Time-frequency Analysis of Musical Rhythm

《Time-frequency Analysis of Musical Rhythm》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

1、Time-frequencyAnalysisofMusicalRhythmXiaowenCheng(Student)DepartmentofMathematicsUniversityofMinnesota–TwinCities;Minneapolis,MN55455E-mail:chen1098@umn.eduTel.612-625-2004,Fax.612-626-2017JarodV.Hart(Student)DepartmentofMathematicsUniversityofKansas;Lawrence,KS66045E-mail:jhart@math.ku.ed

2、uTel.785-864-3651,Fax.785-864-5255JamesS.Walker(Correspondingfacultyauthor)DepartmentofMathematicsUniversityofWisconsin–EauClaire;EauClaire,WI54702–4004E-mail:walkerjs@uwec.eduTel.715-836-4835,Fax.715-836-292412Time-frequencyAnalysisofMusicalRhythmIntroductionWeshallusethemathematicaltechn

3、iquesofGabortransformsandcontinuouswavelettransformstoanalyzetherhythmicstructureofmusicanditsinteractionwithmelodicstructure.Thisanalysisrevealsthehierarchicalstructureofrhythm.Hierarchicalstructureiscommontorhythmicperformancesthroughouttheworld'smusic.Theworkdescribedhereisinterdiscipli

4、naryandexperimental.Weusemathematicstoaidintheunderstandingofthestructureofmusic,andhavedevelopedmathematicaltoolswhich(whilenotcompletelyfinished)haveshownthemselvestobeusefulforthismusicalanalysis.Weaimtoexploreideaswiththispaper,toprovokethought,nottopresentcompletelyfinishedwork.Thepaper

5、isorganizedasfollows.WefirstsummarizethemathematicalmethodofGabortransforms(alsoknownasshort-timeFouriertransforms,orspectrograms).Spectrogramsprovideatoolforvisualizingthepatternsoftime-frequencystructureswithinamusicalpassage.Wethenreviewthemethodofpercussionscalograms,anewtechniqueforana

6、lyzingrhythmintroducedin[34].Afterthat,weshowhowpercussionscalogramsareusedtoanalyzepercussionpassagesandrhythm.Wecarryoutfouranalysesofpercussionpassagesfromavarietyofmusicstyles(rockdrumming,Africandrumming,andjazzdrumming).Wealsoexplorethreeexamplesoftheconnectionbetweenrhythmandmelody(

7、ajazzpianopiece,aBachpianotranscription,andajazzorchestration).Theseexamplesprovideempiricaljustificationofourmethod.Finally,weexplainhowtheparametersforpercussionscalogramsarechoseninordertoprovideasatisfactorydisplayofthepulsetrainsthatcharacterizeapercussion