Abstract
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 traca 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 established as the basic unit for the overall proportions of the cathedral.
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