Greenbaum:SonataforPiano,4–Handsanalysis,pg.1

StuartGreenbaum:SonataforPiano,4–HandsAnalysisbythecomposer23March,2016

background

InSeptember2012,BrisbanepianistLiamVineycontactedmeaboutthepossibilityof

writingaworkforhimandhiswife,AnnaGinberg,whoformtheViney–GrinbergPianoDuo.

IsubsequentlymetupwithLiamandAnnaandwediscussedtheideaofaworkfortwo

pianos,butultimatelyagreedonaworkforonepiano(4hands).Weweresuccessfulin

procuringanewworkcommissionthroughtheMusicBoardoftheAustraliaCouncil,andthe

workreceiveditspremiereattheAustralianPianoDuoFestivalinBrisbaneon23August

2014.

TheVineyGrinbergPianoDuohavesincegivennumerousperformancesofthework

includingwithlivedancechoreographybyLouiseDeleurfortheQueenslandBallet’s2015

DanceDialoguesseason(4Hands12Feet).

Greenbaum:SonataforPiano,4–Handsanalysis,pg.2

pianosandhands

Ihadpreviouslywrittenashorterworkfortwopianos–ForEver(2000)–andmanyworks

forsolopiano;butatthatstagenotyetaworkfortwopianistsattheonepiano.This

presentsdifferentopportunitiesanddifferentchallenges.

Theadvantageofthe4–handmediumisthatmanyvenuesonlyhaveonepiano–orperhaps

havetwopianosbutnotbothgrandormatching.Rehearsalandtouringaremorepracticalif

onlyonepianoisrequired;andthereisalonghistoryof4–handarrangementsandshort-

scoresoforchestralrepertoirethatformanyyearsenabledsymphoniesandballetscoresto

bedisseminatedinintimate,practicalways.The4–handmediumalsoencouragesawide

tessiturawithrichvoicing.

Thatwidetessituraisalsoachallenge–especiallyforlongerworks–becauseitisalltoo

easyfor4–handwritingtobetexturallydense,registrallyunvariedandtooloud,toooften.

Additionallyoneneedstobemindfulofthebassendpianist’srighthandtanglingwiththe

trebleend’sleft(thoughsomerepertoirepiecesplayonthatentanglementcleverlyand

entertainingly).Inanyevent,thesewerewelcomechallengesincontemplatinghowbestto

exploitthemedium.ThisSonataforPiano,4Handspresentsthreedifferentapproachesto

thechallengesof16fingersand4thumbsplayingattheonekeyboard.

Greenbaum:SonataforPiano,4–Handsanalysis,pg.3

GreenbaumSonataProject

Ididnotintendtowriteasonatafromtheoutset,thoughastheworkprogresseditbecame

clearerthatthe20–minute,3–movementformwasturningoutinthisfashion.Aswithmy

othersonatas,noneofthemovementsareactuallyin‘SonataForm’.Post-minimalismwould

beacloser(ifnotcomplete)description.Iusethetermsonatainthemostbasicsenseof‘a

pieceplayed’(asopposedto‘apiecesung’)andconnectingtoacontinuumoflarge-scale

recitalworks.TheSonataforPiano,4–Handsisthe3rdinasequenceof9sonatas(asatthe

timeofwriting:2016)withtheultimateaimofwritingasonataforeverymajororchestral

instrument(ofwhichtherearearound20).Hindemithnotablydidthisandatthehalfway

markofthismajorundertaking,itstillseemsaworthymission.

Thissequenceofsonatas,whichformerepresentstheGreenbaumSonataProject,are

eitherprogrammaticallyconcernedwithourEarthanditsplaceinthelargerUniverseorin

somecasesaremoresimplyabsolutemusic.

programmaticcontext

Runninginparalleltothelogisticpuzzleofdealingwith16fingersand4thumbsisa

contemplationin3movementsoftheSunandEarthinthecontextofanexpandinguniverse:

I.Solar II.TheExpandingUniverse III.Earthrise

LifeonEarthissupportedbytheuniquenatureofourSun(ayellowdwarf)andourdistance

fromit.Recentobservationsofclimatechangeunderlinethetenuousnatureofthis

existence.Itisanticipatedthatoursunwillbecomearedgiantinanother5billionyearsand

Earthwouldeitherbeswallowedbythesun,oritswaterboiledawayalongwiththe

atmosphere.

TheExpandingUniverseisatheoreticalpremiseconnectedtothecosmologicalmodel

knownastheBigBang–acontinuousexpansion,coolingandthinningoutofthematterthat

constitutestheuniverse.

Greenbaum:SonataforPiano,4–Handsanalysis,pg.4

EarthriseisthenamegiventoaphotographoftheEarthtakenbyastronautWilliamAnders

in1968duringtheApollo8mission.ItshowsjustoverhalfoftheEarthabovethehorizonof

themoon–areversalofwhatwewouldnormallyseeoftheMoonaboveourownhorizon.

Thiscaptivatingimage–describedasthe“mostinfluentialenvironmentalphotoevertaken”

–evokesasenseofthebeauty(butalsofragility)ofourhomeplanet.

I.Solar

Theopeningtwobarspresentsa24–notequaverpatterncreatedbyalternatingasequence

of3pitchesinthelefthandagainst4pitchesintheright:

Example1:Solar,sketchforopening

ThisfirstsketchfromDecember2012showshowthenotesaredividedbetweentwohands

onagrandstaffandthentheresultantlinecreatedbelow.

The7pitchesformanascendingmelodicminorscale(orjazzminorscale)inCthatjumpsup

anddownincontourforthefirst17notes,thennaturally(bypermutation)presentsthe7

pitchesasarisingscale.ThisisatechniqueIhaveusedpreviouslybuthasitsoriginsinSteve

Reich’sPianoPhase(1967)whichsets3notesinthelefthandagainst2intheright(creating

a12–notepattern).Reichreferstothistechniqueas‘drummingatthekeyboard’.4against3

isanaturalexpansionofthesametechnique,thoughitdoesincreasethecomplexityofthe

permutation.

Rightfromtheopeningbarsthemusicaleffectisintendedtoevokeimagesofsolarflares

burstingfromthesuninradiantheat.Initiallyasanexplosionofsoundwiththepedaldown,

Greenbaum:SonataforPiano,4–Handsanalysis,pg.5

andthenfrombars3–4withthepedalreleased,lowerchordstillhelddownandupper

patternplayingsoftlyinstaccato:

Example2:Solar,opening

Thisisintendedtoprovideaghostinghalooreclipse-likecontrast.It’salsoatechnical

responsetothechallengesofwritingforpiano4-hands.Thiseffectcanbecontrolledquite

easilywithtwoplayersattheonepianoandexploitsasortof‘depthoffield’inthesound

world,wherethe4-handsmediumcanquicklybecomeoverlyforegrounded.

ThesustainedchordsinPiano2areoftensuspendedharmonies.Thevoicingabovehasan

added9thand11thbutno3rd.Thesesustainedchordsarepunctuatedbysyncopated

anacrusisfigureslikethatfoundatbar8:

Example3:Solar,Piano2,syncopation

TheinfluenceofPinkFloyd,andspecificallyRichardWright’smoody,atmosphericelectric

pianointheopeningofSheep(Animals,1977)isapparent.

Greenbaum:SonataforPiano,4–Handsanalysis,pg.6

Theopening24–notepatterngeneratedfromthe7pitches(4against3)formsthebasisofa

seriesofvariationsthatdefinethe1stmovement.Threedaysafterthecompositionofthe

pattern,ideasforpossiblevariationswerenoteddown:

Example4:Solar,sketchedideasforvariations

Mostoftheseideasfoundtheirwayintothestructure(includingreversenotepatterns,

compressedpatternlength,resultingpatterns,modulationandhemiolavariation).Other

variationsaroselaterincludingaugmentationandpalindromicphrasing,butallmaterialis

drawnfromtheoriginal24–quaverpattern.Anoverviewofthestructurecanbeseenasa

proportionalchartandmightbeviewedasa‘developingvariation’form:

Example5:Solar,developingvariationstructuralchart24-quavermotive chords–contrarymotion transition

retrograde compression retrograde compression augmentation palindrome/polyphony recapitulation

chords–contrarymotion transition coda

TheintroductionofthethemeinretrogradeatletterD(modulationtoEminor)presentsthe

7–notescalenowindescentfollowedbythejumpingcontouroftheremaining17notes.

Greenbaum:SonataforPiano,4–Handsanalysis,pg.7

Additionally,afterthetwo–barretrogradethepatterndoesnotrepeatinthesameregister

butcontinuesitsdescentdovetailingfromplayer1toplayer2:

Example6:Solar,LetterD

Thiscreatesalonger4–barphrasewithbassnoteandupperregisterchordswovenaround

themovingquaverline.AtletterE,themusicagainmodulatesupamajor3rd–thistimeto

Abminor.Thedovetailed4–barphraseremainsbuthasbeencompressedsothatevery

secondbarisin6/8(ratherthan12/8).Thecombinationofthephrasecompressionand

modulationaredesignedtokeepthemomentumgoing:

Example7:Solar,LetterE

LetterGpresentsthefirstbaroftheretrogradeandthenimmediatelypresentsthatin

reverseordertocreateamicro–palindrome:

Greenbaum:SonataforPiano,4–Handsanalysis,pg.8

Example8:Solar,LetterG,palindrome

Theslursarenotpalindromic,butthepitchandrhythmformanexactmirror.Thisisan

exampleof‘developingvariation’(asdistinctfrommoretraditionalthemeandvariations)

andformsthebasisofabuild–upinpolyphonyacrossthe4staves(4hands)leadingtoa

clearrecapitulationoftheopening.

FromletterM,anextendedcodasectionisbuiltaroundadoubleaugmentationofthe

retrogradeandare-orderedretrograde(withdescendingscaleatend):

Example9:Solar,LetterM,doubleaugmentation

Harmonically,theascendingminorpitchstructureholdsthroughout,thoughthevoicingof

chordsisoftenquartal(stacked4ths)ratherthantriadsandconsequentlythemusicismore

modalthantonal.Diatonicclusters(stacked2nds)arealsofeaturedprominently.Theoverall

modulationschemecanbechartedinroughproportionasfollows:

Greenbaum:SonataforPiano,4–Handsanalysis,pg.9

Example10:Solar,modulationchart

Ab Ab E E E

D C C C

TheopeningfirmlyestablishesaharmoniccentreofCbeforemodulatingupamajor3rdtoE

andthenupafurthermajor3rdtoAbandagainbacktoC.ThemovetoDhalvesthe

difference(movingbyamajor2nd),butstayswithinastructureofcentresconnectedby

wholetones.ThecodasectionfromletterMmovesbackuptoaharmoniccentreofE,and

thisisintendedtosubtlycreatea‘tobecontinued’impressionleadingintothesecond

movement(whoseharmoniccentreisE).

Theharmonicqualityofminortonalitiesmodulatingsymmetricallybymajor3rdsisalso

foundinthe3rdmovementofmySonataforViolinandPiano(2000).Withoutconsciously

copyingthat,thereferenceuponreflectiondemonstratesabasictruththatsuccessful

experimentsaremorelikelytoberevisited.

II.TheExpandingUniverse

Almosttwoweeksafterthe1stmovementwasstarted,apitchstructurewassketchedout

fora2ndmovement:

Example11:TheExpandingUniverse,pitchstructure

Greenbaum:SonataforPiano,4–Handsanalysis,pg.10

Thestructureisbasedonastringof9notes(6differentpitches)spanninganoctaveanda

5th(oraperfect12th)fromEtoB:

Example12:TheExpandingUniverse,non–octavingmode

Itisaminorscalewithaminor6thbutno7th(majororminor),sothereforeeitheran

incompleteAeolianmodeoranincompleteHarmonicminorscale.Theintervalofa12this

importantbecauseitcreatesanon-octavingmodethatisreplicated(transposed)bya12th

(notbyanoctave).Thisbranchesoutlikeacycleof5thscreatingadditionalpitches(C#,Bb,

DandG#).Intheory,thatcreatesasetof10pitches–thoughtheBbattheverybottomof

thesketchisneverused.Sotheoverallsetincludes9pitchesandmighttheoreticallybe

describedasnonatonic.

TheeventualpresenceofDnaturalatbar15(entryofpiano1)temporarilyestablishesa

completeAeolianmodeinE.Theremainingtwo‘outside’pitches(C#andG#)onlyappearin

thehigheroctaves(asdeterminedbytheoverallpitchsystemasafixedregisterchord)and

createsubtlebutimportantcrossrelations.The2ndmovementnevermodulates–staying

fixedinrelationtotheharmoniccentreofEthroughout.

Thenon-octavingmodespanningtheintervalofa12thfromEtoBprovidesthecoremotivic

threadfortheentiremovement.Atfirsttherearejust2notes,then3,4,5,6,8andthen(by

bar6)thefull9–notepitchspanisfullyrevealed:

Example13:TheExpandingUniverse,coremotive

Greenbaum:SonataforPiano,4–Handsanalysis,pg.11

Thisenfoldingfrom2notesupto9fansoutfromthemiddle–registrallyexpandingboth

higherandlower.Thefirst9semiquaversoutlinethenon-octavingmode(fromwhichallis

built)andthefollowing7semiquaversstartthesamesequenceforthefirst3notesbutthen

swaptheorderofpitches4+5andalsoswap6+7(pitches8+9areomittedsecondtime

around).Thisisasubtlebutimportantvariationdevice.

Inparalleltotheadditivenatureofpitch,theoverallphrasestructureofthe2ndmovement

isalsoadditive:

Example14:TheExpandingUniverse,phrasestructure

Thegreensectionsshow4barsofmotivicexpansionfrom2notesto6notes.Thelightblue

columnrepresentsabridging8–notebar(2/4metre)leadingtothecoremotivicthread

(showninExample13)of9+7notesmarkedindarkerblue.Thiscompletemotiveexpandsin

lengtheachtimeuntiladdingexpandedpatternsin5/4(markedinorange)andthen6/4

(markedinpurple).

ThismotivicexpansionismainlydelineatedinPiano2.Piano1takesadifferentmorefluid

melodicrole,whichmightperhapsbeinterpretedasourownhumanindividualjourneys

intertwinedwithinalargerUniversalcontext.Theseupperregistermelodiesaccess

transpositionsofthenon–octavingmodethatproducethe‘outside’pitchesofC#andG#.A

mid–movementexampleofthiscanbeseenatbars39–40:

Greenbaum:SonataforPiano,4–Handsanalysis,pg.12

Example15:TheExpandingUniverse,melodicinvention

HerePiano1ismovingmostlyindemi-semiquavertripletsandfreetremoloaffordinga

dance–likequality.

Thefinalsectionofthesecondmovement–letterF–startsoutthesameaspreviouslybut

leadstoafinalcodasectionfromletterGincontrarymotion:

Example16:TheExpandingUniverse,coda

Thisnewgesture(markedinyellowinExample14)getsabbreviatedinthenumberofnotes,

butthelengthofsustainonthefinalnotegetslonger.Thisregistralshapedeliberatelystarts

withbothplayersonaunisonC#andthenspreadsoutacrosstheentirepianokeyboardto

reflecttheexpandingUniverse.

Greenbaum:SonataforPiano,4–Handsanalysis,pg.13

III.Earthrise

Aftertwomovementsofsustainedminorharmoniccentres,thefinalmovementisalmost

entirelyinDmajorthroughout,aimingforareflectionofjoyatviewingthehomeplanet.It

startsandendsthatwayandonlythesecondandthirdoctaveepisodesshowmodal

alternationtotheminor(thoughstillfirmlyfixedinD).WhileclearlyinDmajor,theopening

chordvoicingsshowsuperimpositionofperfect5ths(Amajorandsuch),whichactas

harmoniccolour(likea12thstoponanorgan)thanactualbitonality.Butthiscolouris

presentthroughout.

Themovementisaloosethemeandvariationsbasedaroundan8–barmelodywith

harmonicaccompanimentfirstplayedbypiano2atletterA:

Example17:Earthrise,theme(piano2)withjazzchordsymbols

Here,themelodyiscompletelydiatonic.Thebasslineisalmostcompletelydiatonic(except

foronechromaticpassingnote).Theharmonyinbetweeniscompletelydiatonic.Yet,the

voicingissignificantlymorecomplex.Thejazzchordsymbolsshowchordsinallinversions

Greenbaum:SonataforPiano,4–Handsanalysis,pg.14

(root,1stinversion,2ndinversion)andwithadded7ths,9ths+11ths.Somechords,takenas

isolatedverticalsonoritiesaremoredissonantthantheoverallprogressionseemsata

surfacelevel.Theoverallimpressionismelodicand‘relatively’harmonicallystable:butthe

voicingsandrhythmicphrasingaremorecomplex–influencedbythecontemporaryjazz

idiomofPatMethenyandLyleMaysandthepopsensibilityofJamesTaylor.Additionally,

thefirsttwobarsoutlinetheintervalsofaminorseventhchord,probablyfoundincountless

popularsongsbutBacharach’s1968classicI’llNeverFallinLoveAgaincomestomind.When

writingthisthemeIwasnotthinkingofanyofthoseartists;butsharedmusicalDNAcanbe

observed.

Therhythmicphrasingmovesfromonbeattooffbeatquaverstothefollowingtwo–bar

phrase:ON_ON(ON)|offoffoffoff.Thethirdonbeatisinbracketsbecauseatthe

crotchetlevelitisanoffbeat(4thbeatofthebar).Thefrictionbetweenonandoffbeatsis

commoninLatinrhythmsthoughthiswouldnotappeartobeanexactcommonpattern.

Astructuralchartrevealsahybridofthemeandvariations,internalarchformsandan

extendedcoda:

Greenbaum:SonataforPiano,4–Handsanalysis,pg.15

Example18:Earthrise,structuralchart

Thechartshowschordsbasedonthetheme(nomelody)followedbyaformalexpositionof

themelodictheme.Thevariationsthatfollowareinanarchform,followedbyasmallerarch

formbasedonacompressedversionofthethemeandultimatelyfollowedbyanextended

codaultimatelyleadingtoharmonicandstructuralresolution.

Thevariationsarereasonablyself-evident,mostlyworkingwithin8–barphrases.Whereas

thefirstmovementexploitsthe4handsasanintegratedwhole,andthesecondmovement

Greenbaum:SonataforPiano,4–Handsanalysis,pg.16

reliesonsuperimpositionofdifferentlayers,thefinalmovementtakesantiphonyasthe

basisofdevelopment.Firstlyatthelevelofphrasing(Piano2playsletterAbyitself,

answeredbyPiano1atletterB),andthenatacloserlevelofhocketandclosecounterpoint

foundfromletterC.

Twonotabledevelopmentalfeaturesareanintervalliccompressionofthetheme(letterQ)

andthethemeinretrogradeatthecoda(letterW).Thecompressedintervalthemeatletter

Qretainsthemaintheme’srhythm,butrestrictedtothefirst4notesofamajorscale:

Example19:Earthrise,melodiccompression

AtletterA,notes2to5spantheintervalofaminor7th.ByletterQthosenotesspanonlya

major3rd,makingthethemelessexpansiveandmoreanthemic.Thisreductivetechnique

canalsofoundattheendofthe1stmovementofSchubert’sStringQuintetinC(1828).It’sa

typeofboilingdowntotheessenceofmusicalmaterial.Afterallissaidanddone,thisis

whatisleft.

AfirstdraftofthescoreresolvedthesustainedchordsattheendofletterT.Andmyfriend

(andformerteacherofmanyyears)BrentonBroadstocksuggestedextendingitonthebasis

ofwantingtohearthethemeagain.Iwasinitiallyconcernedaboutredundantrepetition,

butBrenton’sinsightleadmetotreattheendofletterTasa‘false’endingandreprisethe

themewithcompressedintervals,followedbythethemewithalteredbassnotes,leadingto

anotablenewvariationintheformofacoda.

Thecodapresentsthethemenotonlyinretrograde(pitchonly–samerhythm)andthen

applyingisorhythmicoffset,butin3–barphrasing–anothertypeofcompressionalso

designedtoaidmomentum:

Greenbaum:SonataforPiano,4–Handsanalysis,pg.17

Example20:Earthrise,retrograde,isorhythmandfurthernote–orderpermutation

Afterextensive4–barbinaryphrasing,theimpactofthe3–barcompressionhasstrong

impactuponthenarrativeflowofthemusic.Thesyncopatedpatternretainstherhythmic

formofthefirst5notesofthemaintheme,butthenextendsthe2+3quavergroupingasa

cyclealltoitself:

Example21:Earthrise,codarhythm42+32+32+32+3(=24)

Itimplies5/8butincontextthe5–quaverpatterniscyclingonandoffthecrotchetbeatsof

the4/4metrethatanchorsit.

Therateofvariationisalsoturningfasterthanatanyotherstageintheentiresonataand

thealteredharmoniccontextdeliberatelyavoidsthetonic(D)inthebassuntiltheveryfinal

chord.Coupledwiththefirstpresenceofquaverpulsing,theoverallmodificationsare

designedtoheightenboththetensionofthecodaandalso(byextension)thedepthof

resolutionfortheendofthework.

ThefinalresolutionisclearlyinDmajor,howeverthevoicingofthefinalchordisagainmore

complex,includingnotonlytheprimarymajortriad,butalsothe7th,9thand11th:

Greenbaum:SonataforPiano,4–Handsanalysis,pg.18

Example22:Earthrise,combinedvoicingoffinalchord

Thecombineddownwardrolledchordisnotonlyharmonicallyrichinextensions,italso

resolvesthevarietyofcontourcombinationsinrolledchords(upanddown,simultaneous

andconsecutive)previouslyfeaturedthroughoutnotonlythefinalmovement,butthe

entirework.

Greenbaum:SonataforPiano,4–Handsanalysis,pg.19

Worksbythecomposerforfurtherreference

ForEver(2000)

SonataforViolinandPiano(2000),3rdmovement,TheInfiniteHeartbeat

Worksbyothercomposersforfurtherreference

Bacharach/David–I’llNeverFallinLoveAgain(1968)

MethenyandMays–TheGatheringSky(2002)

PinkFloyd(Waters)–Sheep,fromAnimals(1977)

Reich–PianoPhase(1967)

Schubert–StringQuintetinC,1stmovement(1828)

Taylor–NeverSayDie(1988)

Zawinal–Birdland(1977)

Termsforfurtherreference

ArchForm

Depthoffield

DevelopingVariation

FixedRegisterChord

Hemiola

Isorhythm

Non–octavingmode

Nonatonic

Palindrome

Post-minimalism

Quartalharmony

SonataForm

Article©StuartGreenbaum,2016