Musical Analogies

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Musical Analogies in Architecture by E. Toby Morris

Analysis, analogy and the Constructive Principle have long been keystones in designers'efforts to bring the spirit and organizational principles of natural law to their art. Since Ancient

Egypt architects and artists have approached their art as a laboratory for the exploration of the

natural world. Egyptian and Minoan column capitals evoked the beauty and life force of lotusblossoms; the lines and proportions of the Doric Order recalled the strength of tree trunks; and

rational and geometric planning worked side by side with the expressive power of natural form.

With the advent of Pythagorean theory and Platonic philosophy in Classical Greece the scientificmethod was used to analyze the relationships between man, his creations, and his environment;

and architecture was first tied to the laws of musical harmony.This article explores a topic parallel to discussions of design theory and the constructive

principle, namely the use of musical analogies in architectural design. Even as architects study

natural forms and processes to derive "organic" approaches to design, proponents of musicalanalogy in architecture must research the characteristics of musical experience and music's

underlying structural principles in order to formulate sympathetic responses in design. The

article first presents a brief history of musical analogy in architecture -- its goals and products --and then outlines a constructive process of translation for bringing musicality into the

organization and perception of architectural space.

HISTORY OF MUSICAL ANALOGY IN ARCHITECTUREAnalogies drawn throughout history between music and architecture have had one common

purpose: that Music, the most divine and free of arts, become the teacher of worldly andmaterial-bound Architecture. The perceived strengths of music, however, and its place in

assuming this pedagogical role have changed over time. Most famous are cosmological analogies

in which correspondences between the arts were drawn from shared scientific or metaphysicalfoundations: Such were so called "harmonic proportions," linking medieval and Renaissance

architecture to music by means of Pythagorean theory. Less common have been recentperceptual or structural analogies, such as attempts to transcribe music into architecture bygraphic means, or abstractly through an analysis of musical media and perception.

Correspondences drawn between music and architecture have roots in the culture, philosophy

and science of Ancient Egypt, Classical Greece and Pythagorean Theory.(FN1) Pythagoras is

credited with the discovery that pleasingly blending notes or "consonant intervals" could beexpressed mathematically by simple ratios of small whole numbers.(FN2) The unison, for

example, an interval created by plucking two strings of equal length (1:1) and the octave (one

string half the length of the other, or 1:2) are extremely stable and pleasing intervals. The fifth(2:3) and the fourth (3:4) are other such examples. The significance of Pythagoras' discovery is

found in the Plato-Pythagorean concept, which maintained that man's primary relationship to

Nature (and hence to God) is through his perception of active cosmic principles called "Forms"or "Ideas." The presence of simple number ratios in music's consonants was seen as the signature

of a Natural or Cosmic Order, which equated beauty in music with simplicity in mathematics and

geometry.The most important outgrowth of Pythagorean philosophy for architecture was the

development of "harmonic proportions," an aesthetic theory aligning musical ratios with the

proportions of architecture. The Roman architectural theorist Vitruvius Pollio (84-14 B.C.) may

have been the first to mention the art of building according to musical law in his Ten Books on


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Architecture; however, no writing by ancient Greeks is known to have documented or espousedthe use of musical proportions in Greek building design.(FN3)

Medieval Europe saw a rebirth of Pythagorean Theory. In the ninth century with the advent of

polyphony in sacred music it was discovered again that some notes sounded well together whileothers did not. The unknown author of Musica Enchiriadis (c. 860)(FN4) offered this

explanation: "There are several writings of the ancients in which it is convincingly shown ... thatthe same numerical proportions by which different tones sound together in consonance alsodetermine the way of life, the behavior of the human body and the harmony of the

universe."(FN5)

Theologist and theorist St. Augustine was largely responsible for introducing Pythagorean

philosophy to the medieval Christian world through his treatise De Musica.(FN6) Ranking theintervals in terms of their degree of consonance and mathematical simplicity, he leant moral

overtones to the discussion and noted that dissonant (and numerically complex) intervals have

the tendency to strive for perfection by becoming resolved in consonant ones. In an attempt toanchor both music and architecture in metaphysical reality he called for the direct transference of

harmonic proportions to sacred architecture. For him the contemplation of geometry in music

and architecture was seen to play an "anagogical" function: one leading the mind from the worldof appearances to an understanding of the Divine.

As with the Greeks no medieval builder is known to have documented his use of harmonic

proportions in architecture, the only clues to their common application being the proportions ofbuildings themselves. While still largely undocumented in the literature, several modern authors

have noted the use of musical proportions in sacred medieval architecture.(FN7) One notable

example is French theorist Louis Charpentier's analysis of Chartres Cathedral where he found

multiple musical ratios in the proportions of the width of the nave to the hypotenuses of trianglesdrawn to significant points on the nave wall.

Harmonic proportions found widespread acceptance during the Renaissance. RudolfWittkower argues that Italian Renaissance architects strove to elevate their art to the status of a

science by harmonizing it with natural law.(FN8) The words of Leon Battista Alberti typify this

sentiment:

I am every day more convinced of the truth of Pythagoras' saying, that Nature is sure toact consistently and with constant analogy in all her operations: from whence I conclude

the same numbers, by means of which the agreement of sounds affects our ears with

delight, are the very same which please our eyes and our mind. We shall therefore borrow

all our rules for the finishing of our proportions from the musicians, who are the greatestmasters of this sort of numbers, and from those particular things wherein Nature shows

herself most excellent and complete.(FN9)

Commensurable ratios (those ratios of simple integers) were the keystone of all Renaissanceproportions and they are abundant in Palladio's published plans.(FN10)

With the advent of the "Age of Reason" and the birth of the scientific method the basic context

supporting the application of harmonic proportions had irrevocably changed. No longer were thesimple ratios of musical consonances seen as the mark of a cosmic design; in the new world of

causality, patterns were the mark of physical forces and evolution.(FN11) Music's

commensurable ratios stripped of their larger context became merely a curiosity; however,

interest in the musical analogy remained and correspondences between music and other arts


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entered a new stage in which increasing weight was placed on perception and structuralsimilarities.

German Romantic philosopher Friedrich Schelling (1775-1854) called for an architecture

permeated with rhythm, striving to express the Ideal in art, much as Plato had seen it. It was hewho first coined the phrase "frozen music" in his Philosophie der Kunst of 1859: "Music, to

which architecture corresponds among the various forms of the plastic arts, is freed from therequirement of portraying actual forms or figures ... [It is] separated from matter. Architecture,however ... if it is music, then it is frozen music."(FN12)

Eighteenth century theorist Fredrich Schiller acknowledged the fundamental differences

between the arts, but set the stage for structural comparisons and analogies between music and

architecture when he stated:

The plastic arts at their most perfect must become music and move us by the immediacy

of their sensuous presence.... This, precisely, is the mark of the perfect style in each and

every art: that it is able to remove the specific limitations of the art in question withoutthereby destroying its specific qualities, and through a wide use of its individual

peculiarities, is able to confer on it a more general character.(FN13)

Among early twentieth century authors Claude Bragdon took the most inclusive view ofarchitecture as "frozen music."(FN14) From a Theosophical perspective he argued that evolution

proceeds from natural law, which in turn leaves its imprint on the thing evolved. All arts aspire

to this expression, but music, "being unencumbered by the leaden burden of gross physical

matter, expresses it most easily and adequately."(FN15) Other arts, such as architecture, canfreely benefit from association with the facts of mystical harmony and rhythm by analogy to

music's structural components: Rhythm in architecture (as in music) is the key component of

ordering, both at the gross level of building structure and at the finer one of skin articulation.Harmony in both arts consists of a critical relationship of parts to the whole. Finally, pattern and

texture enrich both types of composition. Bragdon's discussion came with one proviso: namelythat, "rules and formulas are useful and valuable not as a substitute for inspiration, but as aguide."(FN16)

Analysis of music's graphic and structural characteristics have been the basis for later

twentieth century analysis and constructive experiments. In 1952 Claude Charpentier showed

how the graphic analysis or rhythm in music begins to resemble an elevation inarchitecture.(FN17) Charpentier's approach was based on drawing parallels between abstractions

of both music (the score) and architecture (the elevation). The rhythms perceived on the staff are

rhythms of the density of ink on a printed page; they are not necessarily the rhythms of the heardcomposition. As such the approach is limited to using music as an inspiration for design

decisions, with no attempt to anchor them in the actual overall mood and specific characteristics

of the music.Reacting to the uniformity of 1960s International Style architecture, Douglas Haskell

suggested that architecture take a cue from jazz and reject regular rhythms of structure and

fenestration in favor of syncopated rhythms and dissonant proportions.(FN18) (His call to actionhas largely come to fruition in the 1990s architecture of dynamic and deconstructed forms.)

Two examples from the world of painting deserve note as they included relatively rigorous

analyses of music's structures for transposition to graphic media.

In the 1940s and 1950s John De Cesare sought a "visual representation of music in


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space."(FN19) Attempting to give form to the overall blending of sound occurring in complexcompositions such as symphonies, De Cesare's compositions involve a visual blending of parts.

His most significant contribution to the development of working structural analogies was the

creation of the "space unit" to replicate duration in music. Duration was represented usingarchitectural techniques of scale. For example, a quarter note was represented as one-half inch

horizontally in his painting. A note then became a triangle with the base representing its durationand the height its pitch. The "space unit" was a genuine attempt to take a musical characteristic(note duration, in this case) and transcribe its effect in the music to another art form.

In 1964 artist Joan Saugrain attempted to depict the structure, order, and relations evidenced in

musical patterning by decomposing music into its component parts.(FN20) Her innovation

consisted of assigning specific responses to music's characteristics of pitch, duration andharmony. Using a simple polyphonic piece by Bela Bartok, Saugrain created a constructed relief

of colored planes representing the notes: Pitch was represented by plane height and color.

Duration was depicted by laying out the note/planes into base and treble lines and allowingspatial placement to correspond to note initiation. Finally musical harmony was suggested by

means of the planar reflectivity of adjacent colored "notes."

In the modern architectural community little has been written about the application of musicalprinciples to design; however, those architects who have declared an interest in music span the

century and a variety of design aesthetics. Le Corbusier stated, "My work, architecture and

painting, is after more than thirty years nourished by the rigors of mathematics because for memusic is always present," and, "music dominates, reigns actually, harmony; and harmony itself

reigns over all things."(FN21) Le Corbusier's and Iannis Xenakis's Philips Pavilion at the

Brussels Worlds Fair (1957) is probably the most famous modern example of a space built to

highlight the characteristics of a specific piece of music.(FN22)Two architects whose names are frequently associated with the word "organic" deserve note:

Frank Lloyd Wright and Bruce Goff. In his autobiography Wright discusses his early debt tomusic: Its poetry, romance and emotional impact impressed him deeply and the young Wright

found release in its "rhythms and syncopations."(FN23) Specific connections between music and

architecture, however, go largely unarticulated in his writing. Bruce Goff, on the other hand, sawin music (and in particular contemporary and experimental compositions) a key to "absolute

architecture": an architecture using the fundamental materials and principles of the art to explore

aesthetic and emotional issues.(FN24) He composed music, explored its pattern generatingqualities, was interested in multi-sensory experience (compositions of light, sound and form) and

encouraged his students to listen to and draw from music's wealth.

A CONSTRUCTIVE PROCESS OF TRANSLATIONWithout question, harmonic theory and its application in systems of proportion profoundly

influenced the historical development of architecture. Nonetheless this body of theory fails to

convince scientists or inspire architects today. What is a rational basis from which to draw

parallels between music and architecture?Most promising is to develop analogies of a structural nature which seek to define the essential

characteristics of each art and enable us to draw useful parallels between them. Through a

constructive process of translation general musical qualities or the specific characteristics of a

given piece may be built into architectural experience. Wassily Kandinsky experimented withmusical analogy in his own work and acknowledged both the strengths and limitations of this

approach:


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Comparison of means among the arts and the learning of one art from another can only besuccessful when the application of the lesson is fundamental. One art must learn how

another uses its method, so that its own means may then be used according to the same

fundamental principles, but in its own medium. The artist must not forget that each meansimplies its proper application, and that it is for him to discover this application.(FN25)

Ironically, "fundamental" research of musical applications in architecture is almost non-existent. While a handful of architects, artists, and theorists mentioned above have exploredvarious musical qualities for application to architecture, none to my knowledge have tried to look

at music as a whole: as an art bound by laws of acoustical perception and consisting of

distinctive underlying elements, structures, and organizational principles. The remainder of this

article presents the outlines of such a comprehensive approach to musical analogy inarchitecture.

Perhaps potential investigators have been halted by music's and architecture's obvious and

substantial differences: Music is sound expressed in the context of time while architecture isforms and space revealed in light. Music occurs sequentially with discrete beginnings and ends,

while the perception of architecture may occur instantaneously or only after repeated visits andmuch time elapsed. Architectural experience, moreover, is far more complex: It is informed by

multiple senses: sight, certainly, but also smell, hearing, and even touch.

THE PERCEPTION OF MOVEMENTThe above distinctions having been made, the experience of time in music and space in

architecture may be closer than they appear at first consideration. Space and time meet mostimportantly through the perception of movement. The quality of movement is an essential aspect

of all music and the first step towards the musicalization of architectural experience may well be

to stimulate the perception of movement in spatial and architectural experience.

While architecture is generally fixed, architectural experience becomes dynamic (and likemusic more mutable) through the movements of the observer. A dynamic sense of rhythm and

tempo can be created in architecture through a choreographed progression of spaces varied in

accentuation, scale, and form. One notable example of this approach in a contemporary contextis the pedestrian tunnel at the Chicago United Airlines terminal designed by sculptor Michael

Heyden and architect Helmut Jahn. Time in this space is firmly orchestrated. Moving along a

conveyor belt the observer's precepts are sequentially and linearly controlled. Like music, the"piece" has a beginning, variations, a climax of fiber optics and sound, and an end.

While most architectural spaces do not lend themselves to such a firmly orchestrated

presentation architecture may embrace the dynamic characteristics of musical movement throughstrategic uses of form, space, and light: Architecture can simulate music's metrical accentuation

through formal emphasis or variation (i.e. irregularly placed and sized columns). It can suggest

movement through interweaving or obscured forms and materials. (Architects practicing in the

organic tradition have long understood the power of curvilinear form, asymmetry and variedscale to elicit the experience of movement.) Strategic uses of natural and artificial light also

enliven spaces. The treatment of surfaces can invigorate forms through varying colors, textures,

levels of embellishment, and the reflectivity of materials. Finally, senses other than sight can beengaged to intensify the experience of time passing (changes in temperature, noise, and smells

may reinforce the experience of movement).


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MUSIC'S ELEMENTS, STRUCTURES, AND FORMBeyond a general appreciation of musical movement and the passage of time so characteristic

of musical experience, architecture which attempts to emulate the perception of music must

address the media, means, and organizational principles which characterize musical experience.

Fortunately musical theory is extremely well developed and the tools of musical analysis providethe entree: Any musical composition can be precisely described by its use of the elements of

sound, the structures which organize them and the overall musical form.

At foundation all sound and music are composed of four basic acoustical elements. They arepitch, duration, loudness and timbre.

Pitch refers to the perceived highness or lowness of a sound and its primary determinant iswavelength or frequency. Pitch in music, and color in visual arts have been frequently compared,

as vibrations in sound (pitch) are analogous to vibrations in light (color). Duration in music (the

time period of a tone from its initiation to its termination) forms a temporal scale which is bestcompared to spatial length in architecture.

Loudness refers to the absolute intensity of sonic material (volume measured in decibels) and

through it emphasis and drama are created. In music "dynamics" refers to the relative intensitiesof a series of tones ("crescendos" and "diminuendos") and may be characterized by leaps of

contrast or smooth transitions of volume. In architecture spatial volume plays a similar role to

loudness and derives its impact by means of contrast.

Timbre we experience as the basic distinguishing quality between notes of the same pitchplayed on different instruments. (Timbre is actually determined by the presence and strength of

the harmonics produced by an instrument.) The musician's manipulation of timbre is akin to the

architect's choice and composition of materials characterized by specific qualities of texture,weight, hardness, temperature, and reflectivity, among others. When we transcribe a piece of

music to architecture we may choose a palate of materials that share characteristics with the

musical instruments or voices. For example, distinct and pure tones may correspond to hard,reflective, conductive, and/or bright materials.

While an understanding of music's acoustical media is critical, the richness of the musical

language and its potential for informing design are only revealed when we look beyond its

individual elements and consider musical structure. The three most important and influentialstructures in Western music are rhythm, harmony, and melody.

Rhythm is the most dominant structural characteristic of most music. It consists of the

durations of sounds and silences, of meter (the "beat," or hierarchy of weak and strong pulses), oftempo (pace), and of changes in loudness. By means of musical rhythm we anticipate what will

follow and as such it is an effective device in the creation and release of tension.

Rhythm is also recognized as a central organizational principle in architectural compositionwhere concepts such as repetition, varied articulation, and a hierarchy of differentiated parts are

key. Rhythm in architecture, however, is rarely expressed with such variety and contrast as in

music. For this very reason architects should study the various ways in which composers and

musicians use rhythm to enliven and give meaning to their art.Harmony is the second most critical structural property in music. Musical harmony is the

blending of tones whereby the impression of musical space, depth, and mood is created.

Consonance and dissonance characterize musical harmony and are played against one another tocreate tension and resolution.

While harmony in architecture is usually defined differently (i.e. as the relationship of parts to

the whole, or of order outweighing complexity), two aspects of musical harmony may beeffectively translated to architectural and spatial experience. First is the character of individual


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chords themselves. To analyze a simple piece of music with this in mind is to look for qualitiesof composition, proportion, density, and the organization of materials into characteristic

groupings. Second is the harmonic character or mood of larger phrases created by "chord

progressions." The chord progression may be compared to architecture's sequence of contrastingspaces and/or materials which elicit alternate feelings of tension and relaxation in the observer.

The concept of musical dissonance, for example, might be expressed in architecture as theintroduction of some unexpected formal twist (the breaking of symmetry, a clash of materials oran unexpected change in scale) subsequently to be resolved elsewhere.

Melody refers to a sequence of pitches of distinctive hoights and rhythm. One of the most

suggestive characteristics of melody is its shape: It has directionality, rises and falls, expands and

contracts. Musical lines describe beautiful shapes on the score and in the imagination of thelistener. These characteristics of melody have implications for the evocation of form in

architecture and for the use and placement of materials. Forms may rise and fall in silhousette

and materials may be treated to create the illusion of melodic horizontality, not characterized byformal linearity but by richly varied shape and emphasis.

Beyond music's elements and structures overall musical form is defined through a number of

devices, most important among them phrasing (or grouping) and orchestration.Melodic phrases are readily expressed in the composition of materials and openings along the

plane of a wall. When considering a piece of music for architectural transposition one may note

its organization into phrases and the differences between first and subsequent repeats of musicalmotifs. Such organization and variations can be integrated into the architectural translations of

melody, harmony, or rhythm.

Orchestration in music consists not only of the choice of instruments but also of the roles and

relationships between them (i.e. instruments as solo voices or as harmonic support).Architectural materials may likewise be organized and placed not only to enclose form, but as

"instruments" with distinct tones capable of engaging with one another in a variety of visual and

functional relationships.

CONCLUSIONSMusical analogies in architecture have enjoyed a long history and likely will continue to

fascinate architects for years to come. While the application of harmonic proportions has fallenfrom vogue, interest in broadening and enlivening architectural experience by analogy to other

arts is as strong as ever. Music has particular appeal. While practicing architects daily confront

the challenges of architecture's functional requirements, social obligations and materialconstraints, musicians freely explore worlds of pure sensation and of artistic and emotional

content, regularly challenging conventions of harmony and composition. Each generation of

architects has approached the musical analogy differently, bringing new world views, analyticaltools, and artistic skills to the task of drawing meaningful parallels; nonetheless, even the

rudiments of transpositional theory are lacking.

The structural analysis and translational process outlined in the latter part of this article is anattempt to address this gap in theory. The exploration of music's elements, structures, and formscan only result in a heightened awareness of musicality, leading designers on new paths in

pursuit of dynamic form, varied spatial sequences, expressive rhythms, and the evocation of

emotion.We make no claims to the objective validity of the interpretations introduced here; the

translation of musical ideas to architectural expression is ultimately subjective and depends to a

large degree upon personal experience and artistic imagination. Nonetheless, any theory or


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constructive process attempting to bridge these arts must be comprehensive and firmly grounded

in the fundamentals of musical expression and perception.

E. TOBY MORRIS is a practicing architect in San Fransisco. He has published articles on

historic structures research and non-profit housing development. He currently teaches design inthe City Planning Department of the University of California at Berkeley. This article is a

condensed version of his Masters Thesis in architecture.

FOOTNOTES1. Tons Brunes, The Secrets of Ancient Geometry (Copenhagen, 1967). Pythagoras, to whom the

earliest analogies between the laws of musical harmony and of the cosmos are usually credited,received his training in mathematics and geometry in Egypt in the sixth century B.C. where it is

held he spent 22 years as a priest of the temple.

2. Hermann Helmholtz, father of nineteenth century acoustical science, found physical and

physiological bases for Pythagoras' discovery regarding the pleasant, smooth quality ofconsonant intervals and published them in his ground breaking work, On the Sensations of Tone

as a Physiological Basis for the Theory of Music, trans. Alexander J. Ellis, 4th ed. (London &

New York, 1912). The harmonious quality of consonances, he argued, and their distinction fromdissonance, depends largely on the harmonic upper partial tones (harmonics), which vibrate (and

sound) along with the note's fundamental tone. The overtone series of a fundamental contains the

octave, the fifth and the fourth, all of which were important to Pythagoras. The overtone seriesalso contains the major and minor thirds and the major triad, intervals around which most

Western tonal music is composed. Helmholtz found that so called "dissonant" intervals in

Western music are those in which few of the upper harmonics or partials of the component tones

are shared. Such intervals cause a beating in the amplitude of the sound produced, which isexperienced as an unpleasant sensation on the basal membrane of the inner ear. When we speak

of a composer's tendency to resolve dissonances in tonal music we are referring to the human

inclination to mirror the laws of harmonics in our compositions.3. See Vitruvius Pollio, The Ten Books on Architecture, trans. Morris Hicky Morgan

(Cambridge, Massachusetts, 1914). Modern research by Albert von Thimus (Die harmonikale

Symbolik des Alterthums, 2 Bde. Koln, 1868 & 1876, Neufruck Hildesheim, 1972) and HansKayser (Paestum. Die Nomoi der drei altgreichischen Tempel zu Paestum, Bildteil Nr. 23,

Heidelberg, 1958) suggests that Greek temple building may have been founded on a system of

"harmonic proportions" (those derived from the simple ratios forming musical consonants)because these ratios occur frequently in temple architecture.

4. Anonymous, Musica Enchiriadis, ninth century, trans. Leonie Rosenstiel (Colorado Springs,

1976).

5. Manfred F. Bukofzer, "Speculative Thinking in Mediaeval Music," Speculum XVII, no. 2(April, 1942): 174.

6. Saint Augustine, Bishop of Hippo, St. Augustine on Music, Book I-VI, trans. R. Catesby

Taliaferro (Annapolis, 1939).7. See Otto von Simpson, The Gothic Cathedral (New York, 1962) and Louis Charpentier, The

Mysteries of Chartres Cathedral, trans. Sir Ronald Fraser (London, 1972).8. Rudolf Wittkower, Architectural Principles in the Age of Humanism, 2[supnd] ed. (London,

1952).


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9. Leon Battista Alberti, The Architecture of Leon Battista Alberti in Ten Books..., Book IX,chapter 5, trans. James Leoni (London, 1726); Re-printed by J. Rykwerk (London, 1955).

10. See Wittkower's discussions of harmonic proportions in Architectural Principles.

11. So forcible was the new science of Enlightenment that the seventeenth and eighteenthcenturies saw the general destruction of the analogy of harmonic proportions. The concept that

proportions could be transferred from the audible world to that of the visible world was attackedby Claude Perrault (Ordonnance des cinq especes de colonnes [1683], trans. John James as ATreatise of the Five Orders of Columns in Architecture, 1722), who in 1683 stated that we are

unaware of any mathematical ratios involved in musical intervals. While disharmonies are

quickly perceived in music and can cause discomfort, there is a large latitude, he argued, to

augment or diminish the dimensions of parts in architecture without substantial consequence.Tommaso Temanza (Vita di Andrea Palladio, 1762) then attacked the problem from a perceptual

viewpoint, noting that the proportions we see are dependent on the relation of the viewer to the

object, which is hardly absolute, being in a state of continual flux as we move through a space.Gotthold Ephriam Lessing ("Laocon, An Essay on the Limits of Painting and Poetry," 1776)

objected to perceptual analogies claiming that the arts represent different realms of human

experience and should not be translated from one to the other. Others, such as Hume (Of theStandard of Taste, 1775) and Archibald Alison (Essays on the Nature and Principles of Taste,

1790), found no place for proportioning by musical analogy and held that beauty is in the eye of

the beholder and that our response to form derives from our associations with it and is entirelysubjective.

12. Friedrich W.J. Schelling, The Philosophy of Art, trans. and ed. Douglas W. Stott

(Minneapolis, 1989).

13. Hugh Honor, Romanticism (New York, 1979), 119. (From "On the Aesthetic Education ofMan," by Schiller.)

14. Claude Bragdon, The Beautiful Necessity, Seven Essays on Theosophy and Architecture(Rochester, N.Y., 1910), 85-96.

15. Ibid., 85.

16. Ibid., 90.17. Claude Charpentier, "La Musique Puet-elle Etre une Source d'Inspiration en Architecture?"

Urbanisime 21, no. 1-2 (1952): 51-9.

18. Douglas Haskell, "Jazz in architecture. It makes more fun and better sense," ArchitecturalForum (September, 1960).

19. John De Cesare, "The Theory of Visual Space in Music," Precis 6 (Spring, 1987): 182-8.

20. Joan Saugrain, "Some Possible Relationships between Composition in Music and Art," TheStructurist 4 (1964): 35-48.

21. Charpentier, 58.

22. The pavilion was built as multi-sensory experience incorporating a piece composed by

Edgard Varese. See Iannis Xenakis, Music. Architecture (Belgium, 1971) and Formalized Music,Thought and Mathematics in Composition (Bloomington & London, 1971).

23. Frank Lloyd Wright, An Autobiography (London & New York, 1932).

24. Sidney K. Robinson, "Bruce Goff and Music," in The Architecture of Bruce Goff, 1904-1982, Design for the Continuous Present, ed. Pauline Saliga and Mary Woolever (Munich &

New York, 1995).

25. Wassily Kandinsky, Concerning the Spiritual in Art, and Painting in Particular (New York,

1947).

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