.