DIMENSIONING AT THE EPICLASSIC SITE OF CACAXTLA, TLAXCALA, MEXICO: AN EXPRESSION OF PAN-MESOAMERICAN COMPLEX THINKING Author(s): Geneviève Lucet Source: Latin American Antiquity , June 2015, Vol. 26, No. 2 (June 2015), pp. 242-259 Published by: Cambridge University Press Stable URL: https://www.jstor.org/stable/43460463 JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at https://about.jstor.org/terms Cambridge University Press is collaborating with JSTOR to digitize, preserve and extend access to Latin American Antiquity This content downloaded from 132.248.9.8 on Sat, 19 Nov 2022 17:50:37 UTC All use subject to https://about.jstor.org/terms DIMENSIONING AT THE EPICLASSIC SITE OF CACAXTLA, TLAXCALA, MEXICO: AN EXPRESSION OF PAN -MESO AMERICAN COMPLEX THINKING Geneviève Lucet This article discusses the measurement system used at Cacaxtla, Tlaxcala, Mexico. It addresses the ideological concepts this system may have expressed, its relationship to other systems used in Mesoamerica, and its implications for evaluating the hypothesis of a Maya presence at Cacaxtla during the Epiclassic. Measurements used at Cacaxtla combine the practical needs of builders with symbolic expression reflected in architecture. Two moduli served as the basis for the dimensioning: the unit of .488 m and its triple, 1.465 m. This measurement was in turn multiplied by 3, 4, 9, and 12 to obtain the lengths of the main spaces, which served as the basis for the dimensioning system used during different phases of construction. In specific places, three anthropometric measures were used. Additionally, the spatial distribution of pillars according to their sizes confirms the coexistence of two zones within the site that express a duality also present in mural paintings. The moduli and units used at Cacaxtla agree to a considerable degree with those identified for the Maya area and, in some cases, with Teotihuacan and the Nahua culture. I hypothesize that this system was shared by several Mesoamerican cultures and lasted from the Classic to the Postclassic periods. Este artículo discute el sistema de medición utilizado en la arquitectura de Cacaxtla, cómo se relaciona con el contexto meso- americano, la información que proporciona sobre la presencia de grupos mayas en el altiplano durante el periodo epiclásico, el pensamiento expresado a través de las medidas de los edificios y la lógica seguida por los constructores para aplicarlas. Las mediciones utilizadas en el sitio epiclásico de Cacaxtla combinan la forma de trabajar de los constructores en el terreno con expresiones simbólicas que se plasman en la arquitectura. Dos módulos constructivos fueron empleados para el dimensionamiento: .488 my su triple, 1 .465 m, el cual a su vez fue multiplicado por 3,4,9 y 12 para definir la longitud de los espacios principales. Estos sirvieron para definir el sistema de medidas de las estructuras utilizado durante las distintas fases constructivas del sitio. Tres medidas antropométricas fueron empleadas en lugares específicos. Además, la distribución espacial de los pilares de acuerdo a sus tamaños confirma la coexistencia de dos zonas dentro del sitio, lo que ratifica una dualidad también presente en la pintura mural. Los módulos y unidades empleados en Cacaxtla tienen muchas coincidencias con los que han sido identificados en el área maya y algunas con Teotihuacán y la cultura Nahua, por lo tanto, este sistema fue compartido entre varias culturas mesoamericanas y perduró desde el clásico hasta el postclásico. are innate to humans independently of their cultural origins (Morley 2010; Morley and Renfrew The use nents dimensioning useof of involves aa system system two of of measurement ofrelated measurement architectural elements: with compo- with pat- the pat2010; Urton 2010). Nevertheless, being based on terns or units and the logic followed by units the that vary from one person to another, such builders for laying out walls, porticos, and patios references generate inaccurate systems- hence that define buildings and open spaces. Both the are need for setting fixed standards. The use of nents involves two related elements: the cultural legacies, acquired knowledge transmitted standardized building measurements is also a tool within social groups and inherited across generathat facilitates the organization of work and com- tions, and thus can serve as indicators of populamunication between the various groups involved tion origins and affiliations. in the process (for instance, those building walls Measuring units and quantifying schemata and the suppliers of timber for roofing). Using a based on anatomical references are practices that measurement unit known to all- referring to it Geneviève Lucet ■ Instituto de Investigaciones Estéticas, Universidad Nacional Autónoma de México, Mexico City, 04510, Mexico (genevieve.lucet@gmail.com) Latin American Antiquity 26(2), 2015, pp. 242-259 Copyright © 2015 by the Society for American Archaeology DOI: 10.7183/1045-6635.26.2.242 242 This content downloaded from 132.248.9.8 on Sat, 19 Nov 2022 17:50:37 UTC All use subject to https://about.jstor.org/terms Lucet] DIMENSIONING AT THE EPICLASSIC SITE OF CACAXTLA, TLAXCALA, MEXICO 243 Cacaxtla and its multiples- ensures the accuracy indispensable for all building projects (Lee 1996). Cacaxtladeis located at a distance of 100 km from Units for measuring distances may differ Teotihuacan, pending on the object measured. A measurement and some of its substructures indicate theainfluence of the metropolis. Nonetheless, its system may also be defined on the basis of combination of different units of different sizes with period of splendor was around A.D. 700-800 and settlement was abandoned during the tenth or without an arithmetic relationship the between (Garcia 1978; Garcia et al. 1995; Molina them. Likewise, when analyzing ancient century buildings 1977). The site belongs to the Epiclassic, a period to identify the dimensioning units used, a degree characterized by complex political, social, ecoof uncertainty and inaccuracy must be taken into account. Several elements come into play that and addcultural movements resulting from the nomic, variations between the ideal initial measurements abandonment of Teotihuacan, the great city of the Classic period. Far from the altiplano , Maya cities and those recorded in the present. These may in- clude: (1) approximations made during construc-survived several centuries more before disappeartion when an anthropometric measure based oning toward the end of the millennium. Cacaxtla is parts of the body was used; (2) lack of precisiondistinguished by its extensive murals that cover during the building process (a tolerance of a fewseveral walls, a long batter or talud , a bench, and two pillars inside a room. centimeters is generally expected, and even more so in preindustrial societies); (3) subsidence and The mural paintings were carefully protected when the inhabitants decided to carry out archibuilding deterioration caused by natural processes or human activities. Furthermore, (4) current mea-tectural modifications resulting in their burial surements, even when taken with laser systems, (Brittenham 2009). They have been an invaluable add one final source of possible error. source of information for studying the history of The first of these factors is built into the systemthe site. Extensive debates have arisen regarding and will be multiplied proportionally in relationtheir unmistakable similarities- but also considto the overall dimensions involved. If the modulus erable differences- with the mural paintings of used is small, the multiplying effect upon repeti- the lowland Maya during the same era. Some aution is greater than if a larger modulus is involved. thors think that the artists came from the Maya Hence, the larger the modulus identified, the lesser area (Graulich 1988; McVicker 1985), while oth- the margin of error. The remaining factors (2-4) ers (Brittenham 2009, 2011) believe they were from the altiplano and would have learned their are related to the measurement taken as a whole trade in the Maya area and hence developed skills and represent an absolute error that in most cases that enabled them to set forth a local discourse does not exceed a couple of centimeters. using Maya styles and techniques. Most scholars The manner of counting also exerts an influrecognize that the rulers who commissioned the ence on measurements. In a decimal system, mul- work were from the central highlands of Mexico; tiples of 10 or 5 are preferred, whereas Mesoamer- ican systems were vigesimal. Divisions becomea more marginal hypothesis is that a Maya group could have conquered Cacaxtla and established a unwieldy when having to handle non-integer reTeotihuacan-Maya shared government (Graulich sults, which are not intuitive; in contrast, this prob- 1988,2001). lem disappears if a tool such as a string is used instead of numerical values: to divide one only If the rulers were local people, their interest in using a Maya style of painting has been interpreted has to fold the string onto itself, so that the mea- as a public declaration of affiliation with the domsurement becomes "a string folded into x equal parts." inant culture of the period and as a way of casting Among Mesoamerican cultures, numbers also may be considered a symbolic representation re- ture of Teotihuacan through the use of an eclectic a veil over their previous affiliation with the cul- lated to worldview. The meanings of the symbolic style of art (Kubier 1978; Nagao 1989). In any essence of constructions would be expressed through the use of specific numbers (Clark 2008, case, the absence of Mayan writing would be explained by the position of the site in a zone in- 2010; Sugiyama 1983, 1993, 2010). habited by speakers of a non-Mayan language This content downloaded from 132.248.9.8 on Sat, 19 Nov 2022 17:50:37 UTC All use subject to https://about.jstor.org/terms 244 LATIN AMERICAN ANTIQUITY [Vol. 26, No. 2, 2015 planned before construction. addition, most (Walling 1982). According to the latter In studies, available evidence indicates a mixture of cultural structures conserve their original lime plaster fin- expressions. The most visible elements are notish, which facilitates taking measurements resystematic indicators of an origin: some could quired in order to know their original dimensions. have been copied, sometimes with a deep knowl- A question of methodology that had to be considered at the outset was to determine whether edge of their meaning and at other times by being reinterpreted with varying degrees of syncretism. one should start by seeking to apply a known sys- New codes of expression may be adopted fortem a of Mesoamerican measurement or by working variety reasons. Pictorial representations, with their empirically on the basis of the measurements found. I opted for the latter approach so as not to high degree of visibility and various expressive bias results with preconceived ideas and not to components- such as style, icons, and forms of rule out the possibility for the existence of a syswriting- are ideal means of conveying a message and so new elements may be imported for political tem that was peculiar to Cacaxtla. purposes. On the other hand, the use of a system ofInitial analyses involved applying statistical calculations to all measurements, but this method measurement in building is anchored to a complex was not useful because it ignored the fact that deand traditional practice that includes planning, degrees of variation between the original design and sign, geometry, and calculation. It is a type of what is currently measured are not invariable for knowledge that is transmitted via practice and man- all categories of architectural elements. In addiifests ancestral cultural heritage. It is part of the way of thinking of the builders, and it may well tion, it was necessary to take into account several prove extremely complicated for them to adapt to other variables in measuring the buildings whether, for instance, the layers of finishing manew systems of measurement.1 A system of measurement in architecture is a cultural good that may terials applied on the core of the structural ele- be regarded as a parameter of identification. ments were taken into account, or just the distances between structural elements. The soluDifferent systems of measurement have been tion for the analysis of data was to group meareported for Teotihuacan and the Maya area. If surements by building type. The first category comparable systems could be attested for other for study was one of the most easily consites, this would offer proof of the existence chosen of cultural connections. At Cacaxtla, such informatrolled. Moreover, it was a category in which the builders might conceivably have been most intertion would provide new parameters for underin the careful application of dimensionsstanding the complex system of relationships ested in namely, the measurements of porticos, the pillars the Mesoamerican Epiclassic, in particular regardforming them, and the spaces separating them. ing Maya presence in the central highlands after the fall of Teotihuacan. The measurements taken were analyzed and compared arithmetically in search of repeating moduli; Methods once such units were identified and verified, they were applied to the remaining building types. The measurements were weighted according to their Architectural composition and style, the arrangement of buildings, and the dimensions of therole sitein the logic of construction and the importance of the object or the space where they were taken. are elements that support the hypothesis that a particular measurement system was used for build- ing Cacaxtla. The monumental core of the site is Prehispanic Dimensioning Systems characterized by the presence of many porticos There are several sources available for the study surrounding plazas and on the edge of the platof measurement systems. Sixteenth-century texts form. This is evidence for the builders having caninserve as a basis for understanding the Nahua sought a regular pattern by using a constant measurement system. The main source is found measurements to establish recurring rhythms (Figin the archaeological sites themselves; however, ure 1). In the same way, the regularity of the buildsome studies have added anthropological and ethings and the proportions of inner and outer space data. indicate that these buildings were thought outnohistorical and This content downloaded from 132.248.9.8 on Sat, 19 Nov 2022 17:50:37 UTC All use subject to https://about.jstor.org/terms Lucet] DIMENSIONING AT THE EPICLASSIC SITE OF CACAXTLA, TLAXCALA, MEXICO 245 Figure 1. Plan and cross sections of the Great Platform of Cacaxtla (Lucet 2013). (1) North Portico; (2) Mo Sunken Patio; (4) Building C; (5) Corridor of the Slope-and-Panels; (6) Building B; (7) Building A; (8) Slope of t (9) Building E; (9a) Superstructure of Building E; (10) Building D; (10a) Superstructure of Building D; (11) Nort (12) Teotihuacan Structure; (13) West Room; (14) Building of the Columns; (15) Hollowed Wall; (16) Venus (16a) Venus Room; (17) South Pyramid; (18) Red Temple; (18a) Red Temple Corridor; (19) The Palace; (19a) the Rhombuses; (19b) Plaza of the Altars; (19c) Portico A; (19d) Portico B; (20) South Portico; (21) Buildin Portico F; (23) Room of the Stairs; (24) West Portico; (25) Plaza of the Eastern Stair. This content downloaded from 132.248.9.8 on Sat, 19 Nov 2022 17:50:37 UTC All use subject to https://about.jstor.org/terms 246 LATIN AMERICAN ANTIQUITY [Vol. 26, No. 2, 2015 Table 1 . Some Aztec Measures According to Various A Length Length Aztec Uniť macpilli "palm of the hand," 1/4 vara .209 .208c orniti yollotli "bone" "heart," .334 1 .23-.334 vara .835 .833 miti "arrow, dart," 1 .5 varas 1 .254 1 .25 cenequeztzalli "stature," height of a man 1.60 1.60d maitl o cemmatl "hand," horizontal braza, 2 varas 1 .672 1 .666 niquizantli Note : All dimensions in m. 'Clark 2008, 2010. bDehouve 2011. ciztetl. dnequetzalli ; the author expresses doubts about its conversion to the metric system. The Nahua measurement system has been ex- and the floor and that would have been divided tensively studied by Victor Castillo (1972) and Marcos Matías Alonso (1984) using information into halves and fifths to obtain smaller measures. found in the narratives of missionaries and their standards were instruments used in various ways More than references to a precise measure, these depending on the object being measured. The use indigenous pupils. The system was built upon multiple anthropometric measures. Understanding of twine has continued until the present time, as its operation and establishing its metric equivashown by research carried out in the Maya area lencies is a complex undertaking because there (Powell 2010). are contradictions among the sources. At times, Exact measurement, recording, and quantificait is difficult to tell when the authors refer to Pre- tion were of concern to the Aztecs, as shown in hispanic or to Spanish units, since some documents such as the Codex Vergara and the Santa measures- such as the arm-span, the rod, or the María Asuncion Codex, dated to around AX). 1539foot- occur in both cultures. 1543, where information on plots of land is acConversions to the metric system may varycompanied by ground features and a census of the greatly (Table 1). For instance, according to Bar-families and owners in the Texcoco zone of the bara Williams and Maria del Carmen Jorge y JorgeValley of Mexico. These documents have served (2008) the "bone" measured .5 m, whereas foras a source for understanding how the Aztecs comDehouve (201 1) it has a length that varied betweenputed the surface of plots of land with remarkable .23 and .334 m. Dehouve relates several measures accuracy (Jorge et al. 2011; Williams and Jorge y to the palm and comments that the yollotli (rod), Jorge 2008; Williams and Harvey 1988). measuring approximately .83 m, seems to have Bruce Drewitt (1987) finds a measurement sysbeen a modular base. In the measurements for the tem with a modulus of .805 m as the basis of the Tlaltecuhtli stone, López Lujan reports that the urban layout at Teotihuacan, according to inforsculpture measures 4.17 m x 3.62 m, i.e., 5 yollotli mation obtained from the survey of the city (Mil- or 15.01 tlaxcitamachihualoni (measuring oneIon 1973; Milion et al. 1973). He also shows the third of a yollotli) by 4 yollotli plus 1 .03 tlaxcita- use of multiples of this unit in correspondence machihualoni or 13.03 tlaxcitamachihualoni (López 2010). with the calendar system. Saburo Sugiyama (1983, 1993, 2010) extends that study and proposes a There were also instruments such as the octá- measurement unit based on a modulus of .83 m catl, a measuring rod; the cemmécatl, a length of that is equal to the Nahua yollotli and the Spanish vara. In addition, he shows that the units used for twine or string made from braided fiber; and the tlalmécatl, a string for ground measurements the layouts of the great pyramids and complexes (Castillo 1972). Francisco Guerra (1960) mentionscorrespond to calendric quantities, so that the ura stick called tlacaxilantli that would have correban space is related to cycles of the Sun, Venus, and the Moon, as well as the 260-day ritual calsponded to the distance between the human navel This content downloaded from 132.248.9.8 on Sat, 19 Nov 2022 17:50:37 UTC All use subject to https://about.jstor.org/terms Lucet] DIMENSIONING AT THE EPICLASSIC SITE OF CACAXTLA, TLAXCALA, MEXICO 247 endar. This is evidence for precise, large-scale and no longer adheres to measurements. Geometry has served as the basis for the complanning of the city with a complex vision of of paintings, bas-relief, or architecture space-time relationships. Following the position same line of work, a value close to this modulus and(Chanfon a world- 1979; Clancy 1994; Harrison 1994; Vinette 1986). The square was a recurring form view representation with the use of significant and expressed the conception of the universe with numbers from a symbolic point of view have been four points oriented along the cardinal directions, sought in the architecture of Teotihuacan (Hasel- bach 2003). in addition to the vertical axis that unites the var- In the Maya zone, Patricia O'Brien and Hanne Christiansen (1986) have studied ten Puuc-style 2001). This spatial perception was part of the con- ious levels of the universe (López and López structures at the sites of Chichen Itza, Uxmal, and ceptual scheme that became generalized in the Kabah, dated to A.D. 750-1000. Following careful measurement and rigorous mathematical study, they identify a double measurement system and validate it with ethnohistorical data. They name Mesoamerican world, especially for ritual spaces. Thus, the plazas and principal interior spaces of Cacaxtla have the proportions of a square or a double square (Lucet 1999, 2013). In architectural composition, the geometric properties of figures the principal unit of 1.47 m the zapal , divided into 16 kab of 9 xóot each or 9 oc of 16 xóot each. served to arrange buildings in a hierarchy, taking Thus, there were 144 xóot in each zapal , and a advantage of axes of symmetry and reflecting a xóot is almost exactly equivalent to 1 cm. Usingcomplex, conscious handling of the spatial qualiethnohistorical data, the authors identify a systemties of shapes. of length measurements related to the foot, the In spite of its close connection to architectural hand, and other body measurements, so that 9 dimensioning, the manner of applying measurexóot could be one hand, 16 a foot (without the ments on the ground has been little studied. Questoes), and 1.47 m the distance along outstretchedtions remain regarding the elements considered arms. In addition, ancient Mayan texts refer toand the order followed in measuring out structures several numbers used in measurements: 3, 4, 9, and plazas, whether measurements were taken and 12 appear in the Chilam Balam ofChumayel ,from the inside or outside of a building, or whether 4 in the Popol Vuh , while 9 was a sacred numberthe rhythm of a façade was paramount and took related to the training of artisans according to precedence over the dimensions of the rooms. Data recorded by Sugiyama (1993, 2010) at TeotiA modulus of 70 cm (Roy all 2010) is reported huacan correspond to the edges of large structures from Paquimé, a site outside Mesoamerica inand theto the axis of symmetry of the Avenue of the Landa's Relación de las cosas de Yucatán. north of Mexico. Dead. O'Brien and Christiansen (1986) measure the exteriors and interiors of buildings without Layout and Geometry distinction, as well as doorways and façade stones. According to Powell (2010), a layout is effected tothe define the inside or outside, and additional conThe dimensions of buildings are in most cases result of the method and instruments used to lay ensure that diagonals have equal lengths. trols them out. Thus, the use of a string as a ground layout tool may lead to solutions that do not al- Data Selection and Collection ways correspond to the base units of measurement. For traditional dwellings, present-day Maya The peo-assignment of architectural measurements ple start their layout with a generally square base, follows a process in which the main elements take and the string is folded in two to draw the circular precedence over secondary elements, which must to relative or residual measurements of ends (Powell 2010). There are variants to thisconform sys- tem, which result from moving the center ofthe theformer. What are the elements that are likely arc being traced, thus varying the final proportions to provide useful information on the system of used at Cacaxtla? of the building. While the initial form may measurements have been based on measurements and geometry, the The importance of each building or room final result is the consequence of tracing a layout within the complex is one criterion. For instance, This content downloaded from 132.248.9.8 on Sat, 19 Nov 2022 17:50:37 UTC All use subject to https://about.jstor.org/terms 248 LATIN AMERICAN ANTIQUITY [Vol. 26, No. 2, 2015 ness of between 5 and 8 cm, and covering it with a space used for religious functions transcends lime mortar 1 to 2 cm and a fine layer of the status of an ordinary building. It thick is the habitat white plaster (Magaloni et al. it 2013). This techof a deity or the place for rituals, and is very likely that this will be reflected its location, dinique results inin a significant difference between measurements taken before and after the applicamensions, and geometry, exhibiting the builders' tion ofhierarchical covering layers and is aorder, variable that the needs ideal of perfection. In this be considered. elements surrounding a tomain plaza- namely, the order to achieve representativespecial data of the building's façades- mayIn have received original measurements, only references to comattention in following aesthetic standards. ponents with original finishes in good condition, Builders would have given special attention to fewlimited deformations,by were the considered. the width of building, aspresenting this is reStructures weresupport measured from points the wall sistance of the materials that theon roof. surfaces because in most cases the cornerlength arrises They knew, at least empirically, that the were damaged or severely rounded. beam Measurement that should not be exceeded for specific section. For the same reason, the measurements points were chosen close to the floor to avoid vertical are deformation in the structures. For each disof lintels above openings controlled. Measurements collected at Cacaxtla were clastance, care was taken to record the data from the sified into simple architectural categories: thesame position of the total station to prevent an inheight of pillars, the space between them, thecrease in measurement errors due to translation of the coordinate system. A laser scanner was used space between central pillars when different from for Building B . To define the constructive modulus the lateral spaces, the width of doorways, the inof Cacaxtla, the data originate exclusively from terior length and width of rooms, the measurethe laser record and, to corroborate the modulus ments of open spaces, and those of staircases, in- found, some distances measured with a tape meacluding their balustrades. With the exception of sure were included. Building B , structures at Cacaxtla are not isolated and do not have a well-defined exterior dimension. In the case of long bays that were subdivided Data Analysis into rooms, only the initial lengths of the spaces Recurrent Measurements in Pillars were included in order not to artificially multiply and Spaces between Pillars a measurement that actually corresponds to a sinThe width measurements of pillars (P) were found gle structure. Where dimensions of all four sides of a room were available, those correspondingto tocluster into two ranges (Table 2): (1) 1.1751.226 m Qi = 1.199 m; a= .014 m; 30 pillars in opposite sides were kept without averaging in or- 11 porticos) and (2) 1.437-1.505 m (pi = 1.467 der to deal directly with the initial measurement m; a = .016 m; 28 pillars in 10 porticos). The disand not a mathematically derived quantity. tances between pillars (I) clustered into three Finally, the structural transformations of the ranges. The first two roughly correspond to the site during the centuries it was inhabited were taken into account (Lucet 1999, 2007, 2013). ranges of P identified above: (1) 1.171-1.211 m Mesoamerican cultures tended to renew their (9 spaces from 5 porticos) and (2) 1.431 - 1.494 m (12 spaces from 5 porticos). The largest number buildings regularly so that dimensions or placeof I values, however, cluster in the range 1.895ments of spaces may have depended on the exis2.02 m (jí = 1.953 m; a - .03; 35 spaces from 10 tence of previous walls or buildings. When the system of construction involvesporticos). suThese ranges of P and I were taken together to perimposing several material layers, it is pertinent to ask whether the measurement should include compute their representative means. The values obtained- 1.198 m, 1.465 m, and 1.953 mthe entire resulting thickness or only the structural represent 44 percent, 40 percent and 0 percent of core. At Cacaxtla, the system consisted of erecting measurements, and 20 percent, 20 percent, and a structural core with tepetate stone and earth, P ap40 percent of I measurements, respectively. In the plying a layer of earth, sand, and lime to a thick- This content downloaded from 132.248.9.8 on Sat, 19 Nov 2022 17:50:37 UTC All use subject to https://about.jstor.org/terms Lucet] DIMENSIONING AT THE EPICLASSIC SITE OF CACAXTLA, TLAXCALA, MEXICO 249 Table 3. Measurements of Widest Central Spaces (C). Table 2. Summary of Measurement Ranges of Pillars (P) and Spaces between Them (I). Building P PI Portico .827-.842 P2 P3 1 .93-1.0 2 2 1.146-1.152 4 1 1 P4 1.175-1.226 11 30 P5 1.437-1.505 10 28 11 1.171-1.211 1.431-1.494 5 5 9 12 13 1.600-1.605 1 3 14 1.747-1.798 1 2 15 1.895-2.02 10 35 16 2.041-2.078 2 5 17 2.114-2.176 1 5 Pandi PI P2 P3 .835 .962 1.149 1.915 4 Building -.037 E Note : All d between cent #M = numbe sured I 12 A Building C 2.876 6 -.052 Building A 2.888 6 -.040 value a Validation Other Measurements To verify whether M is effectively an important modulus at Cacaxtla, its relationship with other measurements at the site was sought. Two porticos have pillar widths P in the range .93-1 m, close to twice the value of M (.976). The central spaces (C) of the porticos of four buildings measure .835 .011 .964 1.149 P4&I1 1.198 1.198 P5&I2 1.464 1.465 .03 .004 .014 .017 slightly less than 4,6, and 7 times Af, with a difference between 3 and 5.2 cm (Table 3). Of the 21 doorways (D) sampled (Table 4), 11 correspond to multiples of M with a difference of less than 3 cm, and three more to multiples of half M . Of the 13 1.604 1.603 .003 14 1.773 1.773 .036 9 measurable staircases (Table 5), five exhibit an 15 1.953 .03 application of M and one more seems to use a 16 2.056 1.953 2.057 .014 multiple of one-third of M. Of the 45 internal room widths (W), 25 vary less than 5 cm with reNote : # = numb spect to multiples of Af, and eight more vary up number of spac to 7.5 cm. Four of these correspond to seven and measurements. nine times M (Figure 2). In three more cases, half 17 of the modulus was used. Of the 15 bays that exceed the tolerable error following sections these ranges of values are remargin, 14 are multiples of Af once the thickness ferred to by these means. of a wall (57 cm) is added. The only remaining Arithmetic Relationship between Values case is solved when two wall thicknesses are added. Only two porticos have W values close to 1 .198 m, The means of 1 .465 m and 1 .953 m (both minus and they exceed the corresponding values of P, /, one millimeter) exhibit an arithmetic relationship and D by 5 cm. Six bays are within 15 cm of the with a common denominator of .488 cm: 1 .465 m modulus, and 13 are close to 1 .953 m. 1.464/3= 1.952/4 =.488 Exterior spaces also exhibit the modular scheme (Figure 2). The North Plaza followed it Such a simple and precise mathematical relationin its two constructive phases, first when it was at ship between the main dimensions of the pillars the same level as the surrounding buildings and and the spaces separating them indicates the use then when it became a sunken plaza (Lucet 1999, of said denominator as the modulus (A/) for the 2007, 2013). In the Plaza of the Altars, one par- dimensions of architecture at Cacaxtla. These were the only dimensional relationships determined between the values of P and /. ticular 40-modulus measurement stands out. The distance between Building F and Portico F, between the South Pyramid and the porticos surrounding it to the east and north, the length of the This content downloaded from 132.248.9.8 on Sat, 19 Nov 2022 17:50:37 UTC All use subject to https://about.jstor.org/terms 250 LATIN AMERICAN ANTIQUITY [Vol. 26, No. 2, 2015 Table 4. Measurements ofwalls Doorways (D). the of building h and the internal rooms measure 9 M minus 4 and 8 cm, respectively. The doorway is not centered; Building Portico B .860 2 -.116 the walls on either side are 12.174 m and 12.083 Patio of the Rhumbuses, South .887 2 -.089 The Palace, room b .907 2 -.069 m long; that is, the first measurement corresponds to 25 M with an error of only 2.6 cm, and the Building D .950 2 -.026 Venus Complex .950 2 -.026 The Palace, room g .950 2 -.026 Portico B .970 2 other is not modular. In summary, the P, /, and D dimensions correspond to exact modulus multi- -.006 ples, as does W if measured before the application Room of the Stairs .971 2 -.005 of plaster. The inside length of the building should Building F .977 2 .001 The Palace, room fc 1.000 2 .024 be 54 M, but it falls short by 12.7 cm. To place the doorway, an integer modulus multiple was Building D 1.175 2.5 -.045 Building D 1.184 2.5 -.036 used from the inner western corner, and hence the wall on the eastern side is shorter. Venus Room 1 .000 2 .024 Patio of the Rhumboses, East 1.396 3 -.068 Building A 1.410 3 -.054 Building C 1.426 3 -.038 Building E 1.441 3 -.023 Patio of the Rhumbuses, West 1.445 3 -.019 The Palace, eastern portico 1.680 3.5 -.028 Venus Complex 1.920 4 -.032 Building B Note : way; #M Comparison with Known Measurement Systems The three recurring measurements at Cacaxtla (1 .198, 1 .465 and 1 .953 m) are different from an- thropometric measures reported Nahua dimensions in m; Dfor =themeasure All measured Discussion - culture. The shortest differs by 5.6 cm from the number of modules; dif value and miti, = d multiple of arrow, a measure that goes fromM. the elbow to the opposite hand and to which a value of 1 .254 Table 5. m has been assigned (Clark 2008; Dehouve 201 1). of Staircases This difference is too large to take it as a corre- Measurements Building Room of the Stairs .98 2 .004 West Slope 1.435 3 -.029 North Plaza, south stairs 3.27 7 -.146 Sunken Patio S 4.07 8.3 .020 Sunken Patio E 4.76 10 -.120 Sunken Patio W 4.78 10 -.100 Sunken Patio N 6.83 14 -.002 Building E, superstructure 6.87 14 .038 South sured and in two porticos they measure, on average, 2.056 m, which is close to the 2.09 m niquizantli. The first portico is located in an initial stage of the Palace and the others correspond to the North Portico and the buildings surrounding the North Plaza on its eastern and southern sides. They are highly visible places, which leads to the assump- Pyramid Note'. #M - spondence. In one of the porticos, however, the I values coincide with the 1 .60 m cenequeztzalli , All dimensions in m; S = measurement tion that a different pattern based on anthroponumber of modules; dif = difference b metric measures was used occasionally. value and multiple of M. The two inner pillars of the Venus Room are .835 m wide, a measurement that corresponds to the constructional modulusthe that has been reported and one of façades Sunken Patio s in Teotihuacan and also to the Nahua yollotli the Patio of the Rhombuses correspo (Castillo 1972; Clark 2008, 2010; Dehouve 2011; modularity. The are Drewitt 1987; Sugiyama 1993, 2010). These measurements of 1983, Building an B ( pillars the were originally wider and were part of afram of conceptual large portico with 12 pillars in ranging 1 .183south application of M: from its example lowed in the to 1.21 m in width that bounded western side has six pillars measuring 3 the M and the a great plaza (Lucet 1999, as 2013). are When this arating them areof 4 M wide, the d cated in the north the inner en porticowall was dividedand in the middle to build a new space, two pillars were left inside. TheIn builders corner of the façade. spite reduced their width and covered them withtwo artistic rhomboidal deformation, the lon western This content downloaded from 132.248.9.8 on Sat, 19 Nov 2022 17:50:37 UTC All use subject to https://about.jstor.org/terms Lucet] DIMENSIONING AT THE EPICLASSIC SITE OF CACAXTLA, TLAXCALA, MEXICO 251 Figure 2. Summary of modular measurements in rooms and open spaces. Light gray: multiple of M; dark gray: m of 3 times M. This content downloaded from 132.248.9.8 on Sat, 19 Nov 2022 17:50:37 UTC All use subject to https://about.jstor.org/terms 252 LATIN AMERICAN ANTIQUITY [Vol. 26, No. 2, 2015 Figure 3. Building B. ing C, and pillar of the Roomthey of the Stairs are 3 zapal a representations; on the north painted wide. The north portico of the Patio of thesouth Rhomblue character with a scorpion tail and on the buses is skirt, 9 zapal long,both and the eastern side of the pillar a woman with a jaguar surrounded North Plaza lost in its second constructive phase meaby Venus Stars. These pillars their construcsures 24 zapal.as All are multiples of 3, a preferred tional character; they remained two stelae within number in ancient Mayan texts (O'Brien and the room and became symbol-laden objects. This Christiansenwhere 1986), as well we as of 4,find 9, and 12. this Acis the only place in Cacaxtla cording assume to Dehouve (201 1), the number 3 is related measurement, and we may the conscious to fire, and additional study is needed to determine use of the yollotli on these pillars to complete their the significance of its use in construction. Theculdisymbolic message and establish references to tural elements from Teotihuacan, to mension of the Venus to Room Venus is no longer aor multielements of the Mesoamerican worldview. ple of 3, but measures 5 zapal. Flora Clancy Only two of the three recurrent measurements(1994) reports the frequent use of 1 .92 m at Tikal (1 .465 m and 1 .953 m) correspond to multiples ofand Naranjo. This is a measure close to 4 M, which strengthens the series of coincidences with the modulus .488 m. The value of 1 .465 m is very the Maya area at Cacaxtla. close to the measurement of 1 .47 m reported by Patricia O'Brien and Hanne Christiansen (1986) We may ask ourselves whether the main modulus is .488 m or 1 .465 m. Both were used as units for the Maya area. Thus, the Cacaxtla modulus is and both may be considered as moduli even if one-third of a zapal and corresponds to 3 oc, the subunit obtained by dividing 1 .47 m by 9; follow-there is an arithmetic relationship between them. The zapal is useful for measuring the main eleing this logic, the third measurement, 1.198 m, would correspond to 13 kob (1.194 m), one-six-ments, such as large rooms and plazas, and a smaller unit is needed to measure smaller elements. teenth of 1 .47 m. This correspondence is too preThe Cacaxtla modulus also appears at Teoticise to be considered a simple coincidence. The correspondence between the Cacaxtla and Mayahuacan, as deduced from the measurements remoduli confirms O'Brien and Christiansen's findported by Jorge Acosta (1964) during excavations ings and proves the existence of a measurement he carried out at the Quetzalpapalotl Palace (Table 6). Acosta concluded that the walls were 2.88 m system encompassing widely separate regions. The unit of 1 .465 m, the Cacaxtla zapal, served high, 6 M minus 4.8 cm. The variations in the as the basis for determining the modulus, and ap- modular framework are insignificant in comparipears recurrently also as a single unit (Figure 2). son with the dimensions of the components and The central room of Building E measures 3 times in view of the construction technique used. The 6 zapal. Building B would ideally have measured repeated use of 10 and 20 and the scarcity of 3 as 3 times 1 8 zapal. The rooms of Building A, Build- multipliers are noteworthy. Not knowing how This content downloaded from 132.248.9.8 on Sat, 19 Nov 2022 17:50:37 UTC All use subject to https://about.jstor.org/terms Lucet] DIMENSIONING AT THE EPICLASSIC SITE OF CACAXTLA, TLAXCALA, MEXICO 253 Table 6. Measurements of the Quetzalpapalotl Palace,but walls oriented on a different axis exparallel, Teotihuacan. hibit a deviation close to one degree from the right angle. Building B (Figure 3) has a more marked Building Stair, building 5 9.80 20 .040 Antesala Width 9.74 20 -.020 Antesala Length 12.65 26 -.038 Tumb Width 1.44 3 -.024 Tumb Length 4.75 10 -.130 Battlement .94 2 -.036 North Door 1.95 4 -.002 Corridor 7.3 15 -.020 Corridor Width .96 2 -.016 Parapet .48 1 -.008 Room Length 8.8 18 .016 Patio Width 8.24 17 -.056 rhomboidal form than the rest of the buildings; one of its diagonals is 54 M long and the other is 55 M long, a difference that increased the deformation of the building. It seems as though these diagonals were measured and laid out differently on purpose so as to maintain the pattern marking the general orientation of the site. In five porticos, pillars and the spaces between them have the same dimensions, which shows that measurements were made computing the thickness of plaster layers that would cover the pillars. In contrast, in the majority of the central Note : All dimensi wider spaces of porticos,betwee bay widths, and doordifference Patio Length ways, the dimension is slightly less than a multiple of M. The opposite is the case for stair widths. Acosta measure These irregularities indicate that the builder deto generalize fr fined the layout of these elements without includcally state that ing the thickness of plaster. This difference in cri- Teotihuacan at teria shows the importance of the regular visual dences would h appearance of porticos. Conversely, for rooms and tailed study. staircases, a practical criterion prevailed. The At Tenochtitlan, the state of the structures structural part was built following modularity and makes a similar study difficult; nevertheless, in then finishes were applied, reducing or increasing 1902 Leopoldo Batres (1990) reported the finding of a sculpted altar upon a pedestal; the measure- pearance of porticos is corroborated by the regular ments 1.45, 1.96, 2.44 and 2.96 m corresponded its dimensions. The importance of the visual ap- to 3, 4, 5 and 6 M, and only one (.885 m) does not measurements of the pilaster widths, the small range of variation in their values, and the small correspond to the modulus. variation within a group of measurements. Xochicalco should likewise be compared to Cacaxtla. It was a great city of the high plateau in The most frequent measurement for the pillars is 1 .198 m and the next is 1 .465 m, whereas most spaces between pillars are 1.953 m wide. Bay the Epiclassic period; in both places shared elements are found, such as the distinctive slopeand-panel structures. These coincidences invite a comparison of their measurement systems, al- widths are close to the latter, and for the doorways, one-half of the modulus was used. though a preliminary review of plans of the Acrop- the measurements from the peripheral sidewalks; olis and the Pyramid of the Serpent does not appear to confirm the use of the zapal or of the this shows that the plaza is an exterior space designed carefully and a primary element in the spatial concept. modulus M. Plazas are multiples of the zapal or of M , taking On the Manner of Architectural Measurement Space-time Relationship The modulus of .488 m and the unit of 1.198 m It is pertinent to ask what the criteria were for appear in various architectural categories and point choosing a specific measure and whether they to the use of a unifying system, in contrast to the changed in the various constructive phases. three anthropometric measures (.835 m, 1.60 m, Cacaxtla is clearly divided into three zones. and 2.056 m) used only for pillars and spaces that Access to the north zone is restricted by a small separate them. Walls at Cacaxtla run north-southstaircase located at the center of the Slope of the or east-west; walls along a given orientation are Battle. The central zone is a plaza that is com- This content downloaded from 132.248.9.8 on Sat, 19 Nov 2022 17:50:37 UTC All use subject to https://about.jstor.org/terms 254 LATIN AMERICAN ANTIQUITY [Vol. 26, No. 2, 2015 front of a sides plaza), the rituals the Great Platform pletely enclosed on its four by of buildings, located at a lower level than thepurposes north zone; served various and were seen byoutgroups of different sizes. passageways Spatial analysis has shown that side entrances are through small be- the southern southern part of thecorners. site was separatedThe from tween buildings on the the northern part through form and access (Lucet southern zone is completely isolated from the pre- 2013). We now see that passageways this separation is also exceding ones. To reach it, two long pressed in the measurements of pillars, and that it must be used, arriving at the Plaza of the Altars. may be the resulttwo of the expression of the a duality In this zone we can distinguish levels: reflected in the architecture. This duality may have lower one corresponds to the Venus Complex and been rooted in theto articulation Cacaxtla es- the the Red Temple; the higher one the that Palace, tablishes with its natural environment and which the two Plaza of the Altars, and the South Pyramid, important gods that personify volcanoes that progressively covered the structures ofthe the lower level over different constructive frame it, since the siteepisodes is equidistant from(Lucet the summits of two active volcanoes, the Iztaccihuatl and 1999,2007,2013). There is a clear difference in the use of mea- the Matlalcueye or Malinche (Lucet 2013). surements in the pillars for the three zones. The Alternatively, if the builders were Olmeca-Xinorth and south zones each exhibit their own di- calanca people, the distinction may be associated mensional schemes, and the buildings separatingwith their origin, given that this group was the rethem use a mixture of both schemes (Figure 4).sult of the cultural mixing of two separate ethnic In the south zone, Ps cluster around 1.198 m, as groups. It may also be linked to a "two-headed happens in Building E in the central zone. The government and its ideology" that Michel Graulich rest of the pillars, including all of those in the(2001:21; translation by author) infers from the north zone, approximate the 1.465 m modulus. pairing of plumed serpent and serpent-jaguar imagery, possibly related to the opposition between The pillars of the peripheral porticos surrounding the Great Platform that face outwards have mea"Maya conqueror in charge of the external govsurements in accordance with the zone to which ernment of the city" and "indigenous character of the Mexican high plateau." they belong. On the north, they measure 1 .465 m and on the south, 1.198 m; in the central part of Graulich's (1988, 2001) interpretation affords an opportunity to establish a direct parallel bethe east side, they measure 1.465 m, and toward tween spatial occupation and meaning of two difthe south, 1 .198 m (the west side was destroyed). ferent dimensional systems. Each of his two govA clear spatial differentiation is thus observed. The I values are mixed, and it seems that the erning groups would have used one of the defined builders aimed to preserve the symmetry and harzones and the central zone, acting as the convergence point for the complex, would have exhibmony of the plazas, using the same measure all ited a combination of the two measures. The around or on opposite sides. The distinctive use of pillar measurements Mesoamerican political system is an open subject of study. Whereas in the Maya area there is evicould be related to the spatial significance of the dence of dynastic systems, in the high plateau zone where they are located. Numerous studies government would have been multiethnic and have sought to decipher the significance of paint- corporate, and its antecedent would be traced ings with iconographie and epigraphic readings, back to Teotihuacan (Blanton 1996; López and finding meanings related to rituals, in particular López 1999). It also must be remembered that to actual or mystical sacrificial rituals, or to wars, the use of a measurement system is a deep exconquests, or proclamations of ethnic provenance pression of a culture and is only with difficulty (Carlson 1991; Domínguez and Urcid 2013; Foncerrada de Molina 1980, 1993; Piña 1998; Urcidreplaced by another.2 and Domínguez 2013; Uriarte 2013; Uriarte and Velazquez 2013). None of these has linked its interpretations with a spatial division of meanings. Conclusions The differences between the creator's vision and Depending on the location of the mural, its degree is measured in the present may vary dependof visibility, and its context (within a room or what in This content downloaded from 132.248.9.8 on Sat, 19 Nov 2022 17:50:37 UTC All use subject to https://about.jstor.org/terms Lucet] DIMENSIONING AT THE EPICLASSIC SITE OF CACAXTLA, TLAXCALA, MEXICO 255 Figure 4. Distribution of P. Dark gray: 1.198 m; light gray: 1465 m. This content downloaded from 132.248.9.8 on Sat, 19 Nov 2022 17:50:37 UTC All use subject to https://about.jstor.org/terms 256 LATIN AMERICAN ANTIQUITY [Vol. 26, No. 2, 2015 ing on the nature of the object measured. With When working with measurements, it is usual this in mind, rather than to incorporating see their association with complex anthropometric meastatistics, I took into account the current state of sures; .835 m, 1 .60 m, and 2.056 m correspond to the buildings at Cacaxtla measurements and their features of the human body.in In contrast, order to decipher the dimensional system to 1 .465 m is associated with theused practical manner lay them out. I focused on spaces with visi- to the of working on the layouthigh and corresponds bility where precision would have been more im- arms length of a string held taut with outstretched portant, namely the porticos surrounding and pinched with the thumb oninner each hand. The modular measures were used inentire the various plazas and delimiting the periphery of the site. Three recurring groups of were stages of measurements construction at Cacaxtla and point to a shared between the pilasters the spaces sepa-The cultural and continuity throughout the Epiclassic. rating them. After averaging them, two complete coincidence of theexhibited system of measurea common denominator: the Cacaxtla construc- ment used at Cacaxtla with that reported for the tional modulus M, measuring .488 m. The widths Maya area could be an indicator of the presence and lengths of rooms, staircases, plazas, doorways, of Maya people in the altiplano , leading to the and central spaces of the porticos turned out to hypothesis be that the builders of Cacaxtla were multiples of M with differences of a few centimeMaya. This would explain the similarities in style, ters. This modulus is also present at Teotihuacan, painting techniques, and architectural configurawhere it was used in the building of the Quetzaltions of the buildings. The need to adapt to a land papalotl. in which a different language was spoken obliged The result is close to units reported by O'Brien and Christiansen (1986) for the Maya area. The the leaders to leave aside hieroglyphic writing. Hence, the discourse was centered on shared zapal corresponds to three times the Cacaxtla iconographie elements (Graulich 1988). Maya modulus, with an error of six millimeters. The za- symbols were interpreted and adapted through pal was divided by 9 or 16 to obtain subunits, artistic bilingualism so as to integrate elements of which explains the third recurring measurement in the Cacaxtla porticos. the written languages of the center (Martin 2013). Additional validation of the modulus was found Until now, the modulus encountered at Ca- in multipliers. The 1.465 m (3 times M) con- caxtla had been recorded only in the Maya area. Nevertheless, I have shown (with reservations due structional modulus and its 3-, 6-, 9-, 18- and 24- to measurements that were not obtained under fold multiples provide the measurements for the strict control) that it was also used at Teotihuacan, main spaces, the dimensions of which were care- in an altar at Tenochtitlan, and in a construction fully planned; these multipliers have also been reported in Mayan writings as numbers associated with building activities. The measurement system of Cacaxtla combines built by Central Mexican or Maya groups at Ciutherefore be necessary to carry out similar analyses of measurements at other sites in order to know two logics: one with a base pattern for the modular whether the zapal was a measurement of Maya dad Vieja, El Salvador (see Note 2). It would system, and another with four stable measures. One origin that was adopted and used in other of these measures is .835 m, used only for the width contexts- whether generally or in isolated cases- of the painted pillars of the Venus Room, which or whether it was part of a wide range of tools has the peculiarity of corresponding to the base modulus of the urban layout at Teotihuacan, thus establishing a relationship of the site dimensions employed by the builders of Mesoamerica, without this necessarily implying a specific origin. What has impeded our ability to generalize from this with the most important astronomical cycles in the kind of work is the need for dependable data that Mesoamerican worldview. Another dimension is must take into account the conditions of the struc- 1 .198 m, used mainly for the pillars and in someture of and the thickness of applied finishes. the spaces between pillars; 1.60 m and 2.056 m So far as we understand it, the use of the zapal appear specifically in spaces between pillars. These (or one-third of it), some anthropometric units, four measures are not divided or multiplied andand do units of .835 m at Teotihuacan, Cacaxtla, and not participate in the modular scheme. in Nahua sculpted stones support the claim that This content downloaded from 132.248.9.8 on Sat, 19 Nov 2022 17:50:37 UTC All use subject to https://about.jstor.org/terms Lucet] DIMENSIONING AT THE EPICLASSIC SITE OF CACAXTLA, TLAXCALA, MEXICO 257 these formed the basis of a dimensional scheme Castillo, Victor Manuel in continual use for centuries in a large portion of the Mesoamerican world. 1972 Unidades nahuas de medida. In Estudios de cultura náhuatl 10: 195-223. Instituto de Investigaciones Histórica, Universidad Nacional Autónoma de México, México, The spatial distribution of the measurements D.F. Chanfon Olmos, Carlos employed for the pillars at Cacaxtla points to their1979 La geometría y la piedra del sol. Revista Churubusassociation with the significance of the spaces; in co:l-29, México, D.F. Clancy, Flora S. this case, it does not appear to be related to calen1994 Spatial Geometry and Logic in the Ancient Maya drical features, as has been reported for other sites. Mind Part 1: Monuments. Proceedings of the Seventh Rather, it reflects a duality present at the site, Palenque Round Table, 1989 , edited by Merle Greene which can correspond to an important division in Robertson and Virginia M. Fields, pp. 237-242. The PreColumbian Art Research Institute. the use of its different spaces. The hypothesis Clark, of John E. a dual government in Cacaxtla leads to the as- 2008 Hands and Hearts. Mesoamerican Voices 3:5-34. 2010 Aztec Dimensions of Holiness. In The Archaeology of sumption that these variations in measurements Measurement. Comprehending Heaven, Earth and Time could reflect spaces built for each of the two ruling in Ancient Societies, edited by Iain Morley and Colin groups, which could have been of different ethnic Renfrew, pp. 150-169. Cambridge University Press, New York. origins. The systems of measurement used in dimensioning Mesoamerican architecture are an integral part of a discourse that goes beyond simply solving a building problem. They are related to symbolic manifestations of the worldview and social Dehouve, Daniele 20 1 1 U imaginaire des nombres chez les anciens Mexicains . Presses universitaires de Rennes, France. Domínguez, Elba, and Javier Urcid 2013 El ascenso al poder del Señor 4 Perro: las pinturas murales del Conjunto 2-sub en Cacaxtla. In La pintura mural prehispánica en México, volumen V, Cacaxtla , edited by María Teresa Uriarte, pp. 547-607. Universidad Nacional Autónoma de México, México, D.F. Drewitt, Bruce Acknowledgments. This research paper forms part of the re1 987 Measurement Units and Building Axes at Teotihuacan . sults of the project La pintura mural prehispánica en México , In Teotihuacan, Nuevos Datos, Nuevas Síntesis, Nuevos organization of the people who used them. which received grants from the program UNAM-DGAPAProblemas , edited by Emily McClung de Tapia and PAPIIT-IN402613; I am especially grateful to Prof. María Evelyn Childs Rattray, pp. 389-398. Instituto de InvestiTeresa Uriarte, coordinator of the project, who made this gaciones Antropológicas, Serie 72. Universidad Nacional Autónoma de México, México, D.F. study possible. Foncerrada de Molina, Marta 1980 Mural Painting in Cacaxtla and Teotihuacan CosReferences Cited mopolitanism. In Third Palenque Round Table, 1978, edited by Merle Green Robertson, pp. 183-198. University of Texas Press, Austin. Acosta, Jorge 1964 El Palacio del Quetzalpapalotl. 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Fondo de Cultura Económica, El Janet C. Berlo, pp. 83-104, Dumbarton Oaks Research Library and Collection, Washington, D.C. Colegio de México, México, D.F. O'Brien, Patricia J., and Hanne D. Christiansen López Lujan, Leonardo 1986 An Ancient Maya Measurement System. American 2010 Tlaltecuhtli. Centro Nacional para las Artes, Instituto Nacional de Antropología e Historia, México, D.F. Lucet, Geneviève Antiquity 5 1(1): 136-151. Piña Chan, Román 1998 Cacaxtla, Fuentes Históricas y Pinturas. Fondo de 1999 La computación visual aplicada a la documentación y estudio de monumentos. El sitio arqueológico deCultura Económica, México, D.F. Christopher B.A. Cacaxtla y el mural O'Gorman: dos estudios de Powell, caso. 2010 The Shapes of Sacred Space: A Proposed System of Ph.D. dissertation, Posgrado en Arquitectura, Universidad Nacional Autónoma de México. Geometry to Lay Out and Design Maya Art and Architecture 2007 Propuesta de secuencia constructiva del Gran Basa-and Some Implications Concerning Maya Cosmology. mento. In Memorias del coloquio internacional: Cacaxtla Ph.D. dissertation, University of Texas at Austin. Roy a sus XXX años de investigación. Instituto Nacional deall, Travis J. 2010 Built to Measure: Reconstructing an Ancient MeaAntropología e Historia, Tlaxcala, México. 20 1 3 Arquitectura de Cacaxtla: lectura del espacio . In Ca-surement System from Extant Architecture at Casas caxtla, edited by María Teresa Uriarte, La pintura mural Grandes. Master's thesis, Anthropology Department, Uni- prehispánica en México, volumen V, Cacaxtla, pp. 19-versity of Missouri. 109. Universidad Nacional Autónoma de México, México, Sugiyama, Saburo D.F. McVicker, Donald 1985 The "Mayanized" Mexicans. American Antiquity 1983 Estudio preliminar sobre el sistema de medida teotihuacana. Paper presented at the XVIII Mesa Redonda de la Sociedad Mexicana de Antropología, Taxco, Guerrero, Mexico. 50(1):82- 101 . Magaloni, Diana, Claudia Brittenham, Piero Baglioni, Rodorico 1993 World vie w Materialized in Teotihuacan, Mexico. Latin American Antiquity 4(2): 103-129. Giorgi, and Lorenza Bernini 20 1 3 Cacaxtla, la elocuencia de los colores . In La pintura 20 10 Teotihuacan City Layout as a Cosmogram: Preliminary Results of the 2007 Measurement Unit Study. In The Armural prehispánica en México, volumen V, Cacaxtla, This content downloaded from 132.248.9.8 on Sat, 19 Nov 2022 17:50:37 UTC All use subject to https://about.jstor.org/terms Lucet] DIMENSIONING AT THE EPICLASSIC SITE OF CACAXTLA, TLAXCALA, MEXICO 259 chaeology of Measurement. Comprehending Heaven, Williams, Barbara J., and María del Carmen Jorge y Jorge Aztec Arithmetic Revisited: Land-Area Algoriths Earth and Time in Ancient Societies edited by Iain2008 Morley and Colin Renfrew, pp. 130-149. Cambridge University and Acolhua Congruence Arithmetic. Science 320(5872):7277. Press. Urcid, Javier, and Elba Domínguez 2013 La casa de la tierra, la casa del cielo: los murales en el Edificio A de Cacaxtla. In La pintura mural prehispànica Notes en Mexico, volumen V, Cacaxtla, edited by María Teresa Uriarte, pp. 609-675. Universidad Nacional Autónoma 1. In 1790, the French Revolution established the use of de México, México, D.F. the metric system, but builders were reluctant to implement Uriarte Castañeda, María Teresa (editor) the decision because they found the previous system based on 2013 La pintura mural prehispànica en México, volumen the duodecimal system much more flexible with its units di- II y III, Cacaxtla. Universidad Nacional Autónoma de visible by two, three, and four; it was only in 1840 that a México, México, D.F. Uriarte, María Teresa, and Erik Velazquez García decree made it obligatory (Fredet 2003). This phenomenon seems to be demonstrated in the con2013 El Mural de La Batalla de Cacaxtla. Nuevas 2.aproxi- of Ciudad Vieja, El Salvador. This city was founded maciones. In La pintura mural prehispànica structions en México in 1524 using a measurement system based on the Spanish Cacaxtla, volumen V, Cacaxtla , edited by María Teresa Uriarte, pp. 677-739. Universidad Nacional Autónoma vara (Fowler 2011). One building, however, is distinguished de México, México, D.F. from the rest; it is situated on a hill outside the grid of the city, Urton, Gary 2010 Recording Measure(ment)s in the Inka Khipu. In The Archaeology of Measurement. Comprehending Heaven, Earth and Time in Ancient Societies, edited by Iain Morley and Colin Renfrew, pp. 54-68. Cambridge University Press. Vinette, Francine with a different orientation, and obsidian objects were found associated with it. It likely served as a lookout postsurveillance being a function entrusted to the Tlaxcaltec, Mex- ica, and Maya troops who accompanied the conquistadors. It has been noted that half the dimensions of the room correspond to the zapal with a difference of only 5 percent. This distinction 1986 In Search of Mesoamerican Geometry. In Native American Mathematics , edited by Michael Closs, pp. 387-^07. University of Texas Press, Austin. in the measurements could be taken as a cultural representation and as a statement about the origin of the builders. Walling Jr., Stanley L. 1 982 A Stylistic Analysis of the Cacaxtla Murals . Estudios de Cultura Maya 13:205-223. Williams, Barbara J., and H. R. Harvey 1988 Content, Provenience, and Significance of the Codex Vergara and the Codice de Santa Maria Asuncion. American Antiquity 53(2):337-351 . Submitted July 22, 2014; Revised October 31, 2014; Accepted March 2, 2015. This content downloaded from 132.248.9.8 on Sat, 19 Nov 2022 17:50:37 UTC All use subject to https://about.jstor.org/terms