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City of Dreams |
by David Bowman
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| Antonio Labacco's description of Alberti's San Sebastiano in Mantua |
It is said that the idea for the church of San Sebastiano originated in the dream of Ludovico Gonzaga, a wealthy, educated and powerful member of the Gonzaga clan that ruled the city of Mantua. Alberti answered his call and made a plan for the church that was started in 1460. Many difficulties with the terrain and lack of interest deteriorated the design of the church much from the original plan. It is a classical composition in the form of Greek cross with the portico added in front. The original drawings of Alberti are unknown, but Italian architect Antonio Labacco left a drawing of the main proportions of the church, copied supposedly from another drawing or a model, but it is considered as the description closest to the original intention. Saint Sebastian, the patron of Alberti’s church in Mantua, was a most Christian man and known as an excellent soldier in the army of the emperors Diocletian and Maximian whose reign begun in 287 according to The Golden Legend by de Voragine. Sebastian uses his good standings to cover up his true mission, which was to help and comfort captured Christians. When the emperor Diocletian became aware of the inherent treason, he commanded soldiers to tie Sebastian to a post in the center of the camp and shoot him full of arrows. He miraculously survived the wounds to reproach emperors for their cruel treatment of Christians. They ordered him beaten to death and body thrown into the sewer to prevent the martyrdom. Saint Sebastian appeared to Saint Lucina revealing her where his body lays in order to be properly buried near the remains of the apostles. De Voragine starts the legend of Saint Sebastian with unusual etymological analysis of the name Sebastian:
Sebastian comes from sequens, following, beatitudo, beatitude, astim, city, and ana, above; therefore one who pursues the beatitude of the city on high, the city of supernal glory – in other words, one who acquires and possesses that city.
It seems that Alberti used exactly this metaphor of the city, the heavenly city, while considering the plan for San Sebastiano. This metaphor alludes to Mantua itself: a prosperous town under influential Gonzaga family. According to Labacco’s description, the floor plan delineates a perfect octagram, and if we consider the metaphor of the city, octagram echoes Vitruvius’ prescription for town planning: a curios scheme of eight winds that has to be considered in order to avoid various illnesses that winds would cause to the citizens if not carefully avoided.
Some have held that there are four winds: the Solanus from the equinoctial east, the Auster from the south, Favonius from the equinoctial west, and Septentrio from the north. But those who have inquired more diligently lay down that there are eight: especially indeed Andronicus of Cyrrha, who also, for an example, built at Athens an octagonal marble tower, and, on the several sides of the octagon, had representations of the winds carved opposite their several currents. - Vitruvius, De Architectura, I.c.VI
Perhaps, Vitruvius alludes more to the compositional principle and a set of proportions based on the geometry of the octagram, than describing a real suggestion for a form of the town, since almost no town was planned in the shape of the octagon. Octagram is a very convenient proportional tool since its irrational geometry is rationalised by series of progressions called Pell’s series. Like Fibonacci progressions approximate the geometry of a pentagram, so does Pell’s approximate the geometry of octagram.
Pell Series
If we consider the ground plan of San Sebastiano, as drawn by Labacco, we find that the whole composition is made of measures coming from the first Pell’s serie:
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2 |
5 |
12 |
29 |
70 |
169 |
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3 |
7 |
17 |
41 |
99 |
239 |
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4 |
9 |
22 |
53 |
128 |
309 |
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5 |
11 |
27 |
65 |
157 |
379 |
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Alberti used the first of Pell’s series, multiplied by two: 2, 4, 10, 24, 58, 140, ... He picked the number 58 for the sise of the largest projection square. The octagramic cross, derived from this progression, has the side of 24 units, since this number stands in front of 58 in the first of Pell’s series.
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| Composition of Alberti’s San Sebastiano is based on rational approximation of geometry of octagram |
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Next thing to do, is to cut the middle square of 24 braccia in half and move the halves towards the sides of the square. This represents the basic scheme of the ground plan of San Sebastiano. A dome is 34 braccia in diameter resting on a square base, while the surrounding aisles are 12 braccia wide. Further measures originate in the repeated procedure, this time with a square of 34 braccia as a starting point. The octagramic cross 34 braccia wide has - rationalised by the progression - 14 braccia for a side. Both numbers are in the same progression: 34 = 10 + 24 while 14 is the sum of preceding factors 10 and 4. Again the central square is split in half and the measures are transfered to the sides of the base square producing measure 20 braccia, which is the breadth of the surrounding aisles. The division of measures goes even further, the starting point now being the square of 20 braccia. The inscribed cross has 8 braccia for a side since 20 = 2 x 10 and preceding factor is 4 or 2 x 4 = 8, the diameter of the half cylindric niches embeded in the frontal walls of aisles. No measure is left out, since according to the recunstruction drawings made by Alberti Olivetti group, the extreme outer measures of San Sebastiano would be 70 braccia, and Number 70 comes immediately after 58 (2 x 29) in the first Pell’s progression.
In this manner the whole sanctuary is composed out of a single Pell’s progression, using only numbers and their combinations from a single progression. It must be said that this is only a geometrical illustration of the manipulation of the factors of Pell’s progressions and this geometrical approach was not necessarily employed by Alberti, the architect could have just picked the suitable numbers from the chosen progression knowing, that however you combinate this numbers among themselves, you will always stay within the system, never loosing the harmonic relation between a part and a whole.
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| Composition of Alberti’s San Sebastiano based on Pell series that rationalize geometry of octagram |
Geometrical illustration of 1st Pell’s progression
Octagram lotus is showing the relations as defined by the 1st Pell’s progression. The ratio of two successive factors in the progression is infinitly approaching √2 + 1. The further we go along the progression line the more accurate approximation of irrational value of √2 + 1 is becoming. Anteceding numbers are obtained by multiplication of the base number by two and addition of preceding number. If we have the progression starting with 1, 2, the next number will be 2x2+1=5, the next 2x5+2=12, 12x2+5=29, and so on.
Labacco leaves three vertical measures: 13 1/3, 33 1/3, and 56 2/3 braccia. These measures are in relation 4 : 10 : 17, and all these measures of the elevation of San Sebastiano are also factors of the first Pell’s progression. While describing the composition of temples Vitruvius describes in detail proportions of the human body and relations among different parts. These relations are always expressed by means of small whole numbers, and it seems that Alberti carefully followed that prescription, since all the extreme dimension of San Sebastiano can be reduced to small whole numbers.
Bibliography:
- Robert Tavernor, On Alberti and the Art of Building, Yale University Press, 1998. A faximile of Labacco’s description is published along with the computer reconstruction of San Sebastiano produced by Olivetti/Alberti Group.
- Jacobus de Voragine, The Golden Legend–Readings on the Saints, Princeton University Press, 1995.
- Vitruvius, De Architectura, Loeb, 1970.
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