Measure and Module of Helmut Spieker’s Marburg Building System 1960–1970

Using the example of the well-known “Marburg building system” by Helmut Spieker (1933–2014), this contribution analyzes how the proportional rules of the Vitruvius tradition, already modified in the modified century, changed as a result of the advancing industrialization of architecture in the 1960s. After 1945, construction had to be done quickly and inexpensively. Ernst Neufert’s Bauentwurfslehre provided the foundation for the production of standardized components in large quantities. Spieker’s system is one of the most important examples of modularized constructions, from the installation and furnishings to the wall and ceiling elements, etc. Although it is based on rational criteria of the norm and the module, Spieker’s method is linked to the tradition of proportion. We examine the question of how the traditional architectural proportion can be made norm-compliant and then translated into a specific construction system.

, who constructed the house for Albert Einstein in Caputh near Berlin (1929), noted that, "mass production of identical parts" affects construction methods just as much as it affects "surface, objects and spaces" (Wachsmann 1961: 54). 2 This fundamental change can be seen in the Germany of 1962/1973in Helmut Spieker's (1933-2014

manuscript Ein Bausystem für Hochschul-Institute (Construction System for Higher Education Institutes) and the brochure Marburger Bausystem
Finally, the constraints surrounding practices of architectural proportion were blown apart by technology after the Second World War. Two systems became valid above all: Bauentwurfslehre (Building Design Theory) by Ernst Neufert (1900-1982 published in 1936 and officially translated into English as Architect's Data (Neufert and Neufert 2012) and the Modulor of Le Corbusier (1887-1965), published in 1948(Le Corbusier 1985. Marcus Frings examined both systems with regard to the golden section (Frings 2002: 20-25) and concludes that, according to Frings, Neufert's system "together with his own normed measures," can be understood as "'an inner law' in the spirit of Antique, Gothic, Renaissance, and Classicism of Palladio and Schinkel" (Frings 2002: 20). Le Corbusier's Modulor, formally deriving from the figure of the square and the golden section (Fig. 3), instead refers to a "normative aesthetics, which propagates the combination of abstract geometry and anthropomorphic measures" (Frings 2002: 25). 7 From then on, both of these systems formed guidelines for an architecture that became more modularized and rationalized. At the same time the golden section gained in importance, as Michael J. Ostwald elaborates (Ostwald 2000: 75-81).
Using Spieker's Marburg Building System as one example among several possible, such as Wachmann und Walter Gropius's (1884-1969) General-Panel-System, constructed between 1941-1952or Angelo Mangiarotti's (1884-1969 building system U70 Isocell of 1968U70 Isocell of -1977, this present contribution investigates the way in which the nineteenth-century rules of proportion that were valid in Modernism have changed with regard to standardization and modules in university constructions in Germany since 1960. 8 In the lecture Funktionalismus heute (Functionalism Today), held in 1965 at the annual meeting of the Deutscher Werkbund in Berlin, Theodor W. Adorno (1903Adorno ( -1969 stated that the "plausible sentence that technology is there for people" hardly suffices with regard to a critical handling of it. 9 In fact, the mechanization of architecture was particularly popular at this time: buildings had to be constructed quickly and at the same time inexpensively. The prerequisite for this was the production of large quantities of components that were as standardized as possible. Nonetheless, this aspect is deliberately neglected in the following investigation. Instead, the question here revolves around the problem of how the traditional understanding of proportions, which are geared towards geometry and aesthetics, are translated into a modular building system centered around human proportions. 7 On Le Corbusier's Modulor, see Passanti (2002: 68-99). 8 For the building systems of Wachsmann/Gropius and Mangiarotti: Herbert (1984: 299-324) ;Nerdinger (2010: 100-103;130-131). From 1949From until 1989 Germany consisted of two countries, the Federal Republic of Germany and the German Democratic Republic. In this paper, 'Germany' refers to the Federal Republic. 9 Adorno (1967: 122). The original reads: Jener plausible Satz, die Technik sei für die Menschen da, ist seinerseits in die platte Ideologie der Zurückgebliebenheit übergegangen.

The Marburg Building System and the Vitruvian Man
The association of the traditional system of measurements, based on human dimensions, with building technology and the standards of architecture and construction that were successively introduced in Germany in the mid-1920s is the subject of Ernst Neufert's Bauentwurfslehre. 10 This standard work, which Walter Prigge calls "one of the most widely used handbooks in the world", is found in Helmut Spieker's remaining library (Prigge 1999: 7). Spieker's copy of the 1956 edition of this book, on the cover of which he has written his name, contains a few margin notes where Neufert addresses the relationship between measure and standard (Neufert [Spieker's personal copy] 1956: 34). 11 On the subject of proportion, the page "Der Mensch. Das Mass aller Dinge" (The Human Being. The Measure of All Things) is especially interesting (Fig. 4).
It shows a version elaborated by Neufert of the well-known male figure in the homo bene figuratus-described, as Wolfgang Voigt points out, in Vitruvius's De architectura libri decem-inserted into a system of circles concentrically arranged around the navel (Voigt 1999: 20-34). In the corresponding passage Vitruvius writes: "But to whatever extent a circular scheme may be present in the  1961-1963/1965. Image: Staatliches Bauamt Marburg body, a square design may also be discerned there" (Vitruvius 1999: 47). During the Renaissance, Francesco di Giorgio, Leonardo da Vinci, Albrecht Dürer, and  Thiersch, Parthenon, proportion system, 1926. Image: Thiersch (1883 others, translated Vitruvius's remarks into the medium of drawing. 12 Neufert's figure, which was featured in publications such as Walter Meyer-Bohe's Handbuch des Bauens mit Fertigteilen (Handbook of Building with Precast Elements) in the early 1960s, corresponds to Dürer's model (Meyer-Bohe 1964: 26). Neufert derives a measurement system based on a geometric system of circles. The horizontal lines applied to this drawing allow length ratios of the depicted male body to be distinguished, starting from the foot and ankle through the knee, pelvis, abdomen and chest to the shoulder, neck and head. The body is divided into five segments using the length marks M and m (Neufert [Spieker's personal copy] 1956: 23;Neufert and Neufert 2012: 27). Spieker's copy contains a special feature: noted in pencil, above and below the marks M and m, are length indications in centimeters in Spieker's handwriting (Neufert [Spieker's personal copy] 1956: 24;Neufert and Neufert 2012: 27). These values are approximations. He derived them from minimum furniture and room dimensions as well as their space requirements, which were depicted on the following page (Fig. 5).
Neufert's page in the Bauentwurfslehre with the title "Abmessungen und Platzbedarf" (Dimensions and Space Requirements) 13 shows a modified version of the Vitruvian Man standing, from the side, and seated. The respective minimum space required in each instance is illustrated using cramped spatial compartments. Furthermore, there are specific numbers related to body lengths and figure postures. The margin notes reveal Spieker's interest in this page. He recorded in red colored pencil the measurement that he considered to be the main one. He numerically reduces the free remaining space in the seated figures at the top right and bottom left  Le Corbusier, Modulor, 1956. Image: Le Corbusier (1985 12 On the relationship of the Vitruvian Man to the centralized church, see Wittkower (1998: 15-40). 13 On the history of this, see Weckherlin (2017: 332-341).  Neufert (1956: 24) and replaces Neufert's value "87 5 cm" with "75 cm". 14 This value corresponds to the height of a table on which the figure at the top right can rest its arm.
The aim of Spieker's addition of handwritten length measurements to Neufert's figure was to develop a module as a starting point for a building system, which would in turn be utilized extensively in the construction of building complexes. As mentioned at the beginning, the building system for the Philipps University Marburg Lahnberge is considered a comprehensive building system derived from a modules. Spieker mentions the following about the prerequisite for it in the brochure "Marburger Bausystem": "The basis for standardization is a set of instruments for coordination as a consistent planning principle for furnishing, installations, finishing and load-bearing structures". 15 The starting point for the Marburg Building System is the module as the smallest unit of the complete system. Spieker's concept of a module differs from that of Le Corbusier's Modulor. It does not operate with the dimensions of human height = 1.829 m and navel height = 1.130 m etc., which in turn culminate in the proportions of the golden section. 16 Rather, Spieker's concept of a module can be understood through Konrad Wachsmann, to whom alone he refers by name. Without referring to the book, he quotes Wachsmann in The Turning Point of Building: The module is the abstract fundamental unit of measurement which, by means of multiplication, subtraction or division, numerically determines the geometrical system of a given modular order. 17 Spieker is guided by this statement of Wachsmann's and its related implications. He bases his module on criteria he presented as early as 1966 in the article "Vorschlag für eine Maßordnung im Bauwesen" (Proposal for a Measurement System in the Building Industry) for a system based on construction, industry, and mathematics that provides "spatial subdivisions, for mobile and fixed furniture, for building elements that depend on human or on technical dimensions". 18 It is neither the unity of proportion nor the perception of the subject, but the module derived from the traditional system of measurements that is conceived of as the condition for architecture. Concerning the size of this module Spieker states: The value of M = 15 cm for the basic module (equal to the width) allows for non-load-bearing wall constructions in various materials; the modular series 15, 30, 45, 60 cm results in favorable furniture dimensions; the value 4 M = 60 cm from the doubling series is a common basic dimension for all spatial dimensions. 19 The dimensional sequence of 15, 30, 45, 60 cm as a module series continues with the "75 cm" derived by Spieker from Neufert's dimension ratios, which in his terminology corresponds to the value 5 M = 75 cm (Neufert [Spieker's personal copy] 1956: 24;Neufert 1980: 9). By adding that "all spatial dimensions" derive from the "spatial movement of the human being" (Anon. [Spieker] 1971: 14). Spieker refers to Neufert's drawings with the variations of the Vitruvian Man and the minimal spaces. 20 Furthermore, he finds the measurement of 75 cm, which he determined as an example, in the "basic measurement of the Asian mat-systems and in the historical double foot". 21 With his mention of the tatami mat, he takes up the discussion on Japanese interiors. The publications Die neue Wohnung (The New Apartment) by Bruno Taut (1880Taut ( -1938Taut ( ) (1924 and Das japanische Wohnhaus (The Japanese Apartment Building) by Tetsuro Yoshida (1894Yoshida ( -1956Yoshida ( ) (1935 show the characteristics of the traditional interiors of Japan. In the 1960s, however, Heinrich Engel's book The Japanese House was key to the understanding of Japanese architecture (1964: 37-43), and shows a variant of the Vitruvian figure (Engel 1964: 53). As Thomas Schmid and Carlo Testa demonstrate (1969: 45), the Committee for Housing of the European Economic Commission agreed upon of M 1 = 10 cm as a basic module in 1959. Spieker, who developed his system around the same time, deviated from it with the module M 1 = 15 cm, i.e., the orientation to the sexagesimal system (Anon. [Spieker] 1971: 14).
Furthermore, Spieker incorporates an additional deviation from the module convention. For Spieker's building system concept, the following is essential: the module M 1 = 15 cm applies solely to the horizontal layout of the building. For the vertical structure, he introduces a slight but decisive deviation from mathematical regularity: Vertical dimensions for floor and ceiling heights need to be derived from the multiplication of the dimensions of a comfortable and uniform stair climb. The tread dimension of 30 cm = 2 M corresponds to 16.5 cm = 1.1 cm as the most convenient climb dimension. 22 This inconsistency is part of the building system: Spieker thereby puts emphasizes on the movement of the human being over mathematical progression. The "modular series 15, 30, 45, 60 cm" quoted by Spieker and the resulting 19 Anon. [Spieker] (1971: 14 van den Boom (1999: 168-175). 21 Anon. [Spieker] (1971: 14). The original reads: …abgeleitet aus dem Bewegungsraum des Menschen und bestätigt als Grundmaß der asiatischen Matten-Systeme und im historischen Doppel-Fuß. 22 Anon. [Spieker] (1971: 14). The original reads: Vertikalmaße für Geschoßhöhen und -sprünge müssen von dem Vielfachen eines bequemen und einheitlichen Treppensteigungsmaßes abgeleitet werden. Dem Auftrittsmaß von 30 cm = 2 M entspricht als günstigstes Steigungsmaß 16,5 cm = 1,1 cm. "favorable installation dimensions" with the "value 4 M = 60 cm" are relevant to the problem of proportion, that is, the transformation of traditional systems of measures in postwar Modernism. 23 They link his building system with the proportion system of the golden section. Indeed, it is not a coincidence that the value M is found above the head of the Vitruvian Man in the formula noted by Spieker by hand in red pencil in his personal copy of the Bauentwurfslehre: "M: m = (M + m): M" (Fig. 6) (Neufert [Spieker's personal copy] 1956: 23).
The equation captures the dimensions of the golden section (Hilpert 1999: 131-143). However, in his discussion of the Vitruvian Man, Neufert refers to the relationship that is relevant to it. Marcus Frings (2002: 18-22) determined that Neufert's figure and measurements are based on the 1854 book Neue Lehre von den Proportionen des menschlichen Körpers (New Doctrine of the Proportions of the Human Body) by Adolf Zeising (1810-1876). Neufert writes: In the past century before all others, A. Zeising achieved greater clarity with his investigations on the dimensional relationships of the human being on the basis of the Golden Section by means of exact measurements and comparisons (Neufert 1956: 23). 24 Zeising's aesthetics were intended to establish the relationship of the proportion of the human body to formal beauty. As part of his historical differentiation, he turned to Johann Joachim Winckelmann (1717-1768), who, in Zeising's view, assumed "in principle a non-continuous proportion" (Zeising 1854: 113). 25 Zeising paraphrases Winckelmann and corrects him at the same time. According to Zeising, Winckelmann states: "As the body relates to the thighs and legs with the feet, so the thighs (without legs and feet) relate to the legs and feet". 26 But Zeising immediately corrects Winckelmann and transfers Winckelmann's relationship of the individual parts of a sculpture to the whole body into the mathematical: "expressed in letters, it would read as: a: b + c = b: c, while according to the principle it should read as: a: b = b: c". 27 Zeising articulates the inconsistency in Winckelmann's conception of beauty in the use of the third factor "c", which is added to the ratio "a: b" (Zeising 1854: 113). As Elisabeth Décultot and Daniel Fulda show (2017: 41-51), with this third factor, Winckelmann merges the Beautiful with the Good. Zeising, however, refrains from doing so. For him, the discontinuity is perverted or erroneous. He insists on establishing the proportional relationship without this factor in favor of a mathematical relationship. Adorno, who actively followed the erection of the new buildings for the Johann Wolfgang Goethe University in Frankfurt by his childhood 25 On the context of Zeising's system of proportion, see Gerber (2017: 67-76 23 Neufert [Spieker's personal copy] (1956: 23). The English editions have a different text than the German. Neufert (1980: 9) and Neufert and Neufert (2012: 27). 24 The English edition of 1980 fails to print Neufert's reference to Zeising at the appropriate place. Neufert (1980: 9). friend Ferdinand Kramer (1898Kramer ( -1985 (Müller-Doohm 2003: 390-391), explains about Zeising's connection between form and geometry in his book Aesthetic Theory: "Entirely, the concept of form should not to be reduced to mathematical relations, as at the time of the older aesthetics, according to Zeising". 28 Similarly, Spieker does not reduce the question of measures to technology: for him, the proportional relationship is not restricted to a mathematical progression. Rather, the ratio is extended using another factor, which in turn allows the comprehensive inclusion of all building elements, which would otherwise be often neglected.

Building Standards: The Furniture as Starting Point
The standardization of architecture necessarily starts with the interior design, which in turn is oriented towards human proportions. This relation between human proportions and furniture is constitutive for Le Corbusier's Modulor. In his patent application of 1945 he says: The invention relates to assemblies for human use, such as furniture, habitats, dwellings, buildings, agglomerations, constituted by the juxtaposition of elements, in particular prefabricated standard elements. 29 Le Corbusier emphasizes in the patent that the aim is to facilitate the manufacture of such assemblies and to obtain a wide variety of shapes, dimensions and configurations from a relatively limited set of suitable standard elements. But overall, as Frings (2002: 25) pointed out, he sticks to the goal of transferring anthropomorphic measures to the buildings, with the help of abstract geometry. The first building completed using the Modulor system was l'Unité d'Habitation in Marseille. 30 Spieker took a similar approach. He used Neufert's diagram of the dimensions and space requirements of a human being to determine the module M = 15, and from this he deduced the sequence of dimensions of 15, 30, 45, 60 cm as a series of modules, from which he derived the fundamental dimensions for the planned building. Consequently, Spieker took the furnishings as the starting point for building planning (Anon. [Spieker] 1971: 12). The fixed and mobile furniture forms the basic unit of the building: "All furniture, and the rooms and building's enclosing it must fit into the uniform system of order in which dimensions, connections and tolerances are regulated" (Anon. [Spieker] 1971: 12). In Spieker's building system, furnishings have a uniform size, which consequently allows for standardization. The publication of the Marburg Building System includes representations of such "standardized furnishing", which ranges from technical installation and laboratory parts to the furnishings of the basement level, shelves and cabinets (Anon. [Spieker] 28 Adorno (2016: 214). The original reads: Vollends ist der Formbegriff nicht auf mathematische Relationen zu reduzieren, wie es zuzeiten der älteren Ästhetik, so Zeising, vorschwebte. 29 Le Corbusier (1945:1). The original reads: L'invention est relative aux ensembles à usage humain, tels que meubles, habitats, logis, immeubles, agglomérations, constitués par la juxtaposition d'éléments, notamment d'éléments standards préfabriqués. 30 On the Modulor and the Unité d'Habitation in Marseille, see Gargiani and Rosellini (2011: 36-45). 1971: 27-37) (Fig. 7). For Spieker, it is not the building's structure that forms the starting point of the design, but the furnishings (Fig. 8).
The method of starting work on the design from the level of the furnishing module is a central theme of Bauentwurfslehre. Neufert states: Today, standardized formats form the basis for the dimensions of furniture for writing and archiving. These, in turn, co-determine room dimensions. Exact knowledge of standard formats (= DIN formats) is therefore important for the architect (Neufert 1956: 12). 31 The sequence that moves from the planar area to space-from paper to desk to building-goes back to the publication of DIN 476 "Paper Formats" decided on by the German Standards Committee in 1922 (Porstmann 1923: 67) (Fig. 9). Neufert refers to Walter Porstmann (1886Porstmann ( -1959, whose writings in 1925 prompted Walter Gropius to introduce DIN 4 stationery and lower case writing at the Bauhaus Dessau (Fig. 10).
There is some evidence that Neufert, who was entrusted with the construction of the Bauhaus building in Dessau from 1925 to 1927, helped initiate this process. 32 In 1917, Porstmann published Normenlehre. Grundlagen, Reform, Organisation der Maß-und Normen-Systeme (Norm Teaching. Basics, Reform, Organisation of  Neufert (1956: 23) 31 The English edition from 1980 has a different text-image structure. For the most part, it contains no historical sources; cfr. Neufert (1980: 4-7). The 2012 English version dispenses with this historical information; cfr. Neufert and Neufert (2012: 4). 32 For information on the history of the standardization of modern furniture, see Porstmann (1928: 1-3). The relation between bureau furniture and the standardization of the modern has also been studied (Rehm 2005: 51-55).
the Measurement and Standard Systems), in which he examined the main problem concerning architectural standardization, which for him was the transition from   1961-1963/65. Image: Spieker (1971 the two-dimensional planar surface to three-dimensional space. Porstmann starts from the rectangle of a piece of standardized paper. To ensure the aforementioned transition he fixed specific proportion: Fig. 9 Walter Porstmann, Standardization of paper, 1923. Image: Porstmann (1923) As a consequence, for every rectangle of space whose edges match this proportion, the proposition holds that it can be doubled to a similar spatial rectangle by placing it appropriately next to another one. 33 Fig. 10 Walter Porstmann, Standardization of paper and furnitures, 1928. Image: Porstmann (1928) 33 Porstmann (1917: 233). The original reads: Demgemäß gilt für jedes Raumrechteck, dessen Kanten dieser Proportion genügen, der Satz, daß es durch passendes Aneinanderlegen zu einem ähnlichen Raumrechteck verdoppelt werden kann. On Porstmann, see Krajewski (2006: 64-140).
In this way he arrives at the proposition central to the architectural norm: "Spatial formats should have a flat format as a lateral surface". 34 This is to guarantee the principle of connection, that is, the alignment of plane and space. These efforts towards architectural standardization, which can be observed since the 1920s, also meet also with criticism. In a 1958 issue of Bauwelt, an article by a member of the German Standards Committee, previously published in that journal in 1932, presents the ten commandments of standardization in a manner that is as satirical as it is distanced, as "Thou shalt not standardize…". 35 Spieker's preoccupation with standardization manifested itself at the highest levels: namely, in his collaboration with the German Standards Committee for the Building Industry. In a January 1966 interview in Bauwelt, Lennart Bergvall, the president of the International Modular Group (IMG), spoke about Spieker's module set at 15 cm and its progression Bergvall (1966: 117, 119). Following the interview, Spieker himself contributed to the discussion with the abovementioned essay "Vorschlag für eine Maßordnung im Bauwesen" . His statements clearly illustrate the significance he attributes to the dimensional system for the establishment of building standards. From the point of view of the mid-1960s, he observes various difficulties with DIN 4172, which was issued in 1955 and was one of the first standards in construction to specify the basic unit or building standard dimension as one eighth of a meter with the module of 12.5 cm. 36 According to Spieker, however, the "reference point for the module formation and the series of numerical series is wrong". 37 At the meeting of the Main Committee on Dimensioning in the Building Standards Committee on 16 November 1965, it was proposed that DIN 4172 be amended. Here, Spieker argues that the octametric system should be abandoned, since the planning and execution of standardized buildings, which are mainly built for industry and administration as well as universities, are oriented to the general development of the module. For the standards committee, this would mean recognizing "for the main modules only the values of 30 and 60 cm". 38 According to Spieker, it is precisely this status quo that guarantees the establishment of a new dimensional system on the basis of newly gained experience. In this case, there are only two possibilities: the "metric foot-inch system" and the "decametric foot system". 39 36 On these standardizations of the construction dimensions: Meyer-Bohe (1964: 25). 37 Spieker (1966: 135). The original reads: Gemessen an den aufgestellten Forderungen zeigt sich außerdem, daß diese Norm den Anforderungen, die an ein Maßsystem zu stellen sind, nicht entspricht -nicht entsprechen kann, weil bereits der Ausgangspunkt für die Modulbildung und die Zahlenreihen falsch ist. 38 Spieker (1966: 135). The original reads: Die Oktametrik aufzugeben, bedetet für den Normenaussschuß daher nur ein Anpassen an eine immer weiter um sich greifende Entwicklung: künfig das Hauptmodulen nur noch die Werte von 30 und 60 cm gelten zu lassen. 39 Spieker (1966: 135). The original reads: Der Weg, der von den internationalen Gremien vorgeschlagen wird, kann als metrisches Fuß-Zollsystem, der andere als dektametrisches Fußsystem bezeichnet werden. 34 Porstmann (1917: 235), emphasis in original. The original reads: Die Raumformate sollen ein Flachformat als eine Seitenfläche haben. 35 Anon. (1958: 18). The original reads: Du sollst nicht normieren…

Spieker's Foot System and Neufert's Intervention
The foot measurement of 30 cm would need to be brought to the measurement system. According to Spieker, it has "had its meaning for centuries as the correct module size". 40 Spieker's insistence on the traditional measurement of the foot is unusual. After all, the European Economic Commission had already decided in favor of the decimal system in 1959. Nevertheless, after a demonstration of mathematical derivations of the metric foot-inch system and the decametric foot system, at the end, he refers once again to the measure with the base of the basic numbers 3 and 1.5, respectively. To a large extent, it was historical considerations that compelled him to say: "The 3 is to be believed to have endured the longest as the basis of a system of dimensions for building". 41 With his reference to duration, Spieker alludes to a higher context. The measure of the foot represents a historical norm in architectural history. Winckelmann's Geschichte der Kunst des Altertums (History of the Art of Antiquity), following remarks on proportion, contains a section on the elaboration of norms. Accordingly, the foot "was the rule among the ancients for all great measurements, and the sculptors measured their statues according to the length of the foot, giving them six lengths of foot, as attested by Vitruvius". 42 In addition, Porstmann provides the historical background for the foot measure as a standard, with its minimally differing sizes: 1 old Parisian or French foot is 0.32484 m, 1 English foot (equal to the Russian) is 0.304797 m, 1 Prussian foot (equal to the Danish) is 0.31385 m, 1 Austrian foot is 0.31608 m, 1 Swiss foot is 0.3 m. 43 The standard is thus the reference value of measurement taken from the human being.
In September 1966, Bauwelt commented on the interview with the president of the Building Standards Committee and Spieker's proposal for a dimensional system. None other than Ernst Neufert himself opposed the change in standard building dimensions as intended by the German Standards Committee on Spieker's initiative. Neufert challenged the president to answer several uncomfortable questions. Even the module M 1 = 15 cm, which Spieker develops on the basis of the Bauentwurfslehre, is targeted by Neufert: 40 Spieker (1966: 135). The original reads: Sie hat durch Jahrhunderte hindurch als richtige Modulgröße ihre Bedeutung bewiesen. 41 Spieker (1966: 136). The original reads: Der 3 ist die größte Dauer als Grundlage eines Maßsystems für das Bauwesen zuzutrauen. 42 For Winckelmann's reception of Vitruvius's proportion, see Wincklemann (1764: 174). The original reads: Der Fuß war bey den Alten die Regel in allen großen Aussmessungen, und die Bildhauer setzten nach der Länge desselben das Maaß ihrer Statuen, und gaben denselben sechs Längen des Fußes, wie Vitruvius bezeuget. 43 Porstmann (1917: 11). The original reads: 1 alter pariser oder französischer Fuß ist 0,32484 m, 1 englischer Fuß (gleich dem russischen) ist 0,304797 m, 1 preußischer Fuß (gleich dem dänischen) ist 0,31385 m, 1 österreichischer Fuß ist 0,31608 m, 1 schweizer Fuß ist 0,3 m. 6. Since a 30 cm jump is probably too large for perforated facades, does not 15 cm automatically offer itself as a module here according to the bisection series 120 -60 -30 cm? 7. Is therefore the intention also to change module of 10 cm, upon which was internationally agreed upon in Sweden, to a module of 15 cm? That is, to change the basic module one more time? 44 Neufert, therefore, opposed Spieker's module M 1. In fact, Neufert extended his rebuttal to Spieker's Bauwelt essay without mentioning his name: Proposal for a Measurement System in the Building Industry is the name of an essay in which a system of measurements is propagated that consistently starts from a pure sexagesimal system in the horizontal direction, on the basis of M = 15 cm, (this measurement is not recognized as a module in any country in the world. This measure is used by the author in a doubling series in the horizontal of 15 -30 -60 -120 cm, etc. 45 The measurement series of the sexagesimal system, which according to him "has been adopted everywhere since the French Revolution", is thus criticized by him as precisely the measure that Spieker derives from Baunormenlehre. 46 Last but not least, Neufert, who led the Institute for Standardization in Darmstadt, felt that his authority in matters of measuring systems and standards was being undermined. Spieker's proposal, which revolutionized the module in terms of an assumed measure specifically derived from the human being, does not conform to either the international resolutions or to the studies of Neufert's Institute for Standardization.

Spatial and Planar Modules: The Differentiation
Spieker's quote (Anon. [Spieker] 1971: 11) from Wachsmann's The Turning Point in Building about the module as the "abstract fundamental unit of a measurement which, by means of multiplication, subtraction or division, numerically determines the geometrical system of a given modular order" (Wachsmann 1961: 54) is strategically motivated. Following the principle establishing the mathematical directives of the mode, Wachsmann then justifies the use of two divergent modules for the construction of a building: one module for the horizontal and one module for the vertical: As a fundamental modular unit need only apply in one direction, it may prove necessary to choose a number of different measurements or modules … For example, processes occurring in the horizontal plane need not necessarily be the same as those occurring in the vertical. In this case, it is true, a linear module might expand into an planar module but the latter could be supplemented by quite a different module for the vertical (Wachsmann 1961: 54).
Wachsmann's remarks about the module for the horizontal and the vertical contain instructions that Spieker implements in his building system. The stair step dimension is decisive: in fact, he does not use the basic module of 15 cm for the vertical building structure, and instead provides for a rise dimension of 16.5 cm, a stair dimension that, according to Meyer-Bohe's extensive tables, is not found elsewhere in any building system of the 1960s (Anon. [Spieker] 1971: 16). Spieker provides an overview of this difference in a diagram (Fig. 11).
Above it, he compares vertical and horizontal dimensions. This demonstrates that the dimensions only match at 165 cm and 330 cm. According to Neufert, this lack of alignment is not found in any other international dimensional series. Neufert considers Spieker's combination of two dimensional systems to be incorrect: "In the vertical, however, he relies on an additive series with M = 16.5 cm, corresponding to a stair rise ratio of 16.5 × 30 cm. This results in a confusing chain of dimensions in the height division". 47 Although the difference seems minor at first, the alignment with the level of the stair tread has a striking effect on the height dimensions of the entire building. After all, Neufert exclaims, "Floor heights, slabs, windows, doors, etc. should also be based on this!" 48 He does not appreciate this difference and states: "One can therefore speak here with good reason of a systematic nonconformity with the 10 cm series and also a non-conformity with the 15 cm series". 49 Spieker, however, insists on this apparent inconsistency between vertical and horizontal measure: "The invariable dimension on which every staircase is based, in a more or less exact manner, determines the 'standard' climb, which has to be regarded as an average dimension". 50 The vertical dimension, despite the difference, still correlates to the statutes of the norm: The fact that it is chosen as the vertical dimension is not meant to imply that there can no longer be other stair risers, but merely to open up the possibility of obtaining standardized parts in serial construction also for the stairs, which are dimensionally coordinated with the chosen floor height and at times the bricks used. 51 Spieker alludes to the traditional norm of the foot measurements as listed by Porstmann, the sexagesimal system of 30 cm, which, as Neufert points out, was the norm in the wake of the French Revolution. Spieker points to this recourse to the historically legitimized dimensions of the foot when he says: If one follows this train of thought, it becomes apparent that the stair step dimension of 30 cm, which is of great importance in the ground plan, and the stair tread dimension of 63 cm lead to the rise dimension of 16.5 cm as the most sensible measurement (Spieker 1966: 136).
Just as the furnishings determine the module in the horizontal dimension, the stairs determine the module in the vertical dimension. The use of the furnishings and the stairs therefore form the prerequisite for the dimension system. Wachsmann establishes this relationship by stating that "processes that occur in the horizontal plane need not necessarily be the same as those that occurring in the vertical," thus pursuing a point of view that is related to an understanding of the dimensions of traditional architecture (Wachsmann 1961: 54). 52 He formulated this statement in line with the passage from Spieker quoted above. There, Wachsmann developed a concept of dimensional differentiation. In his view, if one were: …to strike a balance, in which all the requirements were fulfilled in consistent three-dimensional measurement, then the single resulting fundamental module would be simultaneously identical with a body of modular order. This threedimensional unit of a three-dimensional module may be considered the ideal case; it constitutes a universal system in which it is possible to fix any part in any direction and at any time, both in itself and in relation to any other part (Wachsmann 1961: 54-55).
Ultimately, for Spieker, the task at hand is this combination of architectural module and modular body. As it turns out: Wachsmann, who in 1954 carried out experiments at the Technical University in Karlsruhe at the invitation of Egon Eiermann, under whom Spieker was studying, provides, as it were, the program for the development of the Marburg Building System (Wachsmann 1961: 208). 53 According to Wachsmann, the basic module as the core of a system requires investigations in areas that diverge from one another: "These various approaches must be analyzed and all the dimensional findings reduced to a common denominator before the universal module can be established" (Wachsmann 1961: 55). 54 The latter is composed of twelve sub-modules that form a functional whole. The individual modules consist of material, performance, geometry, handling, structural, element, joint, component, tolerance, installation, fixture and planning modules (Wachsmann 1961: 55). These categories provide the basis for an architecture that, like the university buildings being constructed at the time in Frankfurt, in relation to which Ferdinand Kramer always emphasizes the cognitive moment, is comprised of rational elements (Kramer 1991: 92).

Conclusion
The concept of module developed by Wachsmann, which no longer has much to do with Le Corbusier's Modulor and the Golden Section relevant to it, forms a complex basis for the modular architectural construction of the 1960s. Wachsmann's module categories, which became widely accepted within a very short time, still appear a decade later in Schmid and Testa's publication "Systems Building" (Schmid and Testa 1969: 53-59). Wachsmann's module recurs as a variant of Vitruvian Man. Intellectually the module goes back to collaborations with Walter Gropius in the Fig. 11 Helmut Spieker, diagram of the measure system. Image: Spieker [1971: 16)] 54 On the development of module-based building systems, see Frampton (1987) and Banham (1976).
United States in the mid-1940s. This application of human proportions increasingly shifts to an industrial one (Fig. 12). 55 Similarly, Meyer-Bohe states that the dimensional order of architecture is "related to the human body, or can be schematically prescribed" (Meyer-Bohe 1964: 24). Spieker's module criteria for a system based on function, construction, industry, and mathematics, which are mentioned in 1966 in his essay in Bauwelt and in 1971 in the publication on the Marburg Building System (Spieker 1966: 135;Anon. [Spieker] 1971: 13) are based on Wachsmann's categories as well as their derivation. The difference described by Wachsmann between processes in the horizontal and the vertical, which balances the basic module unified by spatial dimensions, corresponds to the above-mentioned approach of taking into account not only fixed sizes but also certain irregularities in the proportioning of a building. Spieker quite deliberately insists on this inclusion of the irregular. What is initially considered as incompatible is brought together. This procedure allows the supposedly erroneous, the seemingly reversed, to be integrated into the overall structure. As mentioned, Spieker associates such deviating values with harmony. This procedure is quite well-known in aesthetics, and Spieker explicitly refers to it at the end of his Bauwelt essay (Spieker 1966: 136). It corresponds to Zeising's reference to Winkelmann's principle of proportion (Zeising 1854: 112). Zeising suggested that Winkelmann is concerned with the relationship of the body to the Beautiful, the "principle" of which on the one hand satisfies the "spirit" and on the other hand is most appealing to the "sensual perception". 56 In fact, for Zeising, Winkelmann's discussion is characterized by a "very mystical application" of proportion. Regarding an order of dimensions, however, he considers Winkelmann's explanations as valuable, since he intends to prove the validity of the principle "directly on the basis of the structure of the human body". 57 In the 1960s, similar traditional procedures were the subject of a criticism. Adorno argued that such relations, "whether as explicit principles as in the Renaissance, or latent and coupled with mystical conceptions," conceal an approach that produces "not form" but "means of preformation". 58 The geometrically defined dimensions allow for the object to be outlined. For Spieker, the module is thus an instrument for producing architecture as a construction in the age of technology, beyond industrial purposes. At the same time, the module is legitimized by means of a connection to architectural history. Spieker states: Vitruvius created the first writing known to us in which he attempts to prove that a modular order underlies the buildings of the Greeks, especially the 56 Zeising (1854: 112). The original reads: So bekennt sich also Winckelmann ausdrücklich zu dem S. 16 näher besprochenen Proportionalgesetz des Plato, woraus deutlich hervorgeht, dass ihm das darin ausgesprochene Princip als das befriedigenste für den Geist und als das zutreffendste für die sinnliche Anschauung erschienen ist. 57 Zeising (1854: 112). The original reads: Während aber Plato von diesem Gesetz nur eine sehr mystische Anwendung macht, sucht er die Gültigkeit desselben unmittelbar an der Gliederung des menschlichen Körpers nachzuweisen… 58 Adorno (2016: 214). The original reads: Derlei Relationen spielen, sei es als ausdrückliche Prinzipien wie in der Renaissance, sei es latent und mit mystischen Konzeptionen gekoppelt …, ihre Rolle in den Verfahrungsweisen, sind aber nicht Form sondern Vehikel, Mittel zur Präformation. temples. This hypothesis is probably correct, even if his exact specifications are not. 59 Fig. 12 Konrad Wachsmann, Diagram of a Vitruanian Men, 1959. Image: Wachsmann (1961 59 Spieker (1973: 125). The original reads: Vitruv hat die erste uns bekannte Schrift geschaffen, in der er nachzuweisen versucht, dass den Bauten der Griechen, insbesondere den Tempeln, eine modulare Ordnung zugrunde liegt. Diese Hypothese dürfte stimmen, wenn seine exakten Angaben auch im Einzelnen nicht zutreffen.
Funding Open access funding provided by Swiss Federal Institute of Technology Zurich.
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