Archit and Music Harmony Proportion Order

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    National Libraryof Canada Bibliothque nationaledu CanadaCanadian Theses Service Service des thses canadiennesOttawa CanadaK A ON4

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    pages are missing contact the university which grantedthe degree.Sorne pages may have indistinct print especially ij theoriginal pages were typed with a poor typewriter ribbon orif the university sent us an inferior photocopy.Reproduction in full or in part of this microform is governedby the Canadian Copyright Act R.S.C. 1970 c C-30 andsubsequent amendments.

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    Canada

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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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    National Libraryof Canada Bibliothque nationaledu CanadaCanadian Theses Service Service des thses canadiennesOttawa anadaK ON

    The author has granted an irrevocable nonexclusive licence a lowing the National Ubraryof C anada tc reproduce, Ioan olStribute or lellcopies of his/her thesis y any means and inany form or fonnat, making this thesis availableto interested persons.

    The author retains ownership of the copyrightin his/her thesis. Neither the thesis norsubstantial extracts from it may be printed orotherwise reproduced without his/her permission.

    L auteur a accord une licence irrvocable etnon exclusive permettant la Bibliothquenationale du Canada de reproduire, prter,distribuer ou vendre des copies de s thsede quelque manire et sous quelque formeque ce soit pour mettre des exemplaires decette thse la disposition des personnesintresses.L auteur conserve la proprit du droit d auteurqui protge sa thse. Ni la thse ni des extraitssubstantiels de celle-ci ne doivent treimprims ou autrement reproduits sans sonautorisation.

    IS N 315 6636 X

    anada

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    STR CT

    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

    5

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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