## The Proportional Design in Rudolph M. Schindler's Braxton-Shore House of 1930

**Abstract**

Journal of Asian Architecture and Building Engineering
, Volume 8 (1): 7 – May 1, 2009

**Abstract**

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- Taylor & Francis
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- © 2018 Architectural Institute of Japan
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- 1347-2852
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- 10.3130/jaabe.8.33
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The Braxton-Shore house has been considered as an exemplar of 'space architecture' – an architecture of 'space forms' which R. M. Schindler believed distinguished his work from contemporary functionalists and internationalists. To achieve such' space architecture', Schindler utilized a proportional system of a space reference frame as a mental tool. This paper ﬁrst outlines the spatial scheme of the Braxton-Shore house, explains Schindler's space reference frame, and finally interprets the proportional design of the house in analogy with the 'row' system, the Fibonacci and Lucas sequence, and musical ratios. Keywords: Schindler; proportion; 'row' system; the Fibonacci and Lucas sequence; musical ratios 1. Introduction Architecture and Mathematics, March (2003) examines Most writings on the proportional study of Rudolph the mathematics that underlie Schindler's notion of the Michael Schindler's houses have been descriptive 'row'. observations rather than in-depth analyses using Schindler argues in his proportional system of space computational techniques or making pedagogical reference frame that the space architect needs to not inferences. At times, the signiﬁcance of the architect's only improve his mental image of the space, but also p r o p o r t i o n a l s y s t e m h a s b e e n b l a t a n t l y i g n o r e d . possess a proportional system. With the system, the Architectural historians, like David Gebhard (1971), forms of space are freely conceived and precisely considered Schindler's system merely one practical measured in the architect's mind. Forms of space are tool for wood frame structure and construction. It is envisioned 'by being inside of it', just as musicians true that Schindler's unit system was derived from imagine and articulate their music with notes. By 1930, Schindler had sufficient command of practical needs for his space architecture, but it may be his system in organizing his space and space forms a mistake to consider the system without its theoretic to propose a beach house for Mr. And Mrs. Henry implications. In a paper by March (1993a), Schindler's Braxton in Venice Beach, Los Angeles. Although proportional method was interpreted as an analogy Schindler left behind numerous built and unbuilt with classical proportion, much more than a mere projects which demonstrate extraordinary spatial construction tool for the ﬁrst time. When March (1993b) complexity as well as variety, the Braxton-Shore house used a musical analogy to examine the proportional stands out the most. Unfortunately, it was never built, design of the How house; in his paper, 'Dr. How's due to the client's ﬁnancial circumstances at the design Magical Musical Box' he seems to portray 'architecture stage (Park and March, 2003). as frozen music.' R e c e n t l y, P a r k ( 2 0 0 3 ) i n t e r p r e t e d S c h i n d l e r ' s 2. Spatial Scheme of the House 'reference frames in space' as set forth in his 1916 The spatial scheme of the house consists of three l e c t u r e n o t e s o n m a t h e m a t i c s , p r o p o r t i o n , a n d organizational forms – a garage, the residence, and architecture, relating to the theory of 'row' in the the circulation spine. The circulation spine, which context of John Beverley Robinson's articles in the is composed of five horizontal wooden structures, Architectural Record (1898-1899). In a complementary c o n n e c t s t h e h o u s e a n d t h e g a r a g e . R a t h e r t h a n paper in the same issue of the Nexus Network Journal: using concrete, as in the Lovell house of 1928, these structures are made of wooden frames. All space *Contact Author: Jin-Ho Park Ph.D., Associate Professor, volumes of the house are interlocked along the five Department of Architecture, Inha University major structures. #253 Yonghyun-dong, Nam-gu, Incheon 402-751 Korea A courtyard covered with sand occupies the space Tel: +82-32-860-7597 Fax: +82-32-866-4624 between the house and the garage. The rectilinear box E-mail: jinhopark@inha.ac.kr form dominates its spatial outlook, in Gebhard's words, ( Received October 8, 2008 ; accepted January 6, 2009 ) ' …[a] rectangular box into and out of which secondary Journal of Asian Architecture and Building Engineering/May 2009/39 33 ﬁnely proportioned window mullions are inset facing the courtyard, while door mullions face the ocean side. The three bedrooms on the balcony ﬂoor are disposed equally overlooking the Paciﬁc Ocean. The composite roof is used as a terrace; a portion of it is used for sunbathing, a sleeping porch, and a small closet. Fig.1. 1/4 Scale Reconstruction of the Braxton-Shore House, 1930 3. References Frames in Space volumes projected,' and in Giella's words, 'a slightly Although Schindler expressed his early interest top-heavy composition is created by cantilevering out in a proportional system as early as 1916, it was not each successive story from bottom to top.' Various clearly expressed until 1946 when Schindler published box forms are projected, recessed, and interlocked a comprehensive summary of his proportional system along the longitude axis (Fig.1.). It is Schindler's usual in an article, 'Reference Frames in Space' (Schindler, practice and the signature of his designs. 1946). In the article, his idea of proportion is well The ground level preserves an open playground and d e f i n e d a s f o l l o w s : ' P r o p o r t i o n i s a n a l i v e a n d patio for the natural beach sand, forecourt, outdoor expressive tool in the hands of the modern architect fireplace, garage, guestroom, maid's quarters, and who uses its variations freely to give each building furnace (Fig.2.). The ground level is an independent its own individual feeling.' The system for Schindler unit, and there is no interior staircase connecting the is indispensable to the creation of his notion of space ground to the upper level. A major portion of the architecture as a doctrine of spatial organization. house is raised above the lot. The option of the lifted Schindler argued that he started using the system as structure may be suitable for the beach house by the early as 1920. In fact, an analysis of Schindler's Free necessity of allowing the sun and air to reach the entire Public Library project of 1920 demonstrates his use of floor, preserving some part of the site beneath for a the system (Park, 1996). playground, and providing an open outlook to the ocean. On the main level, the architect created a living room two stories in height. It is open to the Pacific Ocean and enclosed by individual bedrooms on the balcony ﬂoor overlooking the living area. Below is the living room, kitchen facilities, dining room, and porches are adjacent to the dining room and kitchen. Inside the main floor, there is little built-in furniture shown on the drawing compared to his other projects so that the inner space remains visually unobstructed. In addition, Fig.3. Schindler's Three-dimensional Grid of Space Cubes The purpose of Schindler's system is to provide a mental structure for conceptualization before pencil meets paper, and, secondly, to communicate to the builders a map locating elements, allowing them to easily scale off dimensions. As such, all locations and sizes of the parts with respect to the whole are precisely identified during the construction process. Thus, no obscure or arbitrarily unrelated measurements are involved in the unit system. In addition, the unit grid system offers the means to visualize 'space forms' in three dimensions. He argued, ' … it must be a unit which he can carry palpably in his mind in order to be able to deal with space forms easily but accurately in his imagination.' Although there are a few exceptions, like the Schindler Shelter project where he used a 5-foot unit module, Schindler recommended 4-foot m o d u l e a s t h e b a s i c u n i t , t o b e u s e d w i t h s i m p l e multiples and with 1/2, 1/3, and 1/4 subdivisions. Among the subdivisions, with only a few exceptions, 1 / 3 a n d 1 / 4 a r e u s e d f o r v e r t i c a l m o d u l e s i n h i s Fig.2. Floor Plans and Elevations of the Braxton-Shore House works. This single unit module with its multiples and (1930) with the 4-foot Square Unit Grid. From Top to Bottom: subdivisions form the basis of all dimensions of rooms Ground Floor Plan, Main Floor Plan, Balcony Floor Plan, South in a cube form (Fig.3.). Elevation, and West and East Elevations 34 JAABE vol.8 no.1 May 2009 Jin-Ho Park There are two reasons for this choice. First, the unit 16-foot the kitchen, 6-foot x 10-foot porch in front, an must be related to the human ﬁgure to satisfy all the 8-foot x 8-foot entrance on the second level, his room necessary sizes for rooms, doors, and ceiling heights; 11-foot x 12-foot, her room 14-foot x 16-foot, and second, for practical reasons, the 48-inch module ﬁts another 10-foot x 16-foot bedroom on the third ﬂoor. the standard dimensions of materials and common The rafters of the horizontal wooden structures are construction methods available in California at that regulated in a 2-foot distance – half of the unit module. time. He utilized his unit system in a square grid H o w e v e r , r o o m d i m e n s i o n s w r i t t e n o n t h e pattern. Numbers and letters are laid out on the grid on construction drawings are found to be inconsistent with the ﬂoor plans in sequence and the vertical module is the real dimensions of the rooms. The construction identiﬁed with an elevation grade (Fig.3.). documents of Schindler provided actually consist The grid was presented on drawings and on the of drawings which other architects might consider house in his earlier designs, yet they disappear from schematic, like the instructions to the builder. the house and, at times, from the drawings. However, Two reasons for this might be considered. First, this this does not mean he abandoned his system; on the difference relies on their stages of design development, contrary, his system remains embedded in the designs e i t h e r c o n c e p t u a l o r p r a c t i c a l , t h a t a r e c o m m o n as an underlying principle. In addition, Schindler practice in the architectural field. Early schematic used the system to measure rooms. In his preliminary designs are primarily a conceptual basis, and they sketches, his room sizes, with the whole numbers on evolve depending on specific practical requirements drawings, are commonly presented. These numbers are in the design process and during fabrication as well as increments of unit multiples with their subdivisions. construction. Thus, room sizes shown on the drawings do not always accord with dimensions measured from 4. Proportional Analysis of the House the drawings, although the former might be what the Unlike the proportional study of the Lovell house architect initially had in mind; rather, the latter is of 1925-26 by Sarnitz (1986, 1988), the proportions of the result of some adjustments. For example, in the the Braxton-Shore house has remained uninvestigated. Braxton-Shore house, the dimensions of the guestroom S a r n i t z ' s a n a l y s i s o f t h e L o v e l l h o u s e p l a n s a n d shown on the drawing are 15-foot by 9-foot, yet the elevations is based on his belief that a simple square real measure of the drawing of the room is 14-foot by and double square determine the overall proportional 11-foot. Before arriving at a ﬁnal scheme of a project, system of the house. exercises of various possible schematic layouts are an There are various sets of drawings of the house in almost universal procedure employed by architects, the Schindler Archive at the University of California including Schindler. at Santa Barbara , including preliminary sketches, Second, various rooms are not rectangular, but structural and sash details, construction drawings, and interlocked, overlapped, and, at times, zigzagged. well-organized presentation drawings. These sources In this case it is not possible to present a simple provide valuable information for the proportional dimensional relationship of room ratios with two terms analysis of the house. a and b, to a : b, or a x b, other than by approximation. On the drawings, dimensions and placements of In fact, Schindler approximately measured the room various spatial forms and details of the house are sizes in a rational manner with his unit system to controlled by Schindler's unit system (Fig.2.). The determine its size of each room and probably their 4-foot unit system is clearly identiﬁed in the plan with proportional relations. numbers and letters, and the 16-inch vertical module Although these inconsistencies may cause confusion in elevation with grades. All major space, details, for this analysis, the collection of room dimensions and structure underlie its subdivisions and multiples serves as an excellent basis for further explorations of where all parts are related to each other in terms of his proportional designs (Table 1.). This proportional simple unit relations to produce a coherent unity. a n a l y s i s s o l e l y r e l i e s o n t h e a r c h i t e c t ' s r o o m Most of the major rooms in the construction drawings dimensions written on the drawings since it maintained are measured in whole numbers and written on the the architect's original intent of room sizes and their drawing as is common in other designs. Although relations to each other before the architect's transfer of rooms are frequently not a simple rectangular form, the ratios to the practical necessities. Schindler approximated those to the whole numbers. It Table 1. provides interesting results on two levels. appears that simple whole numbers with respect to the On one hand, among three fractions that Schindler space reference frame easily grasp its size, as Schindler used, which include 1/2, 1/3, and 1/4, 1/3 of 48 inches implied in his space reference frame system. (16-inch) is not used in room dimensions of the plan. Given the evidence of the ﬂoor plan, the dimensions Instead, the fraction is used only for the vertical of the rooms include the following: a 9-foot x 15-foot module. The 16-inch vertical module measures the g u e s t r o o m , 1 0 - f o o t x 1 0 - f o o t m a i d r o o m , 5 - f o o t room height of the house. It also governs window x 8-foot bathroom, 6-foot x 8- foot furnace on the mullions, door mullions, and the thickness of a series ground level, 24-foot x 27-foot living room, 10-foot x of horizontal structures. Accordingly, it is inferred JAABE vol.8 no.1 May 2009 Jin-Ho Park 35 Table 1. List of All Rooms and their Relations Floor Room Names Room Dimensions Space Reference Frame Ratios Decimal Value of the Ratios Ground Floor Guestroom 15 x 9 3 ¾ x 2 ¼ 5 : 3 1.67 Maid room 10 x 10 2 ½ x 2 ½ 1 : 1 1.00 Bathroom 8 x 5 2 x 1 ¼ 8 : 5 1.60 Furnace 8 x 6 2 x ½ 4 : 3 1.33 Second Floor Living room 27 x 24 6 ¾ x 6 9 : 8 1.125 Kitchen 16 x 10 4 x 2 ½ 8 : 5 1.60 Porch 10 x 6 2 ½ x 1 ½ 5 : 3 1.67 Entrance 8 x 8 2 x 2 1 : 1 1.00 Third Floor His room 12 x 11 3 x 2 ¾ 12 : 11 1.09 Her room 16 x 14 4 x 3 ½ 8 : 7 1.14 Bedroom 16 x 10 4 x 2 ½ 8 : 5 1.60 Bathroom 10 x 6 2 ½ x 1 ½ 5 : 3 1.67 Table 2. Series of Coprime Room Dimensions where the Two Dimensions are Prime to One Another Row Ratios Row-1 1x2, 2x3, 3x4, 4x5, 5x6, 6x7, 7x8, 8x9, 9x10, 10x11, 11x12, ... Row-2 1x3, 3x5, 5x7, 7x9, 9x11, 11x13, 13x15, 15x17, 17x19 , .. Row-3 1x4, 2x5, 4x7, 5x8, 7x10, 8x11, 10x13, 11x14, 13x16, ... Row-4 1x5, 3x7, 5x9, 7x11, 9x13, 11x15, 13x17, 15x19, 17x21, ... Row-5 1x6, 2x7, 3x8, 4x9, 6x11, 7x12, 8x13, 9x14, 11x16, 12x17, ... Row-6 1x7, 5x11, 7x13, 11x17, 13x20, 17x23, 19x25, 23x29, ... Row-7 1x8, 2x9, 3x10, 4x11, 5x12, 6x13, 8x15, ... 13x20, 15x22, .. Row-8 1x9, 3x11, 5x13, 7x15, 9x17, 11x19, 13x21, 15x23, ... Row-9 1x10, 2x11, 4x13, 5x14, 7x16, 8x17,…10x19, 11x20, 13x22,... that Schindler used those fractions separately: 12" coprime rectangles (Table 2.). increments for plans and those of 16" for elevations. All room dimensions of the Braxton-Shore house T h e d o o r h e i g h t i s h i s t y p i c a l 6 f e e t 8 i n c h e s . are to be classiﬁed according to the 'row' system. The The room heights vary, but they are subdivisions row-0 contains two room sizes, which involve a 1:1 and multiples of 16 inches vertical modules. The ratio. Row-1 also contains two room sizes from the room height of the ground floor, including the maid, house, guestroom, furnace, and garage, is 8 feet, but the height of the open playground is 10 feet. The height 2/1, 3/2, 4/3, 5/4, 6/5, ... , 9/8, 11/10, 12/11,.... of the kitchen and the dining room in the second ﬂoor is 8 feet. The height of the two-story high open living Row-2 contains another two room sizes: room is 14 feet 16 inches. The height of His room and another bedroom is 8 foot 16 inches on the third ﬂoor. 3/1, 4/2, 5/3, 6/4, 7/5, 8/6, 9/7, ..., 16/14, .... The height of Her room is 9 foot 8 inches, but that of the bathroom and the dressing room next to Her room The alternate 14x11 room belongs to row-3 along are an exceptional 8 feet 10 inches. A series of five with 27x24 and 8x5: 14/11 = (4+10)/(1+10), 27/24 horizontal structures are 8 feet apart, except for the = (4+23)/(1+23), 8x5 = (4+4)/(1+4). By continuing height of the ﬁrst ﬂoor, which is 8 feet 9 inches. t h e p r o c e s s , t h e d i m e n s i o n s o f a l l t h e r o o m s a r e On the other hand, unlike the complexity of the summarized as the following six row equivalences: s p a c e f o r m s , s u r p r i s i n g l y f e w r o o m d i m e n s i o n s Room sizes Row a n d c o r r e s p o n d i n g r a t i o s a r e i n v o l v e d ; y e t t h e i r 10/10, 8/8 row-0 12/11, 9/8 row-1 interrelationship are worthy of the profound study. 8/6, 16/14 row-2 In the house, twelve different room dimensions and 8/5, 14/11, 27/24 row-3 10/6 row-4 seven different ratios, 1:1, 4:3, 5:3, 8:5, 8:7, 9:8, and 16/10, 15/9 row-6 12:11, are collected. In order to deduce relationship of dimensions and ratios, particular analytic methods are introduced to derive all these ratios. 4.1 The 'row' system The room dimensions of the house are inclusive within Schindler's early notion of 'row'. Schindler used the term 'row', a sequence, 'a following of unequal units with deﬁnite changes' (Park, 2003, March 2003). A page from Schindler's 1916 lecture notes illustrates a particular 'row', which is equivalent to the classical sequence of subsuperparticular numbers (March, 1998a). If a/b is a term in the 'row', the next term is (a + 1)/(b + 1). Schindler's use of the term 'row,' appears to derive from his association with the circle around Fig.4. Plot of Room Sizes in the Braxton-Shore House Classiﬁed Adolf Loos from Vienna. March (2003) generalized the by 'Rows'. From Left to Right, First Row 1/2, Second Row 1/3, theory of 'row,' by classifying a series of 'rows' in the Third Row 1/4, Fourth Row 1/5, and Sixth Row 1/7. 36 JAABE vol.8 no.1 May 2009 Jin-Ho Park These room sizes are also to be classiﬁed according to the regulating principle, or geometric similarity. A total of 8 different equivalences are provided, as shown below. These ratios are further interpreted in terms of their proportional relationships in the following two sections. Fig.7. A Double Square and Pentagon with Root 5 Room sizes Ratios 10 x 10, 8 x 8 1 : 1 8 x 6 4 : 3 ratios on the drawings derive new proportional ratios. 10 x 6, 15 x 9 5 : 3 By computing other ratios of the two series together, 8 x 5, 16 x 10 8 : 5 16 x 14 8 : 7 the remaining three ratios can be constructed (March, 9 x 8, 27 x 24 9 : 8 1998b): 7:4 :: 2:1 = 8:7, 4:3 :: 3:2 = 9:8, and 18:11 :: 12 x 11 12 : 11 14 x 11 14 : 11 3:2 = 12:11. All ratios are derived directly from other previously-used ratios. The implication of these newly constructed ratios with old ones is that all the room ratios become associated each other; thus, a ratio consistency is achieved. Also, it could be said that all of these related ratios are ubiquitous in the Braxton- Shore house plans. This computation is delineated in the following diagrams (Fig.8.). Fig.5. Plot of Room Sizes in the Braxton-Shore House Classiﬁed Fig.8. Geometric Construction of the Room Ratios by Conventional Ratios. Clockwise, First Ratio 1:1, Second Ratio 11:12, Third Ratio 8:9, Fourth Ratio 7:8, Fifth Ratio 3:4, Thus, all room ratios of the project are suggestive of Six Ratio 8:5, and Seventh Ratio 3:5. methods of computation coming out of the geometric and proportional construction. By this method, all 4.2 The Fibonacci and Lucas sequence other room ratios are constructed with regard to each T h e r e l a t i o n s h i p o f t h e s e r a t i o s i n t h e h o u s e other. Schindler might be aware of such ideas as he i s i d e n t i f i e d w i t h t h e e x t r e m e a n d m e a n r a t i o wrote, 'We must realize that "proportion" is not any geometrically incorporated in the regular pentagon. more a simple mathematical relationship (Golden The ratios suggest a possible relationship with the Rule, etc.) which can be applied universally in all Fibonacci sequence, in which each successive number buildings as it was in classical times.' However, it is is equal to the sum of the two preceding numbers, 1, incorrect to suppose Schindler derived his room ratios 1, 2, 3, 5, 8, 13, 21 … and the Lucas sequence, 2, 1, 3, this way or mathematically. Although the architect had 4, 7, 11, 18, 29 … The ratios of successive numbers of no particular belief of 'a simple mathematical relation' both series converge to approximately 1.618, which is or 'Golden Rule', perhaps, some sort of computing known as the extreme and mean ratio. Continuing to procedure may have been involved in the architect's the right in these sequences, the ratios get close to the mind. Schindler could choose the total number of Golden Ratio, which is 1.618 (Fig.6.). r o o m d i m e n s i o n s i n t h e p r o j e c t w i t h r e a s o n s t o reference proportions derived from simple geometry or to practical solutions to the problems of a particular design. 4.3 Musical ratios Since Schindler employs a small number of units and a limited set of factions, any analysis of ratios and proportions will inevitably correspond to musical intervals. Again, it does not mean the musicality is Fig.6. A Graph Showing its Successive Fibonacci Sequence intentional, but it is a necessary consequence as the Moving Closer to 1.618. relations of small numbers make it so. That is not to say that Schindler was unaware of musical proportion. Its proportion with a regular geometrical pentagon In his article, 'Reference Frames in Space,' Schindler can be identiﬁed in the following diagram (Fig.7.). e x p r e s s e d h i s m u s i c a l t h i n k i n g o f t h e r h y t h m i c Ratios including 1:1, 4:3, 5:3, and 8:5 are certainly arrangement of spatial organizations. His criticism among these. Geometric constructions using existing JAABE vol.8 no.1 May 2009 Jin-Ho Park 37 of the 'Golden Rule' is followed by the concept of All the ratios we attribute to Schindler's Braxton- symphonic harmony - a definite musical analogy. Shore house are found in musical divisions of a string Schindler explains his concept as follows: "Rhythm of ratios, or musical ratios within an octave (Fig.9.). is a space relationship. It cannot be achieved by an Room ratios in the project are equivalent to musical arithmetical repetition of the same part but must be intervals like unison (1:1), second (9:8), fourth (4:3), maintained by related spacings of parts, whether sixth (5:3), and a minor sixth (8:5). Schindler himself they are similar or not. As in music, such a rhythmic shortly referred to musical ratios in his early discussion scheme may be simple repetition or the more subtle of proportion on his 1916 lecture notes. i n t e r l o c k i n g o f s e v e r a l r h y t h m s . I t i s p r a c t i c a l l y impossible to maintain such an interlacing rhythmic p l a y o n a p l a n i n d i c a t i n g d i m e n s i o n s b y f i g u r e " (Schindler, 1946). March's musical analogy in the analysis of the How house relies on this. In addition, when Schindler discussed proportion in his notes, he made reference to Claude Bragdon, saying 'SEE BRAGDON'S BOOKS.' Schindler might have referred to Bragdon's book, The Fig.9. An Octave with Musical Ratios on a Piano Keyboard Beautiful Necessity, originally published in 1910. A similar analogy between music and architecture is also The question arises, 'Are 8:7 and 12:11 musical inferred in the book. Claiming, 'architecture is frozen ratios?' In fact, these ratios occur in early Greek music,' Bragdon dedicated a whole chapter of his book tetrachords – enharmonic, chromatic, and diatonic, to 'Frozen Music.' Bragdon explains, "Music depends which are referenced in Vitruvius (1931) in the chapter primarily upon equal and regular divisions of time ... 'Harmonic Principles'. In the chapter, 'equal diatonic' Architecture, correspondingly, implies the rhythmical is Ptolemy's division of the ratio 4:3 (the tetrachord) division of space, and obedience to laws numerical into 12/11.11/10.10/9 = 4/3. It appears that each a n d g e o m e t r i c a l … A l l a r c h i t e c t u r a l f o r m s a n d interval approximates a tone. Ptolemy also has a 'tense arrangements which give enduring pleasure are in their chromatic': 7/6.12/11.22/21 in which the last two essence musical. Every well-composed facade makes intervals 12/11.22/21 = 8/7. harmony in three dimensions; every good roof sings a However, the 'bible' on musical theory in Schindler's melody against the sky" (Bragdon, 1910 and 1978). youth was Hermann Helmoltz's book. Helmholtz (1954) Bragdon's discussion of musical notes follows with has a table in his book, Chapter 10, which indicates a vibrating string: intervals in connection with simple that in modern musical theory all ratios, 1:1, 2:1, 3:2, musical ratios, as in Robinson's articles (1898-1899). 4:3, 5:4, 6:5, 7:6, 8:7, and 9:8, occur and that the ratios He further describes distinguishing characteristic of the 5:3, 7:4, 7:5, 8:5, 9:5, and 9:7 should be counted. ratios, either consonant or dissonant, connecting the Here, he only takes this table up to the number 9, but ears to the eyes. he includes all possible ratios using numbers 1 - 9 Before the Braxton-Shore house was designed, between 1:1 and 2:1. Schindler married his wife Pauline in Chicago, who majored in music from Smith College and may well 5. Summary have introduced him to new musical theory, including The proportional design of Schindler's Braxton- the Californian, Henry Cowell, Arnold Schoenberg, Shore house has been analyzed with regard to the and John Cage. Of course, Schindler had a fundamental 'row' system, the Fibonacci and Lucas sequence, and understanding of music scales since he had taken piano musical ratios. This proportional analysis was based on lessons for seven years in Vienna. hypothetic speculation rather than Schindler's recorded Earlier, Schindler's Austrian mentor, Adolf Loos, documentary evidence. Although speculative, the took Vitrivius' treatise to be his 'bible' according to employed analytic method was valid in the sense that it the painter Oskar Kokoschka (1986). The chapter presented the proportional relationship of rooms in the on harmony (1931) refers directly to musical theory. house and exposed their harmonic integrity. Schindler Trying to decipher the cryptic remarks in this chapter wrote, 'The house of the future is a symphony of "space would lead a curious mind to a book such as Hermann forms" - each room a necessary and unavoidable part Helmholtz's, Die Lehre von den Tonempfindungen, of the whole.' In the design, the architect's approach t r a n s l a t e d a s O n t h e S e n s a t i o n s o f To n e a s a was extremely simple. The composition of various Physiological Basis for the Theory of Music (1954) rooms did not have to follow a mere mathematical play since this was the most available comprehensive of rules, but had to express its relations in size between modern work on the subject. The first edition was r o o m s s o a s t o f o r m a n ' o rg a n i c u n i t y ' : a w h o l e published in 1862; but many editions followed and composed of related parts in an orderly arrangement. the work stood as the 'authority' until well into the All in all, the observation leads to a conclusion that twentieth century. proportional relations of these ratios tie together in 38 JAABE vol.8 no.1 May 2009 Jin-Ho Park a cohesive whole in a single design, thus creating a Notes The Schindler archive is located in the Architectural Drawing complex design. Whether the design was intentional Collection, University Art Museum, University of California at or arrived at by chance, R. M. Schindler must have a Santa Barbara (UCSB). splendid sense of proportional eyes to project such a 2 Schindler documented a series of lectures at the Church school in simple and rational system to a very complex spatial Chicago in a booklet of his handwritten notes. The lecture notes are housed in the Schindler Archive at UCSB. composition. Acknowledgements This work was supported by an INHA University Research Grant. The early draft of this paper was presented at the Matomium Conference, Brussels. The author is indebted to Professor Lionel March for his advice in carrying out this proportional analysis. References 1) Bragdon C. (1910, 1978) The Beautiful Necessity, A Quest Book. 2) Gebhard D. (1971) Schindler. London: Thames and Hudson. 3) Granger F. (1931) Trs. Vitruvius on Architecture, Cambridge: Harvard University Press, Book V, Chapter IV. 4) Helmholtz H. (1862, 1954) On the Sensations of Tone as a Physiological Basis for the Theory of Music, New York: Dover Publications, Inc. 5) Kokoschka O. (1971) Ma Vie, (1971) French translation (Paris, 1986), p. 76. 6) March L. (1993a) Proportion is an Alive and Expressive Tool… . In L. March and J. Sheine (Eds) RM Schindler: composition and construction. London: Academy Edition. 7) March L. (1993b) Dr. How's Magical Music Box. In L. March and J. Sheine (Eds) RM Schindler: composition and construction. London: Academy Edition. 8) March L. (2003) Rudolph M. Schindler: Space Reference Frame, Modular Coordination, and the 'Row'. Nexus Network Journal, vol. 5 no. 2. 9) March L. (1998a) Architectonics of Humanism. London: Academy Editions. 10) M a r c h L . ( 1 9 9 8 b ) A r c h i t e c t o n i c s o f p r o p o r t i o n : a s h a p e grammatical depiction of classical theory. Planning and Design. 26: 91-100. 11) Park J. (1996) Schindler, Symmetry and the Free Public Library, 1920. Architectural Research Quarterly. 2: 72-83. 12) Park J. (2003) Rudolph M. Schindler: Proportion, Scale, and the 'Row'. Nexus Network Journal, vol. 5 no. 2. 13) Park J. and March L. (2003) Space architecture: Schindler's 1930 Braxton-Shore project. Architectural Research Quarterly (arq). 7: 51-62. 14) Robinson J. (1898-9) Principles of Architectural Composition. Architectural Record VIII, 1: 1-25; 2:181-223; 3: 297-331; 4: 434-465. 15) Sarnitz A. (1986) Proportion and Beauty – the Lovell Beach House by Rudolph Michael Schindler, Newport Beach, 1922-26. JSAH, 45: 374-388. 16) Sarnitz A (1988) R. M. Schindler-Architect, 1887-1953. New York: Rizzoli. 17) Schindler R (1946) Reference Frames in Space. Architect and Engineer, San Francisco 165: 10, 40, 44-45. JAABE vol.8 no.1 May 2009 Jin-Ho Park 39

Journal of Asian Architecture and Building Engineering – Taylor & Francis

**Published: ** May 1, 2009

**Keywords: **Schindler; proportion; 'row' system; the Fibonacci and Lucas sequence; musical ratios

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