an introduction to french figured bass exercises

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AnIntroductiontoFrenchFiguredBassExercisesbyDerekRemes

Thetraditionofusingfiguredbassexercises,orpartimenti,toteachharmonygoes

backto16thcenturyItaly.Churchorganistsinthe16thcenturyoftenaccompaniedpolyphonicpart‐musicbyplayingthelowestsoundingvoiceatanygiventime.UseofthetermbassocontinuobecamewidespreadfollowingthepublicationofLodovicoViadana’sCentoconcertiecclesiasticiin1602.Thispublicationwasuniqueinthatthecontinuopartswerenotextractedfromothervoices,aswasdoneearlier,butinsteadwerecomposedindependently.

Itwasnotuntilthe18thcenturythatfiguredbassexercises,alsoknownasthoroughbassexcercises,becameamajortoolforteachingharmony.Duringthatcentury,moremanualswerepublishedonthesubjectthatanyothermusicaltopic.Mostpublicationsfocusedonpart‐writingrules,suchasavoidingparalleloctavesorfifths.Bythelate18thcentury,thoroughbasswasnolongerthedominantcompositionaltechnique,buttheuseoffiguredbassexercisesasapedagogicaltoolcontinued. Aroundtheturnofthe19thcentury,teachersatthenewlyfoundedParisConservatoryturnedtoItalianpedagogicalmethodsfortheircurricula.ReproductionsofmanybassesbyfamousItaliancomposerswereused,althoughLuigiCherubini,whowastrainedinpartimentiinBolognaandwasdirectoryoftheConservatoryfrom1822to1841,contributedmanyexercisesofhisown.Later,graduatessuchasDelibes,FranckandThomas,madeadditionalcontributionstothecurricula.

PaulVidalusedhiscollectionofexercises,BassesetChantesDonnées,inhisharmonyclassesattheParisConservatory.NadiaBoulanger,oneofhisstudents,usedhisbooktoteachgenerationsofstudentsinthe20thcentury.Herstudent,NarcisBonet,recentlypublishedarevisededitionoftheseexercises,ACollectionofGivenBassesandMelodies,whichisavailableintwovolumes.

IntheFrenchtradition,realizationsaretobedoneatsightatthepiano,oftenwhilesingingonevoiceinsolfége.Transpositionscanbedoneinenharmonicallyrelatedkeys,soasnottorequireclefchanges.TherearealsotenbooksofexercisespublishedbyHenriChallan,whichareavailableatonline.Theseexercisesaremorecomplex,andthereforeprobablyintendedtobewrittendown.

PartI:Voice‐Leading&DoublingReviewRealizingfiguredbassesinfourvoicesrequiresanunderstandingofbasicvoice‐

leadinganddoublingrules:• Noparallel5thsor8thsbetweenanyvoice.• Nomorethanan8vabetweenupperthreevoices,ora12thbetweenbass&tenor.• Melodicintervals:2nds,3rds,4ths,5ths,6ths,8ths• Ingeneral,moveaslittleaspossiblebetweenchords,keepingcommontoneswhere

possible,exceptinthesoprano,whichshouldhaveaninterestingmelodiccontour.• Avoiddirect5ths&8thsinoutervoicesunlesssopranomovesbystepandthe

lowervoicemovesby“harmonicstep”(i.e.aperfect4thorperfect5th)

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ChordFunctions:

TonicFunction(T):I,vi,iii(viandiiiareweaker)DominantFunction(D):V,viio,iii(iiiisweak,butisalsovofrelativeminor)SubdominantFunction(SD):ii,IV(IVisweakerthanii)

ChordSyntax:

TDT/TSDT/TSDDT

Thesearethemostcommonpatternsappearingwithinphrases,butotheroptionsarepossiblebetweenphrases.Forinstance,asubdominantchordmightfollowadominantchordthatispartofahalf‐cadence.

BasicDoublingRules:

• RootPositionTriads:Alwaysdoubleroot,exceptdeceptivevidoubles3rd.Ingeneral,chooserootforsoprano.

• FirstInversionTriads:Almostalwaysputrootinsoprano.‐ I6,V6,iii6:doubletheroot‐ IV6:doublethe5thwhengoingtoV;doublerootwhengoingtoI(plagal)‐ ii6andvi6:doublethe3rdbecausethisemphasizestheirsubdominant

andtonicfunctions‐ viio:doublethe3rdtoavoiddoublingtritone

• SecondInversionTriads:Thereare4kindsofsix‐fourchords.

‐ Passing,Neighboring,Cadential:doublethe5th,whichisalwaysinthebass

‐ “Deceptive:”doublesroot,thoughthischordisnon‐standard.Thischordwaslabeledas“deceptive”byNadiaBoulanger,soitisincludedhere.

Example1a:TheFourTypesofSecondInversionChords

• SeventhChords:Ifusingacompleteseventhchord,thenallfourvoicesareusedandnodoublingispossible.Ifincomplete,onlythe5thcanbeomitted,andthenrootmustbedoubled.

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• Note:Adiminished7thchordresolvestodoubled3rd,whichresolvesboth

diminished5thsinward,towardseachother.

Example1b:DiminishedSeventhResolvestoDoubledThird:

StandardRootMotions:Noticethatwhenthebassmovesupbystep,allothervoicesmoveincontrarymotion.Ingeneral,successfulvoice‐leadingoccurswhentheoutervoicesmovecontrarytoeachotherand/orthesopranomovesbystep.Example2:RootMotionsofRootPositionTriadswithTypicalHarmonizations

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PartII:Sequences

RealizingFrenchfiguredbassexercisesrequiresanunderstandingoftheFrenchmethodofanalyzingsequences.IntheFrenchschool,thereareonlytwotypesofsequences,whicharedistinguishedbytheirbassmotion:thecellofthe4thandthecellofthe5th.Bothcellsarepossiblewiththesecondtriadinfirstinversion.

Example3a:TheCellofthe4thandtheCellofthe5thCellofthe4th(C4) Cellofthe5th(C5)Cellofthe4th Cellofthe5th withinversion(C4I)withinversion:(C5I)

Thesecellscanrepeatatanyintervaltoformsequences(bysteporleap,upordown).Herearesomecommonintervalsforsequentialrepetition.Example3b:TypicalIntervalsofCellRepetitionC4repeatingdownadiatonic3rd C5repeatingdownadiatonic2nd

Example3c:TypicalIntervalsofCellRepetitionwithInversionsC4‐Irepeatingdownadiatonic3rd C5‐Irepeatingdownadiatonic2nd

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C4Irepeatingdownathirdhasaproblemthough–therearedirect5thsbetweenthetenorandbassvoices.NadiaBoulangersuggestedthisvoicinginstead:Example3d:MlleBoulanger’sSolutionforC4­IRepeatingDowna3rd

C4andC5canalsobereversed,makingfourpossiblevariationsinall.Example4a:C4andC5withChordsReversedC4Rev.(C4‐R) C5Rev.(C5‐R) C4IRev.(C4‐IR) C5IRev.(C5‐IR)

Theretrogradeversionscanbedistinguishedfromtheregularversionsby

identifyingwhichchordtoneisinthesoprano,(thesopranonoteintheaboveexamplesisalmostalwaysmaintainedthroughouttheexercises).

Herearesomeadditionalsequencesusingretrogradecells:Example4b:TypicalIntervalsofReversedCellRepetitionC4‐Rrepeatingupadiatonic2nd C5‐Rrepeatingupadiatonic2nd

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Example4c:TypicalIntervalsofInverted,ReversedCellRepetitionC4‐IRrepeatingupadiatonic2nd C5‐IRrepeatingdownadiatonic2nd

Cellscanalsomodulate.Thissequencemodulatesupa5th.Example5:AModulatorySequenceusingC4­IRepeatingUpa3rd

AMinor:CMajor: EMinor:GMajor: BMinor:DMajor: Herearesomeexamplesofsequencesfromtheliterature,withanalysesaccordingtotheFrenchschool.Creativeuseofsequencesresultsfromhowthesurfacerhythmisactivated.

Example6a:Mozart,PianoConcertoNo.9,K.271­Mov.3(m.133­137)

Thefollowinganalysisplacesgreaterimportancetothefirstnoteofeach

measurebecauseitismetricallyaccented,ratherthanthehighestnoteineachmeasure.NoticeMozart’sadjustmentofaccidentalsinthesequencetotonicizeG‐minorandC‐minor.(TheaccidentalA‐flatalsotonicizesE‐flatMajor,whichisnotrepresentedinthefollowinganalysis).

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Example6b:C4RepeatingDownaDiatonic3rd

Example7a:Beethoven,ViolinSonataNo.3,Op.12–Mov.3(m.341­45)

BeethovenalsomakesadjustmentstothesequencetotonicizeF‐minor:Example7b:C4­IRRepeatingDownaStep

Example8a:Brahms,ViolinSonataNo.3,Op.108–Mov.3(m.43­47)

LikeMozartandBeethoven,BrahmsalsomakesadjustmentstothissequencetotonicizeA‐Major.

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Example8b:C5­IRRepeatingUpaDiatonic2nd

PartIII:RootPositionExercises

ThefiguredbassexercisespublishedbyNarcisBonetareintwovolumesandarearrangedprogressively,beginningwithrootpositiontriadsandproceedingthroughaugmentedsixthchords.

• RootPositionTriads• FirstInversionTriads• SecondInversionTriads• DiminishedTriads• DominantSeventhChords• Non‐DominantSeventhChords

• TheDominantNinthChord• TheSeventhontheLeadingTone• TheDiminishedSeventhChord• Exerciseswithallpreviouschords• TheAugmentedSixthChord

Thisisthefirstexerciseforrootpositiontriads.Example9a:

Inordertofacilitatereadingatthepiano,identifythelocationandtypeof

sequencesemployed.Rememberthatinsequences,thesamesopranonotefromtheaboveexampleswillbeusedconsistentlythroughouttheexercises.Itisalsohelpfultolabelsopranopitchesoccasionally.Inthenextexamplesomepitchesarelabeledforyouinsolfege.

Knowingthesopranonoteisveryimportantbecauseforrootpositiontriads,allthreeuppervoicesarealmostalwaysarrangedincloseposition(i.e.,withouttheomissionofachordtonebetweenanyvoice)‐exceptforthedeceptivevi,whichdoublesthethird.Therefore,ifthesopranonoteisidentified,thealtoandtenornotescanbeplacedunderiteasily.

AsmentionedinPartI,thegoalofvoice‐leadingistomoveassmoothlyaspossiblebetweenchordswhileavoidingparallel5thsand8vasandmakingthesopranoasmelodicaspossible(i.e.,avoidingcommontones).Sincetheupperthreevoicesareusuallydeterminedbythesopranonote,movingthesopranostepwiseandcontrarytothebasswillusuallyfacilitatesmoothvoice‐leading.

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Example9b:

Hereisthefinishedrealization,whichusuallywouldbedoneatsightatthepiano.Rememberthatforrootpositiontriads,generallytherootwillbeinthesoprano.Noticehowthesopranousuallymovesstepwiseandcontrarytothebass,whilethealtoandtenorareplacedinclosepositionbeneathit.Somevariationsarepossible.Example9c:

Thisisanotherexampleusingrootpositiontriads,withsomesopranopitchesgiveninsolfége(using“fixed‐do”)Example10a:

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Hereitisrealized.Somevariationsareofcoursepossible.Example10b:

Thisisonemoreexampleusingrootpositiontriads.NotethedeceptiveuseofanA‐majortriadinm.13!ThissortoftrickistypicalofVidal’sexercises.Also,m.9containsanerror–adominantfunctionG‐sharpmajortriadleadstoasubdominantfunctionF‐sharpminortriad.Technicallythisisnotcorrect,butperhapsVidalthoughtitwasacceptablebecauseoftheweakrhythmicplacementofthesubdominantchord.Example11a:

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Hereistherealization.Noticeinm.15howVidalusesIVratherthaniv,andiirather

thaniio,whichpreventsusinganaugmentedsecondmelodicallyinthesoprano.Also,noticehowthelastbeatofm.16requireskeepingacommontoneinthesopranotoparallel8vaswiththebass.

An“X”indicatesalocationofaV‐viprogression,whichforvoice‐leadingreasons,doesnotusethetypicaldeceptivevidoublingofthethird.

Example11b:

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PartIV:FirstInversionExercises Realizingexerciseswithfirstinversiontriadsrequiresuseofthe“melodicsixsolution.”Thegoalofthissolutionistoharmonizeaseriesofparallelfirstinversionchordswhileavoidingparallel5thsand8vas.Noticethatintheupperthreevoices,twovoicesmoveparallelwhileonemovescontrary.Parallelfoursareacceptable.Example12:MelodicSixSolution

InPartIitwasstatedthatfirstinversiontriadsmustalwayshavetherootinthesoprano.Whenthissolutionisused,melodicconsiderationsareoverrulingharmonicones,sotherootneednotbeinthesoprano.(Therearealsoexceptionswherethe5thcanbeusedinthesopranoforfirstinversiontriads).

Hereisanexerciseusingfirstinversionchords.Thesolfegepitchesandanalysisofthesequencesareaddedinthisexample.Rememberthedoublingrulesforfirstinversiontriads,whichwereoutlinedinPartI.Itcanbeassumedthatchordswithoutfiguredbassnumbersareinrootposition.However,forsakeofclarity,sometimesa“5”or“5/3”isincludedasareminder.Example13a:

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Hereitisrealized.Thisexampleusesaportionofthe“melodicsixsolution,”aswellasadoubledpedalpoint.Pedalpointscallusuallybeidentifiedbyconsecutivefirstinversiontriadswhichmovebyleap,asinm.17‐19.Example13b:

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Afinalexampleofanexerciseusingfirstinversiontriadsmysopranonotesandanalysis.Thisexampleoccasionallyindicatesthedirectionoftheinnervoiceswithanarrow.Example14a:

Rememberthatii6goingtoVwilldoublethethirdtoemphasisitssubdominantfunction.Thedeceptivevoicingisusedinm.11becauseitavoidsparallel5thsbetweensopranoandtenor.Notethatm.17doesnotusethedeceptivevoicinginordertoavoidparallel5ths.

The“X”inExample14indicatesthatthesefirstinversionchordsaretheproductofvoice‐leadinganddonotrequirethattherootbeinthesoprano.ThisexamplealsousestheBoulangersolutionforC4‐Imovingdownbyathirdinm.6‐7,aswellasadoubledpedalpointattheend(seenextpagefortherealization).

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Example14b:

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PartV:SecondInversionTriads

Rememberthatthereareonlyfourtypesofsecondinversiontriads;passing,neighboring,cadential,andthenon‐standard“deceptive.”Noothersecondinversionchordsshouldbeused.Itisimportanttonotethatallpassing6/4chordshavethesamestructure:twovoicesmovestepwiseinoppositedirection(alsocalledavoice‐exchange),onevoiceisalowerneighbor,andtheotherremainsapedal.Thesefourvoicescanbearrangedinanyverticalorder,solongasthebassmovesstepwise.Example15:Passing6/4Chords

Thisisthefirstexerciseofthesecondinversionchords.Itusesallfourtypesof6/4chords.Example16a:

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Hereistherealization.Noticethattheii6chordinm.19doublestherootbecauseitdoesn’tpreceedaVchordliketheii6inthefollowingmeasure.Thisexamplealsousedadoubledpedalpointinm.15‐16.Example16b:

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PartVI:DominantSeventhChords TheFrenchlabelingsystemforseventhchordinversionsisasfollows.Theplusreferstotheleadingtone.Aslashthroughanumbermeansthatpitchisloweredahalf‐step.

• RootPosition:7/+• FirstInversion:6/5

• SecondInversion:+6• ThirdInversion:+4

Thebasicstrategyforusingdominantseventhchordsistobeginbyrealizingthechordasifitwereatriad,followingthestandarddoublingrules.Thenmoveoneoftherootsdownasteptocreatetheseventhchord.Inthecasethattheseventhisalreadyinthebass,proceedasifitweretheroot.Thefollowingexampleillustratesthisprocedure:Example17:StrategyforRealizingDominaÎtSeventhChords

Rememberthatwhenpossible,theseventhofadominantseventhchordmustbepreparedbycommontoneinthepreviouschord.Mostseventhsinfiguredbassexerciseswillbecomplete–thatis,allfourchordtoneswillberepresented.Ifincomplete,onlythe5thcanbeomitted.Inthatcase,therootmustbedoubledbecausethe3rdandthe7tharetendencytonesandwouldcauseparalleloctavesifresolvedcorrectly.

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Example18a:SeventhChordExercise

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Noticethevariousnon‐standardusagesofthedeceptivedoublinginthisexample:m.17&18useittocreatethe“deceptive”6/4chord;m.27usesitasaresultofresolvingthetendencytoneinthetenor;andm.29&37useittoavoidparallel5thsinthealtoandtenor.Bassmotionunderadominantseventhusuallyindicatesavoice‐exchangewithanuppervoice.Measures19through26createanextendedvoice‐exchange.Example18b:

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ConclusionVII:

Realizingfiguredbassescanbewonderfultoolforlearningharmonyandvoice‐leading.Atthepiano,itrequirestheactiveparticipationofthestudent,ratherthanpassiveobservation.However,itisimportanttorememberthattheseexercisesareonlydistillationsoftherulesthatcomposerstendtofollowmostofthetime.Therefore,theintegrityofeachindividualvoiceshouldbethefinaldeterminantinanysituation. Amasteryoftheprinciplesofvoice‐leadinganddoublingdoesnotmakegreatmusic‐creativityisessential.Theseexercisescanprovideasolidfoundation,buttheyarestillonlyapointofdeparture.Theultimategoalistoleavebehindtherulesandjustmakemusic.

Bibliography:

Bonet,Narcis.ACollectionofGivenBassesandMelodies.I.SantaAnna,Barcelona:DINSICPublicacionsMusicals,S.L.,2006.Print.

Lasser,Philip.KeyboardHarmonyMaterials.NewYork,NY:EuropeanAmerican

MusicalAllianceInc.,2004.Print.Randel,DonM.TheNewHarvardDictionaryofMusic. Cambridge,Massachusetts:

TheBelknapPressofHarvardUniversityPress,1986.Print.

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