Archit and Music Harmony Proportion Order

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rchi tecture and Musicn Rhythm, Harmony and a rd e r

Richard de la RivaSchool of rchi tec tu reMCGill Univers i tyApril 18th , 1990

The sis s ubm itt ed to th e Facul ty of Graduate Stud ies andResearch in p a r t i a l fu l f i l lmen t of th e requirements fo r th edegree of Master o f r ch ite c tu rec Richard de la Riva 1990


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IS N 315 6636 X

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T h i s p a p e r examines t h e r e l a t i o n s h i p o f a r c h i t e c t u r et o music i n t e r m s o f rhythm, harmony and o r d e r i n both t h eGreek A n t i q u it y and t h e e a r l y Middle Ages. T hese b a s i cc o n c e p t s a r e c r u c i a l b e c a u s e t h e y emphas ize f u l l n e s s o fe x p e r i e n c e and d e m o n s t r a t e t h e e x t e n t t o which o u r ownr e g u l a t i n g Experience o f t h e world h as become e m p i r i c a l o rformaI) The d i s c u s s i o n t h u s p l a c e s a r c h i t e c t u r a l t h e o r y Ii t h i n t h e movement o f i d e a s between m yth ic a l th ou gh t andm e t a p h y si c a l c o n s t r u c t ; t p l a c e s a r c h i t e c t u r a l p r a c t i c ew i t h i n t h e movement between b o d i l y ex p eri en ce ~ reas o n i n g .

C e t t e t h s e e x a m i n e l e s l i e n s i n t i m e s e n t r el a r c h i t e c t u r e e t l a musique t r a v e r s l e s n o t i o n s der y t h m e , d h a r m o n i e e t d o r d r e dans l e s p r i o d e s del a n t i q u i t grecque e t du h a u t moyen g e . L t u d e de c e sc o n c e p t s de b a se dmontre l a p l n i t u d e de l e x p r i e n c e d e sphnomnes chez l e s a n c i e n s ; e l l e r v le a us s i l t r e i n t e del e m p i r i s m e ou du formalis me) s u r n o t r e p r o p r e ordonnancedu monde. a t h G r i e a r c h i t e c t u r a l e e s t donc s i t u e dans unmovement d e s i d e s e n t r e l a p e n s e mythique e t l ac o n s t r u c t i o n mtaphysique; l a p r a t i q u e a r c h i t e c t u r a l e e n t r el e x p r ie n ce c o rp o re ll e e t l e r a i s o n n e m e n t


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T BLE OF CONTENTS

INTRODUCTION

1 . THE ANCIENT GREEKS: N APPROXIMATION OF EURYTHMI

A Rhythm and EurhythmFrom f u l l n e s s o f rhythm t o c og ni t i o n o f forrnThe P y t h a g o r e a n kosrnosv i t r u v i u s on eurythrniaThe a r t o f t h e a rc hi t e k to n .Knowledge a s p r a x i s .B The C o s m o l o g i c a l Gro u n d in g o f T heoryThe Gre e k cosmos i s s i t u a t e d .A n a x i m a n d e r s column a nd c os mo gr ap hyThe a p e i r o n and cosmogonyMathmata and t h e P y t h a g o r e a n s c h o o l .E q u i l i b r i u m M easur e and harmonic schemaK a t h a r s i s and p o i e s i s .P l a t o s c r e a t i o n my thThe c o d i f i c a t i o n o f HarmonyGeometry and t h e v i e w i n g d i s t a n c e o f t h e o r i ai n t h e p o l i s .C v i t r u v i u s on t h e T h e a t r e .S y m p a t h e t i c r e s o n a n c e and t h e s o u n d i n g v e s s e l s .Harmonic a c o u s t i c s .D Canons o f C o m p o s i t i o nM u s i c a l modes and a r c h i t e c t u r a l o r d e r s .The body p ro p o rt io ns o f t h e o r d e r s . summ ry

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I I . VESTIGES OF ETERNITYIN THE E RLY MEDIEV L PERIOD

Knowledge and I n t e l l i g i b i l i t y .The pedagogical pro gram and t h e Quadrivium.The August inian veGtigeand t h e Dionysian symbol.Geometrical form as d i v i n e a r c h i t e c t u r e .B Motion an Change.Boethius musical c a t e g o r i e s .The suggested fe-continuum i n te rms o f motion.A r i s t o t e l i a n motion and s u b s t a n c ep o t e n t i a l i t y and change.C. The Experience o f Time.The exper ience o f t ime.A u g u s t i n e s n o t i o n o f t ime:E t e r n i t y and t h e p a s s i n g of t h e p er is ha b l e .Number and t h e Rhythm of Reason.C i r c u l a r movement.D Descent and U p l i f t .The d e s c e n t o f t h e immutablei n t o c o r r u p t i b l e te rms.Musica n a t u r a l i s and musica a r t i f i c i a l i s .The c a t h e d r a l : in strumen t o f God

sounding v e s s e l o f man.The ab bo t S uge r.E. Summary.

CONCLUSION

PPENDIX Personal P r o j e c t .

PPENDIX 2: B r i e f Rsum o f t h e Materia1Evolut ion of Medieval P l a i n c h a n tTowards Polyphony.

BIBLIOGR PHY

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INTRO U TION

ho doubts, then, t ha t our soul havingbecome accustomed to see number, space,movement, bel ieves t h i s and only th is?Pascal , Pensee 89.

In th e physical scheme of th ings which has dominatedthought s ince t he s ev en te en th century, the objec t of sciencei s defined in s t r i c t ly empirical terms. The subj ec t i ved iver s i ty which forms the tex ture of our da i ly r ea l i t i e s isof l i t t l e s igni f icance to the analysis of nature or of ourc i t i e s The generat ion of the world a bui ld ing , a ci ty ora s c i en t i f i c model) cannot be reduced to mechanicalmanipulations unless we make abs t rac t ions of the pa t te rnst h a t give meaning to our l i ves In the f ie ld ofarch i tec tu re we are more fo rtu na te ; d esp ite i t s naivet echnicolour f em the myth of crea t ionnot ions of harmony and composi t ion

survives . Ambiguousst dominate our

vocabulary and f ind t he i r way into our pro jec t s oftentu rn to other f i e lds to the a r t s to music seeking amore profound un dersta ndin g o f the processes of order anddisar ray t ha t we recognize.

The projec t ion of number in to ra t io and into geometryca r r i e s l i t t l e symbolic s igni f icance in the pract ice ofarch i tec tu re today. I t i s the re fore d i f f i cu l t for us tounders tand th a t th is mathematical opera t ion was onceprofoundly analogous to the projec t ion of whole tones frommusical ins t ruments . Both exemplified the con tinuum between


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the phy sica l and s p i r i t u a l world. The experience of v i s u a land a ud it i v e p ro pc rt i o ns s e n s e - p e r c e p t i o n were notseparable . These ideas remained v a l i d in our occiden ta lt r a d i t i o n from the ancien t Greek c i v i l i z a t i o n through theMiddle Ages and t h e Renaissance r i g h t i n t o t h e e a r l yseventeenth cen tury l Reason then began t o draw th e l inest h a t moved both a r t s and sc iences i n t o the burgeonings p e c i a l i z a t i o n s of modern man. Our modern i n h e r i t a n c e ofthe a r c h i t e c t u r a l f i g u r e s has become devoid of symboliccontent . Laid over the c ar te si an g ri d t h e i r l i n e s suggestnegat ive volumes of s p a c e .

The ancien t view centred on t h e realm of l i v i n gbeings hot cold dry and wet were i t s s t a t e s ; i t snumbers and geometry had th e value o f male and femalee n t i t i e s . The experience of l i f e was t h a t of s t r i f e andpresence in a H t h i n g s . This q u a l i t a t i v e grounding madee a r l y Greek correspondences meaningfu l . Pythagorean Harmonysimply emphasized and expanded on t h i s aspec t of r e a l i t y ina r i thmetic geometr ic and musical terms. The permutat ionsof the universe were then understood as t h e most bas ic ofrhythms: the movement of equal and o pp osite f or ce s th elove and a t t r a c t i o n of l i k e for l iKe th e cycle of change a dynamic s t r u c t u r e of harmony and propor t ion . In theEu ro pean M iddle Ages C h r i s t i a n thought and symbol ism \ lasconscious of t h e ancien t metaphysical concepts . In theunderstanding of b a s i c rhythms of l i f e t h e f u l l n e s s oft ime and cycle the e t e r n i t y of God dominated.Theclogy expands experience by bringing th e contemplat ive toi t . This i n t e g r a t i o n ensures a cont inuit y between thoughtand t h i n g between onese l f and a h i e r a r c h i c world.

l Kepler i s often s a i d t o be th e l a s t g r e a t t e n a n t ofsuch a world view.2


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Art as making and archi tec ture as bui ld ing must

become immediate and speak of the essence of rea l i ty .aim has been to e luc ida te some neglec ted aspects of ara queconceptions t h a t have generated meaningful s t ruc tures in thepas t conceptions t ha t may serve a be t t e r understanding ofthe process of crea t ion . l have par t i cu la r ly focused on hmthese ideas connec t music and archi tec ture through theexperience o f rhythm and number in the Antiquity and theear ly Middle Ages. Conceptions such as those of harmony,compos i t i on and o rde r may no t be reusab le in as t ra ight forward way. We cannot simply copy th e works ofthe pas t . Number does not ca rry t ran scendent al or mysticalvalue in the minds of th e many. Revelat ion l i e s elsewherean0, w ith in h im se lf, each ind iv idual must con f ron t the needfo r i t s reappropr ia t ion . A f i r s t s tep towards reve la t ionhO\lever, l i e s in our acknowledgement of the pas t . Themythica l harmony of th e ce l e s t i a l spheres has become mute,e xc ep t th ro ugh the movement of our thoughts .

Behind the awareness which i s basic fo rmetaphysica l renewal , the urgency of th eor ig ina l s i tua t ion pers i s t s ca l l ing as were, upon each generat ion to e s tab lish a newl ink with th e e te rna l and div ine . 2

l would l ike to thank my professor Alberto Prez- cimez fo r his guidance and i ns igh t s . l would also l ike tomention Dr. Marco Frascar i fo r h is kind and enl ightened)encouragement. Impor tant wri t ings by contemporary scho larssuch as those of Rudolf Wittkower and ot to von Simson have

2 Paul Seligman, The Apei ron of Anaximander:in the or ig in and Function of Metaphysical Ideas ,The Athlone Press 1962, p. 165 .

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been i n f luen t i a l and have shed mu ch l igh t . I t remainshowever d i f f i cu l t to deal with these concerns in depth, andone does fee l tha t much of the ava i lable l i t e ra ture whiledescr ip t ive ly impressive, fa i l s very often to ge t to thebottom of th ings . Some very basic quest ions have orientedmy research and, to the ex ten t t ha t they focus on theontological re la t ionship of archi tec ture to music and theworld, they were meant to remain simple and s t ra igh t forward .The in tent ion of th i s paper has been to communicate thepoe t i c s t r eng th of a world-view. The quest ion consequently poses i s whether our present-day s ta te ofa f fa i r s requires a more fundamental conci l ia t ion intomadness th an the ins t i tu t ion or academia of arch i tec tu re

to the Unlimited.radical lypermeable

addresses . L im i t s must once again become

hen arch i tec tu re meets music meets writ ing we canperhapsposi t ion

take measure and consol idate an in teres t ing within th e midst of th ings an ac t ion .

Especial ly Wittkower s Archi tec tura l Princip les inthe Age of Humanism, London and ew York: Academy Edit ions ,(1949) 1988; and von Simson s, The Gothie ca thedra lPrinceton: Princeton Univers i ty Press , (1956) 1988.


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1 . THE ANCIENT GREEKSN PPROXIM TION OF EURYTHMI

and the ancients , who were super ior taus and dwelt nearer to the Gods havehanded down a t r ad i t ia n th a t a l th ingst h a t are sa id to ex i s t cons is t of a one anda Many and contain in themselves thecogna t e p r i n c i p l e s o f L im it andUnlimitedness. Plato , Philebus l6c

A Rhythm and EurhythmRhythm i s t ha t which charac te r izes a f lux or tha t

V hich bonds movement. When the word appeared in ronianphilosophy i t was associated wi th th e word fo rm thearrangement of par t s into a whole. Rhythm becomes form themoment t h a t t i s assumed by th e moving the mobile and thef lu id . Democritus spoke of th e rhythm of atoms and ofthese atoms as cons t i tu t ing a t o t a l i t y ; Aris to t l e spoke ofschema. The rhythm t ha t a s ta tue o r b uild in g embodied wasnot conceived of in s t ruc tu ra l , or even me taphor ic al te rms ;r a the r , trepresented.

spoke of the rap tu re of l i f e t ha t orderThe schemat izat ion of a movement i s in the

recogni t ion of i t s pauses of l tS l imi t s and of t he i rmeasured re l a t ions . I t occurs when specia l ized sense-percept ion f a l l s back upon o r i en t a t i on to es tabl ish acommon ground fo r the experience: schema as re la t ionship .We wil l thus acknowledge rhy thm in the movement of the s ta r sor of animaIs as in t h a t of music dance visua l

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representa t ion and archi tec ture . wil l acknowledge rhythmin the s e t t l i ng of place.

Figure 1. The Music of the Spheres. 5

The formulation of the Pythagorean kosmos evolvedfrom th i s rhythmic understanding of the world. Pythagorase f fec t ive ly demonstrated the underly ing harmony of themovement of the s t a r s through t he p ropor tio n at e re la t ionshipof v ib ra t ing s t r ing lengths to whole tones in music. Themovement of the s ta r s was an absolute phenomenon to whichman s own imperfect and discontinuous act ions were compared.

For a fur ther discuss ion of the or ig ina l experienceof rhythm, see:E. Benveniste , L a notion de ry thme dans sonexpression l inguis t ique J . de psychologie normale e tpathologigue, Par is . XLIV 1951, pp. 401-410.P. Fra isse La psychologie du rythme, Vendme:Presses un ivers i t a i re s de France, 1974.William Sheldon Jordan, Time. Space, and Music:Prologema to the History of Musical T heory, Flor ida StateUnivers i ty Ph.D., 1976, footnote 37, p. 35-37.

Marius Schneider, El or igen musical de lo s animalessimbolos en l a mitologia y la escu1tura ant iguas Barcelona:Ins t i t u to espanol de musico10gia, 1946.5 From Stan1ey s History of Phi10sophy, 1687.Through Kenneth Sy1van Guthrie , The Pythagorean Sourcebookand Library, Grand Rapids, Michigan: Phanes Press 1987,p. 166.

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l Th e a p p r o p r i a t i o n o f rhythmi nvol vement with t h e fo rc e s o f p e r m i t t e dN a t u r e . m n s me suredThere i s a p a s s a g e in t h e Te n Books o f v j t r u v i u s

whose a p p a r e n t o p a c i t y p e r m i t s c e r t a i n s p e c u l a t i o n s t h a t mayf u r t h e r t h i s d i s c u s s i o n . The Roman a u t h o r e f f e c t i v e l y sendsus back t o t h e Greek t r a d i t i o n t o which he wa s i n d e b t e d . Int h e second c h a p t e r o f t h e f i r s t book, v i t r u v i u s i n t r o d u c e st h e f i v e c o n s t i t u e n t s o f a r c h i t e c t u r e . Along withO rdonnance, A rrangem ent o r r e p r e s e n t a t i o n , Decor, andD i s t r i b u t i o n o r economy), he a l s o draws o u t Eurhythmy andSymmetry. From o u r p r e l i m i n a r y j u x t a p o s i t i o n o f rhythm t oharmonie form, we may a d d r e ss t h e n a t u r e o f a r e l a t i o n s h i pmore f o r c e f u l l y s u g g e s t e d in e u r h y th my . Vi t r u v i l l s w ri t e s :

Euryt hmi a e s t v e n u s t a s p e c i e s commodusque inc o m p o s i t i o n i b u s membrorum a s p e c t u s . Haece f f i c i t u r , cum membra o p e r i s c o n v e n i e n t i a su n ta l t i t u d i n i s ad l a t i t u d i n e m , l a t i t u d i n i s adl o n g i t u d i n e m , e t ad summam omnia r e s p o n d e n tsuae symmet ri ae. Item symmetria e s t ex i p s i u so p e r i s membris c o n v e n i e n s c o n se n s u s e xp a r t i b u s q u e s e p a r a t i s ad u n i v e r s a e f i g u r a especiem r a t a e p a r t i s r e s p o n s u s . u t i inhomi ni s c o r p o r e e c u b i t o , pede, palmo, d i g i t oc e t e r i s q u e p a r t i c u l i s symmetros e s t e u r y t h m i a eq u a l i t a s , s i c e s t i n operum p e r f e c t i o n i b u s . L Eurythmie e s t l a b e a u t de l a s s e m b l a g e det o u t e s l e s p a r t i e s de l o e u v r e , q u i en rendl a s p e c t a gr ea bl e, lo rs qu e l a h a u t e u r rpond l a l a r g e u r , l a l a r g e u r l a l o n g u e u r , l et o u t a y a n t s a j u s t e mesure. La P r o p o r t i o na u s s i e s t l e r a p p o r t que t o u t e l o e u v r e a avecs e s p a r t i e s , c e l u y q u e l l e s o n t sparment l i d e du t o u t , s u i v a n t l a mesure d u n ec e r t a i n e p a r t i e . C ar de mesme que dans l ec o r p s humain, y a un r a p p o r t e n t r e l ecoude, l e p i e d , l a paume de l a mai n, l e d o i g t

v i t r u v i u s , A r c h i t e c t u r a , Book l , Ch . I I , 3 ,4 .From t h e H a r l e i a n m a n u s c r i p t 2767 8 th c . o f th e B r i t i s hMuseum; a l o n g wi t h an E n g l i sh t r a n s l a t i o n by Frank Granger.Cambridge: Harvard U n i v e r s i t y P r e s s , 1970.


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l e s a u t r e s p a r t i e s : Ainsi dans l e s ouvragesqui ont a t t e i n t l e u r p e r f e c t i o n , un membre enp a r t i c u l i e r f a i t juger de l a grandeur de t o u tl o e u v r e .

aof

was borrowederm,hethe measured propor t ions

proport ion t h a t p a r t s ofrecognized t h a t t h e not ionappl ied

described

have juxtaposed an e ighth century t r a n s c r i p t i o n ofthe passage in Latin and a seventeenth century t r a n s l a t i o nof t i n t o French in order t o demonstrate t w d i f f i c u l t i e s

Claude P e r r a u l t , t o whom wenoted t h a t t h e word r h i thmus

of i n t e r p r e t a t i o n t h a t a r i s e .are indebted f o r the l a t t e r ,general ly r e f e r r e d t o t h emovement may share . 8 eeurhythmy , as v i t r u v i u sfrom dance and music. I tof chant and dance s t e p s .d i f f e r e n t i a t e both uses However, P e r r a u l t did not c l e a r l yv i t r u v i u s made of eurythmia andsymmetria. In t h i s excerpt , he thus replaced the termsymm etria with p r o p o r t i o n . Our modern notion ofsymmetry as an e q u a l i t y of p a r t s was apparent ly foreign t ov i t r u v i u s o r i g i n a l i n t e n t , which was c l o s e r t o ourconception of proport ion. Both of t h e s e words have l o s tsome of t h e elemental f u l l n e s s t h a t they once h e l d ; so t h a tHe, l i k e P e r r a u l t , may be tempted t o dismiss them j u s t asquickly . e should s t a t e t h a t t h e confusion t h a t i s thusengendered may have been p r e s e n t in V itru viu s h im self , or inthe numerous t r a n s c r i p t i o n s h i s work has knmm. 9 What i sul t i m a t e l y r e l e v a n t , however, i s t h a t t h e s e p r e c i s e words,along with the vague co nnotations th ey i n t i m a t e , remain

Vitruve, Les dix l i v r e sand notes by Claude P e r r a u l tMardaga e d . , 1979, Livre l Ch.d A r c h i t e c tu r e , t r a n s l a t i o n 1 6 8 4 ) , Bruxel les: P i e r r eI I , p. I l .

8 I b i d , Livre 1, Ch. l , note 2 8 , p. 8 .9 In t h e l a s t paragraph of t h i s genera l exposi t ion(Book 1 , Ch. v i t r u v i u s bids our forgiveness f o r h i sshortcomings i n phi losophy, r h e t o r i c and grammar, butassures us of h i s a u t h o r i t y i n the a r t of b u i l d i n g .

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argumentat ion.somewhat a c c e s s i b l e i n t h e c o n t e x t of v i t r u v i u s

v i t r u v i u s wished to o u t l i n e the sc iences necessary tothe p r a c t i c e of a r c h i t e c t u r e . Along with w r i t i n g drawinggeometry o p t i c s a r i t h m e t i c h i s t o r y philosophy andju r i sprudence ; he included music medicine and astronomy.To expla in the re levance of such a connection he equatedthe p r o p o r t i o n of the movement of blood in veins asobserved in t h e human pulse t o the movement of dancingf e e t . IO v i t r u v i u s thus e le vated th e fundamental impor tanceof eurhy thmy above t h a t of vacant words. Claude P e r r a u l t asev en te en th c entu ry p hy sic ia n and a r c h i t e c t himself couldonly examine t h i s comparison with the understanding t h a tpermi t t e d him t o measure the l i f e of organs through thed i s s e c t i o n of dead bodies . 11 His modern speculat ions ont h i s t e x t o f a n t i q u i t y a p p l i e d t h e same educatedo b j e c t i v i t y and words l o s t t h e i r l i f e b l o o d .

v i t r u v i u s discuss ion continues. In t h e same Iayt h a t a musician would not be asked t o heal wounds or

,-

s i c k n e s s a physic ian cannot be expected t o play anins t rument f o r our p l e a s u r e . Both could nonetheless sharean understanding of th e venarum r h i thmo. In the same wayt h a t an a s t r o l o g e r and a musician can speculate on thesyr::pathies and consonance of t h e s t a r s in accordance Iitht h e i r own a r t they should be ~ l t o exchange ideas amongthemselves or with a geometer. 12 This same e s s e n t i a l graspof t h e problem of eurhythmy as t he li fe -r hy thms of the

10 I b i d Livre l Ch. l p. 8.11 P e r r a u l t would eventual ly d i e from a diseasecontracted i n the d i s s e c t i o n of a camel. 2 v i t r u v i u s Q2. c i t . Book l Ch. l 15-18.

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un v rsa r c h i t e c t .

i s what VitruviuS expected of the p r a c t i c i n g

The place a r c h i t e c t u r e occupied as a mechanical a r tunderl ies a l l of the Vitruvian e x e r c i s e . This argument i snot as s t raightforward as it may i n i t i a l l y appear, for itmust address the problem of making. In the Greek t r a d i t i o nthe word techne, which w t r a n s l a t e as art r e f e r r e d t oevery c r a f t created by man, and included the labours ofcarpenters and weavers, as well as a r c h i t e c t s .13 Techner e l i e d on s k i l l and on experience. But th e a rc hit e kto n wasa master c ra f tsman : h i s a r t a l s o d e a l t with mimesis, ther e p r e s e n t a t i o n of r e a l i t y ; and on p o i e s i s , th e inspiredmaking whose source lay in t h e divine o t h e r outs ide ofoneself . Both mimesis and p o i e s i s i ssued from mythicalthought; but as Georges Gusdorf has observed, myth cannotpronounce i t s own name. 4 I t s passage to Logos i saccomplished th rough t h e s y st e m a t i z a t i o n of hiddens i g n i f i c a n c e t h a t was wait ing t o emerge i n t o t h e l i g h t ofr e f l e c t i o n . The depth of myth i s i n balance with i t simmanence; meaning l i e s j u s t below th e surface of t h i n g s .with respec t t o th e often mitigated a u t h o r i t y conceded t ov i t r u v i u s (an aging, perhaps sour p r a c t i t i o n e r ? , w maywell ask ourselves how a m y t h i c a l p r a c t i c e of a r c h i t e c t u r ecan be reduced t o words. may a l s o ask how i t st h e o r e t i c a l w r i t i n g f i t t e d with t h e learned enkukliospa ide ia t h a t dominatd the Latin curriculum.

The enkuklios pa ide ia was t h e program of educationt h a t had emerged from t h e Pythagorean-Platonic legacy as it

Wladyslaw Tata rk iewic z, H is to ry of A e s t h e t i c s , Vol.I , Mouton, Warsaw: Polish S c i e n t i f i c Publ . , 1970, p. 26.4 Georges Gusdorf, Le dialogue du Muthos e t duLogos ; Les o r i g i n e s des sciences humaines, P a r i s :Payot, 1967.

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was t ransmi t t ed in to the Hel len i s t i c age of the Romans. 15I t had const i tu ted a ser ies of disc ipl ines o f t ra n sc enden ta ldigni ty t ha t were to shed an understanding of the or ig ina ls t ruc ture of the universe : ar i thmetic , geometry, astronomyand music communicated fundamental s c i en t i f i c notions.The oratoryd ia l ec t i c and

ar t s wouldrhe tor ic .

thenThis

complete these: grammar,program of education would

l a t e r receive the name orbis doctr inae , or c i r c l e ofknowledge . Education was bel ieved to be a c i rcu la rprocess , th i s forro being complete and perfecto

vi t ruv ius g ra pp le d w ith these preoccupations throughthe wr i t ing of archi tec ture . In doing 5 0 he recognizedh is own t heore t i ca l shortcomings, the shortcomings of aprac t i t ioner ; but on t h i s basis he a l 5 0 defended anotherform of knowledge, the mechanical knowledge in t r ins ic tomaking and bui lding, praxis. In the words of Socra tes ,wises t of a I l men , Vitruvius wished the hear ts of menopened as windows .16 The meri ts and defect s of the mindcould then be t e s t ed aga ins t the knowledge of thedi sc ip l ines t ha t i s p rese nt in the work. These rea l iza t ionsalready l i e open before our (uncr i t i ca l ) eyes. When the t a l en t of the craftsmen i s concealed in t he i r breasts , i ti s d i f f i cu l t to probe the depth of t he i r knowledge.

Yet those craftsmen themselves would of fe rt he i r sk i l l who while they lack weal th ye thave knowledge based on workshop experience:or indeed when they a re equipped with thegracefu l eloquence of the pleader , they cangain the author i ty corresponding to t he i r

15 David L. Wagner, The Seven Liberal Arts andClass ica l Scholarship ; The Seven Liberal Arts in the MiddleAges, Bloomington: Indiana Unive rs it y P r es s, 1986.Gusdorf, 22. c i t . , p. 32.16 V t P f t kruvlus , 22. Cl re ace Boo I I I , 1.

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1 i n d u s t r y and have t h e c r e d i t o f knowing whatt h e y p r o f e s s . 17Th e d e p t h o f v i t r u v i u s own knowledge i s s i m i l a r l y d i f f i c u l tt o p r o b e . I n t h e m i d s t o f p r a c t i c e t h e r e l las no c l e a r

e ~ i n e t i o n between p o i e s i s and t e c h n e between m y t h i c a l an dr a t i o n a l th o u g h t a s l le c a t e g o r i z e them t o d a y .

B Th e Cos mological Grounding o r h o ~

v i t r u v i a n eurhythmy has l e d u s i n t o a d i s c u s s i o n o fth e p l a c e a r c h i t e c t u r e occupied w i t h i n t h e c i r c l e o fknowledge l would now l i k e t o draw on t h e c o s m o l o g i c a lbackground o f t h i s t h e o r e t i c a l t r a d i t i o n .

In c o n t r a s t t o t h e Babylonian p r a c t i c e o f astronomyto which l las i n d e b t e d f o r i t s o b s e r v a t i o n s and methodsth e Greek kosmos l las s i t u a t e d b o t h i n p h y s i c a l andm e t a p h y s i c a l t e r m s . O r g a n i z a t i o n and movements a sp o s i t i o n s d i s t a n c e s and dimensions o cc ur re d a cc ord in g tog e o m e t r i c a l schema. I n t h e s i x t h c e n t u r y B . C . t h eM i l e s i a n s l lere t h e f i r s t t o work o u t su ch a view o f t h en a t u r a l world. 18 Of t h e s e Anaximander w r o t e a book whichl las l o s t i n a n t i q u i t y b u t which l las c e r t a i n l y known r i g h ti n t o t h e f o u r t h c e n t u r y B. C. . 19 The i d e a s h e f o r m u l a t e d

17 I b i d 1-18 T h a l e s A na xi ma nd er a nd Aniximenes l lere a l l t h r e e o fM i l e t u s an Io n i an c i t y . They a r e u s u al l y looked upon a st h e founders o f n a t u r a l p h i l o so p h y .19 T h i s book would a p p e a r t o have been known to b o t hA r i s t o t l e and h i s s u c c e s s o r a s head o f t h e P e r i p a t e t i cS c h o o l T h e o p h r a s t u s . On A r i s t o t le s s u g g e s t i o nT h e o p h r a s t u s composed a h i s t o r i c a l su r v e y o f p rev i o u sp h i l o s o p h i e s . See: P au l S eligm an The A p e i r o n o fAnaximander: A Study i n t h e O r i g i n and F u n c t i o n o f

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c o n t r i b u t e d t o t h e establ ishment of key metaphysicalp r i n c i p l e s .Anaximander drew a map, a pinax, and placed h i s c i t y

a t th e c e n t r e of a c y l l n d r i c a l e a r t h . Aetius l a t e r comparedt h e e a r t h of Anaximander t o a s tone column. Hippolytuswould comment: The form of th e e a r t h i s moist [o rc o n c a v e ] rounded l i k e [ t h e drum] o f a stone column. 20This a nalo gy was l a t e r i n t e r p r e t e d by th e Pseudo-Plutarch asmeaning c y l i n d r i c a l in shape; but we should remember t h a tth e word a n a l o g y comes from t h e Greek analogia , meaningr a t i o correspondence. The c i r c u l a r face , c o n s t i t u t i n g thetop s u r f a c e was t h r e e t imes as wide as t h e drum was high.This was th e s u r f a c e man i n h a b i t e d . The importance of thenumber 3 lay in i t s r o l e as t h e r ep re se nt at i v e of p l u r a l i t yin g e n e r a l incorpora t ing beginning, Middle and end. Thenumber 1 r e f e r r e d t o t h e o r i g i n a l One, or u n i t y . 2 1

Anaximander s conception of th e e a r t h was o r ig ina ls i n c e l e n t i t s e l f d ir ec tl y t o geometr ical r e p r e s e n t a t i o n ; the idea i s perfect1y expressed by a comparison of thee a r t h t o th e stocky rounded stones o f which a Greek columni s composed. 22 This p r o j e c t i o n i s p o s s i b l e throughsymbolic numerical r a t i o and t h e knowledge of th e world t h a tt h e column embodies. Anaximander recovered t h e column fromt h e f i e l d o f myth and o v e r l a i d a symbol ical ly e x p l i c i tcosmological schema. e did not deal with o b j e c t s in

Metaphysical Ideas, London: The Athlone P r e s s 1962,pp. 21-23.20 Ar;alogos means proportionate; from logos speech, r a t i o .21 See: Charles H. Kahn, Anaximander and

o f Greek Cosmology, ew York and London:U n iv er si ty P re ss 1960, pp. 55,56,81-84.22 I b i d p. 81.

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s p a c e per 2 but the e a r t h did r e s t a t equipoise a t thec e n t r e of the heavens. 3 His column demonstrated t h e poten ts i g n i f i c a t i o n the a c t o f b uilding c ar r i e d in to the order ingof the world, and t h a t cosmography wou ld i n v e r s e l y carryi n t o the experience of a r c h i t e c t u r e .

For Anaximander, the o r i g i n of the world arose fromthe Limit less , o r the apeiron - - t h e u n d i f f e r e n t i a t e d chaosfrom which a I l t h i n g s came i n t o being and back i n t o whicha I l th ings melted. e understood t h e v i t a l processes of thesublunary world as a r e t r i b u t i o n of opposi te powers, arend ering o f j u s t i c e : the primacy of t h e ape ir on gua rante edthe permanence of an e g a l i t a r i a n order founded on ther e c i p r o c i t y of r e l a t i o n s an order t h a t was s u pe r i o r t o a I lthe elements and governed them equal ly . 4 e a r e againreminded of h i s geometr ical model: the c y l i n d r i c a l e a r t hwas a t r e s t with no need f o r suppor t because it wase q u i d i s t a n t f r o m l p o i n t s on t h e c e l e s t i a lcircumference. 25 From t h i s c e n t r a l p o s i t i o n the e a r t hcould not f a l l : i t was s t a t i o n a r y because i t experienceda I l e x t e r n a l dominations equal ly . Cosmological and humans t r u c t u r e s enmesh.

3 The e a r t h was surrounded by t h re e t u bu la r wheels ofdimensions 9, 18 and 7 (3x3x3) t imes i t s diam eter of 3.These wheels r o t a t i n g around t h e e a r t h were r s p t ~ v l y thes t a r t h e moon antl the sun wheel. See: Seligman, QP. c i t .pp. 17,18. 4 J e a n - p i e r r e Vernant, Les o r i g i n e s de l a pensegrecgue, P a r i s : Quadrige/Presses U n i v e r s i t a i r e s de France,(1962) 1988 , p. 123. For a more comprehensive

i n t e r p r e t a t i o n see: Seligman, QJ2. c i t . : Kahn, QJ2. c i t . .For some a s t u t e remarks: Eric Voegelin, Vol. IV of Orderand History ; The Ecumenic Age, Baton Rouge and London:Louisiana S t a t e Univers i ty , 1986, p. 189.25 E q u i d i s t a n c e i ssymmetry and j u s t i c e . a l s o d e a l t with inKahn, QJ2. c i t . p. 78.

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un t i l th is moment the i n f in i t e f ie ld underlyingexperience wa3 character ized in terms of Mythos with theMiles ians however we may have a f i r s t r a t iona l iza t ion oft h i s sacred realm In t he i r reconst ruct ion of the order ofnature number was understood as a symbol of physis andgenesis thus s t r iv ing to maintain the whole range oft a c t i l e and temporal Experiences I t was a l iv in g e nti tyencompassing the mani fe sta tio ns o f divers i ty in a unif iedcontinuum Number became the s i t ua t ed or ig in and thesource The fundamental importance of th i s discoveryenta i led the advent of a metaphysical system of thought andwould become the c or ne rs to ne o f the Pythagorean School 26

As the universa l i ty of the pr incip le of numberelevated to the divine th ings unknown in t he i r mathmatawere regarded as par taking from the i r r a t iona l . ThePythagoreans would appear to have emphasized t h i s aspectAgainst the background of the apeiron stood Number asOrder From the tempering of the forces of crea t ionPythagoras introduced the notion of Limit peras andformulated the concept of Harmony Man by the study andcontemplat ion of Number could reproduce a s ta te of harmonyin h is own soul The inf luence music exer ted on man inl e i sure as in h is hea lth demonstrated th i s pr incip le mostreadi ly .

26 As a young man Pythagoras studied under a disc ip leof Anaximander15


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Figure 2. u n i ty Duali ty and Harmony. 7

The f a c t t h a t numerical proport ion under l ies musicalharmony i s sa id t o have been discovered by Pythagoras andhas s ince become common knowledge. Nevertheless therecognit ion of a musical s c a l e from th e i n f i n i t e continuumof tonal f lux remains f a s c i n a t i n g . This t r a n s l a t i o n ofharmonie sounds -into propor t ionate dimensions can beperformed q u i t e simply with a monochord. I t demonstratesthe pervading power of number beyond the realm of sound.s David R. F i d e l e r explains:

phenomenon occurs w en a s t r i n g i sF i r s t , the s t r i n g v i b r a t e s as aThen in two p a r t s , then in t h r e eA cur iousplucked.u n i t .

7 The p r i n c i p l e o f u n i ty underlying number wasexpressed in t h e Monad a l s o represented by the figu re ofthe c i r c l e . One che Monad i s u n i t y . 1x1=1. Two theDyad: the beginning of m u l t i p l i c i t y and o f mattert h e r e f o r e s t r i f e . with the Dyad emerges t h e d u a l i t y ofsubj e c t and o b j e c t , and consequently t h e p o s s i b i l i t y oflogos. with the advent o f th e Triad however the g u l f ofdualism i s bridged f o r i s through the t h i r d term t h a t aRelat ion o r Harmonia j oining t o g e t h e r ) i s obtainedbetween the two extremes. The Triad thus a c t u a l i z e s thep o t e n t i a l exis tence of logos and in th e process r e f l e c t sthe nature o f the One. The continuum Harmony suggested wasa microcosm of the o r i g i n a l u n i t y . For a f u r t h e r discussionof Pythagorean theory see: Kenneth sylvan Guthr ie ThePythagorean Sourcebook and Library Grand Rapids Michigan:Phanes Press 1987. Int roduct ion by David R. F i d e l e r .

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p a r t s , four, and so on. As the s t r i n gv i b r a t e s in smal ler p a r t s higher tones areproduced, t h i s being the s o - c a l l e d harmonieovertone s e r i e s . While they are not as loudas t h e fundamental ' tone of the e n t i r e s t r i n gv i b r a t i n g , with p r a c t i c e t h e overtones cannonetheless be heard. Harmonie nodalp o i n t s occur n a t u r a l l y and i n n a t e l y e x i s t ont h e s t r i n g , dividing i t s length in halves ,t h i r d s , four ths , and so on 8This rhythmic weaving of boundless matter i n t o

d e f i n i t e form was the r e v e l a t i o n of numerical harrnony anunderstanding which examined the phenomenal s i t u a t i o n of manwithin the i n d e f i n i t e r e c e p t a c l e of space. I t c l e a r l yfollowed the Milesians t h a t the word kosmos, meaning o r d e rand 'ornament ' (in th e sense of the b e a u t i f u l l y ordered) ,was conscient iously applied t o the un iverse . P lanetaryd i s t a n c e s and motion were subsequen tl y t hough t t o be r e l a t e dto t h e harmonia of the s c a l e , t h i s being th e long i n v i o l a b l e 1usic of the Spheres .29 Pythagorean thought e f f e c t i v e l ye s t a b l i s h e d a universa l p r i n c i p l e t h a t following epochswould at tempt t o a s s i m i l a t e when studying the physical placehumani t y occupied wi t h i n t h e workings of n a t u r e . In thef i e l d of a r c h i t e c t u r e , t h e manifesta t ion of rhythm andpropor t ion eurhythmy v a r i e d with t h i s understanding ofHarmony.30

8 I b i d , p. 25.29 A r i s t o t l e on t h e Pythagoreans; n the Heavens,Book 9, 290b 12.3 Harmony, as t h e m a t e r i a l and s p i r i t u a l a c t u a l i z a t i o nof Uni t y in t h e world, healed t h e gap i n h e r e n t in theory.I n v e r s e l y , in a world divorced from an encompassing f a i t h ,

d u a l i t y would dominate. e would have t o wait u n t i l theP a r a l l l e des Anciens e t des Modernes of t h e seventeenthcentury , by Charles P e r r a u l t (brother t o the e a r l i e rP e r r a u l t we r e f e r r e d t o , f o r th e f u l l force of t h i sdichotomy t o be f e l t with any c l a r i t y in a r c h i t e c t u r e . Theexperience o f p ro po rtio na l sound was no longer continuous17


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This i s not ta say t ha t Greek thought from the s ix thcentury B.C. onwards) should be dea l t with purely from thestandpoint of metaphysics. Theirs was an awe-inspir ingworld f i l l ed with the presence of mythical gods and enigmast ha t man cannat pretend ta fu lly a ss im ila te . Pla ta woulds ta te tha t a I l th ings a re fu l l of gods. 31 But in contra s tta th e tu rmoil, the re was the s t ab i l i t y of the s t a r s and therecurrence of the seasons as given t a reason and rev ealed innumbers. In contras t ta the uncer ta in ty , there was thec lea r note of the monochord:

The Greek had l i t t l e need ta s imu la te p as sio n.e sought con t ro l and balance because heneeded them; he knew the extremes only taoweIl . When he spoke of the Mean, the thoughtof the tuned s t r ing was never very fa r fromh is mind. The Mean did not imply the absenceof tension, and the lack of passion, but thecor rec t tension which gives out the i:rue andc l ea r note.

The new logos prudently moved within t h i s f i e ld .Divine reve la t ion and pur i f i ca t ion , as experienced in thereckless frenzy of Bacchic or Dionysian fe s t iva l s , no longerharboured absolu te t ru th . Kathars is , as was expressedby the Greeks, s t rove ta pacify the body and purge the soulby l i f t i ng one outs ide of onese l f . Although man partookd i rec t ly of the divine through these r i t e s , the notion ofHarmony as the mean to the extreme passions and des t ruct iveforce of the apeiron es tabl i shed a f i rme r ground fo r

inposi t ive and Arbi t ra ry ,M T Press , 1980.with t ha t of visual harmony.

See: Joseph Rykwert,The Fi r s t Moderns, Cambridge:31 Laws, 899b.9. H.D.F. Kitto, The Greeks, Balt imore: Penguin Books,1970, p. 252.

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experience. The d iv ine madness t h a t re la ted kathars i s top oie sis a lso became subordina te to t h i s generic pr inc ip le .A r a t i ona l i n t e l l e t could not c l e a r l y reduce theauthent ica l ly poet ic elevate techne to i t sdiv ine . Theal lowed manHarmony.33

pr inc ip leto shape

a ru le or to a c ra f t ; nor could itlevel wi thou t the presence of theof th e Mean or of Measure howeverthese forces in to the image of

Pla to as Anaximander dea l t with the problem ofor ig in . In h is use of th e crea t ion motif he had theDemiurge shaping the sens ib le world in a l ikeness of e te rna lforms: reason and l i f e exis ted pr io r to body and physica lcausat ion . The soul was thus bel ieved to partake of thesame s t u f f as t ha t of the body of the universe and was theprime moyer of the ce l e s t i a l spheres . 4

And when the whole s t ruc ture of the soul hadbeen f in i shed to the l ik ing of i t s framer heproceeded to fashion the whole corporeal worldwithin it f i t t i ng the two together cen t re tocentre: and th e soul was woven r i gh t throughfrom the cen t re to the outermost heaven whichi t enveloped from th e outs ide and revolv ingon i t s e l f provided a divine source ofunending and ra t iona l l i f e fo r a l l t ime. The

Plato Republic Book I I 379; Phaedrus 245; Ion533-5. 4 To the Greek the most obvious th ing about motionwas t ha t it needed a force to cause i t . According toPlato th e i r r egu la r i t i e s in the motion of the heavenlybodies were due to t h e i r d iv in e n atu re . Their soul-naturewould inf luence t he i r bodily movement with sorne independencefrom the movement o f th e D iffere nt but it would concur in

the Same the d ai ly r ota tio n from eas t to west as car r i edround by the ou ter sphere of the s t a r s . See thein t roduct ion to Timaeus and Cr i t i a s by Desmond Lee GreatBri ta in : Penguin Books 1987 pp. 12-15.In th e Middle Ages movement also supposed thepresence of a regulat ing soul . t was a widespread be l ie ft ha t th e angels were the movers of plane t s 19


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body of th e heaven i s v i s i b l e but t h e souli n v i s i b l e and endowed w ith rea so n and harrnony,being th e b e s t c r e a t i o n of t h e b e s t ofi n t e l l i g i b l e and e t e r n a l t h i n g s .

In th e Tirnaeus, Plato used t h e power of rnyth t orender th e t ranscenden ta l i n t e l l i g i b l e thus epitornizing th ei n t r i n s i c l irni t a t i o n s o f r r. et aphysic al endeavour . y t h esarne token he endorsed Pythagorean a r i thrnology. The fournumbers of th e f i r s t t e t r a c t y s dorninate h i s d e p i c t i o n ofg e n e s i s . 36 Fur thermore , he t r a c e d t h e place of ageornetr ical c r e a t i o n back t o i t s d is s o l u t i o n i n t o th edimension of c e l e s t i a l c y c l e s . As d i s t i n g u i s h e d from th eo t h e r v a r i a n t s o f r e a l i t y th e c e l e s t i a l c y c l e s appear to bethe very tirne o f t h e i r own r e a l i t y ; we approach a l i m it a twhich r e a l i t y becomes t ime and nurnbers. 37 His experienceof Limit was syrnbolized i n t h e s t r u c t u r i n g of mat ter bygeometr ica l form, through Number, i n th e c y c l i c a l t ime ofthe L i m i t l e s s .

The grand p r o j e c t behind P l a t o s Republ ic had been t odescr ibe th e j u s t c i t y th e unadul t e r a t e d c i t y where th ep r e s e r v a t i o n of musical order was t he m a nif es ta tio n of humanorder . The c o d i f i c a ti o n o f th e musical modes t h a toccurred must a l s o be understood under t h i s l i g h t . ow

P l a t o Tirnaeus, 37.6 The t e t r a c t y s c o n s i s t s of t h e f i r s t four success ivenumbers 1+2+3+4), th e sum of which i s t e n . Hence, th eDecad. Musical ly, t contains th e r a t i o s of t h e s c a l e .Geometrical ly, i t s massing accounts f o r an e q u i l a t e r a lt r i a n g l e . The t e t r a c t y s thus symbolized t h e p e r f e c t i o n ofNumber and of a l l t h e elements which comprise t

7 Voegelin, QP. c i t . p. 82.20


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could one accept char,ge s and innovat ions in an a r t tha t hada t t a ined the l eve l of highes t philosophy and on w o ~pr inc ip les the universe , as the c i ty -s t a t e bu i l t i t s we te rn i ty? Aris to t le had observed t ha t man was a po l i t i ca lanimal . He furthermore believed as Plato did) tha t thei den t i ty of a people and i t s notion of ju s t i ce werein tim a te ly r el ate d to a musical t r ad i t ion : th e n6moi arethe laws t h a t were sung before man knew sc r ip ture . 8Musical modes were in s t i tu t iona l ized as the c i t i zens decidedwhat was conducive to soc ia l cont inui ty . This reasoning i spar t i cu la r ly c lear in the writ ings of Plato . 9 Jus t ice wasperce ived as a matter of proportion, and thus access ib le tobath e th i ca l judgment and s en se exper ie nc e. 40 Archi tec tu ra lorders were s imi la r ly f ixed in to canons of composition andse t in to t r e a t i s e s . 41 These const i tu ted the models tha t thec i ty and i t s in s t i tu t ions must embody: the po l i t i c a l spa cewas not a t odds with the perceived space of the natura lcosmos. In exp lain ing the ra Ie logos played in thein s t i tu t iona l iza t ion of th e pol i s the anthropologis t JeanPier re Vernant emphasises i t s profound respec t of natu re and

8 Ari s to t l e Musica l Probl ems, Ch. XXVIII.39 P l a t a be l i e ved t h a t th e mixing and th et ransgress ions of th e n6moi had brought on th e decadence ofmusic, and consequently of thea t re up to a poin t of generalrebe l l ion agains t the laws of so cie ty Laws, I I I 700-1. ) .

He reac ted again st the fore ign inf luences f e l t in AthensLaws, VII , 798e.) , and proposed proper musica l e du ca tio nProtagoras, 326 b; Republic, 401-2 .) .40 This then, i s what the ju s t i s the proport ional ;th e un ju s t i s what vio la t e s the proport ion . Hence one termbecomes tao grea t th e o ther too small, as indeed happens in

prac t i ce ; fo r the man who ac t s unj ust ly has too much, andth e man who i s unjus t ly t rea ted too l ttl of what i sgood Plato Nicomachean Ethics , 1131 b, 15.41 These anc ien t wri t ings are l o s t ; we know of themthrough vi t ruvius . wil l re turn to t h i s aspect shor t ly .

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i t s d e l i b e r a t e a c t i o n on man: In i t s l i m i t a t i o n s as in i t sinnovations, it i s a c r e a t u r e of the city. , ,42

with A r i s t o t l e , the order o f t h e universe wasdeclared e t e r n a l and ungenerated. He d id not rormulate, ash i s p re de ce sso rs d id , a cosmogony. He did not g ive anyp a r t i c u l a r a t t e n t i o n t o t h e symbolic s h a p e of t h i n g s . Theworld simply was. Movement and change a r e now r e s o l vedd i r e c t l y through p r i n c i p l e s of metaphysics. A r i s t o t l eunderstood k a t h a r s i s in these terms as an outwardmovement of o n e s soul . He t h e r e f o r e emphasized thep o s i t i v e e f f e c t s t h a t music would have on man and remainedopen to the sensuousness of experience. I n s o f a r as theexpression remained proper to t h e s it u a ti on , A r is to tl e wasopposed t o t h e censure of musical mod8s. 43

Plato would have i n s c r i b e d over the entrance t o h i sAcademy t h a t none could e n t e r without being a geometer. Tounderstand geometry was t o have profound knowledge of theordering p r i n c i p l e of the p o l i s . (For a r e n t a l l r a d i i ofequal inf luence i n a c i r c l e ? 4 4 The sphere as a paradigm oft h i s equi l ibr ium was emphasized in the new cosmologies, asin p o l i t i c a l schemas. For example, Hest ia , t h e symbol ofthe new human order on t h e agora, could s i g n i f y forP h i l o l a o s t h e c e n t r a l i z e d cosmic f i r e , f o r o t h e rphi losophers t h e e a r t h t h a t s i t s motionless i n t h e middle ofthe phys ica l univ e r s e . 45 Consequently, t h e ground for

4 Vernant, Q P . c i t . , p. 133.43 A r i s t o t l e , P o l i t i c s , VIII , 1342.44 P l a t o , Gorgias , 508a.45 Vernant, Q P . c i t p. 129. In h i s l a s t chapter ,The w Image of t h e World , the author d i s c u s s e s thegeome tr iz a ti on o f the cosmos and of the p o l i s i n p a r a l l e l t othe new p o l i t i c a l r e a l i t i e s of th e dem ocra t ic p o l i s .


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eurhythmy as par t ic ipatory schema was not los t but anemphasis on che concept of Harmony (as issued frompythagorean-Platonic arithmology) inevi tably led ta i t sformalization in to the th i rd dimension.

Geometry operated through theor ia the viewingdistance of contemplation. Logos was akin ta the visualmode of percept ion in the distance reguired frominvolvement. This development i s manifest in the thea t rewhere man es tabl ished (or acknowledged) a distance betweenhimself and h is world: he did not par t i c ipa te in the groupdance but observed from above in order to be t te r understandh is ro le in the greater tragedy of l i fe as dic ta ted by themovements of the Gods. 6 In the chorus, he wi tnessed aninvolved representa t ion of himself within the destinedschema of th ings . .ne notion of Harmony (and t ha t ofkatharsis) subs tant ia ted the experience. The centra l izedagora reguired such an involvement, but in the thea t re mansa t a t a distance from bodily par t i c ipa t ion ; he couldproj ec t himsel f into the very pos i t ion in i t i a l ly reservedfo r the Gods he venera ted.

c . vi t ruvius on the Theatre

l wish to approach th i s l a s t discuss ion in moreconcrete terms. Vit ruvius pragmatic exposi t ion on thethea t re and i t s acoust ics wil l suppor t th i s approach. There levant chapters of h is f i f th book wil l permit us toconcentrate once again on the essen t i a l re la t ionship t ha tboth music and archi tec ture share.

6 Greek tragedy had grown out of the t r iune choreia ,the fusion of dance, song and rhythmic music. From theorig inal choreia , the chorus of thea tre .See: Tatarkiewicz , QQ c i t . Vol. l pp. 16,45.23


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Simply put ,and of acoust i cspro jec t ed soundthea t re . In theimportance of the

the Vi t ruv ian understanding of harmonyallowed fo r the st rengthening of a

through sympathetic resonance in theth i rd chapter , Vi t ruv ius emphasized thes i t e and the c i rcu la r movement of sound

waves. dedicated the fourth chap ter to Aris toxenestheory on the modulation of the voice and to the l i s t i ng ofh is t h ree musica l sca le s . In accordance with theseenquir ies , he then p re sc ri be d th e in tegra t ion of bronze (orEven earthenware) sounding vases to sol id s tone thea t reswhich he bel ieved to be a cou s ti ca ll y i nep t. 47

. . . bronze vases are to be made in mathematicalra t ios co rresp on din g w ith the s ize of thethea t re . They are to be 5 0 made tha t whenthey are touched, they can make a sound fromone to another of a four th, a f i f th and 5 0 onto the second octave. 48

I f the thea t re was not too la rge these vases , 13 innumber, were to be evenl y spa ced on a t ransverse l ine a t midhe ight . The vases were placed upside down in opencompartments among th e sea t s of the t hea t re t he i remplacement being in accordance with the tone of theenharmonie sca le to which they sounded.

Thus by th i s calculat ion the voice , spreadingfrom the s tage as from a cent re and s t r ik ingby i t s contact the hollows of the severa lvases , wil l arouse an increased clearness of

47 He compares these thea t res bu i l t of so l ids t ha t i sof rubble wall ing, stone or marble which c anno t r esound , tothe thea t res of Rome t ha t have severa l wooden f loors whichnatura l ly resound . vitruvius QJ2 c i t . Book V Ch V 7.48 Ib id 1 .

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sound and by the concord a consonanceharmonising with i t s e l f . 49

For la rg er th ea tre s, Vitruvius recommended three l ines ofvases in accordance with the enharmonie the chromatic andthe d ia to nic scales . The lowest l ine , as fo r the smallert hea t re , was of the enharmonie kind; the second l ine l laschromatic; the t h i rd , dia tonic .

I f [ t he a r c h i t e c t ] a t te n d s to t h e s ecalcula t ions , he wil l the more eas i ly be ableto e re ct th ea tr es adapted to the nature of thevoice and the pleasure of the audience 50

The descr ip t ion i s typ ica l ly vi t ruvian i st echnica l and dry Li t t l e room i s made fo r metaphysicalspecula t ion. In the following chapter however v i t ruv iusdescr ibed the plan of the Roman theat re :

The circumference i s to be drawn; and in i tfour equ il at er a l t ri a ng l es are to be describedtouching the circumference a t in te rva l s ju s tas in the case of the twelve ce l e s t i a l s ignsas t ronomers ca l cu l a t e from th e musica ldivis ion of t he cons te ll at io n s 51The points of the t r i ang les indicated the seven loweras cen t s to th e s ea t i ng and th e r ad i a l geometr ica lcons t ruc t ion upon which the 13 sounding vases must be se t .They a lso d irec ted the l ayout of th e stage. maytherefore specula te t ha t the care fu l cor re la t ion of geometryto ce l e s t i a l s igns and to cosmologically tuned devices waspotent .

49 Ib id , 3.50 Ib id , 6 .51 Ib id , 1 .

.C \..

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Figure 3. The Roman Theatre . 5

In t h e world o f v i t r u v i u s , th e immanence of eurhythmypermit ted th e e la bo ra tio n of p r a c t i c a l harmonie a c o u s t i c sf o r t h e t h e a t r e . The physical propagat ion o f sound was notd i s s o c i a t e d from planimetr ie geometry and musical s c a l e .Consequently, a r c h i t e c t u r e deduced i t s c o n s t r u c t i o n l i n e sfrom t h e harmonie p r i n c i p l e s music revealed . Further t oi n t e g r a t i n g harmonie devices such as th e sounding v a s e s , ab u i l d i n g and i n t h i s p a r t i c u l a r example, t h e t h e a tr e couldbe c a l i b r a t e d much as a musical inst rument was wasunders tood i n i t s r o l e as an instrument of Harmony.

5 From Claude P e r r a u l t s e d i t i o n : Vit ruve , Qg. c i t . ,p . 1 7 3 . V itr uv iu s a ls o described t h e p l a n i m e t r i e geometry ofthe Greek t h e a t r e s : four squares generate t h e layout ,i n s t e a d of t h e t r i a n g l e s . See Book V Ch. V I I I .

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Canons of CompositionThe fo rmal r e l a t i on sh i p between music and

archi tec ture can also be dea l t with a t another l eve l . Boththe musical modes and the arch i tec tu ra l orders had t he i rsources in myth; both evolved in para l l e l towards a morespec ia l ized framing of socia l cont inui ty . Their variousor ig ins blended with those of the people. Plato wrote ofthe fol lowing modes: the mixed or t enor Lydian and theful l- toned or bass Lydian express ive of sorrow; theIonian and the Lydian so f t and drinking harmonies; theDorian and Phrygian expres s ive of courage andtemperance. 5 Each had i t s par t i cu la r qua l i t i e s and eachvaried in scale rhythm theme and inst rumentat ion. In th i ssense each was proper to an occasion as was to a s t a t eof being. The Greeks assoc ia ted these modes to theestabl ishment of the nmoi or l aws tha t they s t r ic t lyobserved.

Equivalent to th e nmoi in music were thearchi t ec tura l canons of composit ion. Vit ruvius describedthe Doric the Ionian and the Corinthian orders . Theseorders were ruled by number andmodule based on the th ickness

propor t ion t he i r basicof the column base. 54

5 Plato Republic Book I I I 399-400.54 Fur ther of these parts whether for t e t ra s ty lehexas ty le or octas ty le l e t one be taken and tha t wil l bethe module or uni t . And of th i s module one wil l be theth ickness of the column. The severa l intercolumniat ionsexcept those in the middle wil l be of two modules and aquar te r ; the middle intercolumniat ions a t the f ront and a tthe back wil l be severa l ly of three modules. The he ight ofthe columns wil l have a j u s t proport ion of modules.Vitruvius 20. c i t . Book I I I Ch I I I 7.

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Vitruvius wrote t h a tpropor t ion cons i s t s in taking f ixed modulein each case both fo r the pa r t s of bui ld ingan fo r the whole by which th e method ofsymmetry i s put in to prac t ice For withoutsymmetry and propor t ion no temple can have regu lar plan; t h a t i s must have an exac tproport ion worked out a f t e r th e fash ion of themembers of f ine ly shaped human body.55

Fig. 4. The Vitruvian f igure 56

Ib id Book I I I Ch. 1 1.56 I l l u s t r a t i on by Leonardo da Vinci ; Accademia Venice.

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Propor t iona lbui ld ings ascons t i t u t edf r i ezes andno t f ixedevolut ion . 57

. i , re la t ionships were accordingly applied taa whole, as weIl as to the par ts tha tit such as columns, cap i t a l s cornices,gables . According to Tatarkiewicz, they wereabso lu tes bu t sub j ec t to ad jus tment andFor example,

the re la t ion of t h e i nt er co lumn ia ti on s wil lbe observed proport ionate ly. For in themeasure by which the spaces between the columngrow, the diameters of the shaf ts are to beincreased. 58

v i t ruv ius chronological ly r e la ted the pa r t i cu l a r i t i e sof each order to the myth from which it issued. The p roport ion of a man s body, i t s s t rength and gracefurnished the Doria :::olumn s dimensions: Finding t ha t thefoot was the s ix th ~ t of the height in a man, they appliedt h i s proport ion to the column. 59 The Doric name issuedfrom the memory of Dorian temples the Ionians had imi ta ted .Depart ing from t h i s i n i t i a l model, they then applied thefeminine s lenderness to the measurement of the Temple ofDiana; the volutes of i t s robed column l ike gracefulcur ling ha ir .60 The th i rd order , which i s cal ledCorinthian, imi ta tes the s l i gh t f igure of a maiden .6l Thephysical re la t ionship suggested in t h i s depic t ion of theorders expands on the audi t ive-mathematical model of thet hea t re and d i rec t ly r e in teg ra tes the body of man in to ourexamination of Harmony. Man s be l ie f in the body-soul

57 Tatarkiewicz, QJ2. c i t . Vol. 1 p. 49.58 v i t ruv ius QJ2. c i t . Book I I I Ch. I I I 10 l l.59 Ib id Book IV , Ch. 1 6.60 Ib id 7 8 .61 Ib id 8.

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c o n s t i t u t i o n o f t h e world perrnitted t h e sympatheticp r o j e c t i o n o f o n e s e l f i n t o a r c h i t e c t u r a l i d e a andgeometrized matter t h e expression of con tinu i t y in theordering process

Fig 5 Column and c a p i t a l .

.

I l l u s t r a t i o n s from Francesco d i G i o r g i o s render ingof t h e Vitruvian t e x t c . 1480 From t h e Saluzziano Codexf o l i o 14v; and t h e Magliabecchiano Codex f o l i o 33v30


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E. SurnroaryTo summarize t h e a n t i q u i t y r e c o g n i z e d th e p rima c y of

a rhythmic e x p e r i e n c e from which t h e a r c h i t e c t drew au n i f i e d u n d e r s t a n d i n g o f t h e world. Rhythm preceded th es e t t l i n g o f m a t t e r i n t o forro; e f f e c t i v e l y bonded dancem usic and p o e t r y i n a s i n g l e e n t i t y i n s e p a r a b l e frommovement and g e s t u r e . Only t h t i m e d id i n d e p e n d e n t a r tforms d e v e l o p . t h s i m i l a r l y moved i n th e rhythmic spheret h a t p re ce de d m eta ph ys ic al r e f l e c t i o n . The d i s c e r n m e n twhich p r o p e l l e d Anaximander s cosmogony t o metaphys icsi s s u ed from t h i s f i e l d and would become d i r e c t l y r e le va nt t ot h e Pythagorean f o r m u l a t i o n o f Harmony. Th e p r o j e c t i o n fkosmos i n t o harmonie s c a l e and i n t o geometry t h r o u g h Numbermarked t h i s p a s s a g e . More t h a n t h e u t i l i t a r i a n embodimento f an i d e a Number r e c o g n i z e d a L i m i t in t h e Unlimitedcontinuum o f e x p e r i e n c e . s we have s e e n t h i s framing o ft h e l i f e w o r l d wa s d e a l t w ith in d i s c o n c e r t i n g l y s implet e r m s through V i t r u v i u s d i s c u s s i o n and a p p l i c a t i o n o feurhythmy. Th e d e p t h o f t h i s c o n c e p t i o n o f a r c h i t e c t u r a lform p r o p o r t i o n symmetry and geometry r e c o g n i z e d t h ep l a c e t h e body o f man occupied i n th e continuum.

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I I VESTIGES OF ETERNITYIN THE EARLY MEDIEVAL PERIOD

Then seek what moves the l imbs of thea r t i f i c e r himself : wil l be number; fo rthey too are moved in the rhythm ofnumbers. And i f you take away the workfrom the hands, and from the mind thein tent ion of making something, and t ha tmotion i s directed toward pleasure youwil l have a dance. Seek then what i t i st ha t gives p le asu re in a dance; number wil lanswer, Behold, i s 1. Augustine, On Free Choice, I I 16, 42.

A Knowledge and In t e l l i g ib i l i t y

Medieval t ru th was human t ru th I t was d i rec t lyaccessible through the i n t eg r i ty of mystery, and ul t imateknowledge was in the Revelation of the mystery of Gad.Reali ty was fe l t and reasoned re l ig iously Ta understandth i s warld, we must place ourse lves within i t s realm. I t scul tu re was faunded on the Judeo -Chr is ti an p resuppos it ionsand deve l aped a c co r d i ng t a He l l en i c narms o fin te l l ig ib i l i ty Latin medieval c iv i l i za t ion thus sends usback ta Sa in t Augustine (354-430 A.D.) , where the wisdam ofChrist ian thealagy guided the o rb is d a ct ri na e

The pedagagical pragram of the Middle Ages hanauredthe a r t es sermocinales t ha t composed what we ca l l thet r ivium: grammar, rhe to r ic and dia lec t ic the t r i n i t y ofthe ar t s of d iscaurse or e laguent ia To these humand isc ip l ines we must add thase t ha t bore on the r ea l i t y ofth e mate r ia l warld, fram the ant ique t r ad i t ion the

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guadrivium a r i thmet ic , geometry, astronomy and music. 63These would come to be ca l l ed the seven l ib era l a rts in thetwelf th cantury.64 As a r t s , they represented the knowledgeman could acquire through prac t i ce and technique; assc iences , they re fe r red to th e pr imordia l mathematicalr e l a t i on sh i p s guid ing th e i n t e l l e c t . There was noseparat ion of the contempla t ive from prax i s . The medievali n t e l l ec tua l understood h is ro le as t h a t of a craf tsman; he laswas

an ar t i s an of thethe cons t ruc t ion

in strumen ts o f the mind and thes i t e . 65 His merchandise was

ci tythe

science he c i rcula ted through h is teaching and h is wri t ings .Hugh of Sain t Victor had then s ta ted t h a t the whole sens ib leworld was l ike a book wri t ten by the finge r of God. 66

the seand of the Creator :

a priv i leged place because ofof nature t proposed. Theuncover the v e s t i g e s of

The guadr iv ium occup iedthe anagogical i n t e rp re t a t ionins t ruments t provided woulddivine wil l l e f t behind by thevest iges were conceived to be pr inc ip le s of cosmic order ,mathematical in character , which ul t imate ly der ive from theuni t y of the one God.,67 Man in the image of God, wouldconceivably have access to knowledge of th e macrocosmthrough the pr inc ip les of divine beauty governing his manmade microcosm, fo r the divine was presen t in a I l order .

63 Gusdorf, QP. c i t . , pp. 167,168.64 Archi tec tu re would not be e f fec t ive ly inc luded un t i lthe Renaissance, fol lowing Albe r t i s theory in h is Ten Books.65 Jacques Le Goff, Le t r ava i l l eu r i n t e l l e c tue l e t lechan t ie r urba in ; Les i n t e l l e c tue l s au Moyen Age, Bourges:Ed . du Seui l , 1957) 1985, pp. 67-69.

66 Gusdorf, QP. c i t . , p. 200.67 Jordan, QP. c i t . , p. 50.Chr i s t i an Pythagoreanism re fe r redverse 20, to confirm t h i s understanding:disposed a I l th ings by measure, number, and

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The place music occupied in the guadrivium was of pivota Iimportance, because music forwarded in s igh t of the inv i s ib lemovements of the human soul and provided a mathematicalmodel of the cosmos. This ins ight could lead the mind fromthe surface of appearances to a d ee pe r c on temp la tio n ofproport ion and geometr ical f igure

Augustine had emphasized these aspects ; he hademphasized knowledge in the in terpre ta t ion of s igns ofsacramentum. Augustine meant t h i s in the t echnica l and inthe s p i r i t ua l sense, as a s ign of something hidden but ofpenetra t ing importance. Beauty was not in the sensual perse , but in the order and un i ty accessible to the i n t e l l ec tin the beauty of the soul The underlying d i s t rus t t ha t hef e l t towards f igura t ive a r t and indeed a I l imagery, kindledh is apprec ia t ion o f meta phys ic al abs t rac t ion He favouredthe non-object ive beauty of both music and arch i tec tu reFor him, music and archi tec ture a re s i s t e r s s ince both are

ch i ld ren of number; they have d ign i ty inasmuch asarchi tec ture mirrors e te rna l harmony, as music echoes i t 68In h is e Musica Augustine had conveyed h is concept ofbeauty in musical terms, through the a r t of number andprec ise proport ion. This appl ied to both v i s ib l e andaudible harmonies, as they both in t imated the same ul t imatet ru th 9 e asked:

And since music somehow i ssu ing for th from themost sec re t sanc tuar ies leaves t r aces in our ot to von Simson, The Gothie Cathedral : the Originsof Gothie Archi t ec ture and the Med ieva l Concept of arder

P rin ce to n: P rin ce to n Unive rs it y P re ss , 3rd edn) 1988, 23 .9 This was however an ear ly work, and in l a t e r yearsh is eva lua t ion of a r t d id change. His judgment became morecondemnatory o f s e ns ua l i t y and f a l s i t y bu t in h isRetract ions he st upheld the bas ic premises of h isphilosophy of number.

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very s e n s e s o r i n t h i n g s sensed by u s , m u s t n tw follow t h r o u g h t h o s e t r a c e s t o r e a c hw i t h o u t f a i l we can? t h o s e v e r y p l a c e s lhave c a l l e d s a n c t u a r i e s ?

c o n t e m p l a t i o n t h u s o v e r t o o k th e e x p l i c a t i o n o f th e o r i g i n so f t h e cosm os; t became more i m p o r t a n t t o r e c o g n i z e t h e\ t r a c e s o r v e s t i g e s ) o f b ea u ty co n firro in g God s p r e s e n c e .The g r e a t themes o f v e s t i g i a and o f imago Dei p e n e t r a t e d th em e d i e v a l u n d e r s t a n d i n g o f p h y s i c a l r e a l i t y t h r o u g hA u g u s t i n e s work, and would o n l y become secondar y in th eu l t e r i o r .development o f s c h o la s tic is m in t h e t h i r t e e n t hc e n t u r y . 7 l A r i s t o t le s a u t h o r i t y t h e n dominated th ei n t e l l e c t u a l d i s c o u r s e and wa s co n d u civ e t o t h e b r e a k froms p i r i t u a I i t y needed f o r t h e e v e n t u a l advancement o f reaso ni n t o e m p i r i c a l a b s t r a c t i o n .

P r i o r t o t h e A r i s t o t e l i a n re s u rg e n c e , a secondh e r m e n e u s i s o v e r l a id t h e Augustinian m o t i f and e x e rc i s e dp r o f o u n d i n f l u e n c e on t h e r e l a t i o n s h i p o f man t ot r a n s c e n d e n t a l r e a l i t y . Th e w r i t i n g s o f D i o n y s i u s th eP s e u d o - A r e o p a g i t e o f t h e f i f t h c e n t u ry had b r o u g h t t o g e t h e rC h r i s t i a n and N e o -P la to n ic t ho u gh t. The Corpus Dionysiacumhad b een a s c r i b e d t o t h e f i r s t b i s h o p o f A t h e n s , d i s c i p l e o fS a i n t P a u l , who l i v e d in th e f i r s t c e n t u ry A D. . 72 Theseanonymous w r i t i n g s a c t u a l l y o r i g i n a t e d in th e l a t e f i f t hc e n t u r y and were b r o u g h t i n t o Fran ce from Rome in th e e i g h t hc e n t u r y , a f t e r having i n f l u e n c e d th e C h r i s t i a n E a s t an dByzantium. Less t h a n a c e n t u ry l a t e r t had become th e

70 A u g u s t i n e , Musi ca, Book 1 ; th ro u g h J o rd a n , .QP.c i t . p . 76.71 Gu sd o rf, . QP. c i t . p p. 1 9 7 ,1 9 8 .72 See: T a t a r k i e w i c z , Q g . c i t . Vol. I I p . 27;von Simson, Q g. c i t . p p. 1 0 3 , 1 0 4 .

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accepted be l l e f in France t h a t the author of t h i s work wasident ica l with Denis, t he i r Patron.

The Dionysian schema i s of the descent of the Onein to matter . Knowledge was in the syrnbolic value of th ings .The symbol revealed i t s e l f fo r what was, fo r anaccomplishment of both t ranscendent a l and physica l rea l i ty .

Thus one can c rea te forms su i tab le fo rheavenly th ings Even from the most miserablepar t i c l e s of matte r , s ince the very mat te rtoo , der iving i t s exis tence from t rue beauty,preserves in i t s whole arranqement cer ta int races of i n t e l l ec tua l beauty.7J

Beauty and goodness are fused in an al l -embracing uni ty .Being conceived as an absolute beauty became a perfec t ionand a power; everything i s sa id to der ive from i t ; contains everything; everything i s di rec ted towards i t . 74From the Dionysian philosophy of Emanat ion : absolutebeauty radia tes and gives for th Emanation, from whichear th ly beauty resu l t s . The church the Eccles ia and thebui ld ing - - represented the world emana tin g from God. The e tap hys ics of l i gh t he developed embodied the analogy ofthe physical world and the mysterious l i gh t of God; i tmerged wel l with August ine s theory of the ves t iges .

Both Augustinian sign and Dionysian symbol rankedsp i r i tua l Experience above ob j ect ive r ea l i ty as we havebecome accustomed to . In the ninth century , Johannes ScotusErigina said t ha t There i s nothing in th ings v i s ib le andcorporea l t h a t do not s ignify something incorporea l and

73through Pseudo-Dionysius, c oe le st i h ie ra rc hiaTatarkiewicz, QQ c i t . Vol. I I p. 34. I I 4 ;

74 Tatarkiewicz, QQ c i t . Vol. I I p. 29.

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i n t e l l i g ib l e 75 This anagogical correspondence of thesens ib le to the sp i r i t u a l through the i n t e l l i g i b l e i t smystery, i s c lea r ly rea l i zed in r e li g iou s a r ch i te c tu r e

Figures 6, 7 . 76

75 Gusdorf , QR. c i t p. 200.76 .FJ.g.Fig .sketchbook.

6: From the Bible moral i se , 13th c Vienna.7: Pla te XXX of Vil la rd de Honnecourt sHere begins the a r t of the elements of drawing 37


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Through the inf luence of Augustine and the PseudoDenis, through th e fragments of the Timaeus t h a t they a l s oi n h e r i t e d , the School of C hartres would l a t e r dramatize thedepict ion of Gad as a master b u i l d e r , a th e or ic u s c re a ti ng ,by means of an a r c h i t e c t u r a l sc ience , t h a t which i se s s e n t i a l l y mathematical . Towards t h e end of th e t w el f t hcentury , t h i s image of th e Demiurge evolved t a become t h a tof the supreme a r c h i t e c t who had b u i l t th e universeaccording t a the mathematical science of geometry. Gad wasoutside of the closed c i r c u l a r space of t h e world; He heldthe world His hand and t r a c e d i t s f i g u r e with a compass.The s i g n i f i c a n c e of an a r c h i t e c t u r a l a c t of c r e a t i o n sendsus back once again t a the Greek conception of kosmos. Fromthe i n i t i a l c r e a t i o n of end less m a t t e r , t h e Demiurgee s t a b l i s h e d a r d e r , or geometr ica l form o rnament inkhaos, or peras from th e a pe iro n.

B Motion and Change

I t i s s i g n i f i c a n t t h a t i n t h e century fol lowingAugustine, Boethius (c. 4 8 0 - 5 2 5 divided th e mathematicald i s c i p l i n e of music i n t o t h re e c at e go ri e s: t h a t of t h euniverse (musica mundana), t h a t of man (musica humana), andt h a t of the instruments (musica i n s t r u m e n t a l i s . The f i r s twas bes t discerned i n a I l t h a t i s i n th e sky, or in thearrangement of el8ments, or in t h e r o t a t i o n of spheres . 8I t sounded across t h e two main regions of being bath thesuperlunary or e t h e r e a l region, t h a t of primordial n a t u r e ;and the sublunary or c o r r u p t i b l e region, c a l l e d t h e work ofnature . I f man experienced the e f f e c t s of superlunary in

von Simson, c i t . , pp. 26-31.78 B o e t h i u s , De n s t ~ u t o n m u s i c a ;Tatarkiewicz, c i t . , Vol. I I , p. 87.

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h is subI unary world, inverse ly , through the study of themusic of the w orld , he could develop h is awareness of theother r e a l i ty . The music of man, h is second category, i sunderstood by anyone who descends into the depths ofhimself . The t h i rd , was the harmony produced by theins truments .

The hierarchy deduced from t h i s ve r t i c a l divis ion ofthe world, the pleni tude also suggested by i t s soul-nature ,were es tabl i shed on an understanding of the l ife-continuumwhich went back to the Pythagoreans, and which i s foreign tous today. This i s perhaps most eas i ly explained throughmo t i on . The medieval understanding of motion wasassociated with a wider concept , t h a t of change , forchange i s l i f e in i t s immanence. This v iewpoin t cer ta in lybecame more exp l i c i t (and r ig id) with the adoption ofA r i s to t l e s phys ics from th e twe l f th century on.Aris to te l i an motion would not be replaced by the mechanist icnotion of in e r t ia un t i l the seventeenth century withGali leo . 79

Aris to t l e reco gn ized fo ur types of motion: comingto-be and passing-away, a l t e ra t ion , growth and diminution,and locomotion ( local -mot ion) . But, more genera l ly : Thefu l f i l lmen t of what e xis ts p ote ntia lly , in so fa r as i t

x s ~ s po ten t ia l ly i s motion. BO nd the motion of a th ingwas movement to i t s proper plar.e: a stone, back to theear th ; f i r e , up towards the heavens. This experience of

79 say m echan i s t ic when a displacement becomes anon-qua l i ta t ive change of posi t ion undergone by a body withrespec t to other bodies . I n e r t i a has t h i s body preservei t s s ta te of r e s t o r of uni fo rm motion, unless acted upon byan exte rna l force. Through phys ic al ob se rv at io n, Gali leosought the l aws , not the causes of th ings . Aris to t l e , Physics 201a, 10. He reformulates th i sin h is Metaphysics, Book XII; The Prime Mover , Ch. I I .

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motion explains sorne of the fascinat ion with ve r t i c a l i t y andheight found in the Gothie cathedral : po t en t i a ll y , theproper place of th e c ath ed ral i s in the heavens; i t s motioni s upwards. The word anagogy i t s e l f is from the Greekanagoge, a l i f t i ng up, .81

For Aris to t le , the motivat ion behind th i s phenomenonwas the love of the outermost sphere, th e primum mobile, whois unloving and unmoved. 82 In the Middle Ages the pr imemover became a loving God. Beauty i s the pr inc ip le of a l las an e f f i c i e n t cause, s ta ted th e Pseudo-Dionysius, s e t t ing a l l in motion and jo in ing a l l in love of rea lbeauty. I t is the l imi t of a l l th ings , an objec t of loveand a f ina l cause 83 Consequently, change was notarbi t rary but integrated an ordered system whereby a l lth ings tended towards t he i r accomplishment. EchoingDionysian thought , Erigina wrote:

God - - because e i s the cause of every love;and because He i s diffused through a l lex is ten t ; and because He co l l ec t s a l l th ingsinto one, and re tu rn s to Himself in ani ne ff ab le r etr og re ss ion while terminat ing inHimself the amatory motions of th e wholecreature ( th e u niv er se l is cor rec t ly cal ledlove . 84

81 From th e ~ o n s Dict ionary of th e Engl ish Language,second edn. , London Glasgow: Coll ins , 1988.82 Aris to t l e developed a concept al ready presen t inPla to . The actual i ty of ( intent ional) substance or formalways presupposes another in t ime, r igh t back to the primummobile . Metaphysics, Book IX , Ch. VIII .83 Pseudo-DionysiLs, e d iv in i s nominibus, V 7 ;through Tatarkiewicz, QP . c i t . Vol. I I , p. 34.84 Johannes Scotus Erigina , e divis ione na turae ;through Jordan, QP . c i t . p. 70.

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In h is Metaphysics, A r is to tl e s ta te d t h a t essence i ssubstance in i t s immanence. 85 explained t ha t the l a t t e r ,being th e cause of being as t h a t which makes a th ing whati t i s must encompass the pr inc ip le of s t ructure whosepresence renders the whole organized. Matter can berecognized as substance, but i t i s matter which underl ieschange , in respec t of place , s ize and qual i ty .86 I t i sthe re fore the essence of th e po ten t ia l sphere w ~ causes ath ing to become ac tua l , as i s from the ac tua l sphere tobe produced from a po ten t ia l one. In such a way hedis t inguished matte r and form, the f i r s t of which i spo t en t i a l l y and th e o th e r ac tu a l ly . , ,8 7 un ity canaccordingly be sa id to l i e in t h i s es sen t ia l movement (ordynamics) of matter towards form (and recogni t ion . Su ch anunderstanding, l bel ieve , br ings us back to our ear l ie rdiscussion of the primordial ground of eurythmia, t ha t whichconcerned i t s e l f so much with the becoming of form. Thecapaci ty fo r motion the re fore lay in the deeper nature ofthe body and in i t s r ela tio ns hip to place . 88 In th e f ie ldof geometry,

po t en t i a l l y ex i s t ing const ruc t ions arediscovered by b ein g b ro ught to ac tua l i ty ; thereason i s t h a t th e geometer s th inking i s inac tua l i ty ; so t h a t the potency proceeds froman ac tua l i ty ; and the re fore i t i s by makingconst ruc t ions t ha t people come to know them

85Oynamic Ar i s t o t l e , Metaphysics, BookConsiderations of Change , ch. I . VIII ; Substance:

86 Ib id , Ch. 8 Ib id , Ch. VIII .88 The apeironmatter , as form i sc i t . , p. 189 .

i s thus pushedplaced in t ime.41

in theSee: di rec t ionVoegelin, ofQP.


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though the s ingle ac tua l i t y i s l a t e r ingenerat ion th an the corresponding potency .89

po t e n t i a l it ypr inc ip le ofrequires t h i s

or end cannotun i ty because th e

involvement.

be dissoc ia tedsubstance o f

fram thethe world

numbers can be described a s s ub sta nc es onlyin so fa r as they have a pr inc ip le of uni tywhich keeps t he i r par t s toge ther ; not , as sornehold, in so fa r as they are mere aggregates ofun i t s . 90

And everything t h a t cornes in to th e world moves towards apr inc ip l e , i . e . an end.

en in sorne cases th e end cons is ts in th eexerc i se of a facu l ty e .g . see ing i s th e endof s igh t , which is sues in nothing e l se butsee ing) , in o thers it i s sorne exte rna l producte. g the bui l d e r s rt produces a house aswell as the ac t of bui ld ing) . Nevertheless ,the ac tua l i t y i s in the former case the endand in the l a t t e r it i s more of an end than i sthe mere potency. For th e ac t of bui ld ing i sin the th ing being bu i l t , and cornes to be andis ) simul taneously with the house. 91

Accordingly concepts such as those of void, or of i n f in i t y t h a t wi l l so a l iena te modern man are a lso rebuffed th e i n ~ n i t does not ex i s t po ten t ia l ly inthe sense t ha t it wi l l ever have separa te andobj e c t ive exis tence: i t i s separab le only inknowledge. For th e fa c t t h a t th e process ofdivis ion never cornes to an end ensures t h a tt h i s ac t iv i ty always ex i s t s po ten t i a l l y , but

9 Aris to t l e , Metaphysics , Book IX, ch .9 .90 Ibic::, Book VIII , Ch. I I I .91 Ib id , Book VIII , Ch. VIII .r

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n o t t h a t t h e i n f i n i t eaccomplished f a c t . 92

C. The Experience of Time

e x i s t s a s an

I n s e p a r a b l e from th e medieval understanding ofmovement was o n e s experience of t ime. The place mortal manoccupied a t t h e c e n t r e of a geocentr ic cosmos did not perm ithim t o take q u a n t i t a t i v e measure of the e n c i r c l i n g bodies ofe t e r n i t y . A harmonie rendering of t h e i r rhythm ic q ual i tywas emphasized. The de pic tio n of t ime was c r u c i a l t o theexp lora tion of man s f i n i t e n e s s through a r t . an tookmeasure of h i s own m o rta li ty a ga in st h i s f a s c i n a t i o n wi the t e r n i t y . Over many generat ions , t h e t a s k of the g r e a tc a t h e d r a l s would thus be c a r r i e d by th e enlightenedf o r t i tude and f l e s h of a communi t y . As they emerged fromthe l i v e o r a l t r a d i t i o n of the many (and of God in to

s u b j e c t t o number andalready s t a t e d t h a t t ime

s c r i p t u r e and n o t a t i o n musicconceived of as ordered motionprop ortion in t ime. 93 P l a t a hadi s a moving image of eterni ty . l I94

and l i t e r a t u r e viere

The f l e s h of man . j u s t as th e stones he l a y s i sweight. His place i s t h a t of t ime. Nurnber measures bothweight and t ime, and more t h e v i t a l music of thosechangeless spheres . Number i s a c c e s s i b l e through sensa t ion ,

92 I b i d Book IX, Ch. VI.93 Dante s w r i t i n g s fo r example, a t t e s t t o t h i s Agradual unfold ing of t h e rhythmic cycle of t ime dominates

the s t r u ~ u r of h i s work. t communicated Love andKnowledge as t was imminently p r e s e n t i n the e xp erie nc e o fl i f e be t through B e a t r i c e s eyes (The ew Life) orthrough th e music of the cosmos.94 P l a t a Timaeus, 37.

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memory and judgment: memory gathers , expic i t , not only thecarnal movements of the mind, animi, t ha t const i tu te therhythm of which we have j u s t spoken, but also the sp i r i t ua lmovements . . . 95 Augustine thus embraces Pythagorean ideas;numbers are fundamental to sa lva tion . The ar i thmet ica lnature of the immutable, as t ha t of a l l p er is ha ble th in gs ,is supported by the sou l -na ture of the universe through thewi l l of the Maker. Spi r i tua l i ty re s to re s de ligh t in theRhythm of Reason .96 Making regui res th i s movement towardsrea l iza t ion , a t ime of re f l ec t ion . I t permits man spar t i c ipa t ion in Eterni ty . Often we wil l speak of thecontemplative qua l i ty of th i s period t ha t seemingly evolvedoutside of t ime. e now rea l i ze , gui t e to the contrary ,t ha t the work was immersed in the inner contemplation ofEterni ty .

The higher th ings are those in which equa l i tyr e s i des , supreme, unshaken, unchangeable,e te rna l ; where the re i s no t ime, because nomutabi l i ty ; whence, in imi ta t ion of e te rn i ty ,t imes in our world are made, ordered, andmodif ied , as long as th e c i rc l i ng skycont inual ly re turns to i t s place of s ta r t ing ,recal l ing t h i t he r the heavenly bodies Soear th ly th ings are subjec t to heavenly th ings ,seeming to assoc ia te the cycles of t he i r own

95 Augustine, e Musica, Book VI, x i i .34 . the nature of number i s apprehended by manthrough an experience a t f i r s t physical f e l t number orrhythm), then in te l l ec tua l ( the number of thought andmemory), and f ina l ly innate number (the judgment of the soulby means of a harmony bestowed upon t by God). See thein t roduct ion to Augustine by Alber t Hofstadter and RichardKuhns in Philosophies of Art and Beauty; Selected Readingsin Aesthet ics from Plato to Heidegger , Chicago: univers i tyof Chicago Press , 1964, 173.96 Augustine, e Musica, Book VI, xi .33 .

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