G. Towards a computational model of melody identification in polyphonic music

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TowardsaComputationalModelofMelodyIdentificationinPolyphonicMusicSørenTjagvadMadsenAustrianResearchInstituteforArtificialIntelligence,Viennasoren.madsen@ofai.at

GerhardWidmerDepartmentofComputationalPerceptionJohannesKeplerUniversity,Linzgerhard.widmer@jku.at

AbstractThispaperpresentsfirststepstowardsasim-ple,robustcomputationalmodelofautomaticmelodyidentification.Basedonresultsfrommu-sicpsychologythatindicatearelationshipbetweenmelodiccomplexityandalistener’sattention,wepostulatearelationshipbetweenmusicalcomplex-ityandtheprobabilityofamusicallinetobeper-ceivedasthemelody.Weintroduceasimplemea-sureofmelodiccomplexity,presentanalgorithmforpredictingthemostlikelymelodynoteatanypointinapiece,andshowexperimentallythatthissimpleapproachworkssurprisinglywellinrathercomplexmusic.

1IntroductionMelodyisacentraldimensioninalmostallmusic.Humanlistenersareveryeffectivein(unconsciously)pickingoutthosenotesina–possiblycomplex–multi-voicepiecethatconstitutethemelodicline.Melodyisalsoanimportantas-pectinmusic-relatedcomputerapplications,forinstance,inMusicInformationRetrieval(e.g.,inmusicdatabasesthatof-ferretrievalbymelodicmotifs[WeydeandDatzko,2005]orQuerybyHumming[Birminghametal.,2006]).Itisnoteasytounequivocallydefinetheconceptof‘melody’.Inasense,themelodyisthemostprominentlineinapolyphonic(multi-voice)pieceofmusic.AlthoughinWesternmusic,themelodyisoftenfoundamongthehighernotes,thisisnotalwaysthecase.Also,evenincomposi-tionsthatareexplicitlystructuredintoindividuallinesbythecomposer(suchas,e.g.,orchestralpiecesconsistingofmono-phonicinstrumentvoices),themelodyisbynomeansalwaysrepresentedby(or‘appearingin’)thesamelinethroughoutapiece.Inaway,whichnotesconstitutethemelodyisdefinedbywherethelistenersperceivethemostinterestingthingstobegoingoninthemusic,orwhattheysensetobethemostcoherentpaththroughthecomplexinterweavingofmusicallines.Thus,thoughourexperiencetellsusthathearingthemelodyisarathersimpleandintuitivetaskforhumans,itisbynomeansasimpletasktobeformalisedinamachine.Inpopularmusic,itissometimesassumedthatthemelodydoesnotchangebetweentheinstrumentspresent.Someworkhasbeendoneonpredictingwhichoneofthetracksina

MIDIfilecontainsthe‘mainmelody’[Rizoetal.,2006;FribergandAhlb¨ack,2006].Inbothcasesastatisticalap-proachwastaken–learningpropertiesofmelodicandnon-melodictracks.Ideasforconvertingpolyphonictracksintomelodicallymeaningfulmonophonicsequenceshavealsobeenproposed[UitdenbogerdandZobel,1998].Thispaperpresentsfirststepstowardsasimple,robustcomputationalmodelofautomaticmelodynoteidentification.Basedonresultsfrommusicologyandmusicpsychologythatindicatearelationshipbetweenmelodiccomplexityandalis-tener’sattention,wepostulatethatthenotesmakingupthemelodylinemaybeidentifiedbycalculatingandintegratingsomemeasuresofperceivedcomplexityovertime.Wewillintroduceasimple,straightforwardmeasureofmelodiccom-plexitybasedonentropy,presentanalgorithmforpredictingthemostlikelymelodynoteatanypointinapiece,andshowexperimentallythatthisverysimpleapproachworkssurpris-inglywellinpickingoutthemelodynotesinquitecomplexpolyphonicmusic.Still,theresultsarestillfarbelowwhatwecanexpecthumanstoachieve,andwewilldiscussanum-berofpossibleextensionsoftheapproachtowardsamorecomprehensiveandeffectivecomputationalmodel.

2ComplexityandMelodyPerceptionThebasicmotivationforourmodelofmelodyidentifica-tionistheobservation,whichhasbeenmademanytimesintheliteratureonmusiccognition,thatthereseemstobeaconnectionbetweenthecomplexityofamusicalline,andtheamountofattentionthatwillbedevotedtoitonthepartofalistener.Avoiceintroducingneworsurprisingmusicalmaterialwillpotentiallyattractthelistener’satten-tion.However,ifthenewmaterialisconstantlyrepeated,wewillpaylessandlessattentiontoitandbecomeha-bituatedoraccustomedtothestimulus.Lessattentionisrequiredfromthelistenerandthevoicewillfallintothebackground[Snyder,2000].Thenotionofmusicalsur-priseisalsorelatedtotheconceptof‘expectation’asithasbeenputforthinrecentmusictheories[Narmour,1990;Huron,2006].Ifweassumethatthemelodyisthemusicallinethatcommandsmostattentionandpresentsmostnewin-formation,itseemsnaturaltoinvestigatemelodiccomplexitymeasuresasabasisformelodydetectionalgorithms.Indeed,theideaofusinginformation-theoreticcomplex-itymeasurestocharacteriseaspectsofmusicaldevelopment

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