Brunelleschi`s Dome and Dufay`s Motet

Transcription

Brunelleschi's Dome and Dufay's Motet
Author(s): Charles W. Warren
Source: The Musical Quarterly, Vol. 59, No. 1 (Jan., 1973), pp. 92-105
Published by: Oxford University Press
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BRUNELLESCHI'S DOME AND
DUFAY'S MOTET
O
By CHARLES
W. WARREN
N March 25, 1436, Pope Eugenius IV dedicated the cathedral at
Florence with its great dome designed by Filippo Brunelleschi,
and the Papal choir performeda motet that Guillaume Dufay had
composed for the event. Both dome and motet occupy special places
in the historyof their respective disciplines, the formeras the most
important achievement of "the fatherof Renaissance architecture,"
and the latter as one of the most impressive occasional pieces ever
written.A great deal has been said about the motet, but there is one
aspect of the music that has been overlooked - its fundamental relationship to the architectureof Brunelleschi. In fact,there are a number of interestingcorrespondencesbetween the structureof the dome
and that of the motet, correspondences involving extraordinaryprocedures on the part of both architectand composer. The relationship
is strikingenough to suggestthat the unique and compelling features
of Nuper rosarum flores- its use of two tenorswith the same cantus
firmus,its isorhythmicand isomelic symmetries,its impressivesonorities, even its overall design - are not purely musical after all, but
the results of a deliberate attempt on the part of Dufay to create a
sounding model of Brunelleschi's architecture.
The significanceof the correspondences between the dome and
the motet can best be appreciated in the context of Brunelleschi's
achievement as an architect.In the eyes of his contemporarieshe was
the firstbuilder of his age to think in terms of the "proporzioni
musicali" of the ancients.' Recent studies have tended to vindicate
this view, finding evidence in nothing that Brunelleschi himself
1 Antonio di Tuccio Manetti, The Life of Brunelleschi, ed. Howard Saalman,
trans. Catherine Engass (UniversityPark, Pa., 1970), p. 51.
92
Brunelleschi's Dome and Dufay's Motet
93
wrote or was reputed to have said, but in the buildings themselves.
According to Wittkower, "the principal formal characteristics of
Brunelleschi's new Renaissance architecture may be summarized
under the terms of homogeneity of wall, space, light and articulation. These homogeneities are the necessary conditions not only to
guarantee coherent metrical development in plan and elevation, but
also to ascertain continued ratios in perspectiveview."2 Leon Battista
Alberti and Leonardo da Vinci may have been the firstclearly to
articulate a metrical and harmonic concept of space based on musical
consonances, but Brunelleschi was the earliest of the Renaissance
masters to emphasize these simple arithmetic ratios in the overall
design of his buildings and to understand the laws of perspective
that are based on them.3
It is easy enough to perceive these "musical consonances" in
churches such as San Lorenzo and Santo Spirito in Florence. They
were designed by Brunelleschi according to a modular scheme that
presupposes a harmonic organization of space.4 In the case of the
dome that he raised over Santa Maria del Fiore, however, the matter
is not so simple. The cathedral was built in the Trecento according
to a gothic systemin which the measurements and dimensions are
derived from a set of simple geometrical proportions based on the
square. In the terminologyof the workshop and the building site,
a due quadri was the same as a two to one proportion and a uno
quadro e mezzo the same as a one to one and a half proportion. Other
proportions were taken from the diagonals of these squares, however, and are incommensurable in termsof harmonic ratios. That is,
a uno quadro il diamitro can only be expressed as V2: 1, while a due
quadri il diamitro is equivalent to V5:1.5
This harmonic incommensurability became exaggerated in actual practice, when in a procedure called "quadrature" a series of
expanding or contractingsquares was taken from the diagonal, as in
the cross of Santa Maria del Fiore (Fig. 1). Here most of the basic
coordinates appear to be related to the large crossing square that is
2 Rudolf Wittkower,"Brunelleschi and
'Proportion in Perspective,'" Journal of
the Warburg and Courtauld Institutes,XVI (1953), 288.
3 On the use of musical proportions in medieval church architecture see Otto
von Simson, The Gothic Cathedral (New York, 1956), pp. 37-38 et passim.
4 Wittkower,op. cit., pp. 288-89.
5Howard Saalman, "Early Renaissance Architectural Theory and Practice in
Antonio Filarete's Trattato di architettura,"The Art Bulletin, XLI (1959),
The MusicalQuarterly
94
circumscribed
bythecentraloctagon.Bydrawinglargersquareswith
sides equal to the diagonal of the smallerand smallersquares with
sides equal to one halfthe diagonal of the larger,the dimensionsof
the entirecruciform
structuremaybe derivedfroma singlequadratureseries.What is interesting
about thisseriesis thatit maybe reduced to a set of ratiosthatcontainthe proporzioni musicali.Multiplyingthe sides of the squares consecutivelyby the numerical
equivalentof -V2:1 (= 0.707) and roundingoffthe reducedseries
to the nearestwhole numbers,one obtainsthe proportions6:4:3:2.0
Accordingto Howard Saalman, the ratios of "simplified"quadraturewerenot unknownto Brunelleschi'spredecessors
and mayhave
been used in determiningthe pier-to-foundation
relationshipsof
Santa Maria del Fiore.7
Measurementsof the dome suggestthat Brunelleschialso used
but on a muchlargerarchitectural
theseproportions,
scale,and that
he conceivedof themin termsof a modularsystemimposedon the
existingdimensionsof the cathedral.Indeed, if we take the square
insidethe octagon (Fig. 1) as a basic module,thesedimensionsmay
-
? "-~
~aj~
~
,
?
?
Fig. 1.
6The complete series of figuresobtained by this calculation is: 101.8, 72.0, 50.8
(crossing square), 35.9, 25.4, 17.9, 12.6, 8.9, 6.3, 4.4, 3.1, 2.2. Dimensions are given in
terms of Florentine braccia (the braccia is about two feet), and are based on
measurements and reports taken from the scale drawings of Bernardo Sgrilli,
Descrizione e studi dell'insigne fabbrica di S. Maria del Fiore (Florence, 1733), Figs.
II, III, and IV, and Giuseppe Molini, La metropolitana fiore7rtina(Florence, 1820),
Figs. II, III, and IV.
7 Saalman, op. cit., p. 98, note 28.
Brunelleschi'sDome and Dufay'sMotet
95
be expressedpreciselyin termsof the ratio 6:4:2:3. Three of these
squaresare containedin thenave,twoin the transept(one on either
side of the crossingsquare), one in the apse, and one and one half
in theelevationof the dome proper,measuringfromthe base of the
tambourto the close of the vault (Figs. 2 and 3, dotted lines).
--
Jim--"lpU
I VY~I~Y
I
I
I|
-
-.
,__
Fig. 2.
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96
These same proportionsmayalso be derivedfroma different
modular schemebased on thetwenty-eight
bracciasquaresof thenave bays
and
solid
Six
of
these
2
3,
(Figs.
lines).
squares are contained in
the nave, four in the transept(two on eitherside of the crossing
square), two in the apse, and three in the elevationof the dome,
measuringfromthepeaksof thearchesto theclose of thevault (one
module to the base of thecupola and two fromthe base to the top).
In effect,Brunelleschireduced the interiordimensionsof the
cathedralto a setof proportions
based on a whole numberratio,and
it is preciselytheseproportions
thatare used in themotetthatDufay
wrotefortheconsecrationof thecathedral.Not onlydo the mensurationsin its foursectionshave a proportionalrelationshipof 6:4:2:3,
but the numberof tactusin each of the sectionsis the same as the
number of braccia contained in the modular scheme based on
braccia squares: one hundredsixty-eight
in the nave,
twenty-eight
one hundredtwelvein the transept,fifty-six
in theapse, and eightyfourin the dome of Brunelleschi.What is more,thereare twentyeightbrevesin each of the two-voiceand four-voicesubsectionsof
the motet,whichmeansthatthe "module" of the motetis the same
as thatof the cathedral:
O 168 t.
'C 112 t.
Triplum
56 t.
0
84 t.
.
Motetus
TenorII
TenorI
6
4
2
3
It mustbe emphasized,however,thatthe lengthof the last sectionof the motetis expressedherein termsof a uniformtactusand
notthesloweror fasterbeat thatwas apparentlyrequiredfortemrnpus
perfectumdiminutumin actual practice.Ornithoparchusreports
thatin the opinion of the "veteres,"referring
to the generationof
the
diminution
of
took
Dufay,
perfectsigns
away a thirdpart and
not a half.8Coussemaker'sAnonymousXII also writes:"If at the
8 "Diminutio: ut veteres sensere: est tertia partis ab
ipsa mensura abstractio."
Musice active Micrologus Andree Ornithoparchi (Leipzig, 1519), Bk. I, chap. viii.
97
beginninga line is placed in the middleof a circlenot havinga dot
inside,as here: 0; in thissortofsonghalfis not takenawaybut only
a thirdpart; thatis to say,it is sung fasterthan if the line were not
placed in the middle."9In practicalterms,the onlyway one could
take away exactlya thirdpart of the speed of the last section of
Nuper rosarumfloreswould be by keeping the speed of the semibreveconstantwiththatof the thirdsection.With a constantsemibreve two breves of tempus perfectum diminutum will be used up
for every three of tempus imperfectumdiminutum:
Ex. 1
(
3:2
This resultsin a breve that loses a thirdpart of its speed, as the
theoristssuggest.Thus the fifty-six
brevesin the last sectionof the
will
in
a
lengthby thirdcomparedto the fifty-six
expand
motet
brevesin the previoussectionand take up the time of eighty-four
tactus.On the otherhand, givena constantsemibrevebetweenthe
two last sections, two breves of tempus perfectum diminutum will
be taken up for every one of tempus perfectum non diminutum,
makingthe finalsectionof themotethalfas long as the first:
Ex. 2
O
1:2
In its overalldimension,then,Nuper rosarumfloreshas exactlythe
same proportionsas the interiorof the cross and dome of Santa
Maria del Fiore. The mensurations
producingtheseproportionsoccur in only one othermotetof Dufay,Magnanimaegentes,written
some two yearslater thanNuper rosarumflores,but in thispiece a
canon doubles the lengthof the firstsection,makinga proportion
of 12:4:2:3.
An examinationof Brunelleschi'sspecifications
forthe dome indicates thatthe correspondencein overall dimensionsbetweenthe
9 Scriptorum de musica medii aevi (Paris, 1864-76), III, 484.
98
architecture
of thecathedraland thatof the motetwas not accidental. The specifications,
dated 1420,are preservedas a notarialrecord
of the FlorentineWoolen Guild and describein summaryfashion
the formand measureof the componentpartsof the dome:
formin the corners.Its thicknessat
. .. the inner cupola is vaulted in five-part
the bottompoint fromwhich it springsis 33/4braccia. It tapersso that the end
theupperoculusis only21/2bracciathick.A second,outer
portionsurrounding
and to vaultit in a
it fromtheweather
cupolais placedoverthisone to preserve
and swellingform.It is 11/4braccia thickat the bottompoint
more magnificent
and tapersto theupperoculus,whereit is only2/3braccia
fromwhichit springs,
thick.10
In this passage Brunelleschidescribeshis dome as having two
shells- an innerone and an outerone separatedby a space (Plate
I). The idea of a double cupola was a startlinginnovation,a tour
de forceof engineeringwhose chief functionwas apparentlyan
estheticone. In fact,it is onlyhere thatBrunelleschiallows himself
to lapse into anythingapproachingextravagantlanguage.An outer
cupola is to be placed over an innerone in order"to vault it in a
and swellingform" ("piu magnificae gonfiata").
more magnificent
This double cupola has a close musicalcounterpartin the double
tenorof Nuper rosarumflores (Plate II). Breakingwith tradition,
Dufayhas two tenorssound thesamecantusfirmusa fifth
apart,and
the effect
is primarilyaesthetic the amplification
of sonority.One
tenoris placed a fifthbelow anotherin orderto harmonizeit in a
and swellingform."
"more magnificent
The mensurationsof the tenorsalso correspondto the thicknessesof the two cupolas. Brunelleschigivesthesemeasurements
as
braccia
for
the
inner
thickness
of
the
at
the
and
shell
tambour
33/4
21/2braccia forits thicknessat the lantern.The inner shell is 11/4
bracciathickat the tambourand 2/ bracciaat the lantern.The first
threemeasurements
have exactlythe same proportionsas the nave,
and
of
transept,
apse the cathedraland the firstthreemensurations
of Dufay'stenors.It maybe no morethana curiouscoincidence,but
the one incommensurate
dimensionin Brunelleschi'sseriesof measurements,the fraction2/sbracciaforthe thicknessof theoutershell
at thetop,does suggesta proportionalrelationshipof 2:3.
toFrank D. Prager and Gustina Scaglia, Brunelleschi: Studies of his Technology
and Inventions(Cambridge,
Mass.,1970),text,pp. 139-40;trans.,pp. 32ff.
--i~ii-~
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i:::i:-:.~:i:i~iiii~iii-i':
-.:-_-ii:i~i:-l---i
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ii~ii
-:l: iii:l~-:--i
....................ii
;''~'''
;
l::'
...............:--ii:-i
:_::................/ql/"
JB
21;,"'a
77,
Plate I.
Santa Maria del Fiore as shown in Bernardo Sgrilli's Descrizione e stud
Maria del Fiore (1733), Figure IV.
IS
flog
(i
'
44
"t ,
i
Oft,I
?
Ita
'vir':4-1
Al
:bijtv
-uttoft";
S:?
Al::~::
:~'
v~ni
CUM 40
loi
lowB" e
Modena, Biblioteca Estense, MS a. X. 1, 11, folios 6
101
is of
One otherpassagein the initialsectionof the specifications
da
la
interestto us. He statesat thebeginning:"Imprima cupola lato
dentroe volta a misuradel quinto acuto neglangoli."The sentence
has been variouslyinterpreted,
but a drawingof the dome by Giovanni Gherardoda Prato, one of the artistsassociatedwith Brunelleschi,indicatesthat the base line of the cupola was divided into
fiveequal partsand that the turnof the vault was determinedby
radii emanatingfromthis line."1Perhaps coincidentally,thereare
fivepointsof imitationin the canon of Dufay'stenors.
relates to the reinforceThe next sectionof the specifications
to be used. "There
materials
kinds
of
and
the
the
mentsof
cupola
are twenty-four
ribs, eight in the cornersand sixteenin the sides.
Each cornerrib has a thicknessof seven bracciaat the outside....
The ribs tie the two vaults together.They convergeproportionally
to the top, where the oculus is." In this passage Brunelleschidescribeswhat is visuallythe mostdistinctivefeatureof the dometheeightcornerribsthatprojectfromtheoutersurfaceofthecupola
and tie the twoshellstogether.Each of theseeightribsis sevenbraccia thick,whichmayrelateto the factthateach of the foursections
of Nuper rosarumfloresconsistsof 8 X 7 breves.More intriguing,
sectionsof themotetDufay
however,is thefactthatin thefour-voice
employsan unusualvariationtechniquein whichthe motivesin the
upper two parts are compressedand elided to accommodatethe
In effect,
themelodiesconvergeproportionally
smallermensurations.
in thesesectionsas do theribsof thecupola:
Ex. 3
rA
of the dome
Next to the ribs,the mostimportantreinforcement
consistsof circlesof strongsandstoneblocks thatgirdle the cupola.
"These blocksare long, and are well linkedby tin-platediron...
11Howard Saalman, "Giovanni di Ghirardo da Prato's Designs concerning the
Cupola of Santa Maria del Fiore in Florence," Journal of the Society of Architectural
Historians, XVIII, No. 1 (1959), 15-16.
102
The firstand second circles are two braccia high, the thirdand
fourthcirclesare 11/sbraccia high,and the fifthand sixth circles
one bracciahigh." These stoneringsgirdlethe cupola at threedifferentlevels, the firstand second side by side at the bottom,the
thirdand fourthat an intermediatelevel, and the fifthand sixth
near the top of the dome. Dufay may have had these reinforcing
blocksin mind when he added extratonesto the textureat the beginning,the middle,and the end of the four-voicesectionsof the
motet (see motetusin black notation). In fact,these extra tones
and are as numerousin roughly
serve as harmonicreinforcement
stone
the same proportionas the
ringsare thick.Justas the thicknesses of the stone rings decrease at the intermediateand upper
tonesin themiddleand at the
levelsso do thenumberofreinforcing
tones
end of the four-voice
sectionsof the motet.Such reinforcing
are not uncommonin the music of the period,but I know of no
otherworkin whichso manyof themare used so systematically.
suggestedby BrunelApartfromthe structuralcorrespondences
leschi'sspecifications,
thereis one otheraspectof Dufay'smusicthat
seemsrelatedto Santa Maria del Fiore- its extraordinary
reliance
on the numberseven. There are 8 x 7 brevesin each of the four
main sectionsof the motet,4 X 7 brevesin each two-voiceand fourvoice subsection,2 x 7 tonesin the cantusfirmus,
sevenlines of text
in each strophe,and sevensyllablesin each line. Furthermore,
the
mostextensiveduos (those in the O and C sectionsof the motet)
are organizedinto phrasesof 4+3 and 3+4 longs.Accordingto the
chiefauthoritieson ecclesiasticalsymbolismin the late Middle Ages
and earlyRenaissance,sevenwas the numberof the Church:12"Wisdom hath builded her house, she hath hewn out her seven pillars"
(Prov. 9:1). In fact,one of the documentshaving to do with the
constructionof Santa Maria del Fiore recordsa paymentof six
barrelsof wineand a sum of moneyforthefundamentiof the seven
columnscalled "ecclesia."13
Number symbolismalso played a crucial role in the consecration of a cathedral.In the ceremoniesprecedingthe Mass, accordof the crossare sprinkledthree
ing to Sicardus,the fourextremities
times,as are the seven altars, while twelve priestscarrycrosses
12Vincent Foster Hopper, Medieval Number Symbolism (New York, 1938), p. 111.
18Cesare Guasti, Santa Maria del Fiore (Florence, 1887), pp. 165-66.
103
In thiscontext,it is not imthroughthe fourpartsof the church.14
probablethatNuper rosarumfloreswas conceivedas a musicalanalogy of the ceremonyof consecration,one in whichthe introitTerribilisest locus isteis used as the basic emblemin a musicalrepresentationof the cathedralas a whole. As we have seen, the first
sectionof the motetrelatesproportionallyto the nave, the second
to the transept,the thirdto the apse, and the fourthto the dome.
of the
Justas thedome servesas a centralspace thatthe extremities
crosssharein common,so the four-voicesectionsof the motetwith
and isomelicstructuremay be regardedas a kind
theirisorhythmic
of "same musical space" that the four partsof the motetshare in
common.The flattenedcontoursof the upper voices,the sonorities
of the double tenor,and the reinforcingtones in these sections
createan audible shiftfromthe linear to the vertical,as if to symbolize a physicalmovementfromone dimensioninto the other,
fromthe extremitiesof the church,that is, into the crossingunder
the vault. The acoustical effectsof these sonorities,it may be recalled,wereby no meanslost on the ears of Dufay'scontemporaries.
of Santa Maria del Fiore,Gianozzo
In hisaccountof theconsecration
Manettirelatesthatas the altar was being preparedforthe Office
of Dedication a piece was performed"by so many varied and
melodious voices,and was sung fromtime to time with so many
symphoniesexaltedtowardheaventhatindeed theyappearedto the
listenersas angelicand divinesongs."15
There can be littledoubt thatthese"exaltedsymphonies,"preand
sumablythoseof Nuper rosarumflores,bear a more interesting
more intimaterelationshipto the architecture
of Brunelleschithan
has been previouslysuspected.If thecorrespondences
describedhere
involvedordinarydevices in the makingof domes or motets,one
could easilydiscountthemas coincidence.But in everyinstancethe
unusual featuresof the dome may be related directlyto unusual
aspectsof the motet.It seemsimprobablethatthesecorrespondences
were accidental,and I doubt that Dufay could have writtenthe
motetas he did withoutsome special knowledgeof the architecture
of the cathedral.Could he have gotten this informationdirectly
14 Mitrale seu de oficiis ecclesiasticussumma, chap. vi, "De consecratione Ecclesiae" (Migne, Patrologia Latina, CXIII, cols. 23ff.).
15Oratio de secularibus et pontificalibus pompis in consecratione basilice florentine, Biblioteca Apostolica Vaticana, Vat. Lat., 2919, 22'.
104
fromBrunelleschi?Certainlythey were both in Florence at the
same time,Dufay as an already highlyregardedmusician in the
papal retinue,and Brunelleschias the masterbuilder chargedwith
closingthe dome and designingthe choir of thecathedral.One has
to weigh the probabilities,but the most logical conclusionis that
theydid meet,and thattheyleftbehindas a recordof theirmeeting
a unique example of "architecturepainting" in the music of the
Renaissance.
The implicationsof thisapparentcollaborationare intriguing,
particularlyin view of the factthatNuper rosarumfloresis one of
the earliestof Dufay'sworks,if not the earliest,to clearlyanticipate
the formand styleof his late Masses. Nearly all of the most imand formalelementsthatcharacterizethe individual
portantstylistic
movementsof the Missa Caput or the Missa Se la face ay pale are
here: the presenceof a fourthvoice acting as a bass, the division
into two or more metricallycontrastedsectionswith introductory
duos,thechantlikecontoursof theuppervoicesand theiroccasional
imitations,the "disparityin the figurationof the upper and lower
voices,which formtwo distinctarchitectural
groups,"'6and, above
the
balanced
of
linear
texture
in the introductory
all,
juxtaposition
duos witha verticalemphasisin the four-voicetutti.'7
One can pointto variousinfluencesin the late Massesof Dufay,
but the real "missinglink" in theirevolutionmay verywell have
been the late motetsof Dufay himself,beginningwith Nuper rosarumflores.It is no mere coincidencethat the motetdisappears
fromhis repertory
just as the tenorMass is introduced.It mayeven
be an illusion; the stylisticand formalapparatusof the motetmay
simplyhave been applied on a largerscale to the textsof the Mass,
so thatthe motet,ratherthan disappearing,was transformed
into a
motetcyclewitha commoncantusfirmus.
In this context,the architecturalallegoryof Nuper rosarum
floresought to be regardedas somethingmore than a unique or
curiousextramusicalexercise,forit is the extramusicalaspectof the
motetthat appears to anticipatethe styleof the tenor Mass. I am
notsuggesting
thattheelementsof styleand formin Nuper rosarum
that
are
flores
typicalof Dufay'slaterMassesdo not appear in music
16Dufay, Opera Omnia, ed. Guillaume de Van (Rome, 1949), III, p. ii.
17See, for example, the opening of the Gloria of the Missa Caput
(Dufay, Opera
Omnia, ed. Heinrich Besseler [Rome, 1960],II, 81).
105
writtenbefore1436, or that theydid not originallyservea purely
musical function.It does seem to me, however,that these componentsare combinedforthe firsttime in Nuper rosarumfloresin
an overallpatternthatis characteristic
of some of his more mature
works.What confrontsus is the very interestingpossibilitythat
certainaspectsof this patternmay have been catalyzedin part by
the architectural
conceptsof Brunelleschiand the acousticalproperties of his awesomedome. In a real and demonstrablesense,both
and
dome and motetreducegothicdimensionsto classicalsymmetry
both
extricate
themselves
from
the
incomharmonic
proportion,
selfmensurabilityof older systemsand emergeas self-contained,
sustainingforms- the verymodelsof Renaissancesensibility.'8
18A version of this paper was read at the annual meeting of the American
Musicological Society in Chapel Hill, N. C., November 12, 1971.

Brunelleschi`s Dome and Dufay`s Motet

Transcription

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