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The western symmetries I have identified are significant in two ways.
It seems to me that neither the construct of symmetry I call subsidiary axes of symmetry of reflection in a series of coördinate forms nor the design principle I call variation in coördinate detail with reflection is derived from the other. Rather, both are developments of the underlying design principle of variation in coördinate detail. This relationship is obvious for variation in coördinate detail with reflection; for subsidiary axes of symmetry of reflection in a series of coördinate forms it is looser. Still, the aesthetic rationales of variation in coördinate detail are to enliven what could otherwise be a dull set of identical elements, to draw the viewer's attention to the elements as individual compositions, and to display virtuosity in the invention (or at least the execution of an extended repertoire) of variant patterns. All of these rationales are apparent in the qiblah arcades of the three Almohad mosques and again in the Alhambra.
The examination of symmetries helps delineate differences in regional traditions and reveals a regional tradition in western Islamic architecture that is persistent, ingrained, and probably habitual. The occurrence of what I call western symmetries in western Islamic architecture is an indicator of the existence of a regional style, originated in Spain and elaborated there and in North Africa. Other such regional traditions exist (see the discussion of Khirbat al-Mafjar, below).
An unanswered question is where the Islamic West found these uses of symmetry. After all, they were not new. As they seem not to appear in Umayyad or ʿAbbāsid architecture in the central Islamic lands I am disinclined to think that the Umayyads of Spain brought them with them from Syria. Local sources of the immediately pre-Islamic period are hardly rich in the relevant sort of decoration. Without claiming to have answered my question, I can sketch a possible answer: these uses of symmetry came from Roman or Late Antique architecture in Spain, which of course was much better preserved in the eighth century when the Umayyads arrived than it is today. They persisted into the eighth century in lost monuments: impressive and well decorated buildings must have existed in Cordoba (which with Seville and Italica, near Seville, was the most important city of southern Spain) before the Vandal invasion of the fifth century and may even have been restored under Byzantine rule, between 554 and 572.1 As Byzantine architecture in the East does not appear to display either of these western symmetries (nor variation in coördinate detail, for that matter), the possibility of a Visigothic contribution in continuation of the Roman tradition cannot be excluded, even if it is thought that after the Byzantine occupation Cordoba “remained a place of no importance under the Visigothic domination.”2 The Spanish Umayyads then drew on local tradition when they arrived (as well as bringing with them concepts such as the idea of the mosque), rather than importing an entire building tradition from the other end of the Mediterranean.3
In support of this notion of survival from Antiquity, and as Roman and Late Antique architecture in Spain is hardly rich in remains or preserved decor, I offer an example from Rome of Antique variation in coördinate detail with reflection. In the mid-fourth century Church of Sta. Costanza, a work of the highest quality for its time, the mosaics of the ambulatory vault correspond in design along an axis from the entry:
A x A
B B
C C
D D
E o E
where o is the entry and x the spot opposite the entry, where the altar should have been and a sarcophagus now rests. The fields E o E are purely geometric; the rest are vegetal and figural, so there is a directional use of ornament.4
In conclusion, symmetry is a feature of nature and has been studied by mathematicians, whose work should be used by historians of art. Constructs of symmetry in art and architecture exist that are not mathematical but artistic; these constructs are significant components of art and attention should be paid to them. Western Islamic architecture exhibits certain uses of symmetry that do not appear farther east. And finally, investigating such uses of symmetry in a rigorous way makes it possible both to discern other approaches to symmetry in other regions of the Islamic world and to dig a little deeper than one might by just saying of a design “it's symmetrical”.
1. Robert C. Knapp, Roman Cordoba, Berkeley, 1983, pp. 69–74, surveys the evidence: essentially, there is none for building in Cordoba during the relevant period. Nothing is known of destruction during the Vandal invasion (p. 71). For the Visigoths and Byzantines, pp. 72–73; it is of note that Corboda was a Visigothic mint.
2. Encyclopaedia of Islam, 2nd ed., s.v. “Ḳurṭuba”. There is very little basis for this or any other view, as the textual sources are extremely sparse—for architecture, nonexistent—and there is essentially no relevant archaeological evidence in Cordoba itself.
3. Dodds, op. cit., who treats the Christian side of this question of continuity, p. 153, n. 63 to p. 61, regards the Great Mosque of Cordoba as containing not only “spolia from churches built under Visigothic rule” but also “arch types and proportions that are our witness of the buildings of the Visigothic period whose remains were lost to the mosque.”
4. A further note on Sta. Costanza, which may or may not be related to the mosques of Qayrawan and Cordoba, in which Ewert believed that there is a pattern to the arrangement of colored column shafts (Ewert and Wisshak, Forschungen zur almohadischen Moschee, v. 1, fig. 20, 36): the pairs of columns supporting the inner side of the ambulatory of Sta. Costanza are all gray except for four red ones at the entry and the opposite bay:
_
R R
G G
. . . . . .
G G
R R
F