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Oxford Music Online article url: http://www.oxfordmusiconline.com:80/subscriber/article/grove/music/06690 Counterpoint (from Lat. contrapunctus, from contra punctum: ‘against note’; Fr. contrepoint; Ger. Kontrapunkt; It. contrappunto). A term, first used in the 14th century, to describe the combination of simultaneously sounding musical lines according to a system of rules. It has also been used to designate a voice or even an entire composition (e.g. Vincenzo Galilei's Contrapunti a due voci , 1584, or the contrapuncti of J.S. Bach's Art of Fugue) devised according to the principles of counterpoint. (See also POLYPHONY, §I.) 1. Discant of the 13th and 14th centuries. The theory of counterpoint, which existed by about 1330, developed from the older theory of discant, but differs from it in ways that a comparison of the two makes clear. The technique of discant occurs in two distinct forms. Works dealing with ‘interval succession theory’ (‘Klangschritt Lehre’) merely list possible single progressions of an added voice for all usual successive intervals of the cantus, considering only the consonances of unison, octave, 5th (and occasionally 4th); for example: ‘If the cantus ascends by a 2nd and the opposed part begins at the octave, then the opposed part descends by a 3rd and forms [with the cantus] a 5th, or descends by a 7th and coincides with the cantus’ (CoussemakerS, ii, 191). General guidelines on compositional technique are found only in the work of Franco and his followers, apart from traditional instructions on contrary motion (see Eggebrecht and Zaminer, 1970; CoussemakerS, ii, 494; AnnM, v, 1957, 35). Franco was clearly concerned to emphasize the consonant or dissonant quality of sounds in the formulation of general statements on compositional technique, but did not go beyond individual aspects (CSM, xviii, 69–73): “Every discant is ordered by consonances … Every imperfect dissonance [major 2nd, major 6th, minor 7th] sounds well immediately before a consonance … The discant begins at the unison, octave, 5th, 4th, or major or minor 3rd [i.e. on any of the ‘consonances’], then proceeds in consonances and occasionally mixes them at suitable points with dissonances, so that when the tenor is ascending, the discant is descending and vice versa. It should be noted that tenor and discant occasionally ascend or descend simultaneously for the sake of the beauty of the piece … and also that consonances are always used in all [rhythmic] modes at the beginning of the perfectio [mensural unit].” Anonymus 2 tried ( c1300) to analyse the role of imperfect consonances in composition technique: ‘Imperfect [consonances] are the major and minor 3rd, which are good in the progression from a 5th to a 5th or from a 5th to a unison and vice versa; and the major 6th, which is good before an octave’ (CoussemakerS, i, 311). KlausJürgen Sachs Grove Music Online Counterpoint

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    Counterpoint(fromLat.contrapunctus,fromcontrapunctum:againstnoteFr.contrepointGer.KontrapunktIt.contrappunto).

    Aterm,firstusedinthe14thcentury,todescribethecombinationofsimultaneouslysoundingmusicallinesaccordingtoasystemofrules.Ithasalsobeenusedtodesignateavoiceorevenanentirecomposition(e.g.VincenzoGalilei'sContrapuntiaduevoci,1584,orthecontrapunctiofJ.S.Bach'sArtofFugue)devisedaccordingtotheprinciplesofcounterpoint.(SeealsoPOLYPHONY,I.)

    1. Discant of the 13th and 14th centuries.Thetheoryofcounterpoint,whichexistedbyabout1330,developedfromtheoldertheoryofdiscant,butdiffersfromitinwaysthatacomparisonofthetwomakesclear.Thetechniqueofdiscantoccursintwodistinctforms.Worksdealingwithintervalsuccessiontheory(KlangschrittLehre)merelylistpossiblesingleprogressionsofanaddedvoiceforallusualsuccessiveintervalsofthecantus,consideringonlytheconsonancesofunison,octave,5th(andoccasionally4th)forexample:Ifthecantusascendsbya2ndandtheopposedpartbeginsattheoctave,thentheopposedpartdescendsbya3rdandforms[withthecantus]a5th,ordescendsbya7thandcoincideswiththecantus(CoussemakerS,ii,191).GeneralguidelinesoncompositionaltechniquearefoundonlyintheworkofFrancoandhisfollowers,apartfromtraditionalinstructionsoncontrarymotion(seeEggebrechtandZaminer,1970CoussemakerS,ii,494AnnM,v,1957,35).Francowasclearlyconcernedtoemphasizetheconsonantordissonantqualityofsoundsintheformulationofgeneralstatementsoncompositionaltechnique,butdidnotgobeyondindividualaspects(CSM,xviii,6973):

    EverydiscantisorderedbyconsonancesEveryimperfectdissonance[major2nd,major6th,minor7th]soundswellimmediatelybeforeaconsonanceThediscantbeginsattheunison,octave,5th,4th,ormajororminor3rd[i.e.onanyoftheconsonances],thenproceedsinconsonancesandoccasionallymixesthematsuitablepointswithdissonances,sothatwhenthetenorisascending,thediscantisdescendingandviceversa.Itshouldbenotedthattenoranddiscantoccasionallyascendordescendsimultaneouslyforthesakeofthebeautyofthepieceandalsothatconsonancesarealwaysusedinall[rhythmic]modesatthebeginningoftheperfectio[mensuralunit].

    Anonymus2tried(c1300)toanalysetheroleofimperfectconsonancesincompositiontechnique:Imperfect[consonances]arethemajorandminor3rd,whicharegoodintheprogressionfroma5thtoa5thorfroma5thtoaunisonandviceversaandthemajor6th,whichisgoodbeforeanoctave(CoussemakerS,i,311).

    KlausJrgenSachs

    Grove Music OnlineCounterpoint

  • 2. Early note-against-note writing.EarlycounterpointdivergesclearlyfromthetheoriesofFrancoandAnonymus2bytakingonlytwopartnoteagainstnotecompositionintoconsideration,thusignoringdissonancesand,atfirst,notevaluesbychangingtheclassificationofthesounds,apparentlylittle,butradically,byreclassifyingthe4th(whichwasamediumconsonanceandbecomesadissonance)andbymakingthedifferenceinqualitybetweenperfectandimperfectconsonancesthebasisofaregularsystem.Textbooks,typically,listconsonances,perfectandimperfect,andproviderulesfortheirsuccession.

    Thesubdivisionofconsonancesalwaysleadstothecontrastbetweentheunison,5thandoctaveasperfectandthe3rdand6thasimperfect.ItisimmaterialwhethertheconsonancesaregivenGreeknames,ashappenedparticularlyintheearlystages,orLatinnames(inotherwords,whether3rds,forexample,weredescribedseparatelyassemiditonusandditonusorjointlyastertia)itisalsoimmaterialwhetherandtowhatextentintervalsgreaterthantheoctavearementionedandclassified,andwhethertheperfectconsonanceswerecalledconsonantiaeandtheimperfectdissonantiae(asoccasionallyhappened).Butterminologyandthenumberofnamedconsonancesdogiveinformationaboutthetraditionsandphasesoftheory.

    Thedifferenceinqualitybetweenthetwogroupsofconsonancesisparticularlyshowninthedirectionsreferringtoimportantsectionsinthecompositionortoparallelpartwriting:thebeginningandendshouldbeperfectconsonancesandthepenultimatenoteanimperfectconsonanceparallelsuccessionsofidenticalintervalsarestrictlyforbiddenwithperfectconsonancesbutemphaticallyrecommendedwithimperfectones.Thisdifferentiationisbasedonthefact,remarkedonbyAnonymus2,thatthreeconsonancesequences(3rdunison,3rd5thand6thoctave)haveparticularadvantages:closemelodicconnectionsthroughconjunctmotion,independentpartwritingthroughcontrarymotion,andchangeinsoundthroughthetransitionfromimperfecttoperfectconsonance(which14thcenturywriterscalledstriving:requirere,tendere).AccordingtothetheoryofMarchettodaPadova(c1318)repeatedlytakenupinthe15thand16thcenturiesthoughwithoutbecomingthenormintheoryorpracticeoneofthetwopartswasalsosupposedtomovebyasemitone,asinex.1.Thisalsodeterminedthebasisofcounterpointevenincontextswhereidealsequencesoccuronlyoccasionally.Thishappenswhenthetheoryoffers,asrecommendations(mandataarbitraria),progressiontonearbynotes,contrarymotion,andalternationbetweenimperfectandperfectconsonances.Forcombinationsthatrespectonlyonemandatumarbitrarium,thestrictprohibition(mandatumnecessarium)ofparallelsimilarperfectconsonancesontheonehand,andthepermittedsuccessionofsimilarimperfect,dissimilarimperfectanddissimilarperfectconsonancesontheother,arebothvalid.Therepetitionofanote,causingobliquemotion,issometimespermittedonlyinthecantus,butmaybeusedineitherpart(oreveninbothsimultaneously,asarepeatednote)itisnothowevertherecommendednextstep.Onthebasisofthesedirections,agivencantusyieldsanoteagainstnotecomposition,inwhich15thcenturytheoristsrequiredtwoessentialqualities:first,differencebetweenthetwoparts,intheinterestsofwhichparallelprogressioninsimilarperfectconsonances,usualinpolyphonyofthe9thcenturytothe13th,wasnowforbidden(Ifonepersonsingsthesameastheotherthatdoesnotfulfiltheaimofcontrapunctusforitsaim[intentio]isthatwhattheonesingsbedifferent[diversum]fromwhattheothersingsProsdocimusdeBeldemandis,1412CoussemakerS,iii,197)andsecond,indeterminatestructure,ensuredbythefactthattherewerealwaysseveralpermittedconsonancestochoosefrom,andthusmanypossibleresolutionsforthepartaddedtoacantus(Contrapunctusistheindeterminatesetting[positio]ofasinglenoteinhighorlowpositionagainstasinglenoteinanycantus.Contrapunctusisrelatedsimply[simpliciter]andwithoutpredetermination[indeterminate]toallsettings[positiones]ofhighandlownotesinthemusicalsystemUgolinoofOrvieto,c1430CSM,vii/2,p.4).

    Ex.1Movementfromanimperfecttoaperfectconsonancewithonepartmovingbyasemitone,fromMarchettodaPadova(c1318)

  • Tohearthisexamplepleaseclickhere

    Musicexamplesfromcounterpointtreatisesmayillustratedifferentfeaturesofthemethodofcomposition.Inex.2acontrarymotionisdominantparallelimperfectconsonancesareusedsparinglywhenonepartmovesbyleaptheothermovesbysteporhasarepetition(theaddedpart,accordingtosometreatises,shouldberestrictedtotherangeofahexachord).Inex.2b,parallelsofuptofoursimilarimperfectconsonancesarerelativelyfrequenttheyusuallyleadtotheadjacentperfectconsonance(asinintervals6,9and20)butcanalsoleadtooneormoreimperfectconsonancesofanotherkind(1415)simultaneousskipsarenotexcluded(1011,1516),butinvolvecontrarymotionandchangeofintervaltype.

    Ex.2Differingmethodsofcompositionfromtwocounterpointtreatises

    Tohearthisexamplepleaseclickhere

    Bywayofcontrastinprecontrapuntalnoteagainstnotecompositions,combinationsofunison,5thandoctave,whereparallelsofsimilarintervalsarenotimpossible,predominateover3rds,whichusuallyonlyserveasabridgebetweenunisonand5th(ex.3)thestillconsonant4thalsosometimesappears,whilethe6thisrare(seetheexamplesinSachs,1974,pp.1212).

    Ex.33rdsservingasabridgebetweenunisonand5th,Alleluya.Altissimus(IFnPalat.472,f.15vb)

    Tohearthisexamplepleaseclickhere

    KlausJrgenSachs

    3. Treatises of the 14th and 15th centuries.Fromthetimeoftheearliestsurvivingtextbooksoncounterpoint,thenumberoftreatisesoncompositiontechniqueincreasedmarkedlyandthetermcontrapunctusquicklycameintouse.Thiswassurelyamatterofcauseandeffecttheexplanationisprobablytobefoundinthenoveltyofthetechniquedesignedfornoteagainstnotecomposition.ThereareisolatedreferencestoacontraponchamensorcontrapointamensinthebriefdiscussionofmusicalgenresandpolyphonicpracticesinPeiredeCorbiac'sProvenalTesaur(c1250),butthereisnomentionofthewordcontrapunctusinmusictheoreticalwritingsuntilitsappearanceinthenewtheoryofcompositionabout1330,sinceallknownauthorsfromJohannesdeGarlandia(c1240)toJacquesdeLige(c1260after1330)usedthegeneraltermdiscantuswhendiscussingcompositiontechnique.

    AmongtheearliestdidacticcontrapuntalworksareprobablythebriefpieceattributedtoJohannesdeMuris,Quilibetaffectans(CoussemakerS,iii,5960a),whichwaswidelyread,andthecompilationofPetrusfraterdictusPalmaociosa,writtenc1336(Wolf,191314).PhilippedeVitry,too,seemstohavetaughtcounterpointevenifnoversionsofthetreatisesattributedtohim(e.g.CoussemakerS,iii,237)canberegardedasauthenticallyhisintheirsurvivingform.

    Mostoftheworksoncounterpointuptothe15thcenturyareanonymous,anditisnotusually

  • possibletofixtheirdatesorplacesoforiginaccurately.TreatisesthathelpestablishachronologyforthedevelopmentofthetheoryincludeGoscalch(1375excerptinSachs,1974),AntoniusdeLeno(c1400CoussemakerS,iii,30728),ProsdocimusdeBeldemandis(1412CoussemakerS,iii,1939),UgolinoofOrvieto(c1430CSMvii/2),JohannesLegrense(c1460CoussemakerS,iv,38396),JohannesTinctoris(1477CoussemakerS,iv,76153),GuilielmusMonachus(c1480CSM,xi)andFlorentiusdeFaxolis(between1484and1492excerptinSeay,1963,p.85).Thereliabilityofthesourcesincreasedwiththeappearanceofprintedworksoncounterpoint,byRamosdePareia(Musicapractica,1482),NicolausBurtius(Musicesopusculum,1487),FranchinusGaffurius(Practicamusicae,1496)andothers.

    KlausJrgenSachs

    4. Contrapunctus diminutus.ThetreatiseCumnotumsit(probablymid14thcentury)containsadefinitionofcounterpointasnothingbutasettingofnoteagainstnote(nonnisipunctumcontrapunctumponerevelnotamcontranotamponerevelfacere)andthebasisofdiscant(fundamentumdiscantusCoussemakerS,iii,60).Discant,thenewerforminthiscase,denotesthemannerofcompositionwhosebasisiscontrapuntalnoteagainstnotecomposition.Thesecondpartofthetreatise(Dediminutionecontrapuncti)elucidatestherelationbetweenthetwotypesofcomposition:sincethecontrapunctusthepartaddedtothetenor,inbrevesofequallengthcanbedividedintosmallernotesinvariousways,theworklistsrhythmicalpossibilitiesofthiskindandillustratesthemwithmusicalexamples.Theexamples(22,accordingtothemostreliablesources)allhavethesametenor,andeachfollowsarhythmicformulatheyareallbasedonthesamenoteagainstnotecomposition,whosedegreeofdiminutionincreasessystematicallyfromexampletoexampleforeachofthefourbasicmensurations,asinex.4(thebeginningoftheexamplesfortempusperfectumcumprolationemaioricitedinSachs,1974,p.146).Theworkillustratesthetechnique,knownfromothertreatises,ofcreatingadiminishedversionofanaddedpart,byfillingoutthebreveunitsorbytheinterpolationofnotes,butdoesnotmentionthedissonances(2nds,4thsand7ths)thatthusoccur.Thelackofsuchcommentprobablydoesnotmeanthatdissonancecouldbeusedfreelybutthatitsapplicationstilllayoutsidethecontrapuntalsystem.Referencestotheuseofdissonance,however,occasionallyoccurin14thandearly15thcenturycounterpointtreatises.

    Ex.4Cumnotumsit

    PetrusfraterdictusPalmaociosasaidthatdissonancescouldappearbriefly,bystepinascentordescenttoaconsonance.AccordingtoAntoniusdeLeno,whoallowednoteagainstnote,twonotesagainstoneandthreenotesagainstone,themiddleofthreeshortnotesofequallengthcouldbedissonant.Anotherworkallowsathirdofasemibrevetobedissonant(CoussemakerS,iii,27)inthesocalledcantusfractibilis.Goscalch,whoapparentlyknewCumnotumsit,wentfurther,andproposedtodividenotesintoparts,i.e.tosingseveralnotesinthecantusinsteadofone.Atthesametimehedemandedobservanceoftherulesofcounterpointandconfirmedtheprohibitionofparallelperfectconsonancesforbothimmediatelyconsecutiveshorternotevalues,andforthecontrapuntalframework.Heconsideredthathavingonlyconsonanceswasimpossibleorverydifficultandirksome,andthusassumedtheuseofdissonance.Healloweddissonanceevenatthebeginningandendofafiguralunit,ifittookuplessthanhalfthevalueofthefigure(or,inthecaseofsyncopation,evenasmuchashalf).

    Inspiteoftheevidentclosenessinmaterialandmethodofnoteagainstnoteandfiguredcomposition,thetwoformswerelargelyseparateintheoryandterminologyuntilTinctoris'sworkpublishedin1477(see6below):mostofthetreatisesdonotmentiondiminutionordissonance,andtherewascriticismoftheextensionofthemeaningofthewordcontrapunctuswhichalready

  • occasionallymeantthesettingofseveralnotesagainstone(seeCoussemakerS,iii,194CSM,vii/2,4).

    KlausJrgenSachs

    5. Three-part composition in the 15th century.Thefirstworksoncounterpointthatallowthreepartcompositionwereprobablywrittennotearlierthanthe15thcenturytheyarenotgenuineextensionsofthetheory(aswasthecasewithcontrapunctusdiminutus)butsimplyexplanationsofhowtherulesoftwopartnoteagainstnotecompositionshouldbeappliedtoanincreasednumberofvoices.Sincetheintervalsbetweenvariouspairsofpartshavetobeconsideredandcoordinatedinthreepartcomposition,thetheoriesdealwithproblemsliabletooccurwhenthenormsoftwopartcompositionareapplied.Mostimportantly,thebasicruleofallowingonlyconsonancesinnoteagainstnotewritingmustbeobserved,butwithtwoprecautions.

    First,sincetwoaddedpartscanbemutuallydissonantalthougheachmustbeconsonantwiththetenor,thuscorrespondingtothenormsoftwopartcomposition,thebookswarnagainstthe2ndcreatedbetweentwoaddedpartsrespectivelya5thanda6thabovethetenor(CoussemakerS,iii,93),the9thresultingfrom5thssimultaneouslyaboveandbelowatenor,andsimilarcombinations(seeSachs,1974,p.127).Second,becausetwoaddedparts,eachconsonantwiththetenor,oftenforma4th,whichintwopartnoteagainstnotecompositionhastobeavoidedasadissonance,treatisesindicatethepossibilityofusingthe4thinthreepartnoteagainstnotecompositionaslongasitremainshidden(Gaffurius,iii,6)bynotinvolvingthebottompart(CSM,xxii/2,p.27).

    Sometextslistthepossiblecomplementarynotesforthecontratenoraswellasalltheusualconsonancesoftenoranddiscant(CoussemakerS,iii,935,4656).Thisclumsymethod,whichinthe16thcenturyevenstretchedtoafourthvoice,showsthatgeneralprinciplesofcompositionhadhardlybeenformulated.Warningsagainstunisonandoctaveasequalorequivalentconsonancesbetweentheaddedpartsarerare(CoussemakerS,iii,92),butshowthateventhentherewasapreferenceforcompletesounds.

    Therulesforthesequenceofconsonancesintwopartcompositionremainedvalidforanincreasednumberofparts.Theorywas,however,notconsistentabouttheprohibitionofparallel5ths.Thepermittingof4thswasbasedontheirincidentalcreation(betweenaddedvoices)andthiscoveredparallel4thsaswell(althoughtheseareseldommentioned,andonlyinthetechniqueofFAUXBOURDONCSM,xxii/2,p.27CSM,xi,39Gaffurius,iii,5).Fromthereitwouldhavebeenasmallsteptoconcedetheanalogousparallel5ths,whichcouldbeexplainedascausedbytheinversionofaddedparts.Occasionallytheywereindeedpermitted(CoussemakerS,iii,466CSM,xi,423),andthatmayjustifyphrasessuchastheoneinex.5.Butothertextsforbidparallel5ths(CSM,xxii/2,pp.1478Sachs,1974,p.131)thislatterpositiongainedacceptanceprobablybecauseadifferencebetweenprimaryandsecondarycomposition,althoughtheoreticallyusefulforchordconstruction,wassubordinatetothegeneralcompositionalviewpointwhererulesofprogressionwereconcerned.

    Ex.5Parallel5thspossiblypermittedbyanalogytofauxbourdontechnique,PierredeLaRue:MissadeBeataVirgine

    Tohearthisexamplepleaseclickhere

    Standardsforthemelodicstructureoftheindividualpartsvariedintheirstrictness:discantandtenorshouldavoidleapsof6thsand7thswhilethecontratenorwasallowednotonlythesebutevensometimesaleapofa9th.Thespecialcharacterofthecontratenorisbasedontheconceptofthesuccessivecompositionofpartscustomaryinthe15thcentury,forwhichBurtius(ii,5)gavetwopossibilities:firstcantus(supranus),thentenor,andlastlycontratenorfirsttenor(usuallyasa

  • givencantusplanus),thensuperius,andlastlycontratenor.

    Thecontratenor,whichisthusaddedtoadiscantandtenorframework,wasinthefirstinstanceafiller(proreplecionesonorumseuvocumSachs,1974,p.131).Theaddedcharacterofthecontratenorisalsotobeseeninthetypicalendings(clausulas,conclusiones)thattheoristshadfixedforthepartssinceabout1500.Theformulaefordiscantandtenorreachthefinalnote(ultima)ascendingordescendingbysteptoproducethe6thoctaveprogression(ex.6ac).Thecontratenor,ontheotherhand,normallya5thbelowthetenoronthepenultimatenote,movestooneofthepossibleperfectlyconsonantfinalnotes,forminganoctaveleap(ex.6a),4thleap(ex.6b),orfalling5th(ex.6c)cadence.Onlywhenthetenorcadencesbydescendingasemitonetomidoesthecontratenor,inordertoavoidadiminished5th,takethe3rdbelowthetenoronthepenultimateintervalandcloseonthe5thbelow(ex.6d).Theantepenultimateinterval,whichcontemporaryexamplesalsoinclude,varieswithincertainlimits.

    Ex.6Formulaeforstepwisediscantandtenorprogressionstothefinalnote,JohannesCochlaeus:Tetrachordummusices(Nuremberg,1511,f.F)

    Tohearthisexamplepleaseclickhere

    Aparticular15thcenturythreeparttechniqueisfoundinthosecompositionswheretwopartsconstantlyruninsimilarimperfectconsonancesbetweenthefirstandlastnote,whileathird,usuallythecontratenor,hascomplementarynotesoralsotakespartintheparallelprogression.GuilielmusMonachusdescribedandprovidedexamplesofsuchpatterns(seeSachs,1974,pp.132ff):withparallel3rds(ex.7a,b),and6ths(ex.7c,d),wherethecontratenoreitheralternatesbetweentheunisonand5th(ex.7a,c),orbetweenthelower5thandlower3rd(ex.7b,d)withparallel10ths,betweenwhichthereisamiddlevoice,eitherwritteninparallel6thsor5ths(ex.7e),orwhichprogresseslikeacantusfirmusinfairlylongnotevalues(ex.7f)orwithsimultaneousparallel3rdsand6ths(ex.7g).Thesepatterns,whichconsiderablysimplifytheconstructionofthreeparttexture,haveadvantagesfortextbookpurposesandforpracticeinimprovisation,buthavelittlevalueforcomposition.

    Ex.7Patternsinwhichtwopartsruninsimilarimperfectconsonanceswhileathirdhascomplementarynotes,fromGuilielmusMonachus(c1480)

    Tohearthisexamplepleaseclickhere

  • (b)Thesamestichron,withembellishmentsbyKampanes,beautifiedbyKoukouzeles(ETMSsc1584,f.123,(c)Thesamestichron,withembellishmentsbyKampanes,beautifiedbyXenosKorones(MSsc1584,f.126v)

    KlausJrgenSachs

    6. Tinctoris.Themosttightlyknit,comprehensiveandimportant14thor15thcenturytreatiseoncounterpointisTinctoris'sLiberdeartecontrapuncti(1477).Counterpointisheredescribedasrestrainedandthoughtoutpolyphoniccompositioncreatedbysettingonesoundagainstanother(moderatusacrationabilisconcentusperpositionemuniusvociscontraaliameffectusCSM,xxii,2,p.14).Itdividesintocontrapunctussimplex(noteagainstnote)anddiminutus(severalnotes,ofeitherequalorvaryinglength,againstone),andcanbeextemporized(mente)orwrittendown(scripto).ButTinctoriscalledtheimprovisedformstraightforward(absolute)counterpoint(orsuperlibrumcantare),andthewrittenformresfactaorcantuscompositus(CSM,xxii/2,pp.105ff).ThisterminologyunknownbeforeTinctorisandusedafterwardsonlywithreferencetohimshouldnotbetakentoimplythattheaimofthetheoryofcounterpointwasimprovisation.Tinctorisseemstohavewantedtoemphasizesomethingelse:that,particularlyincompositionformorethantwovoices,theresultofanimprovisationrelatingseveralpartscontrapuntallytoagiventenor(CSM,xxii/2,p.110)differsfromcarefullyplannedcompositiontheinevitablelackofstrictnessinimprovisationisaconcession,nottheaimofcounterpoint.

    InthefirstpartofhistreatiseTinctorisgaveabasicdescriptionoftheconsonancesandtheirrelationsincontrapunctussimplex.Thetenorandtheaddedpartbothprogresseitherbystep,orinleapsofa3rd,aperfect4thandaperfect5th.Thesecondpartisasurveyofthedissonancesandtheirsystematicapplicationincontrapunctusdiminutus.

    AccordingtoTinctoris,thecorrectuseofadissonancedependsonitsrhythmicandmelodicposition.Theyardstickfortherhythmicpositionofadissonanceisthenotevaluedeterminingthebasicmovementofamusicalpiece,whichTinctoriscalledmensuraedirectio(ornota,secundumquamcantusmensuraturCSM,xxii/2,pp.12438)AdamofFuldacalledthisvalue,actingasapulseorbeat,tactus(1490GerbertS,iii,362),and16thcenturyItaliantheorycalleditbattuta.Inprolatiomaior(ex.8,bars17)itistheminim(transcribedasacrotchet),inprolatiominor(bars911)thesemibreve(transcribedasaminim),andinproportionstheequivalentofthosevalues.Tinctorisusedthefactthatbothvaluesaredivisiblebytwointherespectivemensurationstoformulatethreebasicrulesfortherhythmicvaluesofdissonances(ex.9).

    Ex.8Examplesofthecorrectuseofdissonance,accordingtorhythmicandmelodicposition,JohannesTinctoris:Salvemartyrvirgoque

  • Tohearthisexamplepleaseclickhere

    Ex.9Tinctorissfundamentalrulesfordissonances

    First,ifthefirstpartofamensuraedirectio()orthebeginningofthefirstandsecondparts()isconsonant,adissonanceofequalandsmallervaluecanfollow.Thisrulecoversunstresseddissonances,whosemaximumlengthcorrespondstotheconsonantpartofamensuraedirectio.Unstresseddissonancescanoccuranywhereinthecomposition,butstresseddissonances(i.e.thosefallingonthebeginningofamensuraedirectio,whichappearonlyaspreparedsuspensionsresolvedbystepwisedescent)areforTinctorisalwaysdesignedtoprepareforanimmediatelyfollowingfinalsound(perfectioorconclusio).Thisisusuallyrestrictedtoperfectconsonances,unlessitconcludesaninternalsectionandsimultaneouslyopensacontinuation(asinex.8whereFappearsinparentheses).Becausesyncopateddissonancesarethusdependentonacadence,Tinctoris'sotherrulesarebothrelatedtopropertiesofthepenultimatenoteinaphraseofthetenor.

    Second,wherethereisapenultimatenoteequalinvaluetotwomensuraedirectio,consistingeither()ofasinglenoteor()oftwonotesidenticalinpitchandlength,thefirstpartofthefirstmensuranearlyalwayshasadissonancesetagainstit.Third,ifthepenultimateisequalinvaluetoonemensuraedirectio,thenthefirstpart()canbedissonant,or,whenprecededbystepwisedescendingnotesofequalvalue(),thefirstpartofeachnotecanbedissonant(ex.9).SinceTinctorisformulatedrulesofdissonanceaccordingtothegreatestpermissiblevalueineachcase,itisnotsurprisingtofindthattherhythmicallyshortformulaeofprolatiomaioralsooccurinprolatiominor(inparenthesesinex.8).

    Asregardsmelodicposition,Tinctorisconfirmedthateachdissonanceisprecededbyanadjacent(stepwise)consonance,andthefollowingnotewillbea2ndorveryrarelya3rdaway(ex.8,bar4).Whenadissonanceisintroducedandleftbystep,oneshouldnotreturntothestartingnoteunlessthedissonanceissoshortthatonecanhardlyhearit(CSM,xxii/2,p.141)thus,inTinctorissexamplesthenotacambiatausuallyappearsasthefusa,whilethepassingnotesarealsominimsandsemiminims.Theleapofa3rdfromadissonanceislessrareinTinctoris'sexamples,andin15thcenturymusicingeneral,thanhisbooksuggests,anditalsooccursdescendingfromasyncopateddissonance.Occasionallytheleapofa4thalsooccursafteradissonance,butusuallyitisasubstituteforacambiata(ex.8,bar1:leaptothe3rdaboveinsteadofareturntothepitchoftheprecedingnote,whichappearsinanotherpart).TheeightgeneralrulesofthethirdpartofTinctoris'streatiseofferbothtraditionalnorms(butoftenmodifiedforcompositioninmorethantwoparts)andmoregeneralrecommendationsaboutthewidercontextofcomposition(itsstructureandvarietas)theyareneitherasconcretenorasimportantasthedissonancerules,however,whichforthefirsttimemakepossibleanunderstandingoftheperiod'scompositionaltechniques.

    KlausJrgenSachs

    7. Composition in four or more parts.Theacceptanceintotheoryoffourpartnoteagainstnotecompositionwasanotherextensionofcontrapuntalapportionment:intervalsbetweendiscantandtenorwerefilledoutbytheadditionof

  • twoparts.Thebottomparttakesprecedence,sinceitmustavoidtheformationof4ths(whilemakingthempossiblebetweenotherpartsbysupplyinga3rdora5th),anditissometimesmorepreciselydetermined(e.g.thepenultimatenoteisusuallya5thbelowthetenor).ThelistsandtablescustomarysinceAaron(1523),whoenumeratedpossiblefourpartnoteformations,usuallyfollowtheorderdiscanttenor,bass,altobuttheyillustrateonlytheprocessofcontrapuntaldispositionoftheindividualchord.Theoldmethodofworkingoutthepartsinsuccessionfellintodisuseduringthe16thcenturyasAaronconfirmed,themoderniconsideredallthevoicessimultaneously,thusimprovingconsonanceformationandpartwriting,andavoidingunsatisfactoryunisons,restsorleaps.Thecatalogueofchordsstrictlyavoidssecondarydissonancesand4thsinthebottompart,ofcourse,andfavourscompleteformations(inthesenseoffulltriads).

    AsearlyasCochlaeus(14791552)thereareexamplesshowingthetypicalconcludingformulaeoftheparts(seeex.6),includingthequartavox(altus)theyshowtheinterchangeabilityoftheformulaebetweentheparts(ex.10).Ingeneral,fourwasthemaximumnumberofvoicesin16thcenturycontrapuntaltheoryandfourpartwritingwasthehighestformofcompositionaltechniqueillustratedbyexamplesoffiguralmusic.Gaffuriusmentionedthecreationofafifthpartaccordingtotherulesofcounterpoint(iii,11),andTinctorisuseditinanexample(CSM,xxii/2,pp.107ff).FlorentiusdeFaxoliscontrastedthetwopartcounterpointofthevetereswiththecompositionofthemoderniforthreetosixormoreparts,whichhedescribedascomposition,i.e.thecontrapuntalmethod,extendedtoseveralvoices(Seay,1963,p.87).Eventhoughwritersdiscussedinstancesofgoingbeyondfourpartcomposition,theydidnotdeducefromthemanynewaspectsoftheory.

    Ex.10Theinterchangeabilityofconcludingformualebetweenparts,Cochlaeus(c1504)

    Tohearthisexamplepleaseclickhere

    KlausJrgenSachs

    8. 16th-century counterpoint.Thedevelopmentofcontrapuntaltheoryinthe16thcenturyconsisted,first,ofadrawingtogetherofcontrapunctussimplex,contrapunctusdiminutusandcompositionformorethantwovoices,oftenstillseparateinthe15thcenturysecond,anexpansionofmatterstreatedtoinclude,particularly,themodes,techniquesofimitationandinversion,andtherelationbetweentextandmusicandthird,improved,morepreciserulesfortheuseofdissonance.ThisdevelopmentreacheditspeakinthethirdbookandpartofthefourthofZarlino'sLeistitutioniharmoniche(1558),themostcomprehensiveandinfluential16thcenturyworkoncounterpoint.Itcontainsthebestandmostrefinedanalysisofthecompositiontechniqueusedinsacredmusic,particularlyatthetimeofWillaert,Zarlino'steacheranditsurpassesWillaert'sotherpupilNicolaVicentino'singenious,somewhatearlierbutinmanyrespectsverysimilarL'anticamusicaridottaallamodernaprattica(1555),bothinclarityandindetail.Almostallthemany,usuallyprinted,16thcenturyworksoncounterpointrelatetotheprimapratticastyle.Thefirsttwoattemptstoincorporateinnovationsfromsecularvocalmusicintothetheorywerethusallthemorepioneering:Vicentinousedchromaticmadrigalsasexamplesandrecognizedliberties(inprogression,harmonyandmode)justifiedbytextmeaningortheaffectofthewordsandGalileidiscussedanddefendedfreerusesofdissonance.

    KlausJrgenSachs

  • 9. Zarlino and aspects of dissonance treatment.TheartedelcontrapuntoasthetheoryofpolyphoniccompositionwasforZarlinothecentreofmusicapraticaandatthesametimethemostcomprehensiveamalgamofthemesinallmusictheory.Zarlinonotonlyconsideredindetailalltraditionalaspectsofcounterpointbutalsotriedtodefineadditionalrequirementsandconditionsofpolyphoniccomposition.Thesoggetto,orthematicsubject,iscomposition'spointofdeparture,withoutwhichonecancreatenothing(iii,26),andwhichcanconsistofagivenornewlycreatedcantusfirmus,cantusfiguratusorevenseveralimitativeparts.Thesoggettoinfluencesthechoiceofchurchmode,andthatinturnaffectsthecoordinationofparts.Themodeofthetenor,whichdeterminesthetonalityofthecomposition,isusuallysharedbythesopranoinfourpartcomposition,whilethebassandaltotakeitoverwithchangedcompass(plagalinsteadofauthentic,orviceversa)andthiscorrespondstoadifferenceofalmostanoctavebetweentherangesofthetwopairsofparts(illustratedinex.11onthebasisofthecombinationofsoprano,alto,tenorandbassclefsfrequentinZarlino).

    Ex.11

    Therestrictionsonmodeandcompassaffectimitativetechnique,harmonicstructureandcadenceformation.Zarlinodividedupthepossibilitiesforimitationaccordingtowhethertheleading(guida)andfollowing(conseguente)partshaveequalordifferingintervalpatterns.Theformerhecalledfuga(whoseentriescouldbeattheoctave,5th,4thandunison),thelatterimitatione.Bothfugaandimitationecouldfollowthecanonstrictly(aslegata)ormovefreely(assciolta)initscontinuation,andtakeupeithersomeoralloftheparts(iii,545).

    Theprincipleofharmonywastocreateconsonancesbycombining3rdand5th(or6th),ortheirequivalentsinotheroctaves,tomakeaharmoniaperfetta,or,inmodernterms,atriad.Zarlinoconsideredthetriadwithamajor3rdmoreperfectthanthatwithaminor3rd,anddeclaredthat,whilesuccessionsofmanytriadswithmajor3rdswereharmless,thosewithminor3rdshadaverymelancholyeffect(iii,31).

    Eachmodehaditsownfinalnotesforthenormalcadences(iv,18ff).Thebreakingupofacompositionbycadenceswhich,likethefullstopsinasentence,createdrestingpointsandmarkedoffthesense,wasanimportantpartofthelayout(iii,51).Thecadences,whichnormallyusedsyncopateddissonances,separatedsectionsofthetextfromoneanotherandmadepossiblemusicalvarietyandchangeinthesuccessivepartsofacompositiontheycould,however,alsobedeliberatelyavoided(fuggirlecadenze)infavourofalargercontextifonepartavoidedbyaleaporaresttheexpected(perfect)consonance(asindicatedinex.12a).

    Ex.12Examplesofdissonancetreatment,fromGioseffoZarlino:Leistitutioniharmoniche

    Tohearthisexamplepleaseclickhere

    Zarlino'steachingwasaimedatfourpartcomposition,whichcontainedallperfectionofharmony.ThisconceptofperfectionexplainswhyZarlinotriedtodescribethecharactersofthepartsby

  • comparisonwiththefourelements:thebass,astheearth,wasthedeepestvoice,oftenslowmoving,andcarriedtheharmonythetenorwastheequivalentofwater(itsurroundedthebassandruledthecompositionasregardsthecombinationofmodes)thealtowastheair,andmediatedbetweentenorandsoprano(fire),inwhoseglowitshonethesoprano,asthehighest,moststirringandmostpowerfulvoice,waslikethelifegivingfireofthesun(iii,58).

    Zarlinorequiredthatthemusicshouldsuitthecharacterofthewords,andrelatedthisproblemtotheorderingofmodesandtoparticularaffects(iv,32).Fortextunderlayhemadeasetofruleswhichmaybesummarizedasfollows.Thelengthofasyllableshallbereflectedinthecorrespondingnotevalueorvalues.Noteswiththeirownsyllableinclude,always,thefirstandlastnoteofapieceorasectionandthefirstnoteofeveryligature,andusuallyeverynontiednoteofgreatervaluethanasemiminimorcrotchet(exceptionallyasemiminim,afteradottedminim),butnevernotesofsmallervaluethanasemiminim,orthedotafteranote.Achangeofsyllablecannormallyoccuronlyafternotesofvaluelargerthanasemiminim,exceptthatitmayfollowasemiminimafteradottedminim.Repetitionofwordsispermittedincantusfiguratus(butnotincantusfirmus),aslongastherepetitionsconsistofmeaningfulphrases,notjustindividualwordsorsyllables(iv,33).

    Zarlino'srulesfordissonancemostlyusethesimplestformsofexercise,inwhichtwominims,foursemiminimsoraminimandtwosemiminimsintheaddedparteachsoundagainstonesemibreveofthesoggetto,andalsoconsiderthesuspension(seeex.13).First,sincetwominimsoccuronthedownbeat(battere)andtheupbeat(levare)ofthesemibrevetactus(battuta),andarecorrespondinglyprominent,bothshallbeconsonantunstressednotesmaybedissonantonlyinstepwiseascendingordescendingsequencesofminims.Second,thefirstandthirdsemiminiminagroupoffourmustlikewisebeconsonant,whilethesecondandfourthmaybedissonantinstepwiseprogression.Third,thefirstoftwosemiminimsmaybedissonantwheretheybothdescendbystepafterastressedminim(orasyncopatedsemibreve)Zarlino'sexample(ex.12b)indicatesthatthislicenceisbasedontheelementarycharacterofthethreenotemelodicformula,which,dependingonthefollowingnote,eitherfillsadescending4th(x)orembellishesa2nd(y),forbothconsonant(C)andsyncopateddissonant(S)usesarenormal.Fourth,fornormalsuspensions,Zarlinorequiredconsonantpreparationandstepwisedescendingresolution,whichheillustratedbydecorativefigureswithnoterepetition(whichJeppesencalledPortamentseeex.12catP)andpairedfuse(quavers).Healsodiscussedspecialcasesinparticularhepermittedpreparationbya4thabovethelowerpart(iii,61Jeppesen,quartaconsonans)andundersomecircumstancestheirregularresolutionsof2ndintounisonandof4thintothediminished5th(iii,42).

    Ex.13

    Zarlino'sdirectionsontherhythmicstructureofthecompositionandofindividualpartsarealsoinstructive.Thebeginningmustalwaysbeonthedownbeat.Ifapartenteredlater,itshouldbeafteratleastaminimpause(oftenwithasyncopatedsemibreve).Therhythmicmovementshouldnotbetoofastatfirstsothatitcouldgraduallyspeedupitwasbestfortheaccelerationtobeachievedbytransitiontothenextsmallernotevalue.Theintroductionofsemiminimsafterasemibreveshouldcoincidewiththelevare,notthebattere(iii,45ex.13b).IntwopartcompositionwithasoggettoinsemibrevesZarlinomadeastrictdistinctionbetweentwopositionsofthedottedminimandsemiminimgroup:heusedthestressedpositiononlyatthebeginning(ex.13c,),whiletheunstressedpositionisusedbothinthemiddleofthepieceand,afterarest,atthebeginning().

    ThemanydetailsoncompositiontechniquementionedbyZarlinoareessentialfortheexaminationofprimapraticaworksbuttheyarenotquitecomplete.Twofiguresshouldbe

  • mentioned,eachofwhichcontainsacharacteristicfreedominthetreatmentofdissonance,whichinmodernterminologyiswithconfusingambiguitycalledcambiata.

    Thefirstoftheseisafivenotegroupconsistingoffoursemiminimsdescendingbystep,thesecondandthirdofwhicharedissonant,followedbyastepupwards.Thisformulaisusuallypartofacadenceandgoeswiththepreparationforasuspension.Whatisprobablytheoldestdescriptionofthisusage,byG.M.Artusi(L'artedelcontraponto,i,1586seeex.14a),stressesitsverygoodeffect.ItisunlikelythatStephanoVanneowasreferringtothiswhenheprescribedtheconsonanceofthefirstandlastoffoursemiminimsasthenorm(Recanetumdemusicaaurea,1533).Berardicalledtheirregularlydissonantthirdnoteacambiata(Miscellaneamusicale,1689),andJeppesentermeditarelativelystressedpassingdissonance.

    Ex.14TwotreatmentsofdissonancenotcataloguedbyZarlino

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    Thesecondconsists,mostly,offournotes:anunstressedsemiminimdissonanceleapingdowntothelower3rdtheupper2ndprecedesitandusuallyfollowstheleapinordertobalanceitout.Itappearedinvarioustextbookexamples(ofteninTinctorisex.14bisfromPontio,Ragionamentodimusica,1588),butthereisnoknowndescriptionoftheusagein16thcenturytreatises.Popularityandfreedomindissonancetreatmentseemtobebasedonthegoodstyleofitsmelodicoutline,asintheformulashowninex.14b:theascendingformisrare,butthedescendingformoccursinbothdissonant(theprogressionisusually875)andconsonant(653ex.14c)contexts,andcanevenappear,rhythmicallyextendedandmetricallydisplaced,inapartthatcontinueswiththeresolutionofasuspension(ex.14b,atbrokenbracket).Fux(GradusadParnassum,1725),JeppesenandotherscalledthesemiminimirregularlyleapingfromadissonancecambiataMerrittdescribeditasachangingnotegroup.(Seealso13below.)

    KlausJrgenSachs

    10. Galilei and his innovations, 158791.Galilei'streatisescontainthefirstsystematicattempttoaccommodatethetheoryofcounterpointtotherecentinnovationsincompositiontechnique,attributedparticularlytoCiprianodeRoreandproclaimedbyMonteverdiin1605asthehallmarksofsecondapratica.Theseinnovationsareineffectlibertiesindissonancetreatmentandarebasedontheviewthatdissonancesarenotonlypassingformations,dependentonconsonance,butthemselvescarrymusicalexpression.Galileiparticularlyenrichedcompositiontheorybyallowingthefollowingmeansofmakingdissonancesmoreurgent,sharperandmoresurprising(seePalisca,1956,andRempp,1980).

    First,inaconjunctsequenceoffoursemiminims,two(apartfromtheformsinexx.13aandex.14a)canbedissonantinanyposition,andoccasionallythreecanbeconsecutivelydissonant(ex.15a,b).Second,suspensions,apartfromtheformsinexx.9andex.13a,canberesolvedbyleaptoaconsonance(ex.15c),byprogressiontoanewdissonance(ex.15d),byascenttoaconsonance(ex.15e)and,apartfromtheforminex.14b,simultaneouslywithachromaticallyprogressingaddedpart(ex.15f)theycanoccurseveralatonce(ex.15g).Third,dissonancescanalsosometimesoccurinthestressedpositionwithoutsyncopatedpreparationifaregularresolutionfollows(ex.15h,i).

  • Ex.15VincenzoGalileisinnovationsinthetreatmentofdissonances(158791)

    Tohearthisexamplepleaseclickhere

    KlausJrgenSachs

    11. 16thcentury double counterpoint.Withinthecontextoftheirimitativeandcanonictechniques,VicentinoandZarlinoalsodiscussedthesystematictranspositionofpartsincompositiontootherkeys,whichtheycalledcontrapuntodoppio(Vicentinoalsousedthetermcompositionedoppia,iv,34).Theythusgaveoutforthefirsttimeamethod(considerablyolder,nodoubt)ofproducingespeciallyartificialformsofcounterpoint(Zarlino,iii,56).Thistechniquerequiresanunderstandingoftheharmoniesandprogressionsthatcanoccurinvariousformsofcomposition.Theknowledgeoftherespectivecomplementaryintervalsisfundamental:forharmonicintervalsofthesamekindinthebasic(Zarlino:principale)andintheinvertedversion(replica)alwayscomplementeachothertomaketheinversioninterval.Initssimplestform,anoctaveexchangeoftheupperandthelowerpart,theintervals3rdand6th(imperfectconsonances),2ndand7th(dissonances)andtheunisonandoctave(bothperfect)arepairedcomplementaryintervals.Thiskindofcounterpointisthusmuchthemostproductiveandneedsnospecialtheory.Thepossibilitiesoftranspositionatthe12thand10tharemorelimitedbutcanalsowellbeusedZarlinoespeciallyusedthem,evenwithinthesamepiece(seeex.16).Thecomplementaryintervalsfordoublecounterpointatthe12thand10thareeasilyderivedbyensuringthatthepairsoffiguresadduprespectivelyto13and11(thusa3rdanda10th,forexample,willformdoublecounterpointatthe12th).

    Itisthuspossibletodeducethecontrapuntalconditionsforex.16a,whichmaybeinvertedineitherway:theconsonancesofunison,3rd,5th,octaveand10th(and12th)remainconsonantinordertoavoidunacceptableparallelsthepiecemustprogressincontrarymotionorleapconsonantlyinobliquemotionpassingdissonancesarepossible,butnotsuspensions.Asafurtherformtheauthorsalsotaughtthetranspositionofbothpartsininversion(ex.16d).Inthiscaseallthechangesinintervaloftheprincipaleremainintactinthereplica.Therestrictiononcompositiontechniqueconsistsinthefactthatmelodicformulaethatarepersuasiveonlyinonedirection(ascendingordescending)aretobeavoided.

    Ex.16Thetranspositionofpartsincontrapuntodoppio,fromZarlino(iii,56)

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    KlausJrgenSachs

  • 12. The term counterpoint after 1600.Counterpointhasbeenusedtoconveydifferentmeaningsinliteratureonmusicandmusictheoryfromthe17thcenturytothe20th.Theenumerationofthesemeaningsisessentialifconfusionistobeavoided.First,theconceptofcounterpointhasbeenequatedwiththeartofstrictcomposition(J.P.Kirnberger,17719),thusbeingusedtodescriberegulatedpartwritingregardlessofwhetherthestyleispolyphonicorhomophonic(counterpointisatechnicalcategory,polyphonyastylisticconcept).Second,morenarrowly,counterpointhasbeentakentorefertothetechniqueofpolyphonic,asdistinctfromhomophonic,writing.Third,stillmorenarrowly,theconceptofcounterpointhasbeenconfinedtothetechniqueofvocalpolyphonybefore1600(andinadditionBach'sinstrumentalpolyphony).Fourth,anumberof20thcenturytheoristshaveproposedadistinctionbetweenpolyphony,thecombiningofequalvoices,andcounterpoint,atypeofwritinginwhichthevoicesarebroughtintoreliefagainsteachotherfunctionallyandbyvirtueoftheirrelativeimportance.Generally,however,polyphonyhasbeenusedtorefertomattersofstyleoraesthetics,andcounterpointtorefertomattersoftechnique:polyphonyisanend,counterpointameans.

    Theassumptionthatthetheoryofcounterpointdealswiththehorizontalandthatofharmonywiththeverticaldimensionofmusicisastrivialasitismisleading.Inthestudyofharmony,itisnotjustthestructureofchordsbutalsotheirprogressionsthatmustbedealtwithandsimilarly,inthetheoryofcounterpointitisaquestionnotonlyofmelodicpartwritingbutalsoofthechordsformedbytheparts.Second,thestylisticaimsofcounterpointwhicharedirectedtothesimultaneousdeploymentofcharacteristicmelodicpartsshouldbedistinguishedfromthetechnicalproblemsacomposermustsolveinordertorealizetheseaims,aboveallintheregulationofsimultaneities(joiningconsonancestogether,manipulatingdissonances).Itisthetechnicalrulesratherthanthestylisticmaximsthatprimarilyconstitutethesubjectforstudy.(Aguidetocontrapuntalorpolyphonicstyle,suchasthatofKurth,1917,isnottobeconfusedwithaworkoftechnicalinstruction.)

    Thehistorians'ideathatanepochofcounterpointcanbeidentifiedasdistinctfromanepochofharmony,withtheyear1600representingthedividinglinebetweenthetwo,cameaboutthroughlackofconceptualclarity.Ifharmonyisunderstoodasreferringtoaregulatedjoiningtogetherofsimultaneitiesandthereisnothingtojustifytherestrictionoftheconceptofharmonysimplytotonal,chordalharmonythenmusicbefore1600alsobearsaharmonicimprint,evenifofadifferentkindfromthatoflatermusic.Kurth'sassertionthatearlycounterpointwasbasedonmereintervalliccompatibility,andhencethatthetechniqueofjoiningtogethersimultaneitiesfulfilledonlythenegativeaimofavoidingperturbationsinthelinearexpositionandthusofavoidingobtrusivesequencesofconsonancesorconspicuousdissonances,ismistaken:itiscontradictedbythefactthattheprogressions(incontrarymotion)fromthemajor6thtotheoctave,fromthemajor3rdtothe5th,andfromtheminor3rdtotheunison,werereckonedtobeespeciallyclearandcompelling,andwerethusunderstood(comparablywiththeprogressionfromthechordofthedominant7thtothetonictriadintonalharmony)asharmonicphenomena.Harmonybefore1600differsfundamentallyfromthatoflatertimes:earlierharmonyproceededfromtwonoteintervalsandnotfromthreeandfournotechords(athreenotesimultaneitywasconsideredasecondarycombinationofintervalsratherthanaprimaryentityinitself)andtonalitywasshownlessbychordalsequencesthanbymelodicformulae.

    Kurth'shypothesisthatthelinearpolyphonicdeploymentofmelodicpartswasinhibitedbytonalharmonyisnotwhollyerroneous,butadistortionofthetruth.Aestheticallyitmaybecorrect,inthecaseofnarrowlyrestrictedmusicalperception,tosaythatattentionisdirectedeithertothephenomenonofharmonyandsonorityortothatofmelodyandpolyphonyandnodoubtmanycomposershavedrawntheconclusionthatinorderformusictoremainintherealmofthecomprehensibleeitherharmonyorcounterpointmustcometothefore.Butstrictlyspeakingthecontraryistrue:thefactthatchordprogressionsconstitutemusicalcontinuityandcomprehensibilityfreesthepartwritingfromthenecessitytotakeaccountofaspectsthatwouldbeindispensableincompositionconsistingofintervalsequences.Thustheharmonicandtonalbasisoffreestyleisnottechnicallyanimpedimenttolinearitybutaprerequisitefortheunrestricteddeploymentofthemelodicinmusic.BachtoocontrarytoKurth'sinterpretationofhissimultaneitiesasmereresultantsconceivedharmonictonalityasasupportformelodiclinearity.

  • CarlDahlhaus

    13. Theory after 1700.Counterpointtheory,whichuntilthe17thcenturywastheonlykindofinstructionincomposition,hashadtoshareitsdominantpositionwithharmonytheorysincethe18thcenturyandtherelationbetweenthetwodisciplineshasbecomeincreasinglycomplicated.Freecompositionappearsintheworkofmanytheoristsaspracticalharmonyandintheworkofothers,bycontrast,aslicentiouscounterpointitispossibleontheonehandtoconceiveofthe(theoretical)studyofharmonytheawarenessoftheharmonicsignificanceofnotesasaprerequisiteforstrictwriting,andontheothertoconceiveofstrictwritingthefoundationonwhichfreecompositionasasetofpermitteddeparturesisbuiltasaprerequisiteforthe(practical)studyofharmony.

    Asadidacticdiscipline,counterpointhasbeenjustifiedbothspeculativelyandpragmatically.FuxandPadreMartiniwereconvincedthatthenormsofstrictcounterpointwerefoundedintheverynatureofmusic,which,thoughitmightbetransformedbychangingstylesandfashions,wasnottobedestroyed(freestylewasunderstoodasapermitteddeparturefromstrictstyleratherthanasasuspensionofit).Incontrast,sincethelater18thcenturytherulesofcounterpointhavebeenseenashistoricallyspecific,hencealterable,norms(andthenatureofmusichasbeensoughtintherudimentsofharmony)theyweretakenovereitherinordertoavoidabreakinthecontinuityofthedevelopmentofthestyleofsacredmusic(Albrechtsberger)orinarevivalistspirit(Bellermann).Sincethebreakwithtraditionthatoccurredaround1910,thecustomofcontinuingtoteachcounterpointintheFuxianmannerisgenerallyjustifiedbyarguingthatitispedagogicallynecessarytodisciplinemusicalthoughtbymeansofexercisesindeadmaterial.(NootherstylecanbecodifiedtothesameextentascanthetechniqueofPalestrina.)

    Thedistinctionbetweenstrictandfreestyle,whichcontrapuntaltheorysincethe17thcenturyhastakenasitsstartingpoint,canbeexplainedbyconstructing(inMaxWeber'ssense)antitheticidealtypes:complexesofcharacteristicswhichcoherecloselyandclearly,butalsocontrastwiththecharacteristicsoftheothertype.Strictstyleistheoldertype,passeddownfromthe16thcentury,andtypicalforchurchmusic(inCatholicregions)itisbasedoncantusfirmus,ismodalincharacter,andproceedsfromtwopartwritingthecohesionofitssoundscomesfromintervalprogressionsparallelperfectconsonancesarestringentlyprohibitedandrigorousrulesareformulatedtogoverndissonancesandfalserelationsthedidacticmethodisthesystemoffivespecies.Freestyleisthelatertype,originatinginthe17thcenturyandconstantlyevolving,andtypicalforchamberortheatremusicitisbasedonsuperposedtwopartwriting(Hindemith,1937)betweenmelodyandbass,istonalandharmonicincharacterandproceedsfromfourpartwriting,fromthechordastheprimarydatumthecohesionofitssoundscomesfromchordprogressionstherearelooserregulationsforbiddingparallelperfectconsonancesandgoverningdissonancesandfalserelationsdidactically,rhythmicallydifferentiatedcounterpointisdevelopedfromnoteagainstnotewritingbymeansoffiguration.

    Althoughtheidealtypesofstrictandfreestylearescarcelyencounteredintheiractualforminthehistoryofmusictheorymosttheoristshavetriedtofindsomecompromisebecause,whilerespectingthetraditionofstrictwriting,theyhavenotwantedtoneglecttheapparentrequirementsofthedaytheantitheticalpresentationisnecessary:itservesasapointofreferenceamongtheconfusionofdoctrinalopinions,andevenconstitutesacriterionfortheassessmentofcontrapuntaltheories,sincelogicalflawsalmostalwaysresultfromdeviationsfromidealtypes.When,forinstance,Albrechtsbergerpostulatedthatoneshouldconductaharmonicandtonalanalysisofacantusfirmusbeforebuildingacounterpointonit,itis,strictlyspeaking,notunderstandablewhyheshouldhavestartedoutfromtwopartwriting,hencefromanincompleteandthereforetechnicallymoredifficultpresentationoftheharmony,insteadofbeginningwithfourpartwritingasdidJ.S.BachandKirnberger.AndwhenDehnheldthatinstrictthreepartwritingadissonantsuspensionwasarelationshipnottoanothernote,buttoachord(2/1883),hewasledbythebiasof18thand19thcenturylisteninghabitstoignorefundamentalprinciplesofintervallicwriting,andhismistakehastechnicalconsequences.

    StrictstylecontrappuntoosservatowascodifiedbyFuxinaformwhosedidacticmeritssufficed

  • tomakehisGradusadParnassum(1725)aclassictextbookforatleasttwocenturies.IfFuxconsequentlyappearsasthefounderofapedagogictradition,thecontentofhisbookrepresentstheinheritanceofatraditionreachingbacktoZarlino.Theprohibitionofhiddenparallels,mostsimplyformulatedinthetenetthataperfectconsonancemustbereachedbycontrarymotions,hasbeenexpressedintheformoffourrules(contrarymotionfromoneperfectconsonancetoanotherunrestrictedmotionfromaperfectconsonancetoanimperfectconsonanceunrestrictedmotionfromoneimperfectconsonancetoanotherandcontrarymotionfromanimperfectconsonancetoaperfectconsonance)sincethetimeofDiruta(1609).However,theprohibitionheldgoodonlyfortheouterparts,althoughtheoristsoftenlaiddownstricterregulations.Theclassificationoftherhythmicrelationsbetweencantusfirmusandcounterpointintofivespecies(noteagainstnotetwonotesagainstonefournotesagainstonesyncopationinthesecondvoicecontrapunctusfloridus)canbefoundasearlyas1610inBanchieri'sCartellamusicale(1610).Thisscheme,oftencriticizedandridiculedaspedantic,hasbeenperpetuatedwithapedagogicallymotivatedtenacityitishardlyreconcilablewiththehistoricalrealityofPalestrina'sstyle,whichprovideslessanexampleofcantusfirmuscompositionthanawayofwritingbasedonpervasiveimitationbetweentextuallycharacterized,rhythmicallydifferentiatedparts.Therelativelystressedpassingdissonancelastingasemiminim(crotchet),permissibleincertaincadentialformulaeinPalestrina'sstyle,wasreferredtobyBerardi(1689)asnotacambiata,sincetheconsonanceanddissonancechangetheirusualplacesonthestressedandtheunstressedbeats(ex.17a).Fux,ontheotherhand,usedtheconceptofcambiata(Fux'sappoggiatura)torefertoadissonancethatleapsdowna3rd,whoseorthodoxresolution,asJeppesenhasit(1925),isimmediatelyretrievedwitharising2nd(ex.17b).

    Ex.17Notacambiata(a),afterBerardi(1689)Fuxsappoggiatura(b),afterJeppesen(1925)

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    TheFuxtraditionsomuchpredominatedintheteachingofstrictstyleduringthe18thand19thcenturies(itconstitutedtherudimentsofthestudyofcompositionforHaydn,MozartandBeethoven)thatothersystemscanclaimanyraisond'treonlybyvirtueoftheirdeparturefromhissystemincertainessentialfeatures:atfirstwithcompromisesbetweenstrictwritingandfree,thenlater(fromthemiddleofthe19thcentury)withthetendencytohistoricize.Albrechtsberger(1790)emphasizedthatharmonicandtonalexaminationofthecantusfirmusshouldbeundertakenbeforecounterpointiswrittenCherubini(1835)renouncedthechurchmodesSechter(1854)regardedwritingfortwoorthreepartsasreductionsoffourpartwriting,whichwashisstartingpoint.

    If,inconsequence,strictcounterpointmovednearertofreestyleinthelate18thcenturyandtheearly19ththroughattemptstoassimilateitintothechangingpracticeoftheecclesiasticalstyle,whosetheorywasmouldedbyittheexactoppositehappenedduringthe19thcenturywhenthecombinationofhistoricalawarenessincontrapuntaltheory(Bellermann,1862)withrevivalistendeavoursincompositionalpractice(Haller,1891)ledtoatendencytoseetherulesofcounterpointinanarrower,stricterlight.Itwasdesiredtoreestablish,bothintheoryandinpractice,thetechniqueofPalestrina,theclassicalecclesiasticalstyle,exactly(toquoteRanke'shistoriographicaldogma)asitactuallyhadbeen.Traditionalism,withitsunconscioustrafficbetweenpastandpresent,yieldedtoahistoricismmotivatedpartlybyphilologyandpartlybyaesthetics.Inthe20thcentury,afterthedeclineoftheCecilianmovement,strictstylebecamepetrifiedintomusicalmentalexercisesinadeadlanguagetheLatinofmusicalinstruction.TheapparentlyindispensabledidacticconsiderationscannotalwaysbewhollyreconciledwithhistoricalendeavourstogiveaprecisedescriptionofPalestrina'sstyle:evenJeppesen'stextbook(1930),aparagonofpedagogicexpositionbyahistorian,resultsfroman(unacknowledged)compromise.

    CarlDahlhaus

  • 14. Free style: licentious and harmoniccounterpoint.Inspiteofsecondarychanges,thetheoryofstrictstyleisessentiallythatofanarrowlyconfinedtechniqueofcomposition,historicallyspeaking,thestyleofPalestrinahoweveroneinterpretsthesystemofrulesasanormgroundedintheverynatureofmusic,asabodyofdogmaattachingtoahistoricalstyle,orasrulesofthegamefordidacticexercisesitisunequivocallycertaintowhichfragmentofmusicalrealityitrelates.Theconceptoffreestyle,ontheotherhand,isacatchmentareaforextremevarietiesofstylethathaveprimarilyincommonanegativecharacteristic,theirdeparturefromthenormsofstrictstyle.Theusualprocedure(inappendixestotextbooksoncounterpointorintheinstructionsforpartwritinginpracticaltextbooksonharmony)ofdescribingfreestylesolelyintermsofitspermitteddeviationfromstrictstyle,insteadofapprehendingitfromwithin,intheformofanidealtype,accordingtoitsownpostulates,hasarisenforanumberofreasonssuchdescriptionseemsadeficiency,albeitanexcusableone.Itresults,first,fromthepracticeofisolatingharmonictheoryfromthetheoryofcounterpoint,fromthesplittingupoftherudimentsofmoderncompositionaltechniqueintotwodisciplinessecond,fromthedifficultyofextractingfromaconglomerateofstylesasingleinternally(andnotsimplyinanegativesense)coherentsystemofrulesthird,fromthefactthatevenindividualstyles(suchasBach'scounterpoint)cannotbesoexhaustively,preciselyandsynopticallycodifiedascanthetechniqueofPalestrinaandfinally,fromtheobservationthatthelawsgoverningtheevolutionofcounterpointfromthe17thcenturytothe20thhaveconsistedincounterpoint'sprogressiveemancipationfromthenormsofprimapratica.(Comparethiswiththe15thand16thcenturies,whenthecourseofdevelopmentwaspreciselytheopposite:fromalessrigoroustoastricterregulationofcomposition.)

    Thestilemodernoofthe17thcentury,whichincludedthemonodic,theconcertanteandthemadrigalstyles(asdidMonteverdistermsecondapratica),wasfounded,ontheonehand,aslicentiouscounterpoint,onthetransgressionofthenormsofstrictstyleatransgressiongroundedinthetendencytoemotionalexpressionandpictorialorallegoricalwordpainting.Ontheotherhand,asharmoniccounterpoint,itwasdistinguishedfromtheprimapraticaofthe16thcenturyandfromtheecclesiasticalstylethatpreservedthattraditionbybeingrootedintonalharmony.However,licentiouscounterpointoughtnottobeequatedsimplywithharmoniccounterpoint:noteverydeviationfromcontrappuntoosservatoismotivatedbytonalharmony.ThebestknownsuchdeviationstheirregularitiesinMonteverdi'smadrigals,abominatedbyArtusi,andseenbyFtisastheearliestdocumentofmoderntonalityarisefromothercauses.Thedownwardleapofadissonantsuspensionfroma7thtoa3rd(asinex.18)isinMonteverdianexpressivefigurethatowesitspathostoitsstrikingdeparturefromtherulesofstrictwriting,butthislicencecannotbeinterpretedintermsoftonalharmony(onecannotspeakofmovementwithinthechord).Bernhard(c1657)explainedthisfigure,whichheconsideredamongthetoolsofmusicalrhetoric,asaheterolepsis(arecoursetoanothermelodicpart):theuppervoicechangesitsusualresolution,the6th,forthe3rd,whichreallybelongstothemiddlevoice.

    Ex.18Downwardleapofadissonantsuspensionfroma7thtoa3rd

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    AfteritsuncertainbeginningsinMonteverdi,theuseoftonalharmonyasabasisforcounterpointgraduallyincreasedfromthelate17thcentury,thoughitdidnotbecomeuniversaltheoreticalsignpostsinthisdevelopmentincludethewritingsofMasson(1694)and,particularly,Rameau(1722).Thedevelopmentwasnevercomplete:thebeliefthatinharmonicallytonalmusiceverydetailwasdeterminedbymeansoftonalharmonyisanexaggerationresultingfromoversystematicthinking.Inharmonicallytonalwriting(andalsoincontrapuntalwriting)harmonies,namelytriadsandchordsofthe7th,constitutetheprimary,directlyavailableentitiesfromwhich

  • thecomposerstartedout.Fromthisbasisinharmonythereresultsthedistinctionbetweenchordaldissonances,whichbelongtotheharmony(the7thinthechordofthe7th),andnotesforeigntotheharmony,whichconstituteanexternaladjuncttoit.Achordaldissonancemustberesolved,butneednotbepreparedandforitsownpart,asacomponentoftheharmony,itcanfunctionastheresolutionofanoteforeigntoit.(Inbar4ofMozart'sJupiterSymphonyeventheoctaveisanoteforeigntotheharmony,asuspensionleadingtothe7th.)Naturallya7thdoesnotalwayscountasachordaldissonance,butonlywhenitsresolutioncoincideswithachangeofroot(asinex.19a)andthuswhenthedissonanceisadeterminingfactorintheharmonicdevelopmentasrepresentedbytherootprogression(seeBASSEFONDAMENTALE).Conversely,ifthenotetowhichadissonancerelatesremainsunmoved(asinex.19b),thenthe7thistobeunderstoodasanoteforeigntotheharmony,i.e.asuspension.

    Ex.19The7thasachordaldissonance(a),andasuspension(b)

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    Sincethelater17thcentury,composers'useoffreecounterpointhasbeencharacterizedbythefactthatdissonantfigurestakenfromlicentiouscounterpointaccentedpassingnotesordownwardleapingsuspensionshavebeenconceivedintermsoftherequirementsofharmoniccounterpoint,andhencerelatedtotriadsandchordsofthe7thinsteadoftoindividualnotes.Itistruethatcontrapuntaltheoryadmittedharmonicallyfoundedphenomenaonlyhesitantly.InBernhard'sattempttosketchoutacontrapuntaltheoryofsecondapratica(thus,tocodifywhatisnotreallysusceptibleofcodification),thedissonantfiguresoflicentiouscounterpoint,thestylusluxurians,aredescribedwithoutregardtotheirharmonicpreconditionsorimplications.Phenomenasuchastheaccentedpassingnote(transitusinversus),theupwardordownwardleapingappoggiatura(superjectioorsubsumptio)andtheresolutionofasuspensionbyleap(syncopatiocatachrestica)orbyastepupwards(mora)arescarcelyproblematicandtheirnatureasexceptionstostrictcounterpoint,whichisclearfromthefactthattheyarereferredbacktothenormfromwhichtheydeviate,isnotopentodispute.However,inaquotationfromarecitative(ex.20a),whichBernhardreducedtoabareskeleton(ex.20b)inordertoelucidateitsfreestyleasaparaphraseofapieceofstrictcounterpoint,thusexplainingitasanagglomerationoflicences

    anellipsis(einsteadoffe),aquaesitionotae(c dinsteadofd)andananticipatio(e)theremaybedoubtastowhetheritisnotsimplyamatterofabrokendiminished7thchord.HenceonemayquestionwhetherBernhardwasdescribingwhatheheardorwhetherhismusicalperceptionhasbeenmisrepresentedinhistheoryforwantofotherthancontrapuntalterminology.

    Ex.20Recitative(a)reducedinordertoelucidateitsfreestyleasaparaphraseofstrictcounterpoint(b),afterBernhard(c1657)

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    Intheirdescriptionsoffreestyle,Heinichen(1728)andMattheson(1739),too,startedoutfromthecategoriesoflicentiouscounterpoint:inclearcontradictionofthelisteninghabitsoftheirtime,andeventheirownperceptions,theyexplainedasananticipatiotransitustheunprepareduseofthe7thinthedominant7thchordonastrongbeat.The7th,whichinstrictwritingshouldappearonlyonaweakbeatasapassingnote,isinterpretedasbeinganticipatedonthestrongbeat.Kirnberger(17719),whotookoverthebasicpropositionsofRameau'stheoryofharmony,outlinedatheoryoffreecompositionsustainedbyanawarenessoftonalharmonicimplicationshetookashisstartingpointfourpartwritingratherthantwopartdissonancesareclassifiedeither

  • asessential(dissonantchords)orfortuitous(notesforeigntotheharmony)andembellishedorvariegatedcounterpointproceedsfromthefigurationofaharmonicframework.

    Fromachoralewithcontinuoaccompaniment(ex.21a)theseeminglytwopartwritingimpliesfourpartwritingbythecontinuoKirnbergerevolvedamotiviccounterpoint(ex.21b).Theupperpartdecoratesdissonantchordsmelodically(chordsofthe2nd,a65anda7th)andistobeunderstoodnotasanintervallicprogression(aswhichitwouldbeabsurd)butasfreemovementwithinthechord,withanticipatorydissonances,hencenotesforeigntotheharmony,oneveryfourthquaver.Thepartwritingisjustifiedbythechordsthatconstitutetheimplicitor(inthecontinuo)explicitbackgroundtothecomposition.

    Ex.21Motiviccounterpoint(b)evolvedbyKirnberger(17719)fromachoralewithcontinuoaccompaniment(a)

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    CarlDahlhaus

    15. Bach.AlongsidethestyleofPalestrina,theinstrumentalpolyphonyofJ.S.Bachconstitutesoneofthemodelsthathavedeterminedcontrapuntaltheory.WhereasPalestrina'sstyleallowsbarelyanydoubtoveritsrules,oratleastitsbasicrules,thetechniqueofBach'scounterpointhasnotyetbeenadequatelydescribedandthereissomecontroversyabouttheprinciplesonwhichitisfounded.

    Thehabitofdefiningpolyphonyasacombinationofequalmelodicparts,theprestigeofthefugueasaconsummateexpressionofinstrumentalcounterpoint,andaonesidedconcentrationonorganandkeyboardmusic(asinSpitta'sthesisoftheprimacyoforganstyleinBach'soutput)allcontributedtoneglectofthefactthatanothertypeofpolyphony,bornealongbyacontinuobassandwiththemelodicpartsnotofequalimportancebutgraded,isnotlesscharacteristicofBach'smusicthanisthefugaltype.TodistortthetitleofabookbyHalm(1913),itispossibletospeakoftwoculturesofcounterpointinBach.

    Continuopolyphonyorconcertantecounterpointisfoundedontheprincipleofafunctionaldifferentiationbetweentheparts:thecounterpointishierarchical.InBach'sarias,wherethewritingisundeniablycontrapuntal,thevocalpart,theconcertanteinstrumentandtheunderpinningofthecontinuomakeupakindofthreepartwriting,differingfromfugalwritingprincipallyinthatthepartsfulfildifferentfunctionsthroughoutratherthanfulfillingthesamefunctions(e.g.subject,countersubjectorcharacteristiccounterpoint,complementarycounterpoint)inalternatinggroupings.

    IncontinuopolyphonyofthelateBaroqueperiodthereisacoalescenceofheterogeneoustraditions,anditispreciselybecauseofthisvarietythatitdisplaysanunsurpassedabundanceofcontrapuntalpossibilities.Thesetraditionsincludedtheideaofpolyphonicwritingoriginatingwiththeprimapratica:apolyphonyeloquentineveryoneofitsmelodicpartsmonodicstyleastherealizationofadeclamatoryorcantabile,expressiveorallegoricaltypeofvocalmelodicwritingtheprincipleofconcertantewriting,withwhichthegrowthofidiomaticinstrumentalmotifwascloselyassociatedand,finally,thecontinuoasbearerofchordprogressions,throughwhoseharmonictonaldefinitionalineardeploymentofthemelodicpartswasnotimpededorrestrictedbutrather,onthecontrary,sustained(asalreadymentioned).

    TheideaofdeducingatheoryofBachiancounterpointlessfromhisfugaltechniquethanfromhis

  • typicalconcertantecontinuopolyphonyoughtnottoappeartoostrange.Forinsofarastheperiodbetween1600and1730,whentechnicaldevelopmentsculminatedinBach'scompositionaltechnique,hasproperlybeendescribedasthecontinuoperiod(Riemann)andastheageoftheconcertantestyle(Handschin),ahistorianwillfinditnaturaltoaffirmthatconcertantecontinuopolyphonyrepresentstheessentialparadigm(resultingfromtheparticularcircumstancesofthetime)forBach'scounterpoint.

    SinceKurth(1917)coinedthetermlinearcounterpointatermwhosesubsequentuseasawatchwordheregardedasamisunderstandingthecontroversyoverwhetherBach'scounterpointwasprimarilylinearlyorharmonicallydeterminedhascontinuedtorage.Inordertoavoidanexcessivelyobdurateoppositionbetweenconflictingdogmas,thetechnicalaspectoftheproblemmaybedistinguishedfromtheaesthetic.Technically(orlogically)speaking,Bach'scounterpointisvirtuallyalwaysgroundedintonalharmony,andwherethethematicaspectofhismusiccomesintoconflictwiththeharmonic,itisthethematicratherthantheharmonicthatisadjusted.

    Thedissonancesequenceinbar28oftheInventioninDminor(ex.22a)wouldbeabsurdifitwerenotheardasanembellishmentofthechordofAminor:notesbelongingtothechordinthebasscoincidewithaccentedpassingnotesintheupperpart,andnotesbelongingtothechordintheupperpartwithunaccentedpassingnotesinthebass.Theconverseisrare:thefactthatinbars11and12ofthesamepiece(ex.22b)apassageofcounterpointisinitselfcomprehensibleasaprogressionofintervalswhilethechordalsignificanceofbar11asawholeremainsuncertain

    (oscillatingbetweenGminorwithadded7thandB majorwithalower3rd)representsanexceptionalcase.Consequently,Kurth'stheorythattheharmonyisalwaysaresultantratherthanastartingpointorpreconditionatheoryintendedasasuggestivehypothesis,andhenceunabletobearinterpretationasadogmabecomesquestionableorevenerroneousasanassertionaboutBach'scontrapuntaltechnique.Itcanstillremainreasonableasanaestheticpostulate,orasarequirementtobemetbymusicalperception.Itwillthenmeanthatlistenersareexpectedtogivetheirattentionprimarilytothemovementfeatureoftheindividualpartsandunderstandsimultaneitiesasmeanstosupportthemusic'slineardynamics.

    Ex.22J.S.Bach:InventioninDMinor

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    Thefactthattechnically,orlogically,seenmanysuchmovementfeaturesresultfromthenecessitytoresolvedissonances,andthusthattheenergeticimpetusoriginatesinthemusic'sharmonyratherthaninitslinearity,neednothoweverpreventonefromperceivingaestheticallythedissonancesasmeansofreinforcingmovementfeatures.Thesewillthusbeaccordedaestheticpriorityeventhough,intechnicalrespects,theyrepresentaresultant:whatislogicallyprimarywillappearasaestheticallysecondary,andviceversa.(Theattempttotallytopsychologizethetheoryofcounterpoint,asanencroachmentofamannerofaestheticperceptionintothedescriptionoftechnicalrudiments,wouldunderminethetheory.)

    If,then,Bach'scounterpointisgroundedintonalharmony,itisalsomotivicallycharacterized.NeitherlinesinKurth'ssenseoftheword(whicharetobefoundinOckeghemratherthaninBach)normelodicdesignsthatimitatetherhythmsandpitchesofspeech,butrathermotifsandfigurationsofinstrumentaloriginrepresenttheprimesubstancefoundinBach'spolyphony.(Fuguesubjectsandcountersubjectsarecomplexesofmotifsandfigurations.)

    Inbars9and10ofthebourrefromFrenchSuiteno.6(ex.23),thesimplerootprogressionin5thsandtheformulaicmelodicfiguresovershadowtheirregulardissonances:thecontrapuntaldetailsremainaestheticallyunobtrusive,sincelogically,inthestructureofthewriting,theyaresubsidiary.TheintervalsequencesthatinthestyleofPalestrinaweretheveryessenceofcounterpointhavenowbecomemerelyabyproductofthetonalharmonicandmotiviccharacterizationofthepolyphony.

  • Ex.23Irregulardissonancesovershadowedthroughtheuseofformulaicmelodicfigures,J.S.Bach:FrenchSuiteno.6,Bourre

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    Contrapuntalphenomenathatcannotbeexplainedbyreferencetotheusualcategoriesmayoftenresultfromthesuperimpositionofmelodicpartsthatmoveaccordingtodifferentrhythmiclevels.InthesecondmovementofthetriosonatafromBach'sMusicalOffering,bars4951,theoutervoicesformachromaticchainof6thsand7thsinacrotchetrhythm(thebassbeingthematic).Buttheprogressioncanbereducedtoadiatonicmodelinminims(ex.24),acontrapuntalprocedurethatdatesbacktothe15thcentury.Itistothisdiatonic,reducedversionthatonemustrelatetheinnerpartiftheharmonies,whichdeviatefromthenormsoftonalharmony,aretobecomecomprehensible:thenotesginbar50andfinbar51,whichappeartobedominant7thsleftunresolved,areinfact5ths.Theapparentchordsofthedominant7thareanincidentalresultoftherhythmicandchromaticmodificationofanoriginalcontrapuntalmodel.

    Ex.24Chromaticchainof6thsand7ths(a)reducedtoadiatonicmodel(b),J.S.Bach:MusicalOffering,triosonata,2ndmovt

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    ThefactthatdefiningBach'scounterpointbecomesacomplicatedbusiness,sinceonehastospeakbothofconcertantecontinuopolyphonyandofhierarchicallyorganizedcounterpoint,oughtnotbethoughtadeficiency.ItispreciselytothemultiplicityofhistoricalconditionsonwhichitisbasedthatBach'spolyphonyowes,first,itsabundanceoffiguralmaterial(andthathasalwaysbeenacauseforadmiration)and,second,itsnumerousdeterminingfactors,whichcouldonlyfailtobeappreciatedwhenitwassoughttodeducethecounterpointfromasingleprinciple,thatoflinearity.

    CarlDahlhaus

    16. The Classical and Romantic eras.Theperiodbetweenthelateryearsofthe18thcenturyandthebeginningofthe20thisaccountedoneinwhichcounterpointsanktobeingamereacademicexercise,leavingbarelyrecognizabletracesinthepracticeofcomposersofpianoandoperaticmusic.Yetanimmenselandscapeofmusicalworksbearingaprimarilyhomophonicimprintisrelievedbyisolatedpolyphonicworksorgroupsofworkswhich,inbothspiritandtechnique,recallolderstyles.Archaisticcounterpoint,lookingbacktothemodelsofPalestrinaorBach,wasbynomeanstheonlyonetypescanbecitedthatdistinguishthisperiodfromearliercenturies(providedonedoesnotcutoffaccesstothephenomenathatconstitutethetypicalcounterpointofthe19thcenturybytheuseofadefinitionrestrictingtheconceptofgenuinecounterpointtotheolderstyle).

    TherevivalofPalestrina'sstyle,athrowbackforwhichthespiritoftheRomanticmovementwasresponsible,wassustainedbytheenthusiasticbeliefthatonly16thcenturyvocalpolyphonycouldbetruechurchmusic:amaximsharedbyProtestantwriters(suchasE.T.A.HoffmannandThibaut)andCatholicalike.Sinceitremainedrestrictedtosacredmusic,thisreverenceforPalestrinacouldevenbetotallyreconciledwiththechampioningofmusicalprogresswhichthe

  • NewGermanschoolbelieveditstoodfor:LisztsympathizedwiththeaimsoftheCecilianmovement,andthatleftitsmarkonhiscompositions.Inthe19thcentury,ofcourse,themostimportantaspectofPalestrina'sstyleusedtoinculcateadevotionalframeofmindwasnotsomuchthestricttechniqueofcompositionasrathertheseraphictoneofamusicwhosetempowasdilatedsothatitcouldbemadetoconveythenotionofhallowedstrainsfelttobeemanatingfromsomeGreatBeyond.AlthoughBellermann'sworkinlayingdownpreciserulesforcompositioninthisstyle(1862)cameaboutinconnectionwiththechurchmusicrevival,italsoindicatesthattheobjectivetaskofhistoricalreconstructionbecamedivorcedfromRomanticenthusiasm.

    WhiletherevivalofPalestrina'sstyleappearsprimarilytohavebeenamatterofresuscitationandperformanceofexistingmusic,andonlysecondarilyintrudingintotherealmofcomposition,theinfluenceofBachscounterpointwasofconcerntocomposers:itwasamatteroftheirprofessionalequipment.TheinfluenceexertedbyBachonChopinandMendelssohn,SchumannandBrahmsshouldnotbesoughtsolelyinfuguesandfughettas:itcanalso,andindeedparticularly,befeltintheircharacterpieces.TheproblemthatRomanticcomposerssoughttosolvebyreferringbacktoBachconsistedinthedifficultyofwritinginastrictstylehencewithoutfallingintothetechnicalheedlessnessofthegeneralrunofoperaticandkeyboardmusicwhileproducingworksthatwerepoeticratherthanprosaic(underwhichheadingSchumanncategorizednotjustlightmusicbutalsothemerelytechnicalworkofart).WhattheysawrealizedinexemplaryfashioninthemusicofBachwastheideaofmusicatoncecontrapuntalandfullofcharacter,atoncestrictandeloquent:musicinwhichthecharacteristicandtheeloquentfeaturesofacontrapuntallydifferentiatedtexturewerenotforcedonitfromoutsidebutwereactuallygeneratedbyit.

    IntheinstrumentalmusicoftheClassicalandRomanticerasthefuguerepresentsakindofcounterpointthoughtofasstrict,althoughactuallyitwasaspecialcaseoffreestyle.However,sonataandfugueorrather,sonataformandfugaltechniquewerecloselyrelated:therewasatendencyforthetwoculturesofmusictocoalesceintoathird.Ontheonehand,asdemonstratedbyHaydn'sevolutionfromop.20toop.33,fugueandfugatowereprerequisitesofthematicworkingoutinthetechniqueofClassicalandRomanticdevelopmentsections.Ontheother,asthetendencygrewforthematicdevelopmenttospreadoverentiremovements,itbecamelogicaltocharacterizethedevelopmentsectionbyanintensificationofmotivicworktothepointoffugaltechniqueandthusmarkitoutasdistinctfromtheexpositionandtherecapitulation.InBeethoven'slatequartets,inBrahmsandeveninLiszt,fugaltechniquewasineffectdisplayedasaconsequenceofthematicworking.

    ThecontinuationofthesecondsubjectinthefirstmovementofSchubert'sStringQuintetinC,amelodyincanon,providesaperfectexampleoftherealizationofanideathatconstantlyrecursinthe19thcentury,inoperaticensemblesaswellasinsubsidiarythemesofBrucknersymphonies:theideaofacantabilecounterpoint,orofacontrapuntalcantabilestyle.Thefactthattoaestheticiansthismusthaveseemedahybrid,sinceitfloutedtheconventionwherebycantabilewasassociatedwithhomophonicstyleandpolyphonywithanunbendingthematicstyle,wasseenbycomposerslessasaninhibitingfactorthanasachallengetotransformthiscontradictionintoanaestheticpropositionandthusabenefit.Indeed,itwascharacteristicofthe19thcenturythatittendedtobringtogetherapparentlymutuallyexclusiveopposites.

    ThethematiccombinationsinthepreludetoWagnersDieMeistersingerandinthefinalduetofSiegfriedthesimultaneous,notwhollyunforced,presentationofleitmotifsthathadbeenindependentlycoinedwerefeltbySchenkertobeabetrayaloftheconceptofcounterpointRichardStraussonthecontrarypraisedthemastheonlyadequateformofcounterpointinanageofexpressivemusic(andtooktheideatotechnicalandaestheticextremesinSalomeandElektra,aspsychologicalcounterpoint).Hereitisundoubtedlyamatterofcounterpointasanexpressionofliteraryideas:themotifsarenotrelatedasmelodiclinesbutassociatedaestheticallyassymbolsofideasandemotions,whilebeingtechnicallypiecedtogetherasencrustationsaroundoneandthesamechord(notwithoutfissuresandflaws).Theproceduremaybethoughttechnicallyquestionablebutduringaperiodtypifiedbymusicdramaandsymphonicpoemsgenresbearingastrongliterarystampitshouldnotseemsurprisingiftheseliterarytendenciesinfiltratedcontrapuntaltechnique.Or,toputitanotherway,ifoneisgoingtocondemnliterarycounterpoint,one'sjudgmentmustalsoincludeliterarymusicasawhole.

    Polyphonywrittenaroundchords,andtherelessforitsownsakethanforthefactthatitimpartsaricherandmorevariegatedeffecttotheorchestralsound,hascomeintodisreputeaspseudo

  • polyphony.Thisterm,eitherexplicitlyortacitly,containstheaestheticomoralreproachthatcounterpoint,whichoughttobeanend,hasherebeenrelegatedtotheroleofameans,afactorsubservienttothequalityofsound:insteadofbeingrenderedclearbymeansofinstrumentation,theexactoppositehappensanditismadetoserveasavehicleofsonority.(Instrumentswhosepartsarecharacterizedbyexpressivitymakeabettersonorousimpact,eventhoughthedetailsofwhattheyhavetosayarequiteinaudible.)Inthisjudgmentisconcealedaprejudicethattheparametersofmusicfallintoanunalterablehierarchicalorder:accordingtothis,contrapuntalstructurewouldasamatterofcoursebetheprimaryfactorandinstrumentationmerelysecondary.Intheevolutionofcompositionduringthemid20thcenturythisprejudicehasbeenoverthrown,sothatinretrospectevenahistoricalphenomenonsuchasthedegradationofcounterpointtoameanstowardsrichnessofsonorityappearsinaverydifferentaestheticlight.

    Textbooks,whichfordidacticreasonsareinclinedtosimplifymattersbysettingupclearantitheses,suggestthatcounterpointfunctionsasanoppositetoharmony,thuspromotingtheviewthatanevolutionofharmonyembracingvariedchordalstructuresandmethodsoflinkingchordsmustnecessarilyentailasuppressionofpolyphony.ButinthemusicofBrahmsandWagnertheoppositeispatentlythecase.TheharmonicrichnesscharacteristicofBrahmsformsacorollarytoakindofmelodicallyconceivedbasswriting(insteadofbeingconfinedtoasmallnumberofsupportingnotes)andtherelationshipofsuchabasstothemelodiclinebecomesacontrapuntalframeworkforthecompositionaltechnique.InWagner'sharmonyitistheindividualcharacterizationofchordsbymeansofdissonancesandchromaticvariantsthatcreatesconsequencesinthecontrapuntalwriting:ontheonehandthedissonant,complicatedchordsimpeltheirownpartwritingontheother,sincetherootprogressioninthebassisoftenweakandnotcapableofsustainingitsload,chordsmustbelinkedbymotivicpartwriting.Hencethepartwritingmusttendtowardspolyphonyifthejuxtapositionofchordsistohavetheeffectofacompellingprogression.

    CarlDahlhaus

    17. 20th century.Theemphasisoncounterpointinmusicafter1910canbeseenasacorollaryofthediminishingimportanceoftonalharmony.Chordalcoherencelostitsfundamentalimportance,anddidsoregardlessofwhethertonalitywasdissolved(Schoenberg,Berg,Webern)ormetamorphosed(Stravinsky,Bartk,Hindemith).Thevarioustypesofexpandedtonality(whoseprincipalfeatureisnot,however,expansion)appearashierarchicallyorderedsystemsanalogoustotraditionaltonalitybutitislesschordsthanindividualnotesroundwhichtheyspinawebofrelationships,sothatitismorenaturalforthetonalstructurestobecharacterizedbymelodicandpolyphonicthanbyhomophonicstyle.

    Amongthetechniquesthatdissolvedtonalharmony,biorpolytonalityisnotableforitstendencytopromoteacontrapuntalstyle.Althoughitappearstoproceedfromthesuperimpositionofchordsofdifferentkeys(asinStrauss'sElektra),itispossibletoconsiderthecontrapuntalmanifestation(asinMilhaud)asthetrulyrepresentativeone.Polytonal(orpolymodal)counterpointisaparadoxofcompositionaltechniqueinthatthetonalatomizationofthestyleasawholerequiresaparticularlycleartonalcharacterizationoftheindividualpartsotherwisepolytonalitywhoseaestheticimportconsistsinthepointednessofitseffectwillturnintothegreyongreyoftonalindistinguishability.

    Theproblemsof12notecounterpointinevitablyraisetheproblemsof12notetechniqueasawholehereitisnecessarytorestrictthediscussiontocommentsonsomemisunderstandingsordetailsthathavebeentakenoutofcontext.First,theemancipationofthedissonance,theliberationofdissonancesfromthenecessityofresolution,merelymeansthatthespecificdifferencebetweenconsonancesanddissonances,whichgaverisetothedependenceofdissonancesonconsonances,hasbeenabolished,andnotthatchordsnolongerpossessvaryingdegreesofconsonanceanddissonancewithwhichthecomposercanwork(Krenek,1940).In12notecounterpoint,too,thereisaharmonicgradient(Hindemith,1937).Second,Schoenberg's

  • procedureofformulatinga12noterowinsuchawaythatthefirsthalfoftheoriginalformtogetherwiththefirsthalfoftheinversiontransposeddowna5thforma12notecomplex(whatBabbittcalledcombinatoriality)representsawayoutofthedilemma:fortheprincipleofdodecaphony,thenonrepetitionofnotesbeforearowhasbeenstatedinitsentirety,iscontravenedassoonasincidentalnoterepetitionsareproducedbythesimultaneoususeofdifferentformsoftherow.Wheretherowitselfisaprimarilymelodicprinciple,combinatorialitypresentsitselfasasustainingprincipleofakindofstrictwritingin12notecounterpoint.Third,dodecaphoniccounterpointinSchoenberg(thoughnotinWebern)istobeunderstoodasthematicormotiviccounterpoint.Schoenbergdidnotconstruct12noterowsinanabstractway,butasthematicshapes(thoughnaturallytheywouldbemodifiedforconstructionalpurposes)andtheassertionthatbyvirtueofdodecaphonictechniqueasdistinctfromfreeatonality,whichtendedeithertowardsdependenceonatextortowardsanaphoristicstyleitwouldoncemorebepossibletocomposelargescaleformsininstrumentalmusicsimplymeansthatdodecaphonictechniquepermittedtheformulationofthemescapableofsustainingalargescalemusicalstructure.

    Thetermlinearcounterpoint(Kurth,1917)shouldnotbemistakenasasynonymforaheedlesssortofpolyphonypayingnoattentiontoverticalsimultaneities.Itsdistinctivefeatureisrathertheconceptofmelody,whichservedasthestartingpointfortheadherentsofthenewobjectivitywhentheysetuplinearcounterpointasanantitypetotheRomanticharmonytheydespised:thenotionofakindofmelodicwritingnotreliantonchordsandchordalprogressions,butevolvedfromthealliancesandoppositionsofleapsandsteps,ascentsanddescents,longandshortvalues,indeedakindofstructureofpitchandrhythmrepresentingastateofenergy(Kurth)andstrivingtowardsanequilibriumwhich,however,itcanonlyachieveattheverylast,sothatthemelodicmovementwillnotcometoastandstillbeforethefinalcadence.Counterpoint,however,isinthisstylenothingmorethanmultiplemelody,andissubjecttothesamecriteriaofenergyasisasinglemelody:thepartssupport,enhanceorcontradicteachothertheycrossorcomplementeachother.

    CarlDahlhaus

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