RELATED EXPLORATIONS IN ARCHITECTURAL AND MUSICAL COMPOSITION by NICCOLO WERNER CASEWIT Bachelor of Environmental Design University of Colorado, Boulder 1983 SUBMITTED TO THE DEPARTMENT OF ARCHITECTURE IN PARTIAL FULFILLMENT OF THE REQUIREMENTS OF THE DEGREE MASTER OF ARCHITECTURE AT THE MASSACHUSETTS INSTITUTE OF TECHNOLOGY FEBRUARY 1987 Q NICCOLO WERNER CASEWIT 1987 The author hereby grants to M.I.T. Dermission to reproduce and to distribute publicly copies of this thesis document in whole or in part. Signature of the author Certified by 7 Niccolo Werner Casewit Department of Architecture January 15, 1985 Will'ia Lyman Porter Professor of Architectur and Planning Thesis Supervisor Accepted by Chairperson MASSACHUS Departmfndb Vi ittee for Graduate Students FEB 25 1987 LIBRARIES Q-i I lLibraries M Document Services Room 14-0551 77 Massachusetts Avenue Cambridge, MA 02139 Ph: 617.253.2800 Email: docs@mit.edu http://Ilibraries.mit.edu/docs DISCLAIMER NOTICE The accompanying media item for this thesis is available in the MIT Libraries or Institute Archives. Thank you. RELATED EXPLORATIONS IN ARCHITECTURAL AND MUSICAL COMPOSITION by NICCOLO WERNER CASEWIT SUBMITTED TO THE DEPARTMENT OF ARCHITECTURE ON JANUARY 15, 1987 IN PARTIAL FULFILLMENT OF THE REQUIREMENTS OF THE DEGREE MASTER OF ARCHITECTURE AT THE MASSACHUSETTS INSTITUTE OF TECHNOLOGY ABSTRACT Architecture has been described as "frozen music." To be sure, architecture has many physically static features, yet it can best be understood as a process in motion and as motion. Both architecture and music share attributes of qualitative movement. A composition unfolds in phases of tension and repose, extension, and arrival. Explicit patterns of organization are defined by proportions, gradients of texture and intensity, and always through the experience of space in time. RELATED EXPLORATIONS ... is an inquiry and a proposed demonstration of a parallel process of composition. A landscape, a sonata, and a building design are "composed" synesthetically with respect to their temporal qualities. An agricultural site in Northern Massachusetts is chosen for a new community of artists. The project accommodates artist housing, studios, workshops, and facilities for performances and exhibitions. Perceptual qualities of the site, programs, and formal strategies are illustrated with diagrams, notations, and original photography. Musical scores and design drawings are presented together to aid direct comparison of the mediums. A cassette recording of the sonata for violin in D-major is included with this submission (30 minutes). The cassette will be shelved with the thesis manuscript in Rotch Library. Thesis Supervisor: William Lyman Porter Title: Professor of Architecture and Planning ii CONTENTS ACKNOWLEDGMENTS 1 INTRODUCTION, 3 THE LANDSCAPE -- 19A 20 THE VIOLIN SONATA 36 THE LIVING MUSEUM 47 ABOUT COMPOSING 55 CONCLUSION 67 BIBLIOGRAPHY APPENDIX I 71 77 iii ACKNOWLEDGMENTS The MIT community has given me freedom to explore ideas about composing and composition and I am indebted to many individuals for inspiring my curiosity and intrigue with interdisciplinary thinking and making. First, I would like to thank Professor Bill Porter who has helped me all along with the difficult task of organizing my flourishes and whose knowledge and criticisms of both the music and the architecture were invaluable while I have been at MIT. To Professors Shun Kanda and Fernando Domeyko-Perez for their interest in this project as it relates to the sensual qualities of experience. Professor Alan Fleisher and Judy Dayton Mitchell encouraged me with comments about both music and architecture. David Epstein graciously welcomed my participation in his music analysis course and introduced me to the concepts of structural hearing. To Ralph and Doris Thut whose support and examples of "processual architecture" have been important in my music. And to Dean John de Monchaux who introduced me to Brooksby Farm, the site for this project. Special thanks to my typist Stuart Stephens. To my personal friends, Laurie Friedman, Kevin Thornton, Randy Snow, Erland Ortiz, Billie Hall, Josef Ehrenfellner, Sabine Kluger, and Cathrine Verhulst who have all contributed so warmly-over the years. And finally to my family, Dr. Renate Grumach, Jutta Meinel, Curtis Casewit, and Charlotte Casewit, for their support and encouragement. NICCOLO WERNER CASEWIT, January 1987 1 The Muse She slips in behind the curtain on opening night. Strings are tuned, reeds adjusted, the light dimmed. We take a breath and raise our bows. The opening chord is sounded. She has no time to ask questions. Her mind is ours too. Sonority unfolds. Abandoning ourselves to her instinctual breath, we are transported, beginnings reflect endings; excursion invites return. Gone again, she'll be back. 2 INTRODUCTION Music shows us that movement can communicate ideas through our own physical perception. Music is an elegant means of presenting ideas as experience. Music has the capacity to arouse within us the most sublime associative content. Music is a deliberate construct. A composition in music starts as an interpretative act by the composer. The "act" of composing may be inspired and influenced by natural laws, but the "message" is finally an abstraction. An "artificial" act: the composer gives us something we did not have before. Architecture can be experienced in movement and as movement. Having abstract content like music, it is also relayed through physical mediums: into materials. ideas are transformed When self-reflection occurs, the materials can then be interpreted back to ideas. These "ideas" are expressed in mediums, but they have a life of their own. Architecture is not music, nor are the two translatable mediums. But their relationships to physical principles and their "artificial content" have many qualities in common. 3 Music and architecture are not the same: 1. Music is durationally condensed experience. and instantaneous: Momentary a compact emotional analogue. Architecture is durationally prolonged because it accompanies the real-time experience of life. 2. Their materials are not interchangeable. Visual and aural materials make space in different ways. visual stimulation -explicit space. Tacit like the trunk of a tree -- makes On the other hand, aural stimulation is found in music which can only imply space. All artistic mediums seem affected by the space during transmission. Transmission is a natural phenomenon, while artistic content is artificial. Their configurations can refer to that which is to be "codified" natural phenomena. The transmission of artistic materials is "carried" by the physical medium. J.S. BACH 3. The sequence of "composed" information in music is rigorously controlled, while in the "open" architecture we are proposing sequence is improvisational. Said another way, music programs the order in which materials are revealed, while in a multivalued architecture sequence is only suggested.* *In painting order of observation is also variable, but, unlike architecture and music, the elements in painting can be perceived in simultaneous combinations of its materials. Thus, the "real-time" experience of painting is free of imposed observational order. 4 Methods, Materials, and Procedure in Composition Artistic creation is a very elusive subject; it is difficult to discuss synthesis occuring when we make compositions. We can show and evaluate successive stages of artistic development through sketches and recordings, but this is only the evidence of the story, not the process itself. In fact, the mystery of synthesis is what motivates us because we love being surprised by what we have made! Procedures are more easily discussed, but unfortunately many artists refrain from being rigorously analytical about their creations; musical composition theory is an extraordinary exception: (though healthy dissent is rampant) music theorists have developed a shared nomenclature for describing the elusive -- perhaps because music composition has always been so closely tied to the disciplines of mathematics and philosophy. Our theory for analyzing architecture and even the "natural landscape" is partly based on current theories of structural perception in music. The concepts of prolongation and "continuance" are taken from music analysis sources and applied to architecture in an effort to find a descriptive methodology identifying factors which cortribute to a sensual architecture. ASPLUND 5 The comparison of architecture and music has -been made throughout history with the aid of geometry and mathematics. Music was thought to be the primary "voice" of the universe and therefore a source of truth explained with geometry and philosophy. For Pythagoreans, musical phenomena reflected the natural order which was essentially metaphysical. Musical proportions 1:2:3:4:... were quantifiable terms which belonged to a sublime organization of the cosmos. "Music of the spheres" was later demonstrated empirically by J. Kepler who showed that the ratios of the furthest and closets points along the natural orbits of the planets conformed to the consonant musical harmonies. Thus, the physical phenomena of sound and vibration were shown to explain other physical phenomena through a shared system of ratios. Renaissance architects Alberti, Serlio, and Palladio took heart and began writing various treatises on a rational architecture based on absolute ratios of musical consonance. This was called and is still misleadingly called "architectural composition." The concentration of their efforts seemed to be focused on the harmonious "static" presence of their buildings. We argue that "musical architecture" is not a single static "chord" composing a facade but is a further development of many ratios which are layered in all directions to make moving space. The "composition" of Alberti is a process of division, while the "musical composition" we are proposing is a process of addition and elaboration fundamentally derived from proportional ratios, but also generated from explicit patterns of registration, alternation, and direction. 6 The comparison of musical "objects" and built "objects" can only lead to an analysis which extracts abstractions from abstractions. Such a comparison cannot bring our inquiry to any truly useful conclusions. (We can compare abstractions ALBERTI, PALAZZO RUCELLAI without results until the ultimate abstraction of death concludes our discussion!) Then why are we proceeding? If we can avoid trying to answer the question, "Why do we interpret the way we do?" -- a strictly rhetorical question -and get onto talking about the process of making and experiencing architecture and music, BRIDGE IN TESSIN, BY BLASER OBJEKTIVE ARCH. 1970 useful comparisons between the two might be revealed. EGYPTIAN LABYRINTH 7 Procedure and Process When we reflect on compositional form, we often reduce it selectively into particular parts: the elements of the Sometimes this process of reflection is composition. confused with the design process itself. Reflective process can be analytical and reductive. It requires the interpreter to overlook some information in order to make sense of the rest. Once defined, these elements can be deployed in a procedure "reenactment" a --- but they are not complete ideas. These principles can be considered more or less like diagrams. They are powerful because they are transformable and self-, organizing. PROCESS PROCEDURE Procedure is an analytical prerequisite to process. In other words, procedure initiates a cognitive process which in turn activates the next procedure. Process must be understood as sentience or feeling as distinguished from communicates dynamic. reflective thought or ideas, while procedure perception. 8 Process clarifies these ideas. Surfaces (Foregr.ound) A combination of procedures can be used to evaluate a given completed composition or a composition in progress. The first inclination is to note instances of change of dimension, texture, and rhythm in the "melodic" lines (design or land topography). This gives us an understanding of BROOKSBY FARM FOREST positions and sequences of surface materials only -- like the "facade" of a great building. The next steps are to identify the sequential order of interruptions and continuities and to classify the melodic themes, as climbing, falling, or constant. RALPH AND DORIS THUT, PASING SQUASH 9 Large Groupings (Background) The third way of hearing/seeing is to extract an apparent "Ursatz" which could be linked to the global unity of the movement, and might anticipate both anomalies and thematic developments which occur independent of sequential time. VIENNA ALLISION Connections and Overlaps (Middle Ground) The second approach is more closely detailed observation of local intervals, harmonies, and transitional "passing" references: connectors and extenders within local and sub-reg.ional domains. We then identify the significant volumetric references occurring sequentially. THE DESIGN 10 At some point, just feeling and experiencing an artistic work is not enough. Questions arise: What moves a composition? What defines and constitutes the ingredients of an What experience? supports the sublime content of experience? And finally, what connects and sustains the superimposition of sequential (through memory) and simultaneous (real-time) experiences? Preliminary observations reveal that experience and perception which have GOETHE LIBRARY WEIMAR any complexity at all are made intelligible through structurally significant Motion in architecture progressions which can be and music is'either readily abstracted from continuous or fragmented, sign events. Material the quality of a patterns of gesture, particular sequence is shape, volume, and either direct or duration are the indirect. constituent elements of differences between the sign-event which are direct and indirect formed by the maker. movement give The compositions their dynamic characteristics. 11 i AM C4 4- I: 60 0om~ LL PAW~ II~ i FI ln r I11-1- so r hi ~ '. 4 1I!m -- ' wK11 I THE PERFORMANCE AND EXHIBITION BUILDINGS 12 Prolongations extend a Prolongation and composition through Continuance thematic variations of the essential materials If a sequence is too that the composer has direct it is monotonous, chosen to explore. A predictable, and even composer may start with boring -- very simple ideas or If a sequence is indirect "basic shapes" which to the extreme, we may embody the components of feel lost or disoriented. his themes. Prolongation we go to sleep! Prolongation and is experienced as continuance are elaboration and layering compositional principles gradients of one space which mediate the order into the next. Sometimes of a sequence to insure prolongations become so tension which holds our intense that they attention and sparks our literally lead the expectations of what may composition into totally follow. unexpected "aleatory" situations. In music harmony and in architecture, prolongation is the tacit urge to resist "closure" or an ending. Prolongation is excitement which actually "prepares" a return to I known territory. 13 In the fall, the leaves of trees surrounding the pond drop upon the water. They seem to migrate back to the shoreline from which they came. They are different now. The leaves still seem to belong to the land. They are merely on the water.... I~'~:~ '1 We could see through a series of rooms. We knew where we were going, because it was made for NORTH POND 14 Us-.. Continuance is closely associated with prolongation, but has an entirely different compositional function. Continuance is made evident by economy of means, repetition of motifs, density of articulation, and thematic returns. In architecture, for example, continuance is' experienced in the repetition of details, spacial moves, and like configurations of materials. It asserts a unity even in a highly differentiated design. In music, continuance WEIMAR, ST. PAUL takes us on a sensual "trip" which happens in a time-sequence, but this sequence actually folds back onto itself. One aspect of continuance is rhythm, another is the use of like-forms and spacial dimensions. Continuance is continuation of a natural cycle of tension and release. Temporally speaking, it is breath. NYMPHENBURG, MUNICH 15 The Context of the Thesis The philosophical context is a point of departure for this study. We take the position that all artistic mediums share a common relationship to, and incorporate the fundamental principles of unity and qualitative difference within their particular compositional frameworks. The musical context gives us a model of dynamic process which demarcates psycho-physical time. It is also a tacit example THE NORTH ORCHARD BIRCH of emotional expression through constructive means. Architecture creates Music fills the silence with significant space with significant form. form. Architecture tells us about how to make our C.E. MILLER time; day to day and historically. Architecture gives us references to position ourselves between sky and ground, and from here to there. We see architecture as a commitment to discussion, because it is the most public art of humankind. 16 SOUTH SIDE The natural context is our primary means of transmission and reception of compositional information. Nature is the realm of our senses, and our bodies. Humankind is essentially an "instrument" of nature, and though our creations may alter nature, we must still abide by the natural laws of metabolism, growth, and other physical principles. Nature is our primary constraint but also our only means to share ideas and feeling. F. d. MARTINI 17 The Experiment this study is to show that clarity of The purpose of this study is to determine a new procedure in architecture modification of basic based on temporal explicit control of organization in musical composition. Music and directed tension result architecture are similar art forms, in that they share qualities of sequence and artistic expression, materials, consistent spacial shapes, and the in a high level of which has dynamic length and includes the natural and constructive context simultaneity. They both order experience of events and the which is disciplined by time and the composer and the physiological limitations of human perception and artistic work. memory. imaginations of both the interpreters of the _____________ '4.- .a..--~Z/1~ Our intent is to demonstrate a theory of structural temporality by composing a sonata and a building in a parallel process. The goal of NORTH FIELD 18 The Composition The design investigations consist of three parts which were looked at separately and then combined. These parts are: -- The existing landscape. -- A sonata for violin. -- The buildings which comprise a new artist community. Each part of the total composition was analyzed on its own terms, but most importantly they were viewed in relationship to each other. In the following pages we will present and describe each element, and then proceed with a discussion o-f their interrelationships and how understanding each element of the total composition as a quasi-analogue for the others helped bring out the most in our compositional process. 19 THE LANDSCAPE FELTON ROAD, PEABODY 20 The Landscape The site is an extraordinary expanse of land near Peabody, Massachusetts, about thirty minutes north of Boston. Currently a protected greenspace surrounded by suburban subdivisions and light industry, it functions as a large park for the towns of Peabody and Danvers. The land consists of over 250 acres of agricultural land. "Brooksby Farm" is one of the oldest farms in New England. The Feltons started the farm in the 1650's, cultivating a variety of crops, including predominantly over 90 acres of Much of the terrain is very subtly sloping apple orchards. with recurrent waves which gently lead to thickly forested catchments to the north. The rows of apple trees are planted about 30' on center parallel to the contours, making for uninterrupted views of the open parts of the site. The orchards are on high land which affords the visitor significant views of the land surrounding the farm to the north. We get a sense that the farm is almost scaleless because of its expansive character. In contrast to this, we feel very far away from the hustle of the city, even though the North Shore Shopping Mall is only a mile away. The immediate neighborhoods, industry, and commercial districts which border the site are conveniently hidden by the thick climax forests which border the edges of the site. The site was studied for a complete year during all four seasons. It goes through considerable seasonal transformations: views tend to open up when the trees lose their leaves; the textural surfaces of the trees become more frame-like while expansive ground "waves" become even more apparent during the winter. The site ponds are full during spring and early summer, while being almost empty by the time winter arrives. 21 THE FELTON FARM 1650 THE SEA OF GRASS 22 The study of the site was primarily focused on how one moves through it following its natural gravity, the sense of passage and enclosure, and identifiable qualities of light which contribute to its cohesiveness and variety. A summary of principles and patterns which are relevant to our compositional theories of continuance and prolongation were identified: 1. Despite its expansive, scaleless nature, the site can be reduced to foreground: particular isolated places. These places tend to occur at the bottom of the hills near the forest or actually within forest paths which open up intermediately near the main north pond, areas of water runoff, and low places between land "wave peaks." Middleground areas were identified as places of transition which are part of both larger perceptual catchments and more intimate places defined above as foreground. Middleground portions tended to be like larger (120' x 40') outdoor districts with views limited on one side by the planar edges of the forest. Sometimes these places are occupied by roads or footpaths. Certain middleground districts function as entrances from larger background regions to other background regions. A good example of this is the area around the two large maple trees which form a dominant gate between the main orchard and the small north orchard at the bottom of the hill. PEAR TREES 23 Larger background districts tend to be defined exclusively by the forest's edge perimeter and connections with views beyond the boundaries of the site proper. Quite often they are the higher places on the land and rarely have any particularized features which one can focus on. The background is affected mostly by topology and the thematic of the apple orchards. 2. The apple orchards follow the contours of the site along a general east-west axis. The trees are planted very regularly, and if the channels between the trees are followed they tend to mark the public access to the whole site because there is little change of elevation along these paths. If one follows a diagonal path between successive rows of trees one quickly and comfortably enters into more remote areas of the site that are less public and soon dissolve into the nooks and crannies at the edge of the forest at the bottom of the hill. Thus, the relationship of paths taken with respect to the hill and the apple trees is crucial to the qualitative change of the land as.it is perceived. 3. Because the site is north-sloping, the trees almost always become intermediate filters between the sun and the observer. This is one way in which the trees and the sunlight reinforce each other's dramatic presence. There are a variety of light intensities and textures. Light falls upon the wavy terrain in soft patterns, or in highly contrasting frame-like patterns from behind angling tree trunks and branches. The general lack of light in the forest makes the brief openings or light "slots" extremely vivid. light is stronger. Higher up on the plateau the There is a continuous sense of transparent textural variety to be found here. 24 RUNOFF DISTRICTS 25 s 4, A Al 4F 41 404 BROOKSBT FARM 26 An Excursion through the Existing Site 1 Arrival at the top of a plateau along Felton St. 2 The Felton Farm. 3 Along the gardens of the Felton residence. 4 Panorama at the east ridge. 5 Easing down to a notch between two forests. 6 Young apple tree and a staccato of conifers. 7 The gate between two maple trees. 8 Willows and shrubs at the edge of the forest. 9 Strawberry fields to the right of a small hill. 10 An ocean of grass. 11 Another orchard, only two long rows of pear trees. 12 Slip down a small opening into the forest. 13 Arrival at a long meadow. 14 The north pond lit by the bright sun emerges on the left. 27 15 Follow the meadow to its end marked by a birch. 16 Enter another orchard. 17 Exit into a winding path that opens and closes. 18 Go down to the left to an opening, a small brook. 19 Continue over a slight rise as the path opens up again. 20 Arrival at steep orchard in the shade. 21 Climb up to the edge of a ridge back to the sun. 22 View the expansive orchard. 23 Follow the edge of the forest's highest trees. Z4 Fifteen rows of apple trees. 25 Reach the top of the plateau, completing the excursion. BROOKSBY EDGE BROOKSBY FARM I ir"4P THE PND'l 28 L 1 * .1 4 2<' i~ <V Th 'N ARCHITECTURE TRANSFORMATION 2-9 -M .. -midmeiK - .- PERCEPTUAL DISTRICTS 30 CL. CC w* wt Q DIRECTIONS AND MAGNITUDES 32 * * . eA 4 40 01* 94q a. ., , ee p.p pONARE "4 BOUNDARIES 33 ~- .- ~ ~- .~ / 0- C Q c-p ~.- 0-0- C 0 ~ C INTENSITY OF LIGHT 34 Ul 7/ -j THE VIOLIN SONATA / I. -Ie, -PrAA.-ec, ~VL~ -~1~A~ ~5C. I / 1"~A' '~ /frS/ -Y~ ' 36 The Violin Sonata The initial layers of the sonata for violin were inspired by the moods, contours, and temporal qualities of the landscape. Music was a method of getting directly at the subjective experiences of the land. Lengths, weights, articulation, and texture actually came after the much simpler and shorter "basic shapes" -- the motifs and harmonies which comprised the first impressions of the landscape as it was experienced in movement. In essence a "background" was abstracted and transformed through process into the minimum musical materials of the sonata. These basic motifs have a few easily describable characteristics: A$Jth2d7. immn4 37 SURFACES MIDDLE GROUND BACKGROUND SITE SECTION AL II 4= =-- a I. A~7 I IL 3%k I 1 F F -%I f ~ 38 The sonata is a tonal work, that is, its system of construction is always related to structural references, such as the triad of the "tonic" key D-major. ~ ?"" "" ~-- -== Typical progressions follow the natural tunings of the violin up and down the scale symmetrically in a kind of wave form: I-III-V-II-III-V-I or I-IV-V-I. What is important to understand is that these are very typical progressions for tonal music of all types and do not limit a sonata's overall form or its style. Harmony is simply a series of related magnitudes that are connected with ease -- the mortar and brick of tonal music from rock and roll to Beethoven. Themes are based on contrasting kinds of spaces: such as large slow themes which progress gradually by sharping a note or flatting a note, creating a change of direction with dissonant notes; which descend long flowing themes (like the slope of the Brooksby Site); and highly articulated themes which move moderately and are highly repetitious. a; 39 #- - The motifs and their respective harmonic progressions are just a starting point. Through elaboration, "stretching" inversions, mirrored themes, repeats and reversals --- all describable as procedural techniques musical variation and contrast are made and the sonata starts to grow durationally. At this point the compositional process not only interprets the landscape but begins to overlay new extraneous references. These are harmonies and shapes which are not predicted by the initial themes. They start to define special places, much like architecture when it begins to move beyond a given program of functional LA organization. 120 e. UP THE DIAGONAL 40 The Movements of the Sonata and Approximate Durations I. "The Orchard" -- introduction variations development recapitulation 1A &V04'Von: /j Ps0 4/4 largo vivace presto vivace - ir A 1 IL :9 ai- 7- 914 Ve af-3 viv'~ .1:0 so :VFW. I 41 ~ 1~ - I ~I ~ A TM i i I - - -- Ki 423 Ar InI UJ rt Y 120 d iii II ~J2' ~ 4 W . ~ -- - w j ---NOW*~ THE GATE 42 II. "The Spinning Wheel" -- 6/8 and 2/4 dolce-allegro allegro free composition development allegro presto canon arpeggio DOP. L42/A4*G~4.1 i it 2pase A AL A. 49E 3%111I _ r 43 I I~ I~p I~~ - I _4 - , 04: 7 : F AsHIM 16 IMF1 1 01 r -If 1 a, EmilIP=:IF- .61 11 2; A do dy 1:3 J-MOM 1VF k 4 - 00 10 jE W o'. OVERLAP IRA% '-W Ap I fill I Vill IF Jr dIL j:Rq* 40 dA 01 ALAIN. _Ole PF I dill 0 Pj r-1401 -I ' -4-. -- -r If - / 44 0 29 0 m III. "The Pond" -- 6/8 and 3/4 exposition andante development allegro suite moderato recapitulation presto coda ndt 66' A-AC' 10 k 3 - -~ -..- IW Ofr1 k~ -~ a __ I __ Ua. -H-- I 'I -Aadfr 4 * - -. Js .e a, ~ LW 46 THE LIVING MUSEUM SITE 47 Program for a "Living Museum" The building complex is seen as an invitation to Brooksby Farm and as a suburban extension of Boston's existing artist community. The site is huge, almost scaleless, and seems to require manmade intervention and demarcation of its nuances. The project is a "living museum" for visual artists, dancers, musicians, writers, and others who seek the spiritual reflection and creative concentration that can be found in such a setting. The project is also a place to view the products of the semi-permanent artist/residents; a multi-purpose facility accommodates concerts, and exhibitions. 48 The Architecture The architecture of the artist community is closely tied to The architecture is an the nuances of the site as it is. elaboration of characteristics already found in the landscape -- in effect the architecture becomes simply another voice accompanying the landscape. The architecture follows and leads the landscape in several important ways: The buildings are concentrated at places where overlap already occurs in the landscape. Buildings and the paths between them occupy the edges between larger "background" territories and the smaller "foreground" territories. This is particularly true of the exhibition and performance spaces which introduce the public to the artist retreat. The public buildings are directionally aligned to the natural public access down the slope of the hill and perpendicular to Felton Road which is the main East-West access into the entire site. Felton Road is the primary reference direction because it follows the dominant ridge of Mount Pleasant. Entrances to the main public buildings occur in the same direction, at the troughs of the wave contours. Auxiliary buildings, such as the guest hostel, the workshop, and the artist apartments, tend to follow the given geometries of the forest-field edges which are at relatively equal elevations. This tends to connect these more private buildings with one another while also framing the forest and maximizing the sunlight into the dwellings. 49 Site walls and ground forms are long continuous elements which provide "background" definitions to the site as a The most private and secluded buildings are positioned deep in the forested areas of the site; the studios are thus embedded into the small openings we call "foreground." whole. slopes and give both lines of reference to structural They are readily accessible from existing goals in the landscape such as entries into more paths which penetrate the forests and punctuate the unarticulated textural hiss of the forest. They generally follow the fall-line of the secluded sections along the forest edges at the bottom The studios The site walls also.provide local are highly dispersed within the site and are rather of the main orchards. self-contained "treehouses" which are lifted up into the surfaces for the apple trees to be read, and stopping air above the forest floor to exemplify the individual places to view sculptures and rest while one climbs back and meditative nature of the artistic work which will out of more remote parts of the site to Felton Road. transpire within them. an artist community HOUSING AND WORKSHOP J310 :IPA . i I;a I- 4pp 1 10 1 - i 0 . -r Ogqf!!4-- I ! I 1.4 1 F-..,OoL;l 50 VIA in Outlines of the Architectural Procedure The working methods used to design the architecture were Below is very similar to those used to compose the sonata. a brief outline of the typical procedures which were deployed in the details and larger groupings of the design: 1. Identify the functions and relationships of the parts. 2. Quantify capacities and magnitudes of the parts. 3. 4. Engage parts in a spacial sequence. Modify parts to be continuous with neighboring elements. 5. Define large background themes and factors supporting continuance. 6. Intensify and prolong individual elements. 7. Prolong connections and transitions. 8. Assert differences between parts through contrasting structures and volumes. 9. Recycle through the procedure. Preliminary Space Requirements 20 artist studio-apartments............... 1 sculpture workshop........................ 20, 000 sq. ft. 1,600 sq. ft. 1 multi-purpose performance room (seat 200)..................... ........ 2,000 sq. ft. 1 main kitchen and storage................ 2,000 sq. ft. 1 common dining hall (seats 50)........... 1,200 sq. ft. 5 guest rooms............................. 1,500 sq. ft. Visitor galleries......................... 2,000 sq. ft. Restrooms................................. 1,000 sq. ft. Outdoor sculpture/meditation zones........ Site walls, frames, stairs, and extensive landscape intervention..,....... ........ Approximately 30,000 sq. ft. 52 2.' 2 SCULPTURE 0I... -. NK. PERFORMANCE ARTIST HOUSING STUDIOS .IN THE TREES V K N jt~ -H SOUTH 04 16 WORKSHOP SITE PLAN 80 r020SOUTH STUDIOS IN THE TREES 53 ECTION A-A \ EXHIBITION EFRFORMANCE RESTRAURANT 0 -c-- 7 -C-D - 'I/B- 54 ABOUT COMPOSING "Die Gottheit ist im Werdenden und sich Verwandelnden aber nicht im Gewordenen und Erstarrten." Goethe zu Ekermann 13.2.1829 55 ENTRANCE 56 Relations of Events When an artistic work - has total coherence, the work's capacity for communication and interpretation takes on a profound character. ' Our perceptions are id*, S- continuously altered and modified by our thought and intuition. Thus, it is our psycho-physical engagement with art which enhances the work itself. There is no subject or object in the experience of art, only "events" which can be grouped in relationship to each other. The makers, the mediums, and the interpreters play 5M essential roles in the generation of events. C, 57 A most challenging possibility in composition is finding a way to relate different, even contradictory "events" to each other, and to make the overall experience of a composition accessible to the interpreters. Compositions of any type must somehow relate parts to wholes. This is a subjective activity and cannot be objectified, though the content of composition might be referring to objects like: "the red apple." Both music and architecture are "sign events" that incorporate to varying degrees the different types of signs as outlined by Max Bense in Zeichen und Design. Our study is not about semiotics, but a brief consideration of this theory may help define the general problems of intelligent groupings. 58 A Summary of Max Bense's KOMMUNIKATION (M) Theory of Signs (0) Information Semiotic/aesthetic schema z (I) Transformation SEMIOTISCHES SCHEMA consist of three aspects which make a sign as part of a "communication canal": the object (information) "O", agent the (communicative medium) "M", Generativer Graph thetischer Graph and degenerativer Graph -M-O M-0-1 1-0-M the interpreter (transformation) 'I". 0 0LI The object is semiotically related to the interpreter as: Sign Type Transformation Symbol dicenti Value + or - Index argument always + Icon rhema 4, + or - Sign Examples (a Rolls Royce !+ rich) (a name, which is definite) (the cross, which for some means Christ) There are three types of sign processes: M -> 0 -> I a generated position I -> M -> 0 a thetic process I -> 0 -> M a degenerative process (rock becomes tool which is used by "I") ("I" thinks, makes "M" to mean "0") ("I" sees "O"11 as "M") 59 Bense's discussion differentiates components of a communication system into specific roles and positions. His theories demonstrate to us why artistic mediums are different semiotically, and he categorically includes the agent "M" (means of transmission) as a viable member between the traditional Aristotelian duality of "subjectobject." Composition is accepted as a form of information, as we see it; what follows is that composition is a Large signs can be multiple-valued communicative process. "over-determined" by a synthesis of many smaller signs as transmitted through the agent and transformed by the interpreter. G. Guenther, an authority on cybernetic process, refers to such over-determined systems as "poly-contextuality." We believe that music and open-ended architecture are vivid examples of this type of complexity. Guenther says, that "if something is, It implies, as it must have order and if it appears as chaos, it only means that we have not yet found the code...." Complexity in compositional terms must not be misconstrued- as formal complexity, but rather as a "nexus" of non-hierarchical relationships which can be answered by different interpreters and possibly! I.e., (subjects) as yes, no, A > B, B > A, and A = B can be true at the same time, because of a "poly-context," which is defined as a multitude of interpretations by subjects Thus, Aristotelian logic is Sn. expanded to include many subjects which take different S1 , 32, S3 , ... , positions with respect to an object(s). In this study we refer to "poly-contextuality" as one or more "events." 60 "The temporal processes in much of Beethoven's music are ones in which revolution is possible if 'revolution' means actualizing a future that is not mechanically determined by the past and does not flow easily from human decisions, but that can be summoned only through a momentous struggle, yet is nevertheless profoundly related to the past. In many of his pieces, the wealth of unusual features makes continuity as well as fulfillment something that only an enormous exertion can achieve. The more the future has previously been unimagined and the more profoundly and comprehensively Beethoven seeks to relate the future to its past, the more violent is this struggle. Without such a struggle, continuity would evidently not be achieved, and events that are surprising would also seem arbitrary." SONATE 9~j -.p P-- A Mii Se David B. Greene, Temporal Process in Beethoven's Music p. 7 STEIN AM RHEIN 61 "Bach's music is an aural image of Newtonian time. In the Newtonian worldview, the totality of material entities constitutes a universe in the sense that they all operate according to the same laws which exhaustively explain their behavior. The location, mass, and velocity of every entity at any given time is a function of the location, mass, and velocity of all entities at the previous If one. instant of time. knows the laws of motion, as Isaac Newton believed he did, and if one knew the location, mass, and velocity of all particles at any one time, as Newton did not believe he did, then one could move either forward or backward in time and describe definitively these parameters at all other times. Although things may happen that are not predicted, nothing that is in principle unpredictable, if one had sufficient The data, can happen. pattern of change is fixed and constant.? David B. Greene, Temporal Process in Beethoven's Music p. 7 62 Music and architecture have a lot in common. They are both physically perceived. They both order temporal sequence. Most importantly they reflect a sublime world; both purposefully organize sensual experiences and inspire human interpretation and 7 Le Corbuster ofoa -Mk.e participation. VJF ViYI willB 17 Z. XVZ 7 1 LX I 42 1 z7 4(Z "Architecture is judged by eyes that see, by the head that turns, and the legs that walk. Architecture is not a synchronic phenomenon but a successive one, made up of pictures adding themselves one to the other, following each other in time and space, like music." I4 F. GIORGI Le Corbusier, The Modulor P. 73 MORTITZBURG, G. MAHLER, 4TH SYMPHONY 63 "In the application of form, music can achieve results which are beyond the reach of painting. But painting is ahead of music in several particulars. Music, for example, has at its disposal duration of time; while painting can present to the spectator the whole content of its message at one moment. Music, which is outwardly unfettered by nature, needs no external form for its expression. Painting is still almost exclusively dependent on natural forms and Its business phenomena. is now to test its strength and means, to know itself, as music has done for a long time, and then to use its powers in a truly painterly way, to a creative end." Sechs Bagatellen far Streichquartett A~ eevdMuig gt I (j.C0ao, iieder.migd.c.o Anton Webarn, Op. 9 rit. 0 PA17- -E 0r by UnEvi aw.ed 19-4 A~ylb IBSZby Anl.n Wb...* C-lg- Ul.,.ta. Wassily Kandinsky, Concerning the Spiritual in Art p. 40 w KANDINSKY 64 8 All* .ag...,s. vnrtwdrl tsal Erbe. MinJ... . 7575 - "Repetition as Creator of Form: The principle of repetition, once successfully applied to the understanding of the microcosm of musical composition, now could be applied on a larger scale as well. For if the significance of a small series of tones results clearly only after it has been repeated, it should seem plausible that a series of such small series would also acquire individuality and meaning by way of simple repetition. This is the origin of the two-part form a:a; or, more exactly, a:a2." Heinrich Schenker, Harmony p. 9 BERNINNI, R + D THUT, MUNICH BY WOLFGANG 65 Iro iw~t 'I S4.~ k.. O vLWA XAJ SOUA.&s / 4..14 iLJA Mi, ±sN '.ra g 1. 3M A44f~ ' _h', Vo""" *Ij'e PAczv1 -yG'$ .'CwrO T £i~ ?~'~ ezxaOr A miwvo_ *-4a Ac 'fl krr A~dC/-m4rnj 3AqIU.A-. low~ ThA4~ L~w tN ~ c E WAWS I,) +def -- t 7Tha _M" IV 66 10W C n l.0 k CONCLUSION Translating and Combining Landscape, Music, and Architecture The literal translation from one medium to another is not possible; even if it were it is not valuable or relevant because their forms are different. Nonetheless we think making descriptive comparisons is a fruitful working method. Composing in layers and with movement in mind is useful because it illustrates and inspires a way of thinking which is common to all art forms. Making comparisons between different compositional processes has helped us clarify and define our activities relative to the specific discipline of compositions which we are working in. Making connections between distinct forms of expression is difficult and at times confusing, but a great deal can be learned in the process....- 67 00 ftjui " THE AUTHOR, BY C.W. CASEWIT 69 Architecture is not "frozen music" In time as they are received by the instruments of our senses, space is made. When we dwell on the land music is released; we feel motion and change. A conversation, spinning curves sliding lines which we make together Between Silence You and Me 17 70 Q.. (C 0 H4 Bibliography List of Musical Sources Apel, Willi, Harvard Dictionary of Music, Harvard Press, Cambridge, Mass., 1972. , The Notations of Polyphonic Music, The Mediaeval Academy of America, Cambridge, Mass., 1953. Berry, Wallace, Form in Music, Prentice-Hall, Englewood Cliffs, N.J., 1966. Brye, Joseph, Basic Principles of Music, Ronald, N.Y., 1965. Cooper, Paul, Perspective in Music Theory, Dodd and Mead, N.Y., 1973. Epstein, David, Beyond Orpheus, MIT Press, Cambridge, Mass., 1979. , Tempo Relations: A Cross-Cultural Study, Music Theory Spectrum, Vol. 7, 1985. , Schoenberg's Grundgestalt, Ph.D. Dissertation, Princeton University, 1969. Greene, David, Temporal Processes in Beethoven's Music, Gordon & Breach, N.Y., 1982. Hodgson, Percival, Motion Study and Violin Bowing, Lavender, London, 1934. Lehrdahl, F. and Jackendorf, R., Generative Theory of Tonal Music, MIT Press, Cambridge, Mass., 1983. Meyer, Leonard, Emotion and Meaning in Music, Univ. Chicago Press, Chicago, 1956. , Music, the Arts and Ideas, Univ. Chicago Press, Chicago, 1967. Reti, Rudolf, The Thematic Process in Music, Faber and Faber, London, 1961. , Tonality, Atonality, Pantonality, Macmillan, N.Y., 1958. Salzer, Felix, Structural Hearing, Dover Pub., N.Y., 1952. 72 Schenker, Heinrich, Five Graphic Music Analyses, Dover Publications, Inc., New York, 1969. , Harmony, MIT Press, Cambridge, Mass., 1954. Schoenberg, Arnold, Structural Functions of Harmony, W.W. Norton, N.Y., 1954. Tovey, Donald, The Forms of Music, Meridian Books, N.Y., 1965. Vitali, Christoph, Paul Klee und die Music, Nicolaische Verlagsbuchhandlung, Berlin, 1986. Design Literature Alexander, Chris, Timeless Way of Building, Oxford Univ. Press, N.Y., 1979. Ando, Tadao, Buildings Projects Writings, Rizzoli, New York, 1984. Borissavlievitch, M., The Golden Number, Philosophical Library, New York, 1958. Cham-Magomedaw, Selim 0., Pioniere der sowjetischen Architektur, Verlag der Kunst, DDR, 1983. Le Corbusier, The Modulor, Harvard University Press, Cambridge, Mass., 1943. Creese, Walter L., The Crowning of the American Landscape, Princeton University Press, Princeton, New Jersey. Crippa, Maria Antonietta, Carlo Scarpa, Jaca Book, Milano, 1984. Doci, Gyorgy, The Power of Limits, Shambhala, Boulder, London, 1981. Edwards, Betty, Drawing with the Right Side of the Brain, Houghton Mifflin, Boston, 1979. Freckmann, Karl, Proportionen in der Architektur, Verlag Georg D.W. Callwey, Munchen. Friedman, Martin, Noguchi's Imaginary Landscapes, Walker Art Center, 1978. Fuller, Buckminster, Synergetics, Macmillan, N.Y., 73 1975. Habraken, John, Appearance of the Form, Awater Press, 1985. Halprin, Lawrence, Notebooks, MIT Press, Cambridge, 1972. Harvard University, Proportion, a Measure of Order, Carpenter Center for the Visual Arts, Spring and Summer 1965. Holmdahl, Gustav, Gunnar Asplund Architect 1885-1940, A.B. Tidskriften Byggmastaren, Stockholm, 1950. Kepes, Gyorgy, Language of Vision, Paul Theobald and Company, 1961. Knowles, Ralph, Sun, Rhythm, Form, MIT Press, Cambridge, 1980. , Energy and Form, MIT Press, Cambridge, 1974. Lawler, Robert, Sacred Geometry, Thames and Hudson, London, 1982. Leitner, Bernhard, Sound:Space, N.Y.U. Press, 1978. Lynch, Kevin, The Image of the City, MIT Press, Cambridge, 1960. , Site Planning, The MIT Press, Cambridge, Mass., and London, England, 1984. , Managing and Sense of Region, MIT Press, Cambridge, 1976. , View from the Road (with J. Meyer), MIT Press, Cambridge, 1965. Matthews, W.H., Mazes and Labyrinths, Dover Publications, Inc., New York, 1922/1970. Mossel, Ernst, Vom Geheimnis der Form und der Urform des Seins, Deutsche Verlagsanstalt, Stuttgart und Berlin, 1938. Naredi-Rainer v., Paul, Architektur und Harmonie, Du Mont Buchverlag, Koln, 1982. Palladio, Andrea, I Quattro Libri dell'Architettura, Edizioni il Polifilo, Milano, 1980. Rassmussen, Steen Eiler, Experiencing Architecture, The MIT Press, Cambridge, Mass., 1959. 74 Schon, Donald, The Design Studio, RIBA Publications, 1985. Smith, B.J., Acoustics, American Elsevier Publishing Co., Inc., New York, 1970. Snozzi, Luigi, Progetti e architetture 1957-1984, Electa Editrice, Milano, 1984. Wingler, Hans M., The Bauhaus, The MIT Press, Cambridge, Mass., 1969, second printing, 1976. Wittkower, Rudolf, Architectural Principles, Alec Tiranti, Ltd., London, 1952. On Language, Intelligence, and Philosophy Beardsley, Monroe C., Aesthetics, Hackett Publishing Co., Inc., Indianapolis, Cambridge, 1958, reprint, 1981. Chomsky, Noam, Language and Responsibility, Pantheon, N.Y., 1977. Gotthard, Gunther, Life as Poly-Contextuality, paper. Hofstadter, Douglas, Goedel, Escher, Bach, Random House, N.Y., 1979. Illich, Ivan, A History of Needs, Pantheon, N.Y., 1978. Jung, Carl, Man and His Symbols, Dell Books, N.Y., 1964. Langer, Susanne, The Problem of Art, Routledge and Kegan Paul, London, 1957. Sommer, Robert, The Mind's Eye, Delta Books, N.Y., 1978. Theil, Philip, Visual Awareness and Design, Univ. of Washington Press, Seattle, London, 1981. "Notes on the Description, Scaling, Notation, and Scoring of Some Perceptual and Cognitive Attributes of the Physical Environment," in Environmental Psychology, ed. by H.M. Proshansky and others, Holt, Rinehart and Winston, N.Y., 1970. Tuan, Yi-Fu, Space and Place, Univ. of Minnesota Press, Minneapolis, 1972. , 75 Topophilia, Prentice-Hall, N.Y., 1974. Other Bibliographical Sources Ardlan, N. and L. Bakhtiar, Sense of Unity: The Sufi Tradition in Persian Architecture, Chicago Univ. Press, Chicago, 1973. Arnheim, R., Entropy and Art, Univ. of California Press, Berkeley, 1971. , Art and Visual Perception, Univ. of California Press, Berkeley, 1954. Beardsley, M., Aesthetics, Hackett Pub., Cambridge, 1958. Edgerton, Harold E., Moments of Vision, The MIT Press, Cambridge, Mass., and London, England, 1979. Kandinsky, Wassily, Concerning the Spiritual in Art, Bauhaus Books, New York, 1966. , Point and Line to Plane, Bauhaus Books, Dessau, 1926. Klee, P., Thinking Eye, Lund Humphries, London, 1957. Kuhn, Thomas S., The Structure of Scientific Revolutions, The Univ-ersity of Chicago Press, Chicago, 1970. Malinowski, Bronislaw, A Scientific Theory of Culture, The University of North Carolina Press, 1944, Sixth Printing, 1973. Maur, Karin V., Von Klang der Bilder, Prestel Verlag, Munchen, 1985. Preziosi, D., Architecture, Language and Meaning, MIT Press, Cambridge, 1977. Rossi, A., The Architecture of the City, MIT Press, Cambridge, 1985. Rowe, Colin, Collage City, MIT Press, Cambridge, 1970. Scruton, R., The Aesthetics of Architecture, Princeton Univ. Press, Princeton, 1979. Weatley, P., Levels of Space Awareness, Ekistics 523, Dec. 1976. Xenakis, I., Art/Science Alloys, Pendragon Press, N.Y., 1983. 76 APPENDIX The following pages illustrate significant features found in all forms of composition and also natural phenomena which apply to and describe kinetic compositional form. By kinetic form we mean patterns which imply movement or are experienced while moving through a composition. Traditionally kinematics is defined as 3x/at -of a body changes with respect to time": "position x this is velocity. We mean not only velocity of physical movement but also the velocity of perception which is a psychological movement. It was necessary to develop notation that resembles both musical and architectural patterns. Many aspects of composition would best be illustrated by the actual notations in scores and drawings used in the respective fields. But an attempt is made here to simply diagram what these features are in order to aid comparison. This is a two-dimensional representation of what actually occurs in many dimensions. Mathematical equations describing the physics and the geometry of compositional patterns are included to aid further study. 77 Gestures = A X A--/\/ f(x) shape loudness weight density texture ~_ I W ~t _ brightness color and pitch d\J\.N4 v dB = 10 F = ma d = m/V t = uN B = I/A f =c A + A 1 Xn-1 + o 10( 1) Demarcations upbeat initiation convergence af(t)/at > 0 = at t o f (t) ___ ___ if - an lim an = 0 n +- and 0 divergence allision consonance dissonance closure lim an * and I an 0 n +w , b) and (c.d) and a < b, b > c , d > c, d > b 1:2, 2:3, 3:4. 4:5 5:6, 6:7,U-an n - 1/n, n > 6 ( t /at < 0 if 4 9 Sli = 9 p,- -~~~ -af(t) af Layers surface fU f(xy) 3t where 0 middle ground background sonority 78 _ V(xyz):f(t) _______..____ V(x y za):f(t) S:fft) U A = V + VM A = (xy) Registration point line p(x) L(xy), (b 4 plane f(x) A(xy) = mx + b f(x) ax = a b V(xyz) volume Ax = ax Voice Overlaps imitation| Va= alternation retrograde -- 3w Vb V = (-1 )Vb sin Va = cos(Vb inversion - nVa n + 7T) n 00 - ew b ??? (field theories?) stretto Relative Proportions arithmetic geometric harmonic Note: b = (a + c)/2 ac b b = 2ac/(a + b) See relative scale and harmonic series, page 81_ 79 The Correlation between Pitch and Relative Scale Calculations based on human hearing thresholds reveal that audible wavelengths are comparable to very significant limits of human body sizes and also "social"* scales of perception. The normal human ear can hear a range of tones: fr = 16 Hz to about 20,000 Hz Calculating the wavelength: Ar [Al'Ah] c/fr = Ar (at 15 0 C) c = speed of sound = 340 m/s Al = 340/16 = 21.25 m 69.7 ft (long wave = low frequency) Ah = 340/20,000 = 0.017 m 0.66 in. (short wave = high frequency) The long wavelength (69.7 ft) is a close approximation to the upper limits of social transactional space: it is about the maximum distance from which we can recognize a person's facial expression visually. The shorter. wavelength is an important but minimal hand-size dimension. Another example is not quite as surprising but just as significant. Our most sensitive hearing response threshold is about 3500 Hz. Its wavelength is about 3.8 in. -- this is about the distance between our eyes. We conclude that sonic dimensions are equivalent to intimate visual dimensions. Longer "landscape-sized" dimensions are of course still perceivable to our eyes, while our ears can no longer hear such large wavelengths. 80 "Use size" -- Scale I Melody! - -A I &F I "Room size" parts! Inner -- Scale II IZZ2dP I Xr .42 "Building sizes" I' N El "T M CD0 C) -- u 00 CO L C Cfl\ 1,0 N ....... 1 C LrI . (Y) M 0 ni CN C) Scale III Found structure! Overtone Series fundamental = fn 1 n = series + n=1 exact multiples: fn = D 7 3 Hz, harmonic (1/n)A, geometric nf lowest "'D" we can hear a series in degrees = tan~l(An+l/x) The Series n fn (Hz) A/n (ft) Scale 1 73 146 15.4 7.7 5.13 3.85 3.08 2.6 2.2 1.9 1.7 1.5 1 *4 1.28 1.18 1.1 1.02 0.96 I 2 3 4 5 6 7* 8 9 10 292 584 11 12* 13* 14* 15 16 1168 II octaves! *Only approx. I8 V I16 III V =.- I :V | *~ ,,, ,t * . q * *- 1 a I 1. /* /"'''' Iv j II III viiI* V. vi vii I32 tones of temp. scale. 81 Proportions of the 12-Tone Scale Quotient* Major 1/1 16/15 10/9 9/8 6/5 5/4 4/3 45/32 3/2 8/5 5/3 9/5 15/8 2/1 Key: - 1 1/2 2 II 3 III 4 IV V 6 VI 7 VII VIII Minor - Scale Step Tone Half Small whole Large whole Small third Large third Fourth Large fourth Fifth Small sixth Large sixth Small seventh Large seventh Octave 1.00 1.06 1.11 1.125 1.20 1.25 1.33 1.40 1.50 1.60 1.66 1.80 1.875 2.00 1/$ $/2 1.00 0.94 0.90 0.88 0.83 0.80 0.75 0.71 0.66 0.62 0.60 0.55 0.53 0.50 0.50 0.53 0.55 0.60 0.62 0.66 0.71 0.75 0.80 0.83 0.88 0.90 0.94 1.00 $ = reference to Tonic I 1/$ = interval below Tonic (inversion) $/2 = reference to Octave (Tonic) Other categories: $/1.5 = intervalic reference to fifth above Tonic $/1.33 = intervalic reference to fourth above Tonic Quotient always relative to tonic and the particular interval above. TONIC 1/1 OCTAVE 1/2 82 FIFTH 3/2 FOUR 3/4 Average Common Durational Dimensions of Movement Dim. Ft. 27r(1 800) 27r(1600) Slow Walk (1 mph) Fast Walk (3 mph) (264 fpm) = 11,309 = 10,053 3200 2400 1800 1200 600 500 400 300 200 100 90 80 70 60 50 40 30 25 20 15 10 6 (88 fpm) 128 14 36 27 20 13 7 5 4 43 min. 38 12 9 6.8 4.5 2.3 1.9 1.5 1.13 0.75 0.375 0.33 3 2 1 1 Meditational Walk (0.5 mph) (44 min. 5 6 0 7 5 4 25 12 0 fpm) 257 min. 228 72 54 41 27 13 .6 11 .4 9 .1 6 .8 4 .5 2 .25 2 .0 1 .8 1 .00 1 .36 1 .13 no longer relevant these become program dimensions (see below) Program Durations Number of People Clock Time Max. Min. Studio/work Living Sculpture garden Performance Exhibit Eating Walking Reading Party 1 hrs 4 hrs ? hrs 1 hrs 1 hrs 0.5 hrs 4 hrs 4 hrs 1 hrs 4 8 1 2 2 1 1 2 4 hrs hrs hrs hrs hrs hrs hrs hrs hrs Min. Max. 2+ 2+ 4+ 200+ 200+ 50+ 5 5 10 300+ 300+ 100 6 4 100 3+ 2+ 50+ 83 4- LIBRARY OF ST. GALLEN 84 "he 3m' v- - -. Ep W '~ LIBRARY OF ST. GALLEN, SWISS NAT. TOURIST OFFICE, 1986 85