**4.4 CHARTRES (France), Our Lady's Cathedral : start rebuilding 1194 (after fire damage), dedication 1260**

The design of this French gothic key monument followed the then current design criteria: a ground floor ad quadratum according the église carrée of Villard (**Figure 2a**), and an elevation ad triangulum. Although the available metric documentation [13–17]; [18], p. 84, is not uniform, the evidence of a coherent modulated design is undeniable, including the inevitable smaller or bigger differences

**161**

still another local standard .

**Figure 6.**

*Rubino + author].*

*Architectural Design Canons from Middle Ages and Before: An Inspiration for Modern...*

and deviations, caused by ca. 100 years construction activity by different masterbuilding teams (**Figure 6a**). Similar to what we'll see in Assisi, also in Chartres there is the very first question about what might have been the metric standard applied on the building site because of the confusion in the historic terminology and the uncertainty on the real length unit in practice at that time: or the French "coudée" or cubit of 0,5236 m, or the ancient "pied du Roy" of 0,3236 m or maybe

*Chartres, Our Lady's Cathedral. (a): Plan [13]. (b) Transversal section [16] and author. (c) Ratio's transversal section (drawing from [16]). (d) Hypothetical altimetry design according musical canon [Wikicommons + A.* 

As said, the metric modulus of the medieval church was given by the net passage opening between the apse and the choir or the choir and the nave, in this case signing **14,78 m** (and not the 16,40 m distance between the center-to-center columns axis's, as kept on in most publications)! Our reference publications propose different 'fabricated' measure units, quite close to the "pied du Roy", as e.g. 0,369 m in [14] or 0,333 m in [18], partly inspired by the Christian semantics associated with number three and his multiples. However, none of those are coherent nor with any historic evidence. By reasoning back to front, comparing with other medieval churches, and inspired by the case of the St. Francis Church in Assisi, it seems probable and plausible that the Chartres's bishop in charge, out of respect to the Roman Pope, absolute head of the Christian church, and maybe also out of piety tradition, imposed to practice the ancient roman foot standard of **0,296 m**, applied in Rome and in many Christian church buildings. This same standard was called in France also "pied de Cluny" for the evident reason that the Cluny convent and the Cistercian monks, since late 10th century, were the most active church builders in Europe. Converting on this base, we obtain a most sense full and most Christian symbolic modulus of 14,78 m: 0,296 = **50rf** (roman

*DOI: http://dx.doi.org/10.5772/intechopen.95391*

<sup>12</sup> The analysis of the measured drawings from [12] proves once again that ancient modulation normally refers to the free passable space in between structural elements as walls and piers. Quite rarely also the thicknesses of this elements are included in the modulated design or are part of the allegoric dimensions (except from the Diophantic geometry as it is the case for the Pantheon's exterior wall).

<sup>13</sup> The outside height of the dome shell actually signs only 74 cub. as the roof structure as well as the ground floor quote has been changed in a later period; the initial height should have been also 77 cub. [12].

*Architectural Design Canons from Middle Ages and Before: An Inspiration for Modern... DOI: http://dx.doi.org/10.5772/intechopen.95391*

**Figure 6.**

*Design of Cities and Buildings - Sustainability and Resilience in the Built Environment*

the triangular inserted spaces of the hexadecagonal ring.

**fire damage), dedication 1260**

length, width and height12 .

Bible and the ancestral arithmetic symbolisms passed down from the Pythagorean philosophers. Nevertheless, there is great logic and uniformity in the geometric figures as well as in the choice of integer and simple numbering for the design of

This logic is found in the harmonic multiples of small (metric) quantities, and simple mathematical sequences (e.g. the arched openings connecting the octagon and the hexadecagon sign 10–12-14 cub. (**Figure 5e**). As said, there is preference for prime numbers and biblical numbers, many of them borrowed from the Apocalypse and the there description of the celestial Jerusalem (Apo.21, 9). This Jerusalem is a squared city (the octagon signs the superposition of the terrestrial and the celestial Jerusalem), and was equally long, large and high, with a wall of 144 (=12x12) cub. Also the virtual cube of the chapel volume is equally high and large (inside 72 cub., outside 77 cub.13); the longitudinal side of the squares in the ring-volume signs 12 cub. and the transversal opening signs 11 cub.. The ratio 12:11 has his own semantic with 12 referring to the 12 apostles of Christ or to his presumed 33 year's life time on earth (to read as 12 = 2x(3 + 3), meaning the double nature of Christ (divine and human) living during 33 years; and the 11-quote indicates men's imperfection while Christ's perfection is signed by 12; to be seen also as 11=1/3 x 33 of Christ's lifetime and the metaphysical passage (12=4x3) from a squared central space into

The passages from the octagonal area into the surrounding area sign an opening of10 cub.(with 10 being the 'perfect' quantity). In most medieval churches, the architectural modulus is indicated by the passage opening between apse and choir; this brings us to conclude that also in this case, the metric modulus has been ten cubits (= ~ 4,18 m), eventually in combination with a secondary 12 cub. Quote as a recall at the left and right of the passage opening (**Figure 5e**). The octagon's diameter of 33 ½ cub. is another reference to Christ's life time on earth (**Figure 5d**); the diagonal of the hexadecagonal and the altimetry design, signing the same quote of cub. 72 = 2x3x12 = 3(2x3x4); the external diameters of the octagon (38 ½ cub.) and the hexadecagonal (77 cub.) sign the evident proportion 1:2. Also the number 77 should not be fortuitous because, according the calculations by S. Augustine of Hippo (354–430), (based on the Old Testament history data), the number of generations from Adam to Christ counts 77! [12]. The lecture of this building's dimensions seems a florilège of biblical quotes, a very typical phenomenon in medieval church design .

**4.4 CHARTRES (France), Our Lady's Cathedral : start rebuilding 1194 (after** 

The design of this French gothic key monument followed the then current design criteria: a ground floor ad quadratum according the église carrée of Villard (**Figure 2a**), and an elevation ad triangulum. Although the available metric documentation [13–17]; [18], p. 84, is not uniform, the evidence of a coherent modulated design is undeniable, including the inevitable smaller or bigger differences

<sup>12</sup> The analysis of the measured drawings from [12] proves once again that ancient modulation normally refers to the free passable space in between structural elements as walls and piers. Quite rarely also the thicknesses of this elements are included in the modulated design or are part of the allegoric dimensions

<sup>13</sup> The outside height of the dome shell actually signs only 74 cub. as the roof structure as well as the ground floor quote has been changed in a later period; the initial height should have been also

(except from the Diophantic geometry as it is the case for the Pantheon's exterior wall).

**160**

77 cub. [12].

*Chartres, Our Lady's Cathedral. (a): Plan [13]. (b) Transversal section [16] and author. (c) Ratio's transversal section (drawing from [16]). (d) Hypothetical altimetry design according musical canon [Wikicommons + A. Rubino + author].*

and deviations, caused by ca. 100 years construction activity by different masterbuilding teams (**Figure 6a**). Similar to what we'll see in Assisi, also in Chartres there is the very first question about what might have been the metric standard applied on the building site because of the confusion in the historic terminology and the uncertainty on the real length unit in practice at that time: or the French "coudée" or cubit of 0,5236 m, or the ancient "pied du Roy" of 0,3236 m or maybe still another local standard .

As said, the metric modulus of the medieval church was given by the net passage opening between the apse and the choir or the choir and the nave, in this case signing **14,78 m** (and not the 16,40 m distance between the center-to-center columns axis's, as kept on in most publications)! Our reference publications propose different 'fabricated' measure units, quite close to the "pied du Roy", as e.g. 0,369 m in [14] or 0,333 m in [18], partly inspired by the Christian semantics associated with number three and his multiples. However, none of those are coherent nor with any historic evidence. By reasoning back to front, comparing with other medieval churches, and inspired by the case of the St. Francis Church in Assisi, it seems probable and plausible that the Chartres's bishop in charge, out of respect to the Roman Pope, absolute head of the Christian church, and maybe also out of piety tradition, imposed to practice the ancient roman foot standard of **0,296 m**, applied in Rome and in many Christian church buildings. This same standard was called in France also "pied de Cluny" for the evident reason that the Cluny convent and the Cistercian monks, since late 10th century, were the most active church builders in Europe. Converting on this base, we obtain a most sense full and most Christian symbolic modulus of 14,78 m: 0,296 = **50rf** (roman

foot). The acceptability of this "pied de Rome" unit is confirmed in the converting of some representative dimensions of the building (always considering the only free passable spaces).

However, for want of a recent complete measured drawing, we only note following data (**Figure 6a**):


According our scaled drawings, the nave and choir rectangles sign theoretically (50x21)rf, the aisles (25x21)rf and the crossing (50x42)rf. All quadrangles are semantically considered equivalent with regular squares.


**163**

avant la lettre [7, 20, 21].

*Architectural Design Canons from Middle Ages and Before: An Inspiration for Modern...*

In this limited list, we see more references to number five and his multiples, including the number 100 and 400 as reference to the exclusive hecatompedon quantity (i.e. 100 = 10x10 what means a more than perfect number) and a supple-

To conclude, we have to mention the interesting hypothesis on the relation between architectural geometry canons and the music harmony canons, which seems to find confirmation in the elevation of Chartres's nave (**Figure 6d**). Just as good architecture should bring order in a chaotic space, also harmonic music is as a cosmos imposed upon chaos [19], 251ff. Considering the side-length of the equilateral triangle (= double modulus) as an octave interval, one connects some significant altimetry quotes or virtual lengths from the opposite floor-bottom, with the tierce (lower capitals of central piers), the quart (keystone vault aisles), the quint (passageway triforium), sext or sept (lower threshold nave windows), first octave (impost vault-arch nave), second octave (~ keystone vault-arch nave). This

**4.5 ASSISI, S. Francis Basilica; start 1228 - dedication 1253 (extended in later** 

The S. Francis Basilica at Assisi was built to worship the sepulcher of Francis of Assisi (1182–1226), founder of the mendicant Order of the Minorite Fathers. The work started March 1228, but after two years, mid 1230, the project mission was extended with a second assignment i.e. becoming the representative mother church of the new religious Order. Integrating this new function in the same, still under construction, sepulchral and pilgrimage church, did not seem possible and for want of space on the same site, it was decided to build a fully separated second church on top of the first one, keeping the same external wall's perimeter and a similar inside spatial distribution. Such audacious project got realized after reinforcing the already built exterior walls and after inserting a new type of cross-rib vaulting for the lower church. This phased realization resulted in the actually superposed double-church, characterized not only by two different functions (a Lower devotional Church for S. Francis's tomb and a Upper Church for the Fathers Convent's services), but also by a double architectural and artistic identity: a first late-Romanesque Umbrian Lower Church and a second early-Gothic European

The design of the Lower Church (excluding later extensions) adopted the traditional middle sized Umbrian single-nave and single level church model. The geometry and the arithmetic's on dimensions and quantities of the Lower Church integrated the ancient Pythagorean traditions, modifying them according Christian semantics with tangible imitation of some iconic Christian churches of that time i.e. the S. Peters Basilica of Rome and, as it was built in full crusaders period, also the S. Sepulcher of Jerusalem, and an allegoric record of the since long demolished biblical Temple of King Solomon on Mount Moriah in Jerusalem. This multifaceted mission was realized in a multilayered design, building a quite old-fashioned Romanesque Lower Church and an innovative Upper Church, this last one in the new transalpine (French) gothic style and structure, the very first application of this new architecture in Italy. It's interesting to notice the remarkable coordination in the design of dimensions, forms and structures within two architecturally and structurally so different buildings. Under this prospective, the S. Francis double church is a interesting example of design resilience and flexibility

*DOI: http://dx.doi.org/10.5772/intechopen.95391*

mentary indicator for the 50rf as present modulus.

needs further study before being confirmed.

**decades)**

Upper Church.

*Architectural Design Canons from Middle Ages and Before: An Inspiration for Modern... DOI: http://dx.doi.org/10.5772/intechopen.95391*

In this limited list, we see more references to number five and his multiples, including the number 100 and 400 as reference to the exclusive hecatompedon quantity (i.e. 100 = 10x10 what means a more than perfect number) and a supplementary indicator for the 50rf as present modulus.

To conclude, we have to mention the interesting hypothesis on the relation between architectural geometry canons and the music harmony canons, which seems to find confirmation in the elevation of Chartres's nave (**Figure 6d**). Just as good architecture should bring order in a chaotic space, also harmonic music is as a cosmos imposed upon chaos [19], 251ff. Considering the side-length of the equilateral triangle (= double modulus) as an octave interval, one connects some significant altimetry quotes or virtual lengths from the opposite floor-bottom, with the tierce (lower capitals of central piers), the quart (keystone vault aisles), the quint (passageway triforium), sext or sept (lower threshold nave windows), first octave (impost vault-arch nave), second octave (~ keystone vault-arch nave). This needs further study before being confirmed.

## **4.5 ASSISI, S. Francis Basilica; start 1228 - dedication 1253 (extended in later decades)**

The S. Francis Basilica at Assisi was built to worship the sepulcher of Francis of Assisi (1182–1226), founder of the mendicant Order of the Minorite Fathers. The work started March 1228, but after two years, mid 1230, the project mission was extended with a second assignment i.e. becoming the representative mother church of the new religious Order. Integrating this new function in the same, still under construction, sepulchral and pilgrimage church, did not seem possible and for want of space on the same site, it was decided to build a fully separated second church on top of the first one, keeping the same external wall's perimeter and a similar inside spatial distribution. Such audacious project got realized after reinforcing the already built exterior walls and after inserting a new type of cross-rib vaulting for the lower church. This phased realization resulted in the actually superposed double-church, characterized not only by two different functions (a Lower devotional Church for S. Francis's tomb and a Upper Church for the Fathers Convent's services), but also by a double architectural and artistic identity: a first late-Romanesque Umbrian Lower Church and a second early-Gothic European Upper Church.

The design of the Lower Church (excluding later extensions) adopted the traditional middle sized Umbrian single-nave and single level church model. The geometry and the arithmetic's on dimensions and quantities of the Lower Church integrated the ancient Pythagorean traditions, modifying them according Christian semantics with tangible imitation of some iconic Christian churches of that time i.e. the S. Peters Basilica of Rome and, as it was built in full crusaders period, also the S. Sepulcher of Jerusalem, and an allegoric record of the since long demolished biblical Temple of King Solomon on Mount Moriah in Jerusalem. This multifaceted mission was realized in a multilayered design, building a quite old-fashioned Romanesque Lower Church and an innovative Upper Church, this last one in the new transalpine (French) gothic style and structure, the very first application of this new architecture in Italy. It's interesting to notice the remarkable coordination in the design of dimensions, forms and structures within two architecturally and structurally so different buildings. Under this prospective, the S. Francis double church is a interesting example of design resilience and flexibility avant la lettre [7, 20, 21].

*Design of Cities and Buildings - Sustainability and Resilience in the Built Environment*

• Transversal width of choir-bay (estimated) 6,25 m **→**21rf = 3x7

semantically considered equivalent with regular squares.

• Architectural modulus: 14,78 m **→** 50rf = 2x5x5

ϕ

36,93 m **→** =125 rf = (5x5x5)rf (**Figure 6b**)

the diagonal AB (=side equilateral triangle).

only free passable spaces).

'golden rectangles' (

zone between the towers;

ing data (**Figure 6a**):

foot). The acceptability of this "pied de Rome" unit is confirmed in the converting of some representative dimensions of the building (always considering the

However, for want of a recent complete measured drawing, we only note follow-

• The overall design grid in the choir and the nave signs a sequence of oblong rectangles and squares with slightly variable dimensions, apparently depending on the section of the columns and alternative ratio's in the tracing of a virtual geometric grid. The grid indicates the net squared areas of the quadrangles, separated by the construction strips, corresponding with the width of the vault-arches. The quadrangles can include different semantics such as

related) or 'dynamic rectangles' ( √ related).

According our scaled drawings, the nave and choir rectangles sign theoretically (50x21)rf, the aisles (25x21)rf and the crossing (50x42)rf. All quadrangles are

• Global inside length (from the entrance porte royal to the closing wall of the apse): 130,20 m **→** = 440 rf or 400rf of church passage and 40 rf of entrance

• Global inside width of nave and two aisles: 32,40 m **→** = 109,46 rf or 100rf of passable church area and 9,46 rf for two rows of pillars construction zone;

• Global height from crypt-floor to nave vault: 39,46 m **→** 133,33 rf (to read as separated ciphers, with double reference to the 33 years Christ lived on earth)

triangulum with the modulus BC equal the half-side of the equilateral triangle with top A at quote 25,58 m (= 29,50x1/2 √ 3) , indicating also the impost of the

• As shown in (**Figure 6b**) there is no doubt about the elevation design ad

nave-vaults arches and the bottom of the first outside flying buttress.

• The external transversal section of the nave(including the crypt areas) describes a quasi-squared plane (height 40 m x large 44 m) = 10:11, which signs the already noticed semantics. The capitals of the triforium corridor (quote 19,73 m) sign the geometric middle of the full inside elevation; the overall transversal section on the nave forms a 5:2 rectangle (**Figure 6b and c**).

• The top E signs the intersection of the two vault curves 'at the fifth point', at the height from outside threshold of 37 m in a ratio versus the width of the nave (= modulus) of 14,78 m:37 m = 1: 2,5. The modulus signs half of the length of

• Global height inside the choir (from first outside stair- threshold of the entrance, i.e. the public space area, to the underside of the vault-keystone:

**162**
