An Introduction to French Figured Bass Exercisesderekremes.com/wp-content/uploads/An Introduction to...
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1 An Introduction to French Figured Bass Exercises by Derek Remes The tradition of using figured bass exercises, or partimenti, to teach harmony goes back to 16 th century Italy. Church organists in the 16 th century often accompanied polyphonic part‐music by playing the lowest sounding voice at any given time. Use of the term basso continuo became widespread following the publication of Lodovico Viadana’s Cento concerti ecclesiastici in 1602. This publication was unique in that the continuo parts were not extracted from other voices, as was done earlier, but instead were composed independently. It was not until the 18 th century that figured bass exercises, also known as thoroughbass exercises, became a major tool for teaching harmony. During that century, more manuals were published on the subject that any other musical topic. Most publications focused on part‐writing rules, such as avoiding parallel octaves or fifths. By the late 18 th century, thoroughbass was no longer the dominant compositional technique, but the use of figured bass exercises as a pedagogical tool continued. Around the turn of the 19 th century, teachers at the newly founded Paris Conservatory turned to Italian pedagogical methods for their curricula. Reproductions of many basses by famous Italian composers were used, although Luigi Cherubini, who was trained in partimenti in Bologna and was directory of the Conservatory from 1822 to 1841, contributed many exercises of his own. Later, graduates such as Delibes, Franck and Thomas, made additional contributions to the curricula. Paul Vidal used his collection of exercises, Basses et Chantes Données, in his harmony classes at the Paris Conservatory. Nadia Boulanger, one of his students, used his book to teach generations of students in the 20 th century. Her student, Narcis Bonet, recently published a revised edition of these exercises, A Collection of Given Basses and Melodies, which is available in two volumes online. In the French tradition, realizations are to be done at sight at the piano, often while singing one voice in solfége. Transpositions can be done in enharmonically related keys by changing the key signature, or to other keys using clef changes. There are also ten books of exercises published by Henri Challan, which are available at online. They progress to eventually become rather complex, and can therefore be written down if needed. Part I: Voice‐Leading & Doubling Review Realizing figured basses in four voices requires an understanding of basic voice‐ leading and doubling rules: • No parallel 5 ths or 8 ths between any voice. • No more than an 8va between upper three voices, or a 12 th between bass & tenor. • Melodic intervals: 2nds, 3rds, 4ths, 5ths, 6ths, 8ths • In general, move as little as possible between chords, keeping common tones where possible, except in the soprano, which should have an interesting melodic contour. • Avoid direct 5ths & 8ths in outer voices unless soprano moves by step and the lower voice moves by “harmonic step” (i.e. a perfect 4 th or perfect 5 th )
Transcript of An Introduction to French Figured Bass Exercisesderekremes.com/wp-content/uploads/An Introduction to...
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AnIntroductiontoFrenchFiguredBassExercisesbyDerekRemes
Thetraditionofusingfiguredbassexercises,orpartimenti,toteachharmonygoes
backto16thcenturyItaly.Churchorganistsinthe16thcenturyoftenaccompaniedpolyphonicpart‐musicbyplayingthelowestsoundingvoiceatanygiventime.UseofthetermbassocontinuobecamewidespreadfollowingthepublicationofLodovicoViadana’sCentoconcertiecclesiasticiin1602.Thispublicationwasuniqueinthatthecontinuopartswerenotextractedfromothervoices,aswasdoneearlier,butinsteadwerecomposedindependently.
Itwasnotuntilthe18thcenturythatfiguredbassexercises,alsoknownasthoroughbassexercises,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,whichisavailableintwovolumesonline.
IntheFrenchtradition,realizationsaretobedoneatsightatthepiano,oftenwhilesingingonevoiceinsolfége.Transpositionscanbedoneinenharmonicallyrelatedkeysbychangingthekeysignature,ortootherkeysusingclefchanges.TherearealsotenbooksofexercisespublishedbyHenriChallan,whichareavailableatonline.Theyprogresstoeventuallybecomerathercomplex,andcanthereforebewrittendownifneeded.
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:Alwaysdoubletheroot,exceptdeceptivevidoublesthe3rd.Ingeneral,choosetherootforthesoprano.
• FirstInversionTriads:Almostalwaysputtherootinsoprano.‐ I6,V6,iii6:doubletheroot‐ IV6:doublethe5thwhengoingtoV;doubletherootwhengoingtoI(plagal)‐ ii6andvi6:doublethe3rdbecausethisemphasizestheirsubdominantand
tonicfunctions‐ viio:doublethe3rdtoavoiddoublingthetritone
• SecondInversionTriads:Thereare4kindsofsix‐fourchords.
‐ 1.Passing,2.Neighboring,3.Cadential;doublethe5th,whichisalwaysinthebass,forallthreetypes.
‐ 4.Deceptive;doublestheroot,thoughthischordisnon‐standardandcanbeseenaspartofapassingstructure.Thischordwaslabeledas“deceptive”byNadiaBoulanger,though,soitisincludedhere.
Example1a:TheFourTypesofSecondInversionChords
• SeventhChords:Ifusingacompleteseventhchord,thenallfourvoicesareusedandnodoublingispossible.Ifincomplete,onlythe5thcanbeomitted,andthenrootmustbedoubled.
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• Note:Adiminished7thchordresolvestodoubled3rd,whichresolvesboth
diminished5thsinward,towardseachother.
Example1b:DiminishedSeventhResolvestoDoubledThird:
StandardRootMotionsforRootPositionTriads: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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C4‐Irepeatingdownathirdhasaproblemthough–therearedirect5thsbetweenthetenorandbassvoices.NadiaBoulangersuggestedthisvoicinginstead:Example3d:MlleBoulanger’sSolutionforC4IRepeatingDowna3rd
C4andC5canalsobereversed,makingfourpossiblevariationsinall.Example4a:C4andC5withChordsReversedC4Rev.(C4‐R) C5Rev.(C5‐R) C4IRev.(C4‐IR) C5IRev.(C5‐IR)
Theretrogradeversionscanbedistinguishedfromtheregularversionsby
identifyingwhichchordtoneisinthesoprano(thesopranonoteintheaboveexamplesisalmostalwaysmaintainedthroughoutthefollowingexercises).
Herearesomeadditionalsequencesusingretrogradecells:Example4b:TypicalIntervalsofReversedCellRepetitionC4‐Rrepeatingupadiatonic2nd C5‐Rrepeatingupadiatonic2nd
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Example4c:TypicalIntervalsofInverted,ReversedCellRepetitionC4‐IRrepeatingupadiatonic2nd C5‐IRrepeatingdownadiatonic2nd
Cellscanalsomodulate.Thiscommonsequencemodulatesupa5th.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:StrategyforRealizingDominantSeventhChords
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.
