Doric Measure and Architectural Design 2: A Modular Reading of the Classical Temple
by
Mark Wilson Jones
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Title:
Doric Measure and Architectural Design 2: A Modular Reading of the Classical Temple
Author:
Mark Wilson Jones
Year:
2001
Publication:
American Journal of Archaeology
Volume:
105
Issue:
4
Start Page:
675
End Page:
713
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English
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Updated: November 1st, 2012
Abstract:
Doric Measure and Architectural Design 2: A Modular Reading of the Classical Temple
MARK WILSON JONES
Abstract
The Doric temple is one of the ancient Greeks' most celebrated achievements and one of the great arche types of architectural history. Not only was it the ultimate reference for other typologies (propylaea, stoas, and mis cellaneous civic buildings), it was also, especially in its fifthcentury form, a highly influential source for the later practice of classical architecture. Yet the methods used to design the ancient Doric temple remain a largely unresolved question despite the considerable scholarly effort dedicated to its investigation.
This lack of resolution reflects to some extent lapses of regularity and syrnmetv in Doric temple plans, lapses that \'itru\ius called "the faults and incongruities" that flowed from the notorious problem associated t~th the configura tion of the peristyle and its frieze at the corner. This problem was also compounded in the archaic period by the prevailing reliance on rules of thumb and a successive approach toward making indilidual decisions. But by the second quarter of the fifth centuv, architects had ac quired a greater control over the design process, becom ing able to instill their projects with improved coherence and precision, as well as neater proportions. The most striking manifestation of this shift is the widespread adop tion of a 2:3 ratio between the mldths of triglj~hs and metopes, a relationship that automatically generated col umn spacings equivalent to 5 triglyph widths. This analysis of the facades of 10 relatively well preserved hexastyle temples shows that the triglj~h width was much more than just one consideration out of many; it constituted the veT lynchpin of a filllyfledged modular design method.
Such an interpretation helps to explain the consis tency of temple facades while also, significantly, tallying with the evidence of Vitruvius, our sole ancient author ity. Vitruvius described Doric design in modular terms, and he also chose a module equal to the triglyph width. In the past, scholars have tended either to trace Vitruvius's account only as far back as the Hellenistic period, or alternatively to doubt its legitimacy altogether. It now emerges that \'itruvius perpetuated principles and practices that went well back into the fifth century*
*Halingbegun in 1992, this research was substantially com plete before Part 1 of this article (Wilson Jones 2000a) was conceived; it was the virtue of clarifying metrological issues first that dictated the published sequence. I was fortunate to re ceive agrant from the British Academy to facilitate research in Greece and Italy. I am also much indebted to the British School at Athens for hospitality and for submitting applications for me to inspect various temple sites, as I am to the respective Ephorates responsible. I have benefited from comments re ceived during discussing the ideas set down here with Jos de LYaele, Manolis Korres, and Margaret Miles. Malcolm Bel1,Jim
The form of the classical Doric temple is highly predictable, more so perhaps than any other his toric building type. By the fifth century B.C. the morphology of temples was governed by conven tions that embraced even the smallest details. Ar chitects had especially limited room for maneuver in designing the end facade. They might make the stylobate sit on four steps rather than three, or in troduce extra elaboration at the junction between capital and shaft, but in essence facade design was a quest for perfection through the honing of pro portions, profiles, and refinements.
Intuition suggests the existence of a method (or methods) that enabled architects to produce the highly conventional temples demanded of them.' This same consistency in design also suggests that such methods must have had a metrical component, an assumption supported by at least three kinds of evidence. First is the desire for mathematical har mony pervading diverse ancient architectural texts, whether Babylonian, Biblical, Greek, or Roman, including most notably Vitruvius's treatise.? Second is the relentless numerical content of Greek spec ifications and contracts for structures such as the Telesterion at Eleusis, the Tholos of Epidauros, and the Arsenal of Pirae~s.~
Third is the presence of accurate proportional correspondences in individ ual Doric temples themselves.
Be this as it may, Doric design strategy remains notoriously elusive. Although progress has been made in recent decades, no modern theory satis factorily accounts for the reproducibility of design intentions, especially in temples of the classical period. Not a single fifthcentury Doric temple dis
Coulton, and Dieter Mertens were kind enough to read and comment on an early version of this text dating to 1994; I thank them not only for their encouragement but also for criticisms, which I have tried to address subsequently with the benefit of invaluable assistance provided by Ida Leggio.
' For general arguments relating to design method, see Coulton 1975.
'Wesenberg 1983; Koenigs 1990.
"askey 1905; Noack 1927,1127; Burford 1969; Jeppesen 1948.
675
Amerzcan Journal ofArchaeolog?l 105 (2001) 674713
Fig. 1. Plans of Ionic temples of the Hellenistic period: the Temple of Xthena at Priene (right) and the Temple of Leto at Xanthos (left), 1:200. Note in both cases the 1:l proportion between the column plinths and the paving slabs in between, and the ovrrall proportion of 1:2. Dirrlensions are shown in Attic feet of ca. 29F295 mrn. (After Hansel1 1991. fig. 11)
plays the proportional and dimensional transpar ency of Hellenistic temples in the Ionic mode like those of Athena Polias at Priene or of Leto at Xan thos (fig. 1).4 Instead, specialists will argue inter minably over the foot units used for individual Doric temples (to date a dozen or so values have been published for the Hephaisteion, a score or more for the Parthenon) ." Research has got bogged down largely because of this ~~nproductively
narrow foc~~s,
which often neglects the principles that typically underlie Doric design.Wor is it helpful to avoid grappling with the problem, as when build ings like these are judged "inscr~~table,"
"enigmatic," or somehow too wonderful to be reduced to mere quantities.' This might be said of all creative work, of course, but it is equally true that buildings have to be dimensioned to get built, especially stone ones that adhere to a formal language as exacting as the Doric order.
The metrical opacity of Doric temples is not to be explained by some rnysterious cause, but rather the procedures employed for setting out the over all plan on the one hand, and on the other a series of considered adjustnlents that were made for the sake of obtaining a "correct" elevation. As regards the setting out of the peristyle columns and the platform on which they stand, the stylobate, in the archaic period architects were apparently unable or disinclined to predict what was necessaiy to ob tain a regular colonnade; they preferred to rely on rules of thumb of great conceptual sinlplicityeven
'Koenigs 1983; de Jong 1988; Hansen 1991.
'De Ifaele 1998; Bankel 1983,198413; Sonntagbauer 1998.
"For similar complaints, see Hocker 1986.
'Cooper (1996, 131), for example, quickly disnlisses the apparent lack of metrical clarity at Bassae by recourse to the notion of"\isual commensurabilih." 'Co~llto~l
1974; 1988, 59 ff.: Tobin 1981.
if these might be considered flawed or even per verse from a rational standpoint. As J.J.Coulton and others have demonstrated, it was common in the sixth century for architects to assign stylobates a width:length ratio according to the number of col umns supported. A stylobate cariying a (5 x 12 peri style, for example, would be set out in the ratio 6:12
(i.e., 12). The fact that this proportion did not re late to the axes of the columns, but rather to the edge of the stylobate, generated shortcomings from a rational perspectivesuch as column inter vals and even column diameters that differ from front to flank.This practice was modified over time to minimize inconsistencies, apparently on the ba sis of empirical observation rather than a concern for coherence in the abstract sense. M'hat is more, such rules of thumb, as well as proportions gener ally, were often applied in a successive manner
(more or less following the sequence of construc tion), and here is another reason why the resulting whole might not display proportional simplicity"
Modifications had a special place in Doric de sign over and above the perennial considerations of formal ideals, aesthetics, site, budget, materials, construction, and so on;"' the gauging of them was an art in itself, and this is particular1.l true of the classical period. The various refinements," exacting distortions made to horizontals, verticals, and the size of otherwise standard elements, are but the most famous manifestation of an ethos that embraced diverse aspects of detailed design." The
'This step by step approach is rrlinored in \'itni\rius's (3.5) account of the Ionic order, see Co1llto1ll975,6971; 1988,66. "'Vitr. 5.6.7 and 6.2. Cf. Corilton 1988, ch. 4;Wilson Jones 2000b, ch. 3. "For the state of research on refinements, see Le\\is 1994; Cooper 1996, ch. 9; Pakkanen 1997; Haselberger 1999. I2E.g.,it was comnlon for the architrave to be fractionally
most far reaching modifications stem from the for ma1 conflict inherent in the Doric order, or what L'itruvius called "the faults and incongruities caused by the laws of its sj,n,netria."'" These laws pre scribed a whole triglyph where the entablature turns the corner. \$'hen the thickness of the architrave beam is substantially greater than the width of the triglyph, as was usually the case, the corner triglyph established a mutual antagonism between the ide als of a uniform frieze and colonnade (fig. 2,b) .;" A regular colurnn spacing required the frieze to stretch toward the corner, while conversely a regu lar frieze required the corner colurnns to contract (fig. 2,c), this being the most favored option.li Ac cording to f7itruvius, both solutions were "faulty."
An awareness of the potential irnpact of such modifications constitutes for some scholars an invi tation to tn to reconstruct a chain of decisions lead ing back to a simpler hypothetical original concep tion prior to its modification. Figure 3 shows two types of shift as visualized by Hans Riemann for the Temple of Zeus at Olympia."' The shifts he de scribes, however, arguably characterize not so much a single project, but a co~npaction of preceding developments, which took place over an extended time. Yet it is not clear whether theoretical goals of the kind that were dear to Vitruvius had even been formulated in the archaic period; at any rate archi tects were fully absorbed coping with the basics of Doric composition by means of rules of thumb like those already mentioned.
By the second quarter of the fifth century howev er, architects had acquired a greater control over the design process. Temple superstructures could be resolved according to a more unitarian concep tion (as manifest in neater proportions, the antici pation of the column rhythm in the joints of the krepidoma, increased regularity and, with time, greater coordination between peristyle and cella). Evidently rules of thumb and strategies of modifi cation were either arnended so as to produce bet ter results, or they were overtaken by a more effec tive mechanism of control. \That form might such a mechanism take? For the fifth centul?, there are no written sources to assist us (the building inscrip tions from Piraeus, Epidauros, and Eleusis date to the rnid fourth centmy or later)," so the suniving classical temples themselves must furnish our prirne evidence. Interpretations of these temples
taller than the frieze, likewise the height of the stylobate corn pared to the steps below. Cf. Seiler 1986, 59, n. 208; Bankel 1984a, Abb. 2 and 3.
'"Vitr. 4.3.1; Tornlinson 1963.
"Riernann 1935, 2833; 1951, 304.
I I
I
A. HYPOTHETICAL TIMBER CONFIGURATION
B. CONFLICT OF AXES (due to the use of stone?)
I I I
(F I (WT)/2 I a I I I
C. CONFLICT RESOLVED BY CORNER CONTRACTION
Fig. 2. The Doric corner problem. The typical corner configuration of the classical temple (c) derives from a conflict between the width of the triglyph and the cross sectional width of the architrave (b), a conflict which might, perhaps, arise frorn the transposition into stone of a timber prototype (a). (Drawing by the author)
are to sorne extent subjectixe, however, so they change with changing perceptions and personal agendas. But while it is well to guard against adopting a parti san position, rnodern scholarship must be right to
'"1uben 1976,413; Coulton 1988,604; Slertens 1984a, 1502; Gros 1992, 1213. "'Riemann 1951; cf. 1960, Xbb. 1 for a si~nilar treatment of the Hephaisteion. "Hocker 1986, 235.
Fig. 3. Analysis of the layout of the Temple of Zeus at Olympia according to Riemann (1951, hbb. 2). h hypothetical regular scheme (I) is first modified for the sake of a more generous peristyle depth at both ends of the building (11, a), and then refined to take account of corner contraction (11, b).
distance itself from the early to mid 20thcentury portrayal of Greek architects as master geometers adept at traces r~gulat~urs,
to use a term adopted by Le Corbusier.'Yhe objections then of William Bell Dinsmoor to "intricate geometrical diagrams . . . or the golden section"'%ave since been compound ed by doubts that geometrical methods could have coped with processes of modification and, more fundamentally, that architects of the classical peri od even made extensive use of drawings."' As a gen eral rule, ancient architects exploited geometry for resolving details, especially those involving cuna ture (volutes, moldings, refinements), but not for the composition of whole buildings unless they were concentric or partially concentric in plan (e.g., theaters and amphitheatres). All things being equal, arithmetic was the more convenient, flexi ble tool and hence the dominant force in facade design."
Following the affirmations of Dinsmoor, selective analyses of Riemann,'? and the comparative stud
'*While the heyday for such speculation was the inter~var period, it persisted later, see Bousquet 1952; Koch 1955, 70 81; Tiberi 1964; Brunes 1967; Pannuti 1974; Michaud 1977, appendix 4. For more attention to the constraints of numeri cal expression and hence a possible strategy for reconciling geometrical and arithmetical notation, see Frey 1992 and Bom melaer 2000, and for outline historiography and further bibli ography, see M'ilson Jones 2000b, 26 and ch. 5.
"'Dinsmoor 1950, 161.
"'Coulton 1974, 1975, 1983, 1985, 1988, 5167, esp. 64;
ies of Coulton, current scholarship highlights the importance of arithmetical proportions for both ensembles and discrete elements, a case in point being Dieter Mertens's study of the unfinished tem ple at Segesta (fig. 4).'The facade returns the ra tios 9:4 and 10:7, while the frieze embodies the same play of relationships as that specified in the build ing inscription for the Telesterion at Eleusis many decades later: 10/9 being the aspect ratio of the metopes; 3/5 that of the triglyphs; 3/2 the ratio between the widths of metopes and triglyphs. A coherent set of interlocking proportions is in fact characteristic of Doric entablatures in the classical period, particularly those with the last mentioned proportion. Figure 5 shows the most striking op tions. But just because we can detect certain pro portions does not mean that we understand the processes that engendered them. How did archi tects know what ratio to assign to which physical limits? M"nich were more important and which less so? Why are some types of relationship present in
hlertens 1984b, 137. Nor does it seem helpf~ll to extend the use of the term module to embrace geometrical approaches, as do Kurent 1972 and Pannuti 1974.
"LViIsonJones 1989b, 12935; 1993,42932; 2000b, ch. 5 and 1267.
"Riemann 1935, 1951, 1960.
" hfertens 1984a, 1984b. For general appreciation of the importance of proportion for ancient design, see Riemann 1935,1951; Coulton 1974,1975,1985; Hoepfner 1984; Koenigs 1990; Wilson Jones 2000b.
Fig. 4. Proportional analysis of the facade of the unfinished teinple at Segesta, 1:200.(After Mertens 1984a, Beil. 24)
some buildings but not in others? How do propor tional methods cope with modifications?
In addressing these questions it helps to distin guish between "schematic" proportions and "visu al" ones. Schematic proportions are chosen for their neatness more than their beauty; visual proportions encapsulate aesthetic conventions but are not al ways satisfactory i~umerically.'~ A representative il lustration of the latter is column slenderness. In any one period and geographical area it had a re stricted range, and although there is no shortage of exceptions,"' it was usual to advance slightly with respect to precedent. Ratios between the height and the lower diameter for West Greek temples progress from 4'/3, 4v9,4%, 4%, to 4% over the course of the fifth century;'5impler ratios of, say, 4, 4%, and 5 are notable by their absence. Of course there is an overlap; visually sensitive indices like entabla ture proportions may be mathematically simple (fig. 5), and mathematically simple proportions may be beautiful, but this does not vitiate the utility of the distinction.
\$'hen composing designs, architects juggled these schematic and visual proportions. For exam
"This distinction isanticipated in Claude Penzult'slate 17th centun contrast benveen abstract and customary beauty, see Herrmann 1973.
"Coulton 1979, 1984; Bommelaer 1984b.
"'These ratios apply respectively to the columns of the fol
ple, it is evident that the proportions of the temple at Segesta's facade (fig. 4) can only have been se lected having been checked against the conven tions affecting its components, for the column slen derness of 4% fits predictably with the chronologi cal evolution just mentioned. The successive ap plication of certain ratios does not necessarily favor dimensional neatness, and the values obtained by calculation might have to be rounded off to the nearest whole dactyl (the standard 1/16th subdivi sion of the Greek foot unit). So while at Segesta it seems that design started from the premise of an 80 ft euthynteria and a 64 ft peristyle, the column height was calculated as 4/9 the latter, or 28% ft, and rounded off to 28 ft, 7 dactyls. The typical col umn spacing worked out as 12 ft, 14 dactyls after allowing for contracted corner bays and a wider cen tral bay, which for its part was tuned to 4/9 the col umn height, and so on, calculation by calculation. Potential solutions were presumably tested by trial and error until the desired result was achieved, bringing to mind the sculptor Polykleitos's maxim: "perfection was achieved gradually in course of many calculations."" Only occasionally, as in the case of
lonlng temples: those of Poseidon at Paestum, Athena at Syr acuse,Juno Lacinia, and Concord atAgrigento, and the unfin ished temple at Segesta.
";As translated by Marsden 1971, 107; cf. Pollitt 1974, 15.
the Hephaisteion, were architects able to achieve unified proportions in terms of both the whole and the parts.28
This iterative pursuit of perfection via propor tional calculations and modifications, ever filtered by rules of thumb, the respect for precedent, and visual acuity is certainly plausible in both analytical and historical terms. Nonetheless, it remains a re markably contorted means of guaranteeing the re producibility highlighted at the beginning of this article. So the door remains open to other strate gies, providing they can cohabit with proportional relationships like those just described.
THE MODULAR HYPOTHESIS
My examination shows that from the second quar ter of the fifth century B.C. many Doric temples were designed according to a method that was com patible with proportional manipulation, and yet better suited to both the pursuit of consistency and the very nature of the Doric order: a method based on modular principles. Vitruvius (DParcIz. 4) famously described the design of the Doric temple in modular terms, and modern specialists have en
joyed partial success inducing metrical units for
individual buildings. The starting point for such
research is usually Vitruvius's derivation of a mod
ule by dividing the width of the stylobate.'" But a
design module is more than an abstract metrical
entity. Written sourcesVitruvius includedtesti
fy that Greek architects associated such nlodules
with the width of physical elements, whether of the
hole for the main spring in catapults," columns,
column bases, or plinths (cf. fig. I).'" Physical rnod
ules like these confer practical advantages since
they correspond to serially repeated building corn
ponents, and it is ~vell to qualify analyses which do
not take this lesson to heart. Published modules
are often not modules in this sense but rnore akin
to abstract units of measurement."
"Particularly striking is a 1:3:3:6 sequence between the xvidth of a wpical bay, the height of theorder, the external width of the cella, and the width of the euthynteria. The bay can then be approximately divided by 5 to g\e the height of the wall blocks (each proportioned height:depth:length as 2:3:5), this in turn being approximately equal to the capital height and the ~ldth of the triglphs, 1/2 the lo~ver column diameter. 2/3 the upper column diameter and the width of the metopes, and 3/2 the height of the steps. For the actual 1neasuren1ent5 see the appendix, no. 2.
"'Yitr. 4.3.37; Knell 1985,8595. Cf. hloe 1945; De Z~varte 1996. Tyaddell's (forthcorning) recent derivation of a module eqni~alentto one triglyph ~ldth frorn the width of the krepi donlawill be discussed below in the section on the plan.
( Agrigento, Juno L. ( 1 1 Segesta I1
121 3 I
I Agrigento, Dioscuri I I I I Agrigento, Conmrd I 1
121 3 1
Fig. 5. The proportions of Doric entablatures of the classical period: three ideal schemes each including a 3:2 relationship behveen metope and triglyph and a 1:1 relationship behveen the heights of architrave and frieze. The comparative dimensions for actual temples shown alongside are based on a cornmon triglyph width. The middle set of proportions is also documented hp the inscription relating to the construction of the Telesterion at Eleusis. (Drawing by the author)
"'Aspecified by Philon of Bpzantion in his Btlofiteca, see Marsden 1971, 10715. Lritruvius (1.2.4) also rnentions physi cal features of artillel7 and ships, and "in other things, frorn \arious rnernbers." Cf. 10.10, 10.1 1.
"See Coulton 1989, esp. 86, including the attractive pro posal that the term rmbntec or rmbnt~r(Yitr. 1.2.4 and 4.3.3, but othenvise unattested, see Gros 1992, 1278; Corso and Romano 1997, 1:84, n. 157: 465, n. 133), could refer specifi cally to the square slabs of gridded stylobates like those illus trated in fig. 1.
"'Coulton 1989, 87. For examples ofrnodules/unit~under stood in the rnore abstract sense, see Knell 1973,114; Koenigs 1979; Bankel 1984a; De Zwarte 1996; Hocker 1986, 1993.
Some scholars recognize the frieze as a determi nant of Doric design, and Mhlf Koenigs has predi cated his analyses on the assumption that the widths of triglyphs and metopes should be capable of be ing expressed neatly in terins of rnodules/feet."' But it is necessary to go further; I see the triglyph as the basic nlodule for the Doric temple from around the middle of the fifth century B.C., if not a couple of decades or so earlier. This is both a new idea in :is much as it goes counter to modern scholarship, and a very old onefor it is directly adapted from L'itruvius. As just mentioned, he divided the stylo bate width to yield a module, and then assigned its multiples to major elements of the facade, includ ing one module for the triglyph width. Not only is this the only element of the plan which is one mod ule wide, but Vitruvius links modules, proportions, and triglyphs in two important passages." I suggest that he inverted the chain of command, and that the triglyph was the real progenitor of the system.'"
Enrolling the support of L'itruvius is not without its difficulties. The Greek sources he relied on date mostly frorn the late fourth to the second centuries,'" so it is understandable that his detailed recomrnen dations hardly match the realities of fifthcentury design. Most notably, he sanctioned much more slen der proportions, three rather than ISVO triglyphs per bay and the anathemato Greek architectsof the frieze ending in a half metope."' So was the modular system another later contribution? Silvio Ferri be lieved so, calling it an arid creation of theoreticians who, long after the heyday of the Doric temple, wished retrospectively to set down a perfect model they knew never actually existed.'"\'itruvius and his Hellenistic masters were guilty of pointless digres
" Koenigs 1979.
"Utr. 1.2.4 and 6.3.7. The forrner is cited here in the con clusion; the latter concerns the use of Doric in (Italian) resi dential buildings: "if the columns ofthe peristyle are to be made in the Doric manner, use the rnodulesjust as I have described then1 in the fourth book for Doric ternples and place the col Ilnlns according to those n~odules and the proportions of the triglyphs." (trans. Hoice and Ro~vland 1999).
"\'itruvius's approach has been championed before, nota bly in Aloe's book I nurnili dili'trurlio (1945), but >foe was pri marily concerned ~ith nlodules derived from the column dia meter. an interpretation that has been ignored for the sirnple reason that it does not hold up to scrutiny. Moe's analysis ernbraces triglyph \lidths only in those buildings where this rrleasure is half the col~~nln
diarneter or thereabouts, as in the case of the Hephaisteion. Ilis work is also marred by an o\er ernphasis on the nurnber 27 and a bias toward geometrically inspired elevations.
'"'Gros 1978: M'esenberg 1983, 1984, 1996.
,,
"The introduction of three triglyph bays seems to have taken place in stoas earlier than it did in temples, see Coulton 1976, 11,&6. For a rare instance of the \'itrtivian solution at
sions on how things ought to have been.g?Apart from a minority enthusiasm for modular design (applied to eveiything frorn Stonehenge to Roman town plan ning),"' the method is widel!, disparaged as a me chanical, almost mindless, strategy, one at odds with the free workings of artistic genius and hence the excellence of Greek architecturean antithesis to "real" design." Burckhardt M'esenberg, the author of numerous punctillious exarninations of L'itrurius and his sources, briefly dismisses the possibility that the Greeks themselves used modular methods for ~vhole buildings, admitting it only for details such as the Ionic capital.." Those who accept modular de sign do so only for the fourth century or somewhat later. It is thought to be "possible to establish with some probabili~ that a modular system was not used by Greek architects, at least before the late Hellenis tic period."4g Coming from Coulton, the scholar who perhaps has done more than anyone to crystallize contemporary thinking about Greek design process es, these words cannot be discarded lightly. Yet the following analysis shows a real possibility that, dis counting inevitable distortions, L'itruvius perpetu
ated a practice originating in the classical era.
While modules are generally seen to be less mal leable than proportions, this is not necessarily true. Any mathematical strategy is only as flexible as de signers allow it to be. As is clear from L'itruvius's account, modular terms were not confined to inte gral values; fractions based on halves, thirds, quar ters, fifths, sixths, and so on are also legitimate, al beit progressively less appealing as the terms in crease." The key words for modular design are metl~od and princij~l~
a method implies the intelligent pursuit of improvement; principles are elastic.
Hadrian'sXlla see Kocco 1994.
'Terri 1960. 160: "come e ~izio costante di tutti i teorici, essi hanno volentieri . . . dettato le leggi del perfetto tenlpio dorico che essi ben sapevano nessuno avrebbe rnai costruito." Even more negative is the concludingsentence ofFalus's study (1979,270): "Celui qui exanline les proportions et les princi ples de constiriction des templesgrecs, n'aqu'nne chose afaire, notainment a oublier tout ce qu'il\enait de lire chez\'itrtive."
"'Ferri 1960, 161.
"'Kurrent 1972, 1977.
"For representative cornrnent5 in thisvein, see Koch 1955.
80. "LVesenberg 1994, 96; cf. Coulton 1989, 87. " Coulton 1988. 66; cf. 1975, 68; 1989, 86. For the use of
L'itruvian methods in the first centuq, see gtienne and\'arene 1995. On the other hand, Koenigs (1979) entertains a late fourthcentnndate for his interpretation of modular method. Cf. hlertens 1984b, 144.
"\'itr. 4.3.47 (for a con\enient list see Knell 1985, 88); 10.10.15: 10.1 1.49. Fifths are not used by\'itruvius but they are repeatec!ly by Philon, see Marsden 1971, 113.
Fig. 6.The entablature schemes identified in the preceding figure analyzed in terms of modules (M) equal to the width of the triglyph. Assuming that the triglyph width was set at a multiple of 5 dactyls (d), in this case 30 dactyls, similarly convenient whole numbers of dactyls automatically follow for all major dimensions. (Dra~ving by the author)
In this analysis of modular design, I examine 10 generically similar and relatively well preserved Doric temples with hexastyle fronts and with me topes oneandahalf times as wide as the neighbor ing triglyphs. My prime concern has been compa rability to ensure that the results pertaining to any single temple are neither fortuituous nor mislead ir~g.~The
temples discussed here are those of Zeus
"The Oynpieion at Agrigento is a case in point, see Bell 1980.
'Tor this distinction, see Wilson Jones 2000b, 645.
'This focus on facades has the added advantage of reduc ing the number of measurements examined. Many of the lim its of probable importance present options: for example, was
at Olympia, Hephaistos at Athens, Apollo at Bas sae, Poseidon at Sounion, Nemesis at Khan~nous, the Athenians at Delos, "~lno Lacinia," "Concord" and "the Dioscuri" at Agrigento, and the unfin ished temple at Segesta. The chronological span, beginning with the Temple of Zeus at Olympia, reflects the reduced likelihood that modular prin ciples had wide currency much earlier, while the cutoff point at the start of the fourth century re flects the relative willingness of scholars to accept this kind of interpretation for later periods in any case. The insistence on the canonic, L'itruvian, metope:triglyph width ratio of 3:2 derives from the fact that this relationship enhances metrical reso nance by virtue of its correlate, a .3 triglyph module width for the bay, the typical column spacing mea sured at the axes (fig. 6). Significantly, it is clear that the bay width came into ascendency as a criti cal design constraint (supplanting the stylobate width in the hierarchy of design intentions) around the second quarter of the fifth centurv; the Temple of Zeus is in fact a key witness to this shift."This also is a time when the work of Greek architects exhibits a more definite interest in abstract order ing prin~iples.~'
Emphasis is placed here on the end facade rath er than on either the flanks (which are less easy to compare since they had varying numbers of col umns) or the plan. ,4 general awareness exists that the design of Doric temples tends to work from outside in, but there also is good reason to catego rize the Doric temple as a "facadedriven" design, as distinct from "plandriven" typologies (e.g., the theatre, the stadium, and Ionic temples of the Hel lenistic period)." In other words, the typical Doric temple plan was organized to accommodate, over and above its other functions, a canonic frontage. One symptom is the relative heterogeneity of plan solutions; various options existed for positioning the cella, and for apportioning the pronaos and opisthodomos. And ultimately the adjustments to the plan associated with the corner problem only make sense as devices to obtain the desired eleva tion. For these reasons plans will be reviewed only after scrutiny of the facade is complete, and then only in sufficient depth to gauge if similar princi ples are likely to apply to them too.4y
the entablature height conceived as excluding or including the geison and/or the kya? By omitting the plan we can avoid having to ponder similar choices relating to the width and length of the cella and its different compartments It is also helpful to concentrate on relatively well presen~ed and docu mented buildings, because this minimizes gaps in the measure ments available. The reconstructions at Delos and Rharnnous are relatively reliable; however, it is frustrating to work with
Giebelanstieg =l:L
GeisonL =3T
Fig. 7. Proportional and modular analysis of the facade of the socalled Temple of the Athenians, Delos, according to 1Iertens (1984a, Abb. 80), 1:100.1Iertens's module "E" corresponds to half the triglyph module
proposed here.
I advocate the following procedure for apprais ing individual temples:
Take the actual average triglyph width.
Establish if there is a proximate unit that divides 5 times into column bays as well as neat ly into other important limits in both plan and elevation; the unit that returns the neatest pat tern is a potential design module.
Check that schematic proportions relating to the facade as a whole can be conveniently ex pressed using such a module.
Check that the module corresponds to a di mension that can be expressed in terms of known feet and/or dactyls, the simpler the better.
Review smallerscale components of' the fa cade to see if they can be conveniently ex pressed in modules.
Review the plan likewise.
measurements that are notsecure, and it may be noted that in both cases an improxed pattern would be returned by slightl! different column heights (12% M rather than 12% Rf at De
The temple the Athenians built on Delos around 425 B.C. (fig. 7) will be used to illustrate this proce dure:
The triglyph width is 370 inm.
A module (M) close to this, of 366 mm, di vides into the axial width of the peristyle 24 times, the column spacing 5 times and the height of the order (excluding the geison) 16 times. The discrepancies between the val ues thus calculated and those actually mea sured amount to 0, l, and 10 mm respectively (appendix, no. ,5).
As Mertens has shown, using a module half the size of the one proposed here, salient pro portional relationships can be recast in such modules."' The 2:s ratio between the height of'the order and the peristyle width translates as 16 M:24 M; the 2:s relationship between the entablature height (excluding the gei
10s; 11 Rf rather than 10% M at Rhamnous). '"Mertens 1984a, 2207; Bommelaer 1984a
son) and the typical colunln spacing trans
lates as 3% M:5 hf; the 1:5 relationship between
the entablature height (excluding the gei
son) and the total height of the order (in
cluding the geison) translates as 3% M:16?4
hf; and of course the 2:3 relationship between
the width of the triglyph and that of the me
tope translates as 1 hf:1% hf.
The proposed module equals 20 dactyls or 1% Attic feet, as \\ell as 18 dactyls or 1% Doric feet, both of these being eminently plausible candidates for the unit used for construction.
Several smaller dimensions are modular, in cluding the corner bay (4% hf), the entabla ture height (4 hf), and the depth of the archi trave (2 hf).
Likewise several elements of the plan are modular; for example, the interaxial length of the peristyle is 44 hf.
The Athenians' temple, with its amphiprostyle plan and Ionic traits, might be considered a uni cum." Yet similar modular patterns can be found in normal Doric peripteral temples of an earlier dateprovided the key 2:3 frieze rhythm ancl 3 module bay widths are present. Perhaps the math ematical neatness of the 3 module bay encouraged architects to illstill similar patternsthat is to say nlodular patternsin entire facades. Entablature schemes like those illustrated in figure 6 are proof that numerical harmony can be expressed equally well in terms of proportions and triglyph modules; no doubt the modular approach rose to prominence in large part because this \\as so. Speculation as to the date when this occurred folio\\s in due course; for the nloment it is enough to observe that this clevelopn~ent possibly had taken place by the time of the earliest building in the present group, the Temple of Zeus at Olympia. The typical bay mea sures 5 hf wide and 10 hl tall, while whole modules are used for the height of the entablature, 4 M, and that of the order; 14 M (appendix, no. 1). hfodular patterns, however, are not sufficiently clear to de feat criticism (the krepidoma, for example, seems to evade anv such definition), and all the later tern ples examined respoilcl more positively to the pro cedure just described, save perhaps for the Tem ple of Concord at Agrigento." But rather than ar gue the case for each of the 10 temples in turn, their analyses are presented in the appendix and most of them summarized graphically in figure 8; the quest here is to identify the general principles in common.
THE ANALYSIS OF HEXASTYLE TEMPLE FRONTS
Lirrzits of Il'idth
The main limits of the plan, working inwards, are the overall width (measured either at the eu thynteria or the bottom step of the krepidoma, which rests on it)," that of the stylobate, and that of the peristyle, measured axially. Architects appear to have assigned whole numbers of triglyph mod ules to one or two of these limits, presumably gaug ing the remainder on the basis of the chosen col umn diameter ancl other considerations of detail (table I)."
Table 1. Salient hfodular Limits of Width
O\erall Width of Axial IZ'iclth IZ'idth St~lobate of Peristlle
llith a thee step krepzdomn
OIL mpia, Zeus Bassae, Apollo Athens, Hephaisteion Sounion, Poseidon Rhamnous, Nemesis Segesta, unfinished
mi'th n four st~p krepzdoma
Agrigento, .June Agrigento, Concord Agrigento, Dioscuri Delos, Athenians' Apollo
"Bornrnelaer 1984a.
"The actual triglyph nidth here is considerably larger than the proposed 1nod~11e (although this is not an insuperable obstacle, as nil1 be arg~led belolc),\\.bile there are no obvious modular patterns either on the long side of the pelist~le or in
293
30
30
29%
30
30
3 2
3 2
32?
30%
the layout of the cella.
'.'Asqualified for each entl? in the appendix.
"'TVhole nmnher dues are sho~cn in bold throughout the tables.
'2===== k===== 261iz 29 d d : &==&==== 27112 32 4 d
, C===== u= 26213 30 '  : & &==== AGRIGENTO 27112 32 4: __1 'Dioscuri' 3 t 15 11215
yL_ 30 ..>, ,.A, , ,i' ;7 &=== U= 27 32 ? ' ,. , , , 44. : 331137 : ;l _I: _I
'
L
i b 26115 : &=== 29315 ======5 U= 30
Fig. 8.Slodular interpretation of eight Doric temple facades of the classicalperiod. Each facade is scaled to a common triglyph \vidth or module of 1 unit. (l)ra\ving by the author)
25 M WlDE PERISTYLE: HYPOTHETICAL INITIAL CONCEPTION
25 M WlDE PERISTYLE WlTH CORNER CONTRACTION
24 M WlDE PERISTYLE WlTH CORNER CONTRACTION
Fig. 9. The t~co most popular modular schemes for Doric temple facades, one ~vith an axial peristyle ~cidth of 25 modules (b),the other 1vit11 an axial peristyle ~cidth of 24 modules (c). Both can be derived from a hypothetical ideal conception based on regular bays 5 modules wide without corner contraction (a). (Dra~ving by the author)
The starting point for the krepidoma of a temple with three steps was often an overall width of 30 modules, while 32 was preferred for those with four. Alternatively, or at the same time, the axial width of the peristyle was typically made a whole number, either 24 or 25 modules. These options signal dif ferent approaches toward the corner problem. In the latter, the 23 module axial width of the frieze was simply transferred to the peristyle, a solution which had a theoretical appeal in so much as 23 M equals 3 bays of 3 M (fig. 9,a). This, however, took no account of corner contraction, which then forced the typical bay to exceed 3 modules by around 1/5 (fig. 9,b). Conversely, a 24 M peristyle anticipated corner contraction and allowed the typical column spacing to remain either exactly or close to 5 modules (fig. 9,c). At Delos this solution was obtained exactly, whereas at Sounion and Segesta the cho sen contraction created discrepancies of a dactyl or two. At the Hephaisteion, on the other hand, a val ue of 24% M cornbined with 5 M normal bays and relatively mild contraction.
Although the width of the stylobate frequently corresponds to half nurnber values (26%and 2% M), that fact that whole numbers are rare suggests that this lirnit was usually a subordinate consider ation, in contrast to archaic practice when it repre sented a fundamental constraint.'Wn occssions, however, as at the Temple of the Dioscuri at Agri gento, the stylobate width could be important and it is interesting to note that the number of modules used here, 2'7, is the salne as that which Vitruvius would have used for such a design."' I'Vhether the prirne consideration was the peristyle or stylobate, the difference between their width is often 2% M, an amount that allowed for the popular colurnn diameter of around 2% modules, plus the oversail between the columns and the edge of the stylo bate."
The tolerances between predicted values and their real counterparts are srnall; those for the whole number values (e.g., 25 or 30) listed in table 1 are frequently less than 1 crn, and only on two occa
"Riemann 1951, 295, 302; Coulton 1974; 1988, 5960.
'"'itru\ins actually di~ides the stylobate of a hexashle tem ple into 29% parts, but this assumes a wider central bay with three sets of triglyphs (i.e., 7% ht).Deducting the difference hehveen 7% M and 5 M yields 29% ht 2%M = 27 M. Cf. Moe 1945, esp. fig. 27. For the possibili? that the Temple of Aph aia has a 27 ht wide stylobate, see below.
.
"This value of 2% ht may have been conceived as 2% M on some occasions, by virtue of~chich the diameter equals 4/9 of a 5 M column spacing. By contrast, at hegina, Athens, and Sounion the conceptual column diameter is likely to have been 2 M, even if this value is not precisely matched in reali?,
Height of Height of
Order Order Height of
Temple inc. Geisoll exc. Geison Column
:Mainln?zd and idands
Olympia
Athens
Bassae
Sounion
Rhamnous
Delos
Sicil~
Agrigento, Juno Agrigento, Concord Agrigento, Dioscuri Segesta
sions do they exceed 3 cm. A notional mean error lies somewhere between 1 and 1% cm, that is to say less than 0.1 % or one in 1,000 compared with the average of the distances involved (ca. 15 m).i8 As

might be expected, tolerances tend to be smaller for well presened marble buildings, and larger for poorer presened ones in humbler material.
The devil's advocate might object that the 2:3 trig1yph:metope rhythm necessarily generates a to tal frieze width of 26 triglyph modules, and hence a peristyle width (measured at the column axes) in the region of 24 to 25 M. But the design of the krepidoma was an independent issue, and there is no reason, deliberate intention apart, why its width should so frequently match either 30 or 32 M." This width measurement suggests that a modular con ception could embrace the very first course of con struction above the foundations, at the same time as furnishing one of a series of "proofs" in favor of the present proposals.
""Indi\idual tolerances are wen in the appendix. Those relating to the axial width are 6 mm (Bassae), 3 mm (Hep haisteion) ,13 mm (Segesta) ,10 mm (Juno) ,24 mm (Concord), ca. 2 mm (Rhamnous). and 0 mm (Delos). It should be borne in mind that the modules proposed in each case represent my hest guess; only a 1 mm error for a module would generate a discrepancy of ca. 2% cm. In addition, there are no doubt nu merous occasions when I have not been able to identi6 deli ations that are caused not by error but by deliberate minor adjustments or rounding off to whole dactyls, as suggested in my reading of the plan at Sounion belolc.
'"It might be argued that a 30 M overall t+idth could have been generated by proportional calculation (30 h.1is 6/5 x 23 ht and 3/4 x 24 hl), but there is no clear proportional explana tion for combinations like 30 and 24% M or 32 and 25 hf.XUternatively it might be argued that the use of the column nurnber rule to set out the krepidoma, coupled with the deci sion to make 1/6th of its width equal to the typical column spacing, and this in its turn equal to 5 triglph ~+idths, necessarily generated overall ~+idths of 30 hl. Such a procedure,
Limits of Height
In terms of modular simplicity the height of the order, measured either including or excluding the geison, usually took precedence over the column height, as shown in table 2. When the pediment and the flanks were capped by a terracotta kyma, it seems that it was excluded for metrical purposes, whereas if the kyma was made of marble it was more likely to be in~luded.~'
Other significant measures could be the height of the order plus krepidoma, the height of the or der plus pediment, or the total height (i.e., order plus krepidoma plus pediment). Although there are instances of neat modular values in this last re spect, definite patterns cannot be discerned since only about half of these buildings are presened up to the peak of the pediment, and in some of them the total height converges only approximately on round numbers." Furthermore, where the kyma is lost it is difficult to be sure if it was included in the
holvever, is less likely to result in simple measurements for the nominal trighph ~+ldths than if these Icere the starting point. h'or does it is explain the choice of 32 M in the Sicilian exam ples. And since there is no reason !thy rules of thumb should lead to the same neat result, it is furthermore significant that the projection of the euthynteria relative to the axes of the peristyle was freqnently and accurately defined by jumps of tvhole or half modules. The overallu.idth less the peristyle~+idth is 5 hl at Bassae (~+ith a tolerance of 2 mm). 5% M in the Hep haisteion (tolerance 15 mm), 6 ht at Segesta and Rhamnous
(tolerances 17 and 1 mm, respectively), and 7 Mat Agrigento, in Juno Laciniaand Concord (tolerances 9and 10 mm, respec tively).
""At Rhamnous the entablature measures 4 M including the kyma. At the Temple of Concord it seems possible that the (lost) k>maconspired to make the total height of the order 16 M, i.e., half the 32 ht overall width.
"'At Bassae, for example, the total height of the building exceeds 20 M by a substantial 8 cm or so.
Table 3. Modular Relationships between Limits of Width and Height with Reference to Width of Peristyle
Temple Axial Width of Peristyle Height of Column
Bassae Sounion Delos Agrigento, Concord Segesta 25
25
24
2 4
24
25
24
24
24
,Vote: Tolerances cited are as follo~vs:
"34 mm (13.231 m x 3/5 = 7.939 m versus 7.973 m).
h5 mm (13.231 m x 9/20 = 3.954 m versus 5.939 m).
'21 mm (ca. 12.320 m x 2/3 = 8.213 mversus 8.192 m).
"20 mm (ca 12.320 m/2 = 6.160 m versus 6.140 m).
'10 mm (8.79 m x 2/3 = 5.860 m versus 5.870 m).
' 16 mm (15.427 m x 3/4 = 11.570 m versus 11.554 m).
"3 mm (21.030 m x 7/12 = 12.268 m versus 12.233 m).
"9 mm (21.030 m x 4/9 = 9.347 m versus 9.338 m).
'6 mm (21.030 m x 7/10 = 14.721 m versus 14.717 m).
design height or not."' It is nonetheless clear that the krepidoma height was typically not assigned a whole number of modules, which suggests it was primarily determined by conventions governing the height of the stepsb3 In fact the steps were tied to human scale and could not simply increase or decrease like the rest, so a big temple has a relative ly low krepidoma and a small temple a relatively tall one. The pediment, too, often does not correspond to a simple modular expression. I suspect that it was more important for the combined height of krepidoma and pediment to make a whole or half number of modules.64
Modulated Proportions
It is highly significant that modular dimensions tend to complement salient schematic proportions. For example, in both the Hephaisteion and the temple at Bassae the 2:l relationship between the
'j2A case in point is the temple at Segesta, ~vhere a total of 21 M including the kyma may be conjectured given that this particular value corresponds to 3/2 the height of the order, 7/8 the width of the perishle, and 7/10 the ~+idth of the eu thynteria.
6'In addition, convention demanded that the step formed by the stylobate ~vas taller than the steps below, and this may have caused departures from modular values that otherwise ~vould have been simple. At the Hephaisteion, for example, the height of two lower steps are on average 344 mm tall, sug gesting that the notional height of the krepidoma is 3 x 344 mm or 1032 mm, which exceeds 2 M (1027 mm) byjust 5 mm.
6"n temples with a three step krepidoma the sum of these heights is 5 Mat Olympia, 3% M plus 1 dactyl at the Hephaist eion, 5 ht plus 2 dachls at Bassae, 5 M less 2 dactyls at Sounion,
Height of Height of Height of Order Order Facade exc. inc. Geison exc. Geison Pediment Ratio
overall width and the height of the order is ex pressed with didactic clarity in terms of modules, 30:15." The peristyle width was usually a more im portant reference, however; it might relate to the height of the order including the geison, to the height of the order excluding the geison, to the height of the columns, or possibly even to the height of the whole facade excluding the pediment (ta ble 3). On other occasions the width of the stylo bate was important. This could be simply related to the height of the order excluding the geison or the height of the column (table 4).
Schematic proportions also influenced the de sign of the bay. As is well known, at Olympia the column height is twice the bay width, 10 and 5 M respectively." Otherwise the entablature was includ ed in this type of relationship on the front and/or the flank, either measured with or without the gei son (table 5).
3%M at Segesta. In temples with a four step krepidoma the same sum produces 6Y2 M at.4grigento (Concord) and 7 M at Delos.
"The tolerance benveen the ideal 2:l ratio and the exe
cutedvalue is 10 mm at the Hephaisteion (15.420 m/2 = 7.710
m versus 7.700 m), and 34 mm at Bassae (13.874 m/2 = 7.937
m versus 7.903 m) .The same relationship, this time expressed
as 32 M to 16 hl,can be reconstructed for the Temple of the
Dioscuri at Xgrigento assuming it to have had a 32 M euthjm
teria ~+<dth
like its predecessors, the temples ofJuno Lacinia and Concord.
"This same 2:l proportion appears approximately and un accompanied by ~vhole numbers of modules at the Temple of Juno Lacinia (and also at the Temple ofAphaia at Aegna).
Table 4. Modular Relationships between Limits of Width and
Height with Reference to Width of Stylobate
Height of Height of Width of Order Column in Temple Stylobate exc. Geison Modules Ratio
Olympia 26% 13% 2:la Agrigento, Dioscuri 27 15 9:5" Agrigento, Juno 27% 13% 2:l' Athens 2 62h 11% 12:5" Bassae 27% 11% 22:9'
vote: Tolerances cited are as follo~vs:
" 40 mm (27.680 m/2 = 13.840 m versus 13.800 m).
" 15 mnl (13.860 m x 5/9 = 7.700 m versus 7.685 m). It may also be noted that the
same relationship is seen with a tolerance ofjust 4 mnl at Aegina (13.810 n1/2 = 6.905m versus 6.909 n~).
12 mnl (16.930 m/2 = 8.465 m versus 8.477 m).
9mm (13.720 m x 5/12 = 5.717 mversus 5.712 m).
'8 mm (14.547 x 9/22 = 5.951 m versus 5.959 m).
Table 5. Modular Relationships for Column Bays
Height of Height of Typical Order Order Column Temple inc. Geison exc. Geison Spacing Ratio
Bassae 15 5 3: 1 Athens 15 5 3: 1 Rhamnous, Nemesis 13% 5 11:4 Agrigento, Juno 13% 5 11:4 Agrigento, Dioscuri 15 5 3: 1
Figure 6 highlights the tendency for entablatures the compilation of specifications, works on site, and to work out neatly in modular terms. In addition, the provision of materials and skills from outside their height could be simply related to the column the immediate locality of each individual project spacing, the former either including or excluding would have been unnecessarily complicated. the geison (table 6). Part 1 of this study focused on the anthropomor
Alternatively, the entablature height could be phic metrological relief from the island of Salamis, related to that of the order. At the Temple of Con only the second known document of its kind after cord a 1:4 relationship excluded the geison, but the one in Oxford. Together, these two reliefs con otherwise it was more usual for the geison to be firm the relevance of the following "international" included in the calculation. Measured in this way, standards: the 294296 mm "Attic" foot, the 325 the entablature height is 1/4 that of the order at 328 mm "Doric" foot, and the Egyptian royal cubit Bassae and Sounion, and 2/7 at Olympia. The thrust of 522525 mm (which implies the existence of a of all this is that proportions and modules are not "Samian" cubit of the same length, and hence a inherently hostile: if so desired, both may be tai 348350 mm "Samian" foot). lored in mutual harmony, even when the simplicity In addition, the Salamis relief returns a 306308 of one had to be sacrificed to the other." mm unit, which could be either a local foot or the
"common" foot mentioned by Herodotos. There is 1Metroloa also mounting evidence in favor of a 298300 mm
The next premise (4) of the procedure for iden "Ionic" foot, giving a total of five safe havens in a tifying triglyph modules holds that candidates still uncertain environment. Indeed, metrical anal should be convenient expressions of units of mea yses of Greek buildings frequently point to units sure widely used by the Greeks. Exceptions may be other than these standards, as if to negate their uni admitted, but if this were not the general rule, then versality. It is important to highlight the fact that
"'At the risk of making too crude a distinction, proportions opposed to modules at the temples at Agrigento and Rham appear to have had the upper hand at Ollmpia and .Athens, as nous.
Table 6. Modular Relationships for Entablatures
Height of
Trabeation
Temple inc. Geison
Olympia (front)
Delos
Sounion
Bassae (flank)
Agrigento, Juno (both)
Agrigento, Concord (flank)
Delos (front)
Segesta (flank)
Rhamnous, Nemesis
the recourse to modular practices offers a sort of "escape route" out of this impasse, for the modules used for the design and construction of individual buildings do not have to be fullblooded units of measureas long as they are related to them.bR In deed the present modular hypothesis provides fur ther support for the "international" standards, in so far as triglyph modules frequently convert to con venient expressions of Doric, Attic, or "common" feet (table 7).
The recurrence of 5 dactyl multiples (e.g., 20, 25, 30, 40) is reminiscent of Roman architects' pre diliction for standardized shaft lengths in multi ples of 5 ft, again 20, 25, 30, and 40. Just as in the Imperial period, the size of shafts was a major factor in Corinthian design, one fundamentally bound up with column proportion^;^' this pattern strongly suggests that triglyph modules represented a ma
jor factor in Doric design." It also confirms that the Doric foot was recognized over a wide geographical area. The appeal of multiples of 5 may be linked to the fact that this number is one of the bases of Greek counting systems, but it also brings a specific ad vantage in this context. The web of proportions set in train by the 3:2 frieze rhythm happens to gener ate denominators of 5 (since 3 plus 2 equals 5), so modules in multiples of 5 units naturally foster com mensurability. For example, figure 6 shows how sim
"Hocker 1993, esp. 458. Cf. Hoepfner 1984, 14.
"Wilson Jones 1989a; 2000b, 1478, 155.
"'Additional triglyph widths are easily accessible in publica
tions, e.g., the 11 West Greek temples treated by Mertens (1984a, Anhange C, 5) and the 11 assorted Doric buildings at Olympia described in the first volume of the German excava tion reports (Ol~mpia1). Mertens's list yields widths that sug gest nominal modules that include 50 dachls, 3 ft (48 dachls), 45 dactyls, 2% ft or 40 dachls, 30 dachls, and 25 dactyls. Of the Olympia treasures no less than five converge on a single mod ule of 20 dachls. Although none appear in those examples, multiples of 2% dactyls may also have been used; for a set of 12% dactyl wide triglyphs, as defined by mason's marks, see Hoepfner 1984, 22.
Height of Typical
Trabeation Column
exc. Geison Spacing Ratio
ple dimensions for all the main components of the entablature follow from a triglyph width of 30 (6 x 5) dactyls."
Meanwhile those triglyph modules which cannot be expressed in whole dactyls correspond to frac tional multiples of Doric feet, which happen to fa vor metrical neatness in the buildings in question. Whether or not it is significant that the triglyph module of the Temple of Zeus at Olympia corre sponds to 2 Egyptian royal cubits and 3 Samian feet, at 16/5 Doric feet this unit made the 10 M column height, the 5 M typical bay, and the 2% M width of the capitals respectively 32, 16, and 8 Doric ft. At Segesta a module of 8/3 Doric ft allowed the over all width of the front to be 30 M and 80 ft, that of the peristyle to be 24 M and 64 ft. At Rhamnous the use of a 7/6 Doric feet module made the overall width 30 M and 35 ft, that of the peristyle 24 M and 28 ft (fig. 10). Out of the 10 temples under study, only at Bassae is the specification of a module in terms of feet something of a puz~le.~
DETAILED DESIGN
The design of some components of a Doric tem ple facade was tightly constrained by formal and technical factors. For others there was more lati tude for choice, the capital being a case in point; it could be relatively tall or short, for example, with
"Here too is a potential explanation for the frequent oc currence in temple dimensions of multiples of 1/5 M,and not just the fractions 1/2,1/4, and 1/8. Discountingminor adjust ments, the nominal column spacing of the Temple of the Dioscuri at Agrigento is 125 dachls, while that of the Temple ofJuno Lacinia at Agrigento is 150 dactyls; see the appendix, nos. 6 and 8, and hlertens 1984a, Ahb. 53, .Abh. 70.
'2Amodule of 529 mm might correspond to 9/5Attic feet, 13/8 Doric feet, or perhaps 25 dachls of a foot of ca. 338 mm, assuming that this might he equated with the 335 mm foot proposed by Cooper (1996,131), although none of these op tions is especially con~incing. The first produces the most round dimensions for important overall limits, hut few at the level of details.
Temple
Olympia, Zeus Segesta, unfinished Agrigento, Juno Agrigento, Concord Bassae, Apollo Athens, Hephaisteion Sounion, Poseidon Agrigento, Dioscuri Delphi, Athena Rhamnous Delos, Athenians'
Nominal Ideal Design Module
Actual Width Doric Feet Attic Feet Common
in mm mm and Dactyls and Dactyls Feet
" 1044 mm = 2 Egyptian cubits, 3 Samian feet, and 31/z ft of 298300 mm
out adversely affecting the conventions bearing on other parts of the elevation. Architects were there fore frequently able to tailor the salient dimensions of capitals (height, breadth, and diameter at the junction with the neck of the shaft) to harmonize with other parts of the order, in particular the lower diameter of the column and/or the widths of trig lyphs and metopes. A virtually identical set of neat proportions characterizes the Hephaisteion and the temple at Sounion, as summarized in table 8.
Put another way, the dimensions involved can be expressed cleanly in terms of triglyph modules: the capital height corresponds to 1 M, the metope width and upper column diameter to 1% M, the lower column diameter to 2 M, and the abacus width to 2% M. (Interestingly enough, some of these values match those that Vitruvius recommends for his ver sion of the Doric tem~le.'~) It might be objected that this web of relationships is so simple that all the dimensions cited could be expressed neatly in terms of any other. There are several instances, how ever, where expressions work out particularly well in terms of triglyph modules (see the appendix). The frieze height, for example, is typically clearly related to the triglyph width (the most common ratios being 3/2, 8/5, 5/3, or 9/5), but is by con trast often relatively awkward in terms of other di mension~.~"
Another factor was a concern to generate conve nient values of feet; at Segesta, for example, the modular values for the height and the breadth of the capital conspired to produce 3 and 7 feet re spectively. At a smaller scale, however, modular de
'3Namely the modular valuesfor the column diameter, cap ital height, and metope width.
'%t the Temple of Concord, for example, the frieze/trig
sign seems to have been less manageable, and the subdivision of capitals was typically finalized accord ing to proportional relationships and whole num ber values of dactyls.'"
The size of certain elements may have been gov erned by rules of thumb couched in triglyph mod ules. In particular, architrave beams converge on a thickness of 2 M (actual values range from a mini mum of 1%to a maximum of 2% M). The nominal 2 M ideal made sense, in fact, in terms of construc tional logic, since it meant that where architraves were made out of two beams side by side it was pos sible to canre the corner triglyphs out of one of them alone. M'hat is more, architraves tend to be slimmer than 2 M where they are made of marble, and fatter when made of lower grade local stone. Here then is a rule of thumb informed by practical concerns.
Ironically, the widths of the metopes and trig lyphs themselves were the most difficult to resolve as neat modular values. The frieze ideally should be regular, with alternate triglyphs standing axially over column centers and with whole triglyphs at the cdmers. But in reality the distribution of trig lyphs and metopes was affected not only by the cho sen solution to the corner problem but also by three further factors: the modular scheme chosen for the facade as a whole (whether the peristyle width was 24 M as opposed to 25 M); the thickness of the architrave/beam; and the presence or not of in ward inclination of the peristyle. In practice, par ticular combinations of these factors meant that the theoretical dimensions for triglyphs and metopes had to be compromised. Indeed, in some cases the
lyph height of 9/5 M corresponds to 36/25 and 54/85 of the height and the width of the capital.
"Cf. Coulton 1979.
Table 8. Ideal Relationships between Components of the
External Orders of the Hephaisteion and the Temple of
Poseidon at Sounion
Metope Width Lower and Upper Column Abacus Dimension Column Diam. Diameter M'idth
Triglyph width (M)
= capital height 3/2
Metope width
= upper diameter
Lower diameter

scansion of the frieze was probably not finalized until its length could be verified physically once the architrave was actually in place. Only in about half of the temples examined do the average trig lyph widths agree within 5 mm of their hypotheti cal values, while in some examples the discrepan cies are substantially greater.'"
Actual triglyph widths larger than the nominal ideal tend to occur in temples with a 25 M wide peristyle since this demanded the frieze to expand slightly with respect to the theoretical 1 M:lM M rhythm (as in fig. 9,b). The more marked devia tions occur in those examples of this type of scheme that also have an architrave beam fatter than the nominal guide value of 2 M, this being a further source of increment in the overall width. The tem ples at Agrigento are the most extreme examples from the present sample since they have not only a 25 M peristyle width and unusually fat architraves, but also no inward inclination to act in mitigation. Although the majority of the triglyphs and metopes at the west end of the Temple of Juno 1,acinia were made 23 cm larger than their ideal widths, this was still not enough to avoid some supplementary stretching toward the corner (fig. 11) ."
Column spacings that are larger on the front than on the flank is a wellknown characteristic of many Doric temples, which in archaic times is in large part explained by laying out the stylobate accord ing to column number ratios.jx Although by the sec
'"his divergence helps explain why scholars have been so ready to dismiss modular design: indeed, if analyses are predi catedon actualsunreyed triglyphuidths they are bound in many cases not to produce significant patterns.
"The triglyphs on theflanks, at 614 mm. are almost exactly equal to the nominal ideal of 30 Doric dactyls, while those of the central bays on the west front average 634 mm. Here thc triglyphs and metopes at the corners are respectively 5 and 7 cm bigger than those nearer the center, see Mertens 1984a,
100. , '" Coulron 1974; 1988, 5960; cf. Tobin 1981.
2/1 9/4
4/3 3/2

9/8
ond quarter of the fifth century some architects were evidently able to calculate the stylobate to produce a regular peristyle, differences in rhythm persisted in temples like that of Juno Lacinia. This could be attributed to the continued application of rules of thumb, but it could just as well be explained in terms of modular design. The phenomenon occurs in temples that have 25 M peristyle widths and there fore frontal rhythms that are slightly larger than 5 triglyph modulesevidently there was a desire to reclaim for the flank spacing the ideal whole num ber value (table 9).
Fig. 10. Modular and dimensional interpretation of the plan of the Temple of Nemesis at Rhamnous, 1:250. Modular values are shown in bold typeface, foot values in normal typeface. (After Miles 1989, fig. 3)
Table 9. Relationships between Column and Frieze Spacing (in M)
Column
Spacing,
Temple Front
Bassae 5%
Agrigento, Juno 5
Segesta 474
This principle also seems to hold true at Seges ta, even though the typical column rhythm on the front is narrower than that on the flanks. (It does not apply to the design of the Temple of Concord, however, which seems to follow a rather unusual 10gic.'~)
THE PLAN
Could modular design have influenced not just the rhythm of the flank elevation but also the layout of the whole plan? While a detailed examination of this question falls outside the scope of this study, it is possible to intimate a positive response courtesy of others' researches.
As mentioned in Part 1, the metrical units that have been induced by scholars for Doric temples frequently turn out be related to triglyph modules. Riemann's generic starting point for temple de sign is predicated on a 10 unit wide column bay (fig. 3,I). Clearly the same scheme can be expressed with bays 5 triglyph modules wide, while all his val ues for the temple at Olympia (fig. 3,IIb) can be similarly divided by 2 to reveal a plausible modular ~pecification.~'
Parallel conclusions apply to the Athenians' tem ple at Delos and that of Juno Lacinia at Agrigento. As we have already seen, at Delos Mertens also de
'"he design of this temple was predicated on that ofJuno Lacinia, its predecessor further along the sacred ridge at Agri gento. Mertens (1984a, 108 ff.; 1984b) has pointed out, both buildings share not only stylistic and typological affinities but the same overall width. More to the point, the reprise of the 30 Doric dactyl module arguably lies at the root of the connection. U'hile the plans are almost identical, the later elevation was "improved" byvirtue ofan upward revision of the column height; meanwhile the column distribution~vas adjusted for the sake of a better alignment behveen the columns and the trigl\phs. This adjustment resulted in a further increase in the typical widths of the triglph, now some 2% cm greater than the nominal module. But whereas in the earlier project the flank returned to the nominal ideal rhythm, here the ac tual triglphwidth usedfor the front\vas carried around to the flanks, where it in effect governed the scansion by acting as a slightly largermodule, this time 31 dactyls (appendix 1, no. 8). Apart from the desire for regularity, perhaps another motive
Frieze Spacing, Front Column and Frieze Spacing, Flanks
5% 5% 5 5 5 5
tected the use of a module corresponding to half my triglyph module throughout the building, so not only his elevation (fig. 7) but also his plan can now be reread halving his numbers (fig. 12) ." The axial width is 24 M, the length of the cella is 36 M, the depth of both porches is 4 M and the total axial length 44 M, values which relate simply to the 4 M entablature and the 16 M height of the order. As regards the temple at Agrigento, several scholars converge on a module/foot around 307308 mm,82 this likewise being half my triglyph module (which might either be identified as 30 Doric dactyls or two "common" feet). Once again it is enough to take the plan analyzed in terms of these feet and halve the numbers shown to yield modular values (fig. 13). (It may be noted that the overall cella width at the toichobate, 16 M, is half the overall width of the euthynteria, while the interior width of the cel la, 12% M, is half the axial width of the peristyle." Either exact or approximate, these relationships are not uncommon in other temples.)
A modular reading similarly infused with whole number values and simple fractions is obtained in the case of the Hephaisteion by taking Jos De Waele's plan and multiplying his foot values by 3/8; this is the same as reducing R. De Zwarte's module by 9/10.X4 At Rhamnous the triglyph mod
for this unusual course of action lay in the consequent elonga tion of the later temple. Emulation through mimesis often involved just such a combination of identical and enlarged dimensions, (see M'ilson Jones 1999; 2000b, 76,7980, ch. 8). In addition, the architect of the Temple of Concord may have been attracted by achieving a stylobate length equal to 64 of the original 30 dactyl modules.
"Riemann 1951. Meanwhile, Grunauer (1981,273) advo cates the use ofa module of 421 mm, this being approximately equivalent to 2/3 the triglyph module proposed here.
*I Mertens 1984a, 2207. *'DeUraele 1980; Ceretto Castigliano and Savio 1983; Hocker 1986, 1993.
'IThe peristyle is 25 M wide and nominally 60 M long (dis counting corner contraction), the exact length being tailored in favor of a stylobate ratio of 9/4. '"e Zwarte 1996; De WTaele 1998.
Fig. 11. Socalled Temple ofJuno Lacinia, Agrigento, detail of frieze showing the variation in size of triglyphs and metopes. (Mertens 1984a, Abb. 48)
ule corresponds to 6/5 of the foot unit sustained by Heiner Knell, revealing an approximate double square plan, 30 x 60 M at the euthynteria (fig. 10) ."
At Segesta the plan rectangles of both the eu thynteria and the peristyle fall out as whole num ber modular expressions. The former measures 70 M long x 30 M wide (admirably suiting the 7:3 ratio identified by Mertens) while the latter measures 64 x 24 M. It is true that these ideal lengths were executed with a substantial error (18 cm or one third of a percentage point) by the usual standards of accuracy encountered in this study;'Qerhaps this has to do with modifying the theoretical modu lar values for the sake of round numbers of feet. By this token the 64 M or 1702/3 ft length of the peri style would have become 170 feet."
Aside from individual examples, it is also inter esting to consider the patterns that emerge in the light of comparative analyses. In his extensive study dedicated to the problem of laying out temple sty lobates, Coulton demonstrated how the rule of thumb based on column numbers came in the clas sical period to be applied more often to the krepi doma or euthynteria. Thus a temple with a n x N
'"ell 1973, 10814. Curiously both the internal length of the cella and the overall length of the naos fail to match exactly 20 and 40 M, dimensions that \vould not only relate as
2:3 to the dimensions of the euthynteria, but also as 3:2 and
3:l to the 13% M internal width of the cella. No doubt 20 and 40 M represent the original intentions; I wonder if exactitude was discarded for the sake of a clever floor pattern that used whole slabs ofjust two sizes for all the spaces containedwithin the peristyle. For contrasting analysis, see De M'aele 1991.
*6The theoretical ideal of 64 M or 36.043 m for the interax ial length of the peristyle, measures about 18 cm more than the actual value of 53.866 m, representing a discrepancy of 0.32%.
*'If the target was 170 feet instead (appendix, no. lo), the reduction would explain why the ideal bay of 5 M or 13% ftwas
peristyle has an overall width to length ratio of n:N. In his coverage of those peripteral buildings that are studied here, he highlighted the ensuing ra tios of 6:15 for the temple at Bassae, 6:14 for the temple at Segesta, 6:13 for the Hephaisteion and the temple at Sounion, and 6:12 for the temple at Rhamno~s.~~
It can hardly be a coincidence that in all but one instance (at Sounion) these significant column number ratios perfectly complement strik ing modular expressions: 30:75 M at Bassae, 30:70 M at Segesta, 30:65 M at Athens, 30:60 M at Rham nous. We may therefore refine Coulton's rule as regards the second half of the fifth century into the formulation: "lay out the overall limits of temple platforms with a number of triglyph modules that in each direction correspond to the number of col umns supported multiplied by 5."XY A forthcoming publication by Gene Waddell comes to parallel con clusions on the basis of Coulton's and supplemen tary data.Y0 There is a key difference with the present interpretation, however, in as much as Waddell believes the triglyph module to be derived from the krepidoma, rather than, as I see it, the other way aro~nd.~'
executed not as 13 ft, 5 dactyls, but 13 ft, 4% dactyls. In the absence ofa similarly solid metrical foundation it is difficult to speculate as to the reason why the flanking bays of the temple at Bassae exceed the ideal 3 M by as much as 3 cm.
"Coulton 1974, table 1.
'Wternatively, it can be encapsulated by the formula OT;W = 3n M, OvL = 3N M.
""iTaddell forthcoming. I am grateful to Gene kt'addell for sight of his manuscript in November 2000.
"In this regard hvo obsen~ations are especially telling. First is the pattern described earlier in the choice of triglvph mod ules equivalent to round numbers like 20,25, or 30 dactyls or simple fraction of feet, for this makes more sense if design started from this premise as opposed to, say, taking a krepido ma/euthynteriawidth based on site dimensions or budgetaiy
Coulton also argued that once the column num

ber ratio rule passed over the stylobate in favor of the krepidoma, the stylobate width itself came to be calculated on the basis of the typical bay width, namely the formula StW = BayW (n + k), where n is the number of bays and k is an arbitrary correction factor, typically either 1/4 or 1/3. If we now couch this formula in modules, then the stylobate width for a hexastyle temple with 5 module bays should equal either 5 x 5% M = 26% M, or alternatively 5 x 5% M = 26% M. This is more or less the same range of stylobate widths encountered in practice for tem ples with 5 M wide bays. The stylobate widths of the temples at Rhamnous, Sounion, Olympia, Delos, Segesta, and Athens are 26%, 26%, 26%, 26%, 26%, and 26% M respectively. So in terms of stylobate widths, the present proposals are in accord with Coulton's analysis, and yet they arguably better ex plain the repeated presence of the half modular value of 26%.%
It would be a mistake, however, to convey too sim plistic an impression. While the plans of individu al Doric temples conform to general patterns, they also display a conflict, tension, or dialogue (the appropriate word varies) between overall measure ments based on proportional schemes and those calculated as the aggregate of their components. Since it was i~npossible almost by definition to get everything to harmonize, ideals had to be sacrificed, sometimes component measurements, sometimes overall ones. A case in point is the temple at Sounion, with its minor departures from an other wise remarkably coherent conception. Heights of 12 M and 16 M for the columns and the order marry well with the 20 hf length of the cella, the 24 M peristyle width, and the 64 hf total length (appen dix, no. 41, and not only do these dimensions cre ate numerous simple interrelations, but the last mentioned corresponds to 100 Doric feet, making the temple a true hekntolr~pedon.There was a price to be paid for achieving this, however, that is to say flank bays 2 dactyls less than the 12.5 dactyl (5 M) ideal," as well as an euthynteria width of 740 dac tyls rather than the more obvious figure of 750 dac
constraints and then dividing it. Second is the superioraccura cy of the predicted dimensions using my dimensionally simple nominal triglyph modules as opposed to values derived from fractions of the krepidoma \\ldth. Waddell makes the point, ho~vever,that the column number ratio rule for the krepido ma seems to have existed before the diffirsion of modular de sign of the type I describe.
')'The popular value of 26% M means that the stylobate\\ldth conveniently measures 2% hl more than the 24 M interaxial width of the peristyle.
"'Ten normal bays of 123 d t 2 corner bays of 115 d + 2
1 1 5 / JN:IOE JN=IOE JEqII
Fig. 12. Modular interpretation of the plan of the socalled Temple of the Athenians at Delos, 1:200. Modular values are sho~vll in bold typeface. (..Uier hlertens 1984a, Abb. 79)
tyls or 30 M.q4At the same time the wish to either reduce the extent of corner contraction or to as sign whole number dactyl dimensions to the col umn spacing seems to have led to a peristyle width of 601 dactyls rather than the ideal 600. The diag nosis of temple plans calls for repeated checks of this kind, and is best addressed in a separate publi cation. The previous examples are sufficient to spec ulate that modular principles may have guided the design of entire temples, inside out and outside in. The number of variations on a theme echoes and amplifies Riemann's insight that the Greek ar chitect "knew how to construct in an elastic man ner his number co~mos.""~
offsets from the peristyle axes to the euthynteria of 70 d = 1230 d t 230 d + 140 d = 1600 d (or 100 ft or 64 M).
"'The offset from the peristyle axes to the euthynteria of 70 d (2% hl) was no doubt derived from the calculation of the length given in the preceding note. Thus the theoretical cal culation of the euthynteriawidth yields an interaxial peristyle width of 24 M or 600 d + offsets to the euthynteria of 70 d = 600 d t 140 d = 740 d.
"Riemann 1051, 19.5 (he had in mind specifically the ar chitect of the Hephaisteion).
reading into doubt. Or perhaps the pattern detect ed in terms of the triglyph width is in this case a reflection of the use of the lower column diameter as a module (this being twice as great). Nonethe less, bearing in mind that Bankel has drawn atten tion to other types of modular corresp~ndences,~~ it seems quite plausible that the designer of this temple experimented with an early formulation of a modular approach to design, the experience of which went on to be exploited by those architects who elaborated the methods described here for later temples.
Relatively few hexastyle temples from the fourth century are well preserved, but positive signs of modular design may be observed at least in those of Athena Pronaia at Delphi and of Zeus at Nemea. As one might expect, the plan organization is com parable to previous examples, with familiar combi nations for the width of euthynteria, stylobate, and peristyle (30, 27, and 24% M respectively at Delphi; 30, 27%, and 25 M at Nemea).loo Equally predict able is a lightening of proportions in elevation that is, an increase in modular values for the col umns coupled with a decrease for the entablature: 13 modules being used for the column height at Delphi and 14 or so at Nemea; in both cases the entablature height excluding the geison shrinks to 3 M.""
The question remains whether the same meth ods were used for other types of building. As anticipated in Part 1, the octastyle Parthenon may con form to analogous principles. Berger's Proportionsrnodul of 858 mm is 12 mm greater than the actual trig lyph width of 846 mm, a discrepancy that, as we have seen, is consistent with the adjustment of the frieze during the detailed phases of design. In other words, the Proportionsmodul is simply the triglyph mod ule. Given the controversy over the original, unexe
"Bankel (1993, esp. 146) identified two types of modules, one based on a denominator of 30 Attic dactyls, the other on a denominator of 11 Attic dactyls. For contrasting analysis see De Zwarte 19941995.
lw'Assumingamoduleof408mmor 20 Doric dactylsat Delphi, 30 M makes 12.240 m (actual value ca. 12.270 m); 27 M makes
11.016 (actual value 11.011 m); 24% M makes 9.996 m (actual value 10.025 m).Assuming a module of 732 mm or 40 Attic dactyls at Nemea, 30 M makes 21.960 m (actual value 21.957 m); 27% M makes 20.130 m (actual value 20.085 m); 25 M makes 18.300 (actual value somewhere between 18.25 and
18.34 m).For measurements, see Michaud 1977; Hill 1966.
'"At Delphi 13 M makes 5.304 m (actualvalue 5.282 m); 3 M makes 1.224 m (actual value 1.218 m).At Nemea 14% M makes 10.329 m (actual value 10.325 m); 3 M makes 2.196 m (actual value 2.184 m). I have not studied the temples ofAth ena Alea at Tegea and of Zeus at Stratos; for metrical analyses, see Bankel 1984a.
cuted, intentions behind the Parthenon's Doric com panion on the Acropolis, the Propylaea,In2 it would be unwise to attempt here a rapid analysis of its plan. Suffice it to observe that a nominal module of 36 Doric dactyls or 40 Attic dactyls may be inferred from the actual triglyph width of 726 mm, and that the heights of the columns fit 8, 12, and 14 such mod ules.lO"
The marble tholos at Delphi (ca. 380370 B.C.) makes a telling counterpoint. As a circular structure, it presents neither the corner problem, nor any dif ferentiation front and flank. We might therefore expect the building to be an unblemished example of modular design, and indeed it is. The starting point was a 20 Doric dactyl (411 mm) wide triglyph. The canonic 5 M column spacing yields 100 dactyl bays (on the face of the frieze), while the circuit of 20 columns generates a total circumference of 100
M. Key linear dimensions include the overall diam eter of 36 M and half of this, 18 M, for the height of the order,In4 while 20 modules was the likely target for both the diameter of the cella and the total height of the facade, krepidoma included."'' The tholos is in effect a veritable manifesto for modular design.
MOTIVATIONS
The explanation for the rise of modular design can be sought at a number of levels, including prac tical advantage^."'^ The new method helped resolve the problem of the Doric facade via schemes that could be scaled to taste (subject to regulating dif ferentially the height of the steps). It enabled solu tions to be codified in an easily transmittable form from architect to architect, from place to place and from generation to generation."" Thus it acted as the key to mimesis and the guarantor of universali tysubject, of course, to variation, whether result ing from a degree of incompleteness in the pub
lo2 See De Waele 1990 for previous interpretations of its design.
IU'The column heights are as follo\vs: Pinakotecca, 5.839 m or 7.93 M; west porch, 8.84m or 12.01 M; eastporch, inc. plinth, 8.850mor 12.02M; central block (Ionic), 10.28 mor 13.97M.
"'Assuming 5 drums per column, as proposed byhandry andBousquet 19401941 (cf. Seiler 1986, abb. 28; Bommelaer 199'7), as opposed to the 4 drums restored by Charbonneaux and Gottlob 19251931.
""Pending a more detailed analysis, I base this hypothesis on my own measurements, supplemented by those of Char bonneaux and Gottlob 19251931; handry and Bousquet 19401941; Seiler 1986, 5671.
''"ace Wesenberg 1994, 96.
""On the question of transmission see Coulton 1983. In my view the modular hypothesis sits well with the broad thrust of his arguments.
lished description or deliberate modification. Mod ular design facilitated the calculation of interrela tionships between different members, and it would have been necessary to specify dimensions in feet and dactyls only at an advanced stage of design. The calculation of corner contraction was doubt less rendered more immediate by being couched in triglyph widths, since this dimension was inher ent in the calculation itself. Modular methods al lowed designers to quickly predict the visual con sequences of any new variation, since comparison with existing buildings w7as SO easy. Given an aware ness of precedent it would have been a simple mat ter to envisage the effect of changing, say, the height of the order from 15 to 15% or 16 modules.
Modular design was not formulaic, however; it did not offer recipes for passive copying. There were options that were more popular than others, to be sure, but the onus was very much on individu al architects to create the appropriate modular or ganism that suited their own reinterpretation of the temple theme. Did particular personalities among them Libon at Olympia, Iktinos at Bassae, and the elusive "Hephaisteion architectmfavor particular types of modular solution? Precisely because of the universality of these proportional and modular schemes (and the likelihood that they were codified in treatises or manuals), they are not much help for the purposes of attribution. To judge by the proportions of their capitals, the Parthenon and the Propylaea might be ascribed to the same hand, yet the sources name Iktinos and Kallikrates for the former and Mnesikles for the latter."'8
Modular design offered theoretical advantages as well. It has been argued that the Doric temple w7as fundamentally modular in character, in as much as it might be interpreted as an assembly of modu lar dedications (columns, triglyphs, metopes, roof tiles, and so on) financed by subs~ription.'~Wore to the point, modular design represented a strate qvfor retrieving mathematical harmony for the Doric
<,
order, for in spite of what Vitruvius called the "faults and embarrassments" associated with the corner problem, the salient dimensions of temples could still be a whole number of modules simply related to one another. Contrary to a popular prejudice, as we have seen, modules and proportions could re

lasMiles1989, 241; Bankel 1993, 145.
lo' Fehr 1996.
"OE.g., ITitr. 9.5.1.
'I' Bommelaer 2000.
''2PreiRhofen 1984; Koenigs 1990, 1213.
"'Vitr. 1.3.2; 3.1.1; 3.1.6; 3.6.7; 6.2.1; 7. pref. 1214. Cf. Pollitt 1974, 1422, 2568; Knell 1985, 304; Gros 1989; zd.
inforce one another. Different architects may have stressed one aspect more than the other, but the ideal was for both to work together, as is especially clear in the temples at Sounion, Delos, Segesta, and of Juno Lacinia at Agrigento. In fact Vitruvius often sho~~s
some difficulty in neatly separating the two concepts.l1° And it seems that the way modules in fifthcenturv practice tended to be selected with proportional harmony in mind also reconciles a per ceived opposition between the design principles of adding the parts to create the whole on the one hand, and subdividing the whole to create the parts on the other."'
The rise of modular design earlv in the fifth cen tury coincides with an increased attention to math ematical harmony, as architects began to master the formal difficulties of Doric design. This is about the time when the Greekswho were the first to conceive of ethics and aesthetics in terms of num ber"2in~ested intellectual energy in design the ory. The concept of symn~etria,the commensurabili ty of number, proportion, shape, and measure, came to the fore as the central principle underlying per fection in art, architecture, and any kind of fabrica tion. It is the most important single element of Greek theory as preserved by Vitruvius, for he used symmetria far more than any other critical term and repeatedly gave it explicit emphasis.""n contradistinction to the uncertain and the relative, metri cal exactitude was held to be a guarantor of the certain and the absolute,"%nd in these terms the modular design of the Doric temple enhanced its objective beauty.
Architects probably learned much from an ex change with sculptors, who were coming to master the lifelike representation of dynamic human pos tures. The aims of sculptors working with statualy parallel those of architects working with the Doric order: in both cases the idea was to reproduce time and again variations of recognizable models with out resorting to ~opying."~
The analyses of some archaic statues reveals principles which have much in common with those documented here: a defi nite modularity; a care to coordinate modular val ues and arithmetical ratios; the selection of appeal ing or convenient numbers for the size of the base module and overall dimensions. The Kuros froin
1990,xi, 5660; Wilson Jones 2000b, ch. 2.
"'I Koenigs 1990, 123.
'"On the importance of mimesis to ancient architects, see Wesenberg 1994, 98. For discussion in the context of the Roman period, see Wilson Jones l993,1999,2000b,esp. 79, 7980, 1236, 156, 174.
Fig. 14. Modular interpretation of the Tenea kuros according to Xhrens ( 19681 971, Abb. 9). Modular valurs are shown in bold typeface, dactyl values in normal typeface. Thr width of each small squarr measures 1 module or 2Y2 dactyls; the width of each large square measures 4 modules or 10 dactyls.
Tenea, for example, seems to have been set out using a module of 2% dactyls, multiples of which determined several critical limits of the statue (fig. 14),while the total height is the same number, 30, as that which fixed the overall width of so many hexastyle temples."' Paradoxically, at this relative ly early date modular methods of the kind de scribed here were not used for temples, while sculp tors abandoned such schemes (on account of their relative rigidity) just at the time when modular de sign came to be taken up in architecture. This cross over may be explained on the one hand because
l1%erger 1990, 15960; cf. Ahrens 19681971.
"The limits of a limb, for example, can be sized as aspecif ic dimension proportioned to other key measurements ~vhile not fitting into a grid of thr kind used for the Tenea kuros. For an appreciation of such dynamics, see Bergrr 1990,160 ff.
l'XVitr. 3.1.1. For a possible connection between Vitrutian Man and the metrological relief from Salamis, see Part 1 (Wil
the sort of modular design practiced by archaic sculptors, inspired by the square grids of the Egyp tian canons, w7as illsuited to the differentiated Doric peristyle. On the other hand, it may well have been classical sculptors' freer conception of the relation between mathematics and form, which showed ar chitects the way to achieving symmetria without being tied to a homogenous, inflexible straitjack et."' Thus we can better grasp the thinking behind Vitrurius's famous parallel between the symmetria of the wellformed body and that of a welldesigned building in Book I11 (a connection explored from another angle in Part 1 of the present study).'I8 The same concept is also explicitly linked with modular design based on triglyphs: "Symmetm'a is a proper agreement between the members of the work itself, and relation between the different parts and the whole general scheme, in accordance with a certain part selected as standard. Thus in the human body there is a kind of symmetrical harmo ny between forearm, foot, palm, finger, and other small parts; so it is with perfect buildings. In the case of temples, symmetria may be calculated from the thickness of a column, from a triglyph, and also
from an embater."""
After the architects of Doric temples perceived the virtues of a modular approach, there could not have been a more appropriate base unit than the triglyph width. The triglyph played a decisive role in the very origins of the Doric order, and undoubtedly carried a potent symbolic charge, even if its nature still eludes consen~us.~"' Over the centuries down to the Roman period some parts of the Doric order changed substantially, yet the triglyph remained essentially the same; it was the true leitmotif of the Doric order. It was inti mately linked to the corner problem and other adjustments related to the formal resolution of the frieze. In effect the new status of the triglyph as the metrical fulcrum of design during the Classi cal period is but the mathematical expression of this architectural reality.
CONCLUSION
The case for modular design may rest: we have the evidence, the motivation, and a witness. The evidence presents itself in the accuracy with which
son Jones 2000a).
""Vitr. 1.2.4, as translated by M.H. Morgan with this au
thor's emendation of "also" instead of "even" on the last line.
For the significance of the term embater, see supra, n. 31.
l'OWeickenmeier 1985. My oun study of this problem is in
prepaixtion.
Doric temples return modular measurements, in the marriage between those modular values and simple proportions, and in the consistent resolu tion of the basic triglyph module in terms of docu mented units of measure. The motivation lies in the desire for universality for method, for harmo ny, and for resolving the problem of the Doric cor ner in the most economical and transmittable fash ion. The witness is Vitruvius, our main ancient au thority, who had at least indirect access to Greek sources. Indeed it would be strange if his account of Doric design did not have some validity despite its theoretical nature; if there might be such a thing as a maxim for interpreting Vitruvius, never is he wholly right, but never is he wholly wrong. Accord ing to the analysis presented here he was right enough about the basic principle; modular design was practiced by Greek architects from the early classical period, and was the core of a procedure that gave birth to many of the finest architectural landmarks of the ancient world.
DEPARTMENT OF ARCHITECTURE .4ND CIVIL
ENGINEERING
UNIVERSITY OF BATH
BATH BA2 7AY
UNITED KINGDOM
M.W.JONES@BATH.AC.UK
Appendix
1. TEMPLE OF ZEUS, OLYMPIA, CA. 470 B.C. The proposed triglyph module is 1,044 mm, equivalent to 16/5 of a Doric foot 326.25 mm long (as well as 2 Egyptian royal cubits and 3 Samian feet). Because this module cannot be expressed in whole numbers of
dactyls, it was probably often necessasy to round off theoretical values to the nearest suitable dactyl. Measure ments are taken from Bohn 1892 (pls. VIIIXVI); Grunauer 1981 gives some slightly different values.
Modular Analysis ofMeasurements
Component Dimensions Triglyph Module Doric Feet Adjusted towhole Dactyls Metric Value Actual Value Difference in cm
itfeasures of ulidth Euthynteria width
Stylobate width
Axial width of front
Typical column spacing
Column diameter
Upper column diameter
Abacus width
Metope width
Triglyph width
measures of height Krepidoma
Column"
Trabeation excluding geison
Height of order exc. geison
Trabeation including geison
Order including geison
Pediment
Total to apex of pediment
.'Grunauer (1981, 273) calculates 10.52 m for the peristyle columns, 10.44 m for those of the pronaos.
Salient Relationships
Typical Triglyph Metope Abacus Trabeation Column Column Component Dimensions Width Width Width Height Spacing Height
Triglyph width 3/2 5/2 4/1 5/1 10/1
Metope width 5/3 8/3 10/3 20/3
Abacus width 8/5 2/1 4/ 1
Trabeation height 5/4 5/2
Typical column spacing 2/ 1
2. HEPHAISTEION, ATHENS, CA. 450 B.C.
The proposed triglyph module is 514 mm, which might be either 25 dactyls of a Doric foot of 329 mm, or 1% feet (28 dactyls) of an Attic foot of 293.7 mm, the latter being more conveniently divisible into hal\es, quar ters, and eighths (cf. Riemann 1951, 306 n. 40; 1960, esp. 188). Measurements are taken from Koch 1953; see also Dinsmoor 1941; Riemann 1960; hell 1973; De Zwarte 1996; De Waele 1998.
A\lodular Analysis of,\leasurements
Triglyph Metric Actual Difference Component Dimensions Module Value l7a1ue in cm
Measures of width
Euthynteria width Stylobate width Axial width of peristyle Typical column spacing Corner colum spacing Typical stylobate block Width of abacus Lower column diameter Depth of architrave, initially? Upper column diameter Metope width Width of wall blocks Triglyph width External width of cella, initially Internal width of cella, initially
,\leasurer of hezght
Krepidoma, initially? Column Trabeation excluding geison Trabeation including geison Order including geison Facade excluding pediment Pediment Total to apex of pediment Wall blocks Capitals
"The extra~vith respect to the ideal value may be attributed to the addition of a dactyl to the height of the topnlost step (vertical edge of stylobate) as compared to the steps below.
Sali~nt Relationships
Component Dimensions Triglyph Width Capital Height Metope Width Upper Column Diameter Lower Column Diameter Abacus Width
Triglyph width Capital height  1/1
Metope width  
Upper column diameter  
Lower column diameter  
3. TEMP1.E OF APOLLO, BASSAE, C4. 430 B.C.
The proposed triglyph module is 529 mm, a unit which might possibly be 9/5 Attic feet of 293.9 mm. Measurements are taken from Cooper et al. 19921996.
Triglyph Metric Actual Difference Component Dimensions Module Value Value in cm
,l.lensures of width
Euthynteria width 16.134
Width at bottom step 15.874
Stylobate width 14.547
Axial width of front 13.231
Typical column spacing (front) 2.725
Lower column diameter 1.137
Upper column diameter 0.927
Width of abacus 1.1701.230
Width of metope (flanks) 0.802
Width of triglyph 0.533
Depth of architrave beam 1.0101.070
Internal length of cella ca. 17.000
External width of cella ca. 8.470
Internal width of cella (measured
between opposing antae) ca. 6.620
il4easures of height
Stylobate
Column
Trabeation including geison
Order including geison
Total height excluding kyma, initially?
Total height excluding kyma, actual
Capital height
Geison
Measures of length
Length at bottom step 7 5 39.675
Axial length of peristyle 7 0 37.030
Typical column spacing (flank) 5 2.645
Salient Relationships
Upper Lower Triglyph Capital Metope Column Column Abacus Component Dimensions Width Height Width Diameter Diameter Width
Triglyph width 1/1 3/2 7/4 17/8 9/4 Capital height 3/2 7/4 17/8 9/4Metope width 7/6 17/ 12 3/2Upper column diameter 17/14 9/7 Lower column diameter 18/17
4. TEMPLL OF POSLIDON, SOUNION, (;A. 435 B.c.?
The proposed triglyph module is 512.5 mm, equivalent to 25 dactyls of a Doric foot 328 mm long. Measure ments are taken from Plommer 1950 and Knell 1973; cf. Blouet et al. 1838.
iWodular Analysis of l\.feasurem~nts
Triglyph Doric Adjusted Metric Actual Difference
Component Dimensions Module Dactyls Dimension Value Value in cm
Measur~s of width
Euthynteria width
Stylobate width
Axial width of peristyle
Typical column spacing
Corner column spacing
Abacus width
Lower column diameter
Cpper column diameter
Metope width
Triglyph width
Measur~s of height
Stylobate (initially 2 M?) 2%0
Column 12
Trabeation up to geison 3%
Order excluding geison 15%
Trabeation including geison 4
Order including geison 16
Pediment excluding kyma
(initially 3 M?) 2Y10! Total excluding kyma 2 I? Capital 1 Geison %
Measzr res of length
Euthvnteria length 64 1600 32.800
Internal length of cella 20 500 10.250
Salient Rela fionshibs
Cpper Lower Trigl~ph Capital Metope Column Column Abacus Component Dimensions Width Height Width Diameter Diameter Width

Triglyph width 1/13/2 3/2 2/ 1 9/4 Capital height 3/2 3/2 2/1 9/4Metope width 1/1 4/3 3/2Upper column diameter 4/3 3/2Lo~\er column diameter 9/8
The proposed triglyph module is 366.25 mm, equivalent to either 20 dactyls of an Attic foot 293 mm long, or 18 dactyls of a Doric foot 325.6 mm long. Measurements are taken from Courby 1931; cf. Mertens 1984a, 2207. The following table assumes an Attic foot.
Modular Anclljszs of Measurements
Component Dimensions Triglyph Module Attic Dactyls Ad,justed Dimension Metric Value Actual Value Difference
in cm
Mrasures of width Width at bottom step
Stylobate width
Axial width of peristyle
Typical column spacing
Corner column spacing
Abacus width
Lower column diameter
(initially 2%?)
Upper column diameter
Metope width
Triglyph width
Width of soffit of architrave
121msurrs of hright Krepidoma
Column (alternatively 12% M)
Trabeation excluding geison
Order excluding geison
Trabeation including geison
Order including geison
Pediment
Total (initially 24 M?)
Capital
Geison
ilfeasures of length
Length at bottom step
Stylobate length
Axial length of peristyle
External length of cella
Axial depth of porticoes
"The excess height of the orderwith respect to the ideal value of 16M might be attributable to the (unusual) presence of a k!ma
bed molding benveen the frieze and the geison, if not a slight overestimate of the column height by Courby.
Salirnf Rrlationshzps
Upper Lower Triglyph Capital Metope Column Column Abacus Component Dimensions Width Height Width Diameter Diameter Width
Triglyph width 1/1 3/2 7/4 =9/4 19/8
Capital height 3/2 7/4 =9/4 19/8
Metope width 7/6 =3/2 19/12
Upper column diameter =9/7 19/14
Lower column diameter 19/18
The proposed triglyph module is 381 mm, equivalent to 1% Doric feet of 326.5 mm long. Measurements are taken from Knell 1973, 10814 and Miles 1989.
Modular Analysis of lZleasurements
Triglyph Doric Metric Actual Actual Component Dimensions Module Feet Value Value, Knell Value, Miles
lZleasures of wzdth
Euthynteria width
Stylobate width
Axial width of peristyle
Typical column spacing, front
Corner column spacing
Corner column spacing, adjusted
Abacus width
Abacus width, rounded off
Lower column diameter
Upper column diameter
Metope width
Triglyph width
Triglyph width, rounded off
Cella width
Internal width of cella
iMeasures of height
Krepidoma 2%
Column (initially 1 I?) 10%
Trabeation up to geison 3
Order excluding geison 13%
Trabeation including kyma 4
Trabeation inc. kyma, rounded off 
Order inc. kyma (initially 15?) 14%
Total to top of pediment 20
Total to top of pediment,
rounded off 
Capital %
Geison and kyma 1
iMeasures of length
Euthynteria length 60
Axial length of peristyle 54
Cella length initially 40?
Cella length adjusted 
Typical column spacing, flank 5
Salzent Relationshzps
Upper Lower Triglyph Capital Metope Column Column Abacus Component Dimensions Width Height Width Diameter Diameter Width
Triglyph width 5/6 3/2 3/2 15/8 2/ 1
Capital height 9/5 9/5 9/4 5/3Metope width 1/ 1 5/4 4/3Upper column diameter 
5/4 4/3
Lower column diameter 16/15
7. TEMPLE "OF JUNOLACINIA," AGRIGENTO, CA. 455 B.C.
The proposed triglyph module is 616.5 mm, equivalent to 30 dactyls of a Doric foot 328.8 mm long. Measurements are taken from Mertens 1984a.
Component Dimensions
~Zleasures of width
Euthynteria width Stylobate width Axial width of front Spacing of intermediate bay Abacus width Depth of architrave, beam Lower column diameter Upper column diameter Metope width Triglyph width Cella width, toichobate Internal width of cella
~Zleasures of height
Stylobate Column Trabeation up to geison Order excluding geison Facade up to geison Facade including geison Capital Geison (cf. Temple of
Concord)
measures of length
Stylobate length = 9/4 SW Axial length of peristyle Cella length, walls Interior length of cella Typical column spacing Triglyph width
Salient Relationships
Component Dimensions
Triglyph width
Capital height
Metope width
Upper column diameter
Lower column diameter
Triglyph Doric Adjusted Metric Actual Difference Module Dactyls Dimension Value Value in cm
61%
59%
4 5
2 4
5
1
Upper Lower Triglyph Capital Metope Column Column Abacus Width Height Width Diameter Diameter Width
7/5 3/2 7/4 9/4 14/5 15/14 5/4 45/28 2/1 7/6 3/2 28/15 9/7 56/35 56/45
8. TEMPLE "OF CONCORD," AGRIGENTO, CA. 43; B.C.
The proposed triglyph module is 616 mm, equivalent to 30 dactyls of a Doric foot 328.5 mm long. Measure ments are taken from Mertens 1984a, 108.
Triglyph Doric Adjusted Metric Actual Difference
Component Dimensions Module Dactyls Dimension Value Value in cm
~Zleasures of width
Euthynteria width
Stylobate width
Stylobate width, based
on SL x 3/7
Axial width of peristyle
Typical column spacing
Corner column spacing
Abacus width
Lower column diameter
Upper column diameter
Metope width
Triglyph width
~Zleasures of height
Stylobate Column 3% lo'/s
Trabeation up to geison 35/8
Order excluding geison 14%
Order including geison 15%
Facade excluding pediment 18%
Pediment 3%
Total excluding terracotta 2 2
Capital 1%
Geison block 1
~Zleasures of length
Stylobate length 64 Axial length of peristyle 6 1% Typical column spacing 5l/5
Alternatively, several measurements of length relate better to a module of 638 mm (this being closer to the average actual triglyph width of ca. 641 mm):
~ZlodularAnalysis oflZleasurements
Triglyph Doric Adjusted Metric Actual Difference Component Dimensions Module Dactyls Dimension Value Value in cm
~Zleasures of length
Typical column spacing 5
Column diameter (9/4 M) 2
Column 10%
Trabeation up to geison 3%
Order excluding geison 14%
Metope width 1
Cella length to walls 45%
9. TEMPLE "OF THE DIOSCURI," AGRIGENTO, CA. 420 B.C.
The proposed triglyph module is 512.4 mm, equivalent to 25 dactyls of a Doric foot 327.9 mm long. Measurements are taken from Mertens 1984a, 117.
Modular Analjsis 0f~2leasurements
Triglyph Doric Adjusted Metric Actual Difference
Component Dimensions Module Dactyls Dimension Value Value in cm
hfeasures of width
Euthynteria width
Stylobate width
Axial width of front
Spacing of typical bay
Abacus width
Depth of architrave, beam
Lower column diameter
Upper column diameter
Metope width
Triglyph width
~Zleasuresof height
Column 11Y5
Trabeation excluding geison 33/5
Order excluding geison 15
Geison block l?
Order including geison 16?
Capital 1%
 
Salient Relationships
Upper Lower Triglyph Capital Metope Column Column Abacus Component Dimensions Width Height Width Diameter Diameter Width
Triglyph width 4/3
Capital height 
Metope width 
Upper column diameter 
Lower column diameter 
710 MARK LYILSON JONES [AJA 105
10. UNFINISHED TEMPLE, SEGESTA, BEFORE 409 B.C.
The proposed triglyph module is 875.7 mm, equivalent to 8/3 Doric feet 328.4 mm long. Measurements
are taken from Mertens 1984a, 39.
iModular Analjszs 0f~2leasurernents
Component Dimensions Triglyph Module Doric Feet Adjusted Dimension Metric Value Actual Value Difference in cm
lZleasures of width Euthynteria width Stylobate width Axial width of front Abacus width Lower column diameter Upper column diameter Metope width Triglyph width Depth of architrave beam
iMeasures of height Stylobate Column Trabeation excluding geison Order excluding geison Order including geison Facade (order t stylobate) Pediment Total including stylobate Total including kyma Geison Capital 22x2 102/3 3% 14 1 4% 164/5 ~3~/5 20% 2l? % 1%
iMeasures of length Euthynteria length, initially? 70 Euthynteria length, adjusted? 69% Axial length, initially? 64 Axial length, adjusted? 63% Typical column spacing 5 186 170 13%
Salient Relationships
Component Dimensions Triglyph Width Capital Height Metope Width Upper Column Diameter Lower Column Diameter Abacus Width
Triglyph width Capital height Metope width Upper column dimension Lower column dimension  9/8  3/2 4/ 3  7/4 14/9 7/6  9/4 2/ 1 3/2 9/7  21/8 7/3 7/4 3/2 7/6
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