derivative analysis and serial music: the theme of schoenberg's

ALMADA,CarlosdeLemos.(2016)DerivativeAnalysisandSerialMusic:theThemeofSchoenberg’sOrchestralVariationsOp.31.PerMusi.Ed.byFaustoBorém,EduardoRosseandDéboraBorburema.BeloHorizonte:UFMG,n.33,p.1‐24.

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DOI:10.1590/permusi20163301

SCIENTIFICARTICLE

DerivativeAnalysisandSerialMusic:theThemeofSchoenberg’sOrchestralVariationsOp.31

Análisederivativaeamúsicaserial:OtemadasVariaçõesparaOrquestraop.31deSchoenberg

CarlosdeLemosAlmadaUniversidadeFederaldoRiodeJaneiro,RiodeJaneiro,RiodeJaneiro,[email protected]

Abstract: Themainobjectiveof thispaper is to investigate thederivative relationsbetween the constituent elements of the theme of Arnold Schoenberg’sOrchestralVariationsOp.31anditssourceofbasicmaterialorGrundgestalt,atheoreticalprincipleelaborated by the composer. After a bibliographical revision concerned with theorigins andmotivations for the formulationof the concept, thepaperdiscusses theproblematic issue of the presence of thematic development in Schoenberg’s serialmusic, taking as reference analyzes by some authors (RUFER, 1954; BOSS, 1992;HAIMO,1997;TARUSKIN,2010).ItisalsoproposedthattheGrundgestaltofatwelve‐tonepiece canbemanifestedaccording to two levels, abstract and concrete,whichadjusts to the analyticalmethodology adopted in this study, described in a specificsection of the paper. The results obtained reveal an extraordinarily organic andeconomicthematicconstruction.Keywords:derivativeanalysis;Grundgestalt;developingvariationinserialmusic;ArnoldSchoenberg’sserialmusic.Resumo:Esteartigotemcomoobjetivoprincipalinvestigarasrelaçõesdederivaçãoentre os elementos componentes do tema das Variações para Orquestra op.31 deArnoldSchoenberg)esuafontedematerialbásico,ouGrundgestalt,conceitoteóricoelaboradopeloprópriocompositor.Apartirdeumarevisãobibliográficaconsiderandoasorigensemotivaçõesparaaformulaçãodoconceito,édiscutidaaquestãosobreapresença de desenvolvimento temático em obras seriais de Schoenberg, tomandocomo referência análises realizadas por alguns autores (RUFER, 1954;BOSS, 1992;HAIMO,1997;TARUSKIN,2010).Propõe‐seaindaaqueaGrundgestaltdeumaobraserial possa semanifestar em dois níveis distintos, porém associados – abstrato econcreto,oqueseajustaàmetodologiaanalíticaadotadanesteestudo,sumarizadaem


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uma seção específica do artigo. Os resultados obtidos revelam uma construçãotemáticaextraordinariamenteorgânicaeeconômica.Palavras‐chave: análise derivativa; Grundgestalt; variação progressiva em músicaserial;músicaserialdeArnoldSchoenberg.

Dataderecebimento:03/12/2015.

Datadeaprovaçãofinal:18/03/2016.

1‐Introduction

This paper is part of a broad research project which aims to systematically study

musical variation under analytical and compositional perspectives, theoretically

groundedontheprinciplesofdevelopingvariationandGrundgestalt,bothelaborated

byArnoldSchoenberg(1874‐1951).Thepresentcaseaddressesaspecificbranchof

the former approach, named thematic derivative analysis (henceforward, TDA), an

original methodology developed and consolidated during the research. TDA is

intendedtoinvestigateifthestructureofatheme(oragroupofthemes)ofagiven

musical work could be explained under the bias of gradual and progressive

transformations(i.e.,throughdevelopingvariation)fromareducedsetofbasicideas

(theGrundgestalt).Thisconceptionimpliesanorganicandeconomicconstruction,and

can be historically, and stylistically associated to the formalist‐organicist Austro‐

Germantradition,representedespeciallybyMozart,Beethoven,Brahms,Schoenberg,

andBerg.ThisstudypresentsthefirstapplicationofTDAtoaserialwork,throughthe

examof thederivativestructureof the themeofSchoenberg’sOrchestralVariations

Op.31.Themainobjectiveofthisapproachistoinvestigatewhetherthemethodmay

be also suitable for non‐tonalmusic, a perspective supported by analyzes of other

authors.

2–TheprinciplesofdevelopingvariationandGrundgestalt

ElaboratedbyArnold Schoenberg, the correlatedprinciples of developing variation

andGrundgestaltmaybeconsideredthemainandfar‐reachingofhiscontributionsfor


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compositionaltheory.BothcanbeassociatedtothetrendofOrganicism,aconception

for musical creation that strongly influenced romantic Austro‐German composers,

especiallyMozart,BeethovenandBrahms(MEYER,1989,p.189‐200).Thelatterwas

considered by Schoenberg as the most talented master of thematic development

(SCHOENBERG,1984,p.398‐441)andthisaspectwascertainlyoneofthemainfactors

thatinfluencedtheconsolidationofhisowncompositionalstyle,basedessentiallyina

kindofsynthesisofWagnerianandBrahmsianattributes(FRISCH,1993,p.xv‐xvi).In

fact,theemploymentofderivativeprocessesintheconstructionofhismusicalworks

is perhaps the most distinctive trait of Schoenberg’s creative personality (HAIMO,

1997,p.352),presentnotonly inhis tonalphase (1893‐1908).AsStephenCollison

argued,theconceptofGrundgestalt(normallytranslatedas“basicformat”)was

formulated by Schoenberg in 1919, during the early stages of hisdevelopment of the twelve‐tone principle … to demonstrate acontinuity between the compositional processes of the classical‐romantic Viennese school and his ownmusic, be it tonal, atonal ortwelve‐tone.COLLISON(1994,p.20)

Therefore, contrary to the common sense, the theoretical formalization of organic

musical construction by Schoenberg was primarily intended not to explain

developmentalthematicproceduresadoptedbyBrahms(amongothers)and,ofcourse,

byhimselfinhistonalphase,butrathertoreinforcethathisrecent(atonal/pre‐serial)

workswerestillbuiltwiththesame“receipt”thatcharacterizehiscreativestyle:the

gradual,economic,pervasiveandprogressivetransformationfromalimitedgroupof

basicideas.

JosefRufer,oneofSchoenberg’spupils,wroteabookaboutthetwelve‐tonemethod

basedonhisownclassroomnotes,Schoenbergwritings,andcorrespondencewithhis

master.RuferdefinesGrundgestaltinitiallyasakindofintermediarystagebetweena

motiveandatheme(RUFER,1954,p.viii).Inthesamepassage,theauthorstressesthe

necessity of distinguishing clearly the concepts of Grundreihe (basic row) and

Grundgestalt:


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Thelatterisawidemusicalconcept;theformerbelongstotwelve‐tonemusic and is part of the latter.(…) in Schoenberg’s music theGrundgestaltasthe ‘firstcreativethougth’ isofprimary importance,butnottheseries,whichisderivedfromtheGrundgestalt.(op.cit.,p.ix)

One candeduce frombothdefinitions thataGrundgestaltofagivenSchoenbergian

serialpiecemayoperateconsideringtwostructuralperspectives:(1)onasurfacelevel,

with the Grundgestalt being formatted as a concrete musical material, like the

“intermediary stage” mentioned by Rufer. This concrete Grundgestalt corresponds

ultimately to the “conventional”conceptionof thisprinciple,normallyassociated to

tonal,organic‐constructedmusic(composed,forexample,byBeethovenorBrahms);

and(2)onabasiclevel.Inthiscontext,theGrundgestalt,the“firstcreativethought”of

acomposition,canbeviewedasanabstractidea(presumablyassociatedtoaspecific

intervallicconfiguration),fromwhichthetwelve‐toneseriesisderived.Bothkindsof

Grundgestaltenwillbeconsideredinthisstudy,beingidentifiedasGs(superficial)and

Gb(basic).

Among innumerable definitions already written about the principle of developing

variation, theoneproposedbyEthanHaimoseemstobethemostcompleteand,at

sametime,sufficientlygeneralizingtoencompassSchoenbergserialprocedures:

Developingvariationisaspecialcategoryofvariationtechnique,onethat implies a teleological process. As a result, later events – evenmarkedlycontrastingones–canbeunderstoodasoriginatefrom,orgrowoutof,changesthatweremadeintherepetitionsofearlymusicalunities.Therefore,truedevelopingvariationcanbedistinguishedfrompurely local varied repetitions that have no developmentalconsequences.Developingvariationoffersthepossibilityofforwardsmotion,permittingthecreationofneworcontrasting(butstillrelated)ideas,whilelocalvariationaffectsonlythepassageinquestion.

Inother terms,developingvariationcanbeviewedasapowerfulprocess,which is

responsible not only for producing musical material with several degrees of

resemblance with the basic idea (considering its two levels), but also capable to

organizethismaterialaccordingtothestructuralfunctionsoftheformalsectionsofa

givenmusicalpiece.

Probablyduetoageneralmisconceptionthattonalityisasinequanonconditionfor

organicmusical construction, there are relatively few academic studies devoted to


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derivative analysis of thepost‐tonal repertoire.However, there is notnecessarily a

directrelationbetweenthematerialandthemannerwithwhichitismolded.Infact,

Schoenberg’s compositional style (no matter which of his phases or the adopted

melodic‐harmonic idiom is considered) can be summarized as based on extensive

motivic‐thematic transformational treatment. Evidently, the absence of the familiar

environmentestablishedbytheactionofthefunctionalforcesinherenttotonalitycan

representactualdifficultiesfortheanalyst.Formalboundariesinnon‐tonalcontexts

arefrequentlyblurred(orevendisappear),sincetherelativestabilitycausedbylocal

andglobalcadentialpointsisvirtuallysuspended.Inotherwords,thissortofmusic

lacksunequivocalreferentialpointsforahierarchicalstructuralorganization.

In spite of this, some authors have proposed convincing analytical approaches

addressing the derivative thematic treatment present in Schoenberg’s late tonal,

atonal,andserialmusic,whichhavebecomeimportantreferencesforthispaper.The

firstof theseanalyseswasmadebythecomposerhimself,encompassingtwoofhis

pieces:theatonalFourOrchestralSongsOp.22(composedin1913‐16)andthetheme

fromtheOrchestralVariationsOp.31(concludedin1928),whichispreciselythefocus

ofthepresentstudy.Bothwereoriginallypresentedin1931‐32asbroadcastlectures

attheFrankfurtRadio,beinglatertranscribedandpublished.1Intendedprimarilyto

presenthisnewmusictothecommonpublic(althoughrelativelywellinformedand

interested), the analyzes of these pieces are comprehensibly not so deeply and

systematicallyasitisnowadaysnormallyrequiredofanacademicstudy.Moreover,as

it is frequently pointed by modern commentators, 2 Schoenberg argumentation

sometimesisvague,ellipticandevenarbitrarywhileidentifyingandlabelingmotives

andtheirderivationsinhisanalyzes.Anyway,thesestudiesarerareandextraordinary

opportunitiestoexamineSchoenberg’smodusoperandiconcerningthedevelopment

ofmusicalideas.Inthisaspect,JackBossformalizedamethodologyforsystematical

motivic‐transformational analysis and applied it to the examples presented by

1ThetypescriptofthetwolecturescanbereadinthesiteoftheArnoldSchoenbergCenterofVienna(availablein:http://schoenberg.at/index.php/de/archiv/texte).

2See,forexample,EPSTEIN(1980,p.17),LEIGH(1998,p.i)andCONLON(2009,p.116),amongothers.


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SchoenbergintheOp.22lecture(BOSS,1992),usingamathematicalapproach,insome

aspectssimilartoTDA(describedinthenextsection).

Justoneyearafterhismaster’sdeath,JosefRuferpublishedhisbookonthetwelve‐

tonemethod(RUFER,1952/1954).Besidesadetailedexplanationaboutitspostulates

and the multitude of compositional possibilities extracted from analyzes of a vast

groupofSchoenberg’sserialworks,theauthorpresentsanoriginalperspectiveabout

the correlationsbetween theGrundgestalt (considering implicitly both its levels, as

previouslymentioned)andthemannersusedforelaborationandmanipulationofthe

series.AfterdemonstratinghisownmethodologyinananalysisofBeethoven’sPiano

Sonata Op.10/1, Rufer proposes to extend its application to twelve‐tone music,

stressingthefactthatBeethovenianandSchoenbergianthematictreatment,apartthe

differences of their respective harmonic idioms, are essentially equivalent (RUFER,

1954,p.38‐45;seealsop.55‐78).

InadetailedprospectonWesternmusicfrom1900‐1950,RichardTaruskindevotesa

longchaptertotheanalysisofrepresentativeserialworksbySchoenberg,Bergand

Webern(TARUSKIN,2010,p.675‐741).Theauthorespeciallyemphasizestherelations

betweentheconceptofGrundgestaltandthechoiceoftheintervallicstructuresforthe

pieces’ respective rows, aswell as thevariousmannerswithwhich theirmusicare

formattedthroughuseoftechniquesforserialmanipulation.

EthanHAIMO(1997)discussestheemploymentofdevelopingvariationtechniquesin

theinstrumentalintroductionofScene2(Act1)oftheoperaMosesandAaron.Hisfocus

addressesthegradualtransformationsufferedbyabasicmotiviccell(aGs,inthiscase,

accordingtoourterminology)resultinginamultitudeofderivedformulations.Haimo

is especially interested in thewayswithwhich Schoenbergmanipulated the serial

formsinordertomoldthedevelopmentalprocessestohiscompositionalintentions.

Impressedbytheanalysisresults,whichdenotesanotableflexibilityintheuseofthe

twelve‐tonetechniquebythecomposer,andaclearpriorityofthemotivic‐thematic

treatmentoverthemethodprotocol,theauthorconcludesthat


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Serial ordering and developing variation might seem incompatibleconcepts, the one suggesting strict order, the other implyingspontaneityandfreedom.InSchoenberg’stwelve‐tonematureworksserialorderinganddevelopingvariationarenotinconflict.Nordotheymerecoexist.Rather,theycomplementoneanother,dependingononeanotherfortheirveryviability(HAIMO,1997,p.363)

In our understanding, the plainly conscious, and confident use of this sort of

malleability for expression of ideas represents an importantmark of Schoenberg’s

trajectory: a long‐expected reconciliationbetweenhismost essential compositional

characteristic, based on extensive motivic developmental construction (someway

neglected since theabandonmentof tonality), and theneedsandconstraintsof the

twelve‐toneidiom.

Being composed just someyearsbeforeMosesandAaron, theOrchestralVariations

Op.31 denotes clearly a similar flexible serial construction in favor of a thematic‐

oriented conception. 3 , The Op.31’s theme results from a remarkable interaction

betweenformal,serialanddevelopingvariationprocedures,asitwillbedemonstrated

onthefifthsectionofthispaper.

3–Thethematicderivativeanalysis

The thematic derivative analysis (TDA) was originally conceived as a method for

systematicalexaminationoforganic‐constructedmusicalpieces.Itwasfirstlyapplied

totheanalysisofthethematicstructureofSchoenberg’sFirstChamberSymphonyOp.9,

andsincethenanumberofotheranalyzesweremade,encompassingdifferentperiods,

worksandcomposers.4

Comparedtoothersimilaranalyticalmethods,TDAisbasedonadistinctivepremise,

namely, that the derivative process can be operated hypothetically on two levels:

3ForadetailedanalysisonOp.31’serialorganization,seeLEIBOWITZ(1997,p.11‐219).

4SeeALMADA(2011a‐b;2013a‐b)andMAYR&ALMADA(2014).


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concreteandabstract.Whiletheformerisconcernedwith,sotospeak,conventional

development,thatis,basedontransformationof“real”musicalideas,thelatterneeds

further explanation. Variation on abstract level occurs based on a given abstracted

musicalstructure.Inthesis,anymusicaldomainmaybeconsideredasreferentialfor

abstractdevelopment(dynamics,timbre,articulation,texture,etc.),butrhythmicand

pitch sequences are certainly the most efficient candidates for analytical practical

purposes.DerivativeprocessesonabstractandconcretelevelsinTDAarelabeledas

developingvariation,respectively,offirstandsecondorder.

The formalization of TDA is based on this assumption, namely, the duality of

abstract/concretelevels.Themainelementsofthemodelcanbebrieflydescribedas

follows:

(a) The basic unity, the Grundgestalt (G) is normally segmented into motivic

elements,namedGrundgestalten‐components(Gc’s),labeledwithboldcapitals,

asshowninFigure1.GandGc’sarepartofconcretelevel(evidently,Ginthis

casecorrespondstotheGsclass).Thesubsequentstagesoftheprocessoccuron

theabstractlevel;

Figure1:AhypotheticalGrundgestaltanditstwoGc’s.

(b) Two abstracted sequences are obtained from each Gc: an intervallic and a

rhythmic sequences (Figure 2). They are namedGrundgestalten‐abstractions

(Ga’s),andindentifiedwiththesameletteroftheGaoforigin(inlowercase),

thedomainconsidered(“i”fortheintervallicsequence,“r”fortherhythmicone),

andtheirrespectivecontents,notatedasnumericstrings.5AGaisrepresented

5 The numeric conventions adopted are the following: (a) for intervallic sequences: the integersrepresentquantitiesofsemitonesandtheplusandminorsignalscorrespondtothedirectionsoftheintervals (respectively, upward anddownward); (b) for rhythmic sequences: the integers representdurations(1=16thnote,2=8thnote,andsoon),andthesignals,theoccurrenceofonset(+)orrest(‐).


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in the analysis in two complementary versions: inmusical notation and in

graphicformat,withitsidentifierdatainsertedinafull‐linerectangle;

Figure2:Ga’sabstractedfromtheGc’sofFigure1

(c) TheGa’sarethereferentialelementsforthephaseofdevelopingvariationof

firstorder(DV1).AGrundgestalt‐variant(Gv)isobtainedthroughapplication

of a transformational operation (as, for example, inversion, augmentation,

permutation,etc.) toaselectedGa.AGv is labeledwith thesame letter(and

domain)oftheGafromwhichitoriginates,beingnumberedaccordingtothe

order and generation of its production, and graphically represented by a

dashed‐linerectangle(Figure3).Thisprocessmayberepeatedoverandover

again,resultinginanindefinitenumberofgenerationsofGa’s;

Figure3:SomepossibleGv’sresultedfromtransformationofGa’sofFigure2.6

6AsitcanbeobservedinFigure3,intervallicvariationdoesnotconsidertranspositionoftheoriginalsequence,justthetransformationsoperatedinitsintervals.


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(d) AreturntotheconcreteleveliseffectedwhenintervallicandrhythmicGa’sare

crossedover,yieldinga“real”musicalunity(asakindofmotive),classifiedas

Pheno‐variant(Pv).APvisidentifiedwithintegersinsertedingrayrectangles,

accordingtotheirorderofcreation.Eventually,aPvmaybecomeareferential

formforproductionoffurthervariants,throughsomesortoftransformation(in

this case,normally a free,non‐canonicoperation),which corresponds to the

developingvariationofsecondorderprocedures(DV2).Thesedescendantsare

numberedaccordingtotheirderivation,asshowninFigure4.

Figure4:AhypotheticalPv(basedonelaborationsontheabstractforms–

Figures2‐3)andapossibledescendant.

(e) Figure5summarizestheelementsabovepresented.


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Figure5:ThestratifiedstructureofTDA:(a)Grundgestalt;(b)Grundgestalten‐

components;(c)Grundgestalten‐abstractions;(d)Grundgestalten‐variants;(e)

basicPheno‐variants;(e)descendantPheno‐variants.

4–TheanalysisofSchoenberg’sVariationsforOrchestra

theme

TheOp.31’s theme is presentedby the cellos after a33‐bar orchestral introduction

(withthefirstviolinjoiningthelineinthelast7bars),beingsupportedbyarelatively

simple, transparenthomophonic texture formedbywoodwinds,Frenchhorns,harp

andcontrabass.

Before beginning the derivative analysis, it is appropriate to examine the theme

accordingtoitsserialandformstructures,sincebothelementscontributetoclarify

certainofSchoenberg’schoicesforhisdevelopmentalprocedures.


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4.1–Serialstructure

The Op.31’s row presents an ingenious construction based on the symmetrical

propertiesofthetritone.AscanbeseeninFigure6.a,twotritones(Bb‐E/C#‐G)are

strategicallypositionedinthefirstandsecondhexacords(ordernumbers0‐1/7‐8).

Figure6:Schoenberg’sOp.31:therow’sprimordialform(P‐0).

AspointedbyTARUSKIN(2010,p.706‐707),theconjunctionofbothintervals(forming

acircleofminorthirdsorthe“diminished‐seventhchord”)canbeproperlyconsidered

asthe“basicshape”forthewholework,oritsbasic‐levelGrundgestalt(Gb),according

tothepresentterminology(Figure6.b).

Moreover,itisremarkablethatSchoenbergpreferentiallyusesinthepieceareduced

numberofserialformsforobtainingthepitch‐structure(againaccordingtotheminor‐

third circle): P‐0, P‐3, P‐6, P‐9, I‐0, I‐3, I‐6, I‐9 (and their respective retrograde

versions).ThisgroupformswhatisdesignedbyTARUSKIN(2010,p.689)asa“row

complex”,akindof referentialmatrixwhichcouldbecompared toa “tonic region”.

Theseformsshareanimportantproperty:allofthemmaintainasinvariantthetritones

1and2(or,takingthemasformingaunity,Gb)inthesamepositions(Figure7).


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Figure7:Schoenberg’sOp.31:therowcomplex.

Thetheme’sserialstructure(Figure8)isobtainedfromasubsetoftherowcomplex:

P‐0/R‐0 and I‐9/RI‐9 (the remaining forms are employed in the accompaniment).

Straightanddashed‐linerectanglesidentifythepresenceoftritones1and2(aswillbe

seen,theirpositionsinsomepointsofthemelodiclinearebynomeansarbitrary).

Figure8:Schoenberg’sOp.31(mm.34‐57):thetheme’sserialstructure.


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4.2–Formalanalysis

The themeof theOp.31 canbeconsideredasanexampleofpracticalapplicationof

someabstractformalconfigurationsdescribedtheoreticallybySchoenberginhisbook

Fundamentalsofmusicalcomposition(SCHOENBERG,1990).Asitwasdemonstratedin

apreviousstudy(ALMADA,2009,p.37‐39),thethemecanbeviewedonabroadlevel

of organization as a “small ternary form” (a‐b‐a’), with its main section (a) built

accordingtothemodelofthe“period”,subdividedinto“antecedent”and“consequent”

(Figure9).Therecapitulativesection(a’)presentsaresumedversionofa,whilethe

contrasting section (b) is formatted as a simple “proposal‐response” pattern. Both

strategies correspond to Classical‐Romantic procedures, as stated by Schoenberg

(1990, p.119‐126). Figure 9 proposes a stratified formal analysis of the theme,

consideringatmostfourlevelsoforganization.

Figure9:Schoenberg’sOp.31(mm.34‐57):thetheme’sformalstructure.


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Acomparisonbetweentheserialandtheformalstructures(Figure10.a‐b)revealsan

almost perfectmatch of the respective segmentation, with a unique exception, the

passageofmm.39‐40,labeledas“seg.#4”inFigure9.Atfirst,thebeginningoftheserial

formRI‐9atthispointcouldsuggesttheoccurrenceofarelativelyimportantformal

boundary(i.e.,consideringlevel1orlevel2,liketheremainingchangesofserialforms).

However,theseg.#4functionsasameresubordinatesubsectionofthesecondpartof

the antecedent. Considering the notorious predilection of Schoenberg for clarity,

symmetryandlogicintheserialsegmentation,thisdiscrepancymayatfirstseemquite

enigmatic. The central reason of this particular choice may be explained by the

positionsandfunctionsattributedtosomeofthetritones1and2inthemelodicline.

AssuggestedinFigure10.c,Schoenberg’sintentionwasprobablymotivatedbyaneed

of expressing an adequate relation of similarity between the beginnings of the

antecedentandtheconsequent,bymaintainingthetritone1asaninvariant,common

element. Since it isproducedbypitchesofnumber8‐7 inRI‐9, itwasnecessary to

anticipatetheentryofthisserialformintwomeasures,withpitches11‐9formingthe

lastpartoftheantecedent.7Anyway,asitwaspointedbyEthanHaimoinhisanalysis,

thiscasecanbeseenasasimple,butclearexampleofhowSchoenbergsubordinates

theserialprocedurestotheneedsofthemotivictreatment.

Figure10:Schoenberg’sOp.31(mm.34‐57):comparisonbetweenformaland

serialstructures.

4.3–Derivativestructure

7Inadditiontothismotivicapplication,itisplausibletoconsiderthatthetritonespositionedattheendofsectionsaandb(indicatedbytheshadingrectanglesinFigure10.c)couldexertasortofharmonicfunction,analogoustotheperfectandhalftonalcadences.


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TheapplicationofTDAtotheOp.31’sthemestartswiththeproperidentificationofits

“concrete” basic shape (more precisely, its Gs, the surface‐level Grundgestalt), the

sourceofmaterialfororganicconstruction.AsshowninFigure11.a,Gsissegmented

intothreeoverlappingGc’s(A,BandC).Figure11.bpresentsthesixGa’sabstracted

fromthethreeGc’s.ItisnoteworthythattheabstractionsfromCcanbealsoexplained

asresultingfromelaborationofpreviousforms(Figure11.c).Thisisameaningfulfact,

sinceitimpliesthatthedevelopingvariationoffirstorderisactingwithinthelimitsof

theGrundgestalt.

Figure11:Schoenberg’sOp.31:theGsandGc’sA,BandC(a);Ga’sA[i],A[r],B[i],

B[r],C[i]andC[r](b);possiblederivationofC[i]andC[r](c).

Figure12presentsthederivativeanalysisoftheantecedentofsectiona(mm.34‐40),

consideringthreesuperimposedplans:themusicalsurface(a),andtheconcrete(b)

andabstractlevels(c).Asitcanbeobserved,theeventsoftheconcretelevelunfoldin

adiachronicalsequence.Onthecontrary,theabstractlevelshows,sotospeak,timeless

elaborations(albeitateleologicalorderbealwaysimplicit),searchingtoexplainthe


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derivations of the concretematerial. Four basic Pv’s canbe identified:1 and2 are

overlappedforms,directlyderivedfromGcA,throughintervallictransformationofthe

originaltritone(itisalsonoteworthythepresenceoftheabstractvariationb2[r]inthe

rhythmicstructureofPv2);Pv3canbeclearlyviewedasaconcretetransformationof

GcC,butalsoassubordinatetoamorebasicform(4),ora“superordinatePv”,resulted

fromanoperationofhybridizationconsideringtherhythmicstructuresofGc’sBand

C.ImmediatelyfollowingPv4thereisacaseofemploymentofthelinkagetechnique:8

theminor second that closesPv4 (B‐C) is used (not casually, transposed a tritone

upwards: E#‐F#) to initiate the subsequente fragment, which yields a second‐

generationPv(41).

8WalterFrischdefineslinkage:“Thistechnique,bywhicha“new”Ideaevolvesspontaneouslyfromaprecedingone,isadistinctlyBrahmsianone(…)”(FRISCH,1984,p.15).ItisaveryinterestingfactthatthisauthorsuggeststhatSchoenberghasintuitivelyassimilatedthisimportantconstructiveprocedurefromanalysisofthemusicofhismasterBrahms,whichcanbeinferredinaspecialexampleinsertedinSchoenberg’sbookonform(SCHOENBERG,1990,p.65).InthisbriefexcerptSchoenbergpresentsanoriginalsentencecomposedinBrahmsianstyle(opposedtoaclassicalone) inwhichthere isaclearapplicationofthelinkagetechnique.Frischconsidersthattheoccurrenceoflinkageinacompositioncorrespondstoanunequivocalevidenceofdevelopingvariation.


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Figure12:Schoenberg’sOp.31:derivativeanalysisoftheantecedentofsectiona

(mm.34‐40),consideringthemusicalsurface(a),theconcretelevel(b),andthe

abstractlevel(c).

The derivative analysis of the consequent (mm.41‐45) is shown in Figure 13. The

abstract level presents only two rhythmic transformations of the hybrid (B+C),

properly illustrating the action of DV1. In the concrete level we can observe the

presenceoffourdescendantPv’s,ofsecondandthirdgenerations(11,31,42and42.1),

remotely derived from the respective referential forms. The basic Pv 6 can be

interpreted as resulted from the overlapping of these forms. As an alternative (or

complementary) analysis for Pv 6, we could consider its rhythmic structure as

remotely derived from the combination of Gc’s A and B (i.e., directly from the

Grundgestaltnucleus).Itisalsonoteworthythatthesuperpositionofthesevariants,

intensified at mm.42‐43 in a chain‐like manner, corresponds to a process of

liquidation,9clearlyintendedtoclosesectionaasasortofsubstituteforaconventional

tonalcadence.

9AccordingtoSchoenberg,“liquidationconsists ingraduallyeliminatingcharacteristic features,untilonlyuncharacteristiconesremain,whichnolongerdemandacontinuation(…).Inconjunctionwithacadence or half cadence, this process canbeused to provide adequatedelimitation for a sentence.”(SCHOENBERG,1990,p.58)


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Figure13:Schoenberg’sOp.31:derivativeanalysisoftheconsequentofsectiona

(mm.40‐45),consideringthemusicalsurface(a),theconcretelevel(b),andthe

abstractlevel(c).

Figure14showstheanalysisofthecontrastingbsection.Weobserveherethepresence

ofonlyonebasicconcreteform(7)andfourderivedPv’s(11.1,21,61and71),which

resultedfromtheintensificationofDV2processandseemstoreinforcetheintended

elaborativefunctionofthispassage.

Figure14:Schoenberg’sOp.31:derivativeanalysisofthesectionb(mm.46‐50),

consideringthemusicalsurface(a),theconcretelevel(b),andtheabstractlevel

(c).


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Therecapitulativesectionfinalizesthederivativeanalysis(Figure15).Aspreviously

stated(c.f.Figure10),sinceitisusedinthispassageatransposedandinvertedserial

form(I‐9)inrelationtothatoneemployedinthemainsection(P‐0),itisnotsurprising

thattheeventsofmm.46‐47correspondtotheexactinversionoftheinitialbarsofthe

Grundgestalt. However, as shown in Figure 15, an alternative derivation can be

proposed, based on another application of the linkage technique. Under this

perspective,thefragmentemployedtoconcludethecontrastingsection(Pv61)serves

asbasis for initiating the recapitulationof themainmaterial (61.1).Anotherdouble

analyticalinterpretationcanalsobeproposedfortheconclusivesegment,bothofthem

ultimatelyoriginatedfromformsofsame“family”:Pv’s4and41.

Figure15:Schoenberg’sOp.31:derivativeanalysisofthesectiona’(mm.51‐57),

consideringthemusicalsurface(a),theconcretelevel(b),andtheabstractlevel

(c).


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Finally,inordertoprovideaclearoverviewofthederivativerelationsinvolvedinthe

analysis,twogenealogicalchartswereelaborated.Figure16presentsthelineagesof

abstract forms produced through developing variation of first order. As can be

observed,whilesomeGa’sareconsiderablyprolific,bothabstractionsfromC–c[i]and

c[r]–are,sotospeak,infertile.Thisisconsistentwiththeconsiderationspreviously

presented (see p.15), concerning the possible derivation of Gc C from the

Grundgestalt’snucleus(A+B).

Figure16:Genealogicaltreeoftheabstractderivativerelationsinthethemeof

Schoenberg’sOp.31.

ThegenealogyofthePv’s,obtainedthroughDV2processes,isshownFigure17.The

schemereinforcesthegerminalinfluenceofGc’sAandB incomparisonwithC: just

oneofthesevenbasicPv’s(3)isdirectlyderivedfromthelatter.


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Figure17:Genealogicaltreeoftheconcretederivativerelationsinthethemeof

Schoenberg’sOp.31.

5‐Conclusion

The derivative analysis applied to the Op.31’s theme demonstrated Schoenberg’s

extraordinarycapacityforextractingamaximumofmaterialfromaminimalgroupof

musicalideas.Itisespeciallynoteworthythatthecomposer,indoingthis,showedthat

hewasnot at all constrainedby the rigid (and, as it is consideredbymostpeople,

inflexibleand“cerebral”)twelve‐tonepostulates.AsSchoenbergconstantlyarguedin

thedefenseofthisnewmodeofexpression(manytimesagainstskepticears),hewas

doingintheserialpiecesexactlythesameashedidinhistonalphase:simplythematic‐

orientedmusic. As affirmsEthanHaimo in his analysis ofMosesandAaron, almost

exactlycontemporary to theOrchestralVariations, in thisepochSchoenberg’sserial

treatment reached such degree ofmaturity and sophistication that allowed him to

subordinate the manipulation of the row forms to a preferential constructive‐

structuralforce:thederivativeprocess,arealtrademarkofhisentirecreativecareer.


23

Moreover,thisstudyaimedtoproposeanewandinstigateperspectiveconcernedto

theprincipleofGrundgestalt(notcasuallyelaboratedduringtheformalizationofthe

twelve‐tonemethod),byconsideringitsexistenceintwodistinctlevels:oneabstract,

basic,oridealized,priortotheproperconstructionoftherow;whiletheotheroneis

concrete,superficial,formedby“real”musicalunities,apotentialseedforthewhole

composition, fromwhichmost (or even all, as in the present case) of the thematic

elementscanbederivedthroughgradualandprogressivedevelopment.Theanalysis

of the Op.31’s theme revealed a perfect integration between its formal, serial and

derivative structures, which in turn can be considered as firmly associated to the

proposeddual‐naturedGrundgestalt.Furtherstudiesareplannedinordertodeepen

andrefinethisanalyticalapproach.

References

1.ALMADA,C.(2009).“AspectosdaconstruçãotemáticadeArnoldSchoenbergapartirdeseusescritosteóricossobreforma”.PerMusi.BeloHorizonte:UFMG.n.20,p.34‐43.

2.________(2011a).“Avariaçãoprogressivaaplicadanageraçãodeideiastemáticas”.SimpósioInternacionaldeMusicologia.2.RiodeJaneiro:UFRJ.p.79‐90.

3.________(2011b).“Avariaçãoprogressivaaplicadanageraçãodeideiastemáticas”.EncontroInternacionaldeTeoriaeAnáliseMusical.2.SãoPaulo:UNESP‐USP‐UNICAMP.p.10‐22.

4.________(2013a).“SimbologiaehereditariedadenaformaçãodeumaGrundgestalt:aprimeiradasQuatroCançõesOp.2deBerg”.PerMusi.BeloHorizonte:UFMG.n.27,p.75‐88.

5.________(2013b).“ConsideraçõessobreaanálisedeGrundgestaltaplicadaàmúsicapopular”.PerMusi.BeloHorizonte:UFMG.n.29,p.117‐124.

6.COLLISON,S.(1994).Grundgestalt,developingvariation,andmotivicprocessesinthemusicofArnoldSchoenberg:Ananalitycalstudyofthestringquartets.Tese(DoutoradoemFilosofia)–King’sCollege,Londres,ReinoUnido.

7.CONLON,C.(2009).ThelessonsofArnoldSchoenberginteaching:TheMusikalischeGedanke.Tese(DoutoradoemFilosofia)–UniversityofNorthTexas,EUA.

8.EPSTEIN,D.(1980).BeyondOrpheus:Studiesinmusicstructure.Cambridge:TheMITPress.


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9. FRISCH,W.(1984).Brahmsandtheprincipleofdevelopingvariation.LosAngeles,EUA:UniversityofCaliforniaPress.

10. ________(1993).TheearlyworksofArnoldSchoenberg(1893‐1908).LosAngeles,EUA:UniversityofCaliforniaPress.

11. HAIMO,E.(1997).“DevelopingvariationandSchoenberg’sserialmusic”.MusicalAnalysis.v.16,n.3,p.349‐365.

12. LEIBOWITZ,R.(1997).Introductionàlamusiquededouzesons.Paris,França:L’Arche.

13. LEIGH,M.(1998).Grundgestalt,multipieceandintertextualityinBrahms’Op.117,118and119.Tese(DoutoradoemFilosofia)–UniversityofNottingham,Nottingham,ReinoUnido.

14. MEYER,L.(1989).Styleandmusic.Chicago,EUA:UniversityofChicagoPress.

15. RUFER,J.(1954).Compositionwithtwelvenotes.Londres,ReinoUnido:Rocklife.

16. SCHOENBERG,A.(1929).VariationenfürOrchesterOp.31.Partitura(78p.).Orquestra.Viena,Áustria:Universal.Disponívelem:http://imslp.org/wiki/Special:IMSLPDisclaimerAccept/118325Acessoem:15/1/2016.

17. ________(1984).Styleandidea:selectedwritingsofArnoldSchoenberg.Londres,ReinoUnido:Faber&Faber.

18. ________(1990).Fundamentalsofmusicalcomposition.Londres,ReinoUnido:Faber&Faber.

19. TARUSKIN,R.(2010).MusicintheearlyTwentiethCentury.Oxford,ReinoUnido:OxfordUniversityPress.

Noteabouttheauthor

CarlosAlmadaismasteranddoctorinMusic,professorattheSchoolofMusicoftheUniversity of Rio de Janeiro, composer and arranger. As a scholar, he haspublished several papers on subjects related to theory and musical analysis,especiallyconcerning the principles of developing variation andGrundgestalt.He isalsoauthorof fourbooksadressedtopopularmusictheory:Contrapontoemmúsicapopular(UFRJ,2013);Harmoniafuncional(UNICAMP,2009),Aestruturadochoro(DaFonseca,2006),Arranjo(UNICAMP,2001).

derivative analysis and serial music: the theme of schoenberg's

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