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The interior unfolds the mechanical version

Urban IV, residing in Viterbo, follows the progress of his chapel with interest and growing satisfaction. A harmoniously proportioned edifice has been planned for the site of my father's humble shoemaker's shop in the heart of bustling Troyes and those formidable nuns of Notre-Dame have acquiesced to this worthy endeavor with remarkably little grumbling. Let my mason proceed with the internal details of the plan, the pontiff muses. Time to ask Thomas Aquinas's advice about the subjects of a glass program devoted to the Corpus Christi and to see if he might also have time to compose an appropriate liturgy...

Figure 3

The overlapping squares JKLM and NOPQ, laid out as the second step of the operation, create a smaller square about the center of the plan (MROS: 15.33 meters per side). The inscribed square TUVW, with a side of around 10.85 meters comes close to the square of the crossing measured to the center of the piers (average 10.58 meters)--the error is some 2.5%. Extending lines of the crossing out to the great squares fixes the spatial corridors of the have and transept.
Next, the diagonal of half the crossing square (XV) is rotated to form TY whose segments TU and LTY (6.71 meters) are in a golden section relationship to one another. UY defines the approximate width of the aisle.

Fig.3. Saint-Urbain, Troyes: mechanical version generation of crossing and aisles (Davis)

Figure 4

The crossing and aisle dimensions (as built: VU=10.58 x UY=6.54 meters) are used to construct a rectangle (bl). This golden section unit is repeated in each transept arm (bl,b4, their exterior porches (b3,b6), and the lateral choir chapels (b2,b5). Once the central vessel supports are designed, the intermediate aisle shafts will be placed on the axis of the arcade span.

The interior unfolds-the square sequence

Urban IV, residing in Viterbo, follows the progress of his chapel with interest and growing satisfaction. A harmoniously proportioned edifice has been planned for the site of my father's humble shoemaker's shop in the heart of bustling Troyes and those formidable nuns of Notre-Dame have acquiesced to this worthy endeavor with remarkably little grumbling. However, Urban is too busy worrying about Manfred's armies, finding French military aid, and the fall of the Latin emperor in Constantinople to give serious thought to planning details of Saint-Urbain. My nephew, Cardinal Ancher, assured me that I hired the best master mason in France, sighs the weary pontiff, I'll pray he creates an inspired building...

Figure 5

In this scenario the interior design of Saint-Urbain unfolds out of a sequence of inscribed squares (S3-S6). The fifth square (S5: 9.25 meters) in the series corresponds closely to the width between the buttresses of the central portal of the west porch. However, it is the sixth square (S6: 6.54 meters) that generates the interior spatial relationships. Set in the center of the plan, the diagonal from the midpoint of one side is rotated to establish a new line (TU) that is used as the dimension of the crossing square. Extending the lines of the crossing demarcates the width of the central vessel and the transept.

Once the crossing square is laid out, the aisle could be generated as in the mechanical version (see figs 4.5). Its width could also be determined by simply extending the side of the crossing (TU or VW) by the distance of a side of S6 (6.54 meters). This alternative reveals an approach that is based to a greater degree on the repetition of a module.

The interior unfolds-the symbolic generator

Urban IV, residing in Viterbo, follows the progress of his chapel with interest and growing satisfaction. A harmoniously proportioned edifice has been Planned for the site of my father's humble shoemaker's shop in the heart of bustling Troyes and those formidable nuns of Notre-Dame have acquiesced to this worthy endeavor with remarkably little grumbling. But now, muses the pontiff, the real act of architecture is at hand, one that will turn a mere Pile of stone into a celestial structure. As my mason and I agreed, sitting squarely in the center of Saint Urbain will be perfection...