isthecontactareabetweenthebowandthestring ProceedingsoftheStockholmMusicAcousticsConferenceAugust692003SMAC03StockholmSwedenthenormalloadandistheshearyieldstressasafunctionoftemperatureThete ID: 241475
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ProceedingsoftheStockholmMusicAcousticsConference,August6-9,2003(SMAC03),Stockholm,SwedenBOWEDSTRINGPHYSICALMODELVALIDATIONTHROUGHUSEOFABOWCONTROLLERANDEXAMINATIONOFBOWSTROKESStefaniaSeranCCRMA,DepartmentofMusicStanfordUniversity,Stanford,CA,USADianaYoungMIT,MediaLab,Cambridge,MA,USAABSTRACTCombiningaphysicalmodelwithabowcontroller,weproposeatechniquetovalidatebowstrokesinavirtualinstrument.1.INTRODUCTION isthecontactareabetweenthebowandthestring, ProceedingsoftheStockholmMusicAcousticsConference,August6-9,2003(SMAC03),Stockholm,Swedenthenormalload,andistheshearyieldstressasafunctionoftemperature.ThetemperatureoftheshearingrosinlayercanbeestimatedfromthecurrentslidingvelocitybypassingitthroughanappropriatelinearÞlter[9].ThebowwidthismodeledbydiscretizingtheregionofthestringincontactwiththebowusingÞnitedifferencesandcalculat-ingthecouplingbetweenthewavespropagatingalongthestringandthefrictionalinteractionbetweenthebowandthestringateachpoint.Oncethevelocityofthestringatthecontactpointhasbeencalculated,thewavespropagatingalongthestringaremod-eledusingdigitalwaveguides.Moreprecisely,transversalandtor-sionalwavespropagatingtowardthebridgeandtheÞngerboardaremodeledaspairsofonedimensionaldigitalwaveguides.TheoutgoingvelocityatthebridgeisÞlteredthroughthebodyÕsresonancesandcorrespondstotheoutputwaveformsperceivedbythelistener.Apreliminaryversionofthismodelhasbeende-scribedin[3].Theblockdiagramstructureofthecompletebowedstringphys-icalmodelisshowninFigure2.Initdelaylinescorrespondtotravelingwavespropagatingfromthebowpointtothebridgeandthenut;LPandAPrepresentrespectivelythelowpassÞltersthatsimulatelossesandtheallpassÞltersthatsimulatedispersion.Theinputparametersofthemodelcorrespondingtotherighthandoftheplayerarebowpositionrelativetothebridge(normalizedbe-tween0and1,where0correspondstothebridge,1correspondstothenut,0.5correspondstothemiddleofthestring),bowpres-sure,bowvelocity,andamountofbowhairincontactwiththestring.ThemodelhasbeenimplementedasanexternalobjectintheMax/MSPenvironment. Figure1:Simpliedstructureofthebowedstringphysicalmodelusedinthesimulation.3.ABOWCONTROLLERThebowcontrollerusedintheseexperimentsisacommercialcar-bonÞberbow,adaptedbyaddingacustommeasurementsystem. BOWSTRINGINTERACTION LPAP NUT TRAVELING WAVESBRIDGE TRAVELING WAVES Figure2:Renedblockdiagramstructureofthebowedstringphysicalmodelusedinthesimulations. Figure3:Dataowfortheviolincontroller.ThesystemiscomprisedofanelectricÞeldsensorformeasur-ingbowposition(tip-frog/bow-bridgedistance),commercialac-celerometersfordetecting3Dacceleration,andfoilstraingaugesformeasuringthestraininthebowstickproportionaltonormalforceonthestringandtheorthogonalforcecorrespondingtoßex-iontowardandawayfromthescroll.Fromthesesensors,theparametersofbowvelocity,bow-bridgedistance,downwardforce,andbowwidth(usingtiltinformationprovidedbytheaccelerometersandthesecondstrainsensor)maybeisolatedfrombowinggesturesandusedasinputtothephysicalmodel.Theimplementationofthemeasurementsystemisminimalandmaintainstheplayabilityoftheinterfaceinmostscenarios.Thoughsomewhatheavierthanusual(almost30gheavier,includ-ingbattery),theresultingbowhasareasonablebalancepointandremainswireless.Themicrocontroller,battery,RFtransmitter,andaccelerome-tersarehousedonanelectronicsboardmountedonthefrog,whilethestrainsensorsaremounteddirectlytothebowstickaroundthemidpointofthebow.Theaccelerationandstraindataistransmit-tedwirelesslytoabaystationboard.Thebowboardalsosendstwosquarewavesignalstoeitherendofaresistivestripthatrunsthelengthofthebowstick,actingasanantennaforthepositionmeasurement.Theresultantsignalisreceivedbyanantennamountedbehindthebridgeofthevio-lin,andthissignalisconnectedviaacabletoasmallbaystationboardthatdeterminesthedifferentamplitudesofthetworeceivedsignals.Thepositioninformationisthencombinedwiththeaccel-erationandstraindatastreamandoutputthroughaserialbustothecomputerrunningthephysicalmodel.Thecompactnessofthisgesturemeasurementsystemallowsforaneasytestsetupinalaboratoryorperformanceenvironment. ProceedingsoftheStockholmMusicAcousticsConference,August6-9,2003(SMAC03),Stockholm,SwedenForadetaileddescriptionofthebowcontroller,see[10].4.EXPERIMENTALSETUPIntheseexperimentsweusedaMacintoshG4computertoruntheMax/MSPimplementationofthebowedstringphysicalmodel.Thegesturaldatafromthebowcontrollerwasconnectedviaaserial/USBconvertertoaUSBportofthecomputer.Theantennausedforthemeasurementofbowpositionwasmountedbehindthebridgeofanelectricviolin(Jensen).Thisvi-olinwaschosenforthesetestsforeaseofaudiorecording,aswellastheabilitytoplaytheaudioproducedbythemodelandtheun-ampliÞedviolinsoundtogether.RecordingsofboththeviolinaudioandthebowcontrollerdataweremadesimultaneouslywithintheMax/MSPenvironment.Thegesturedatawasthenusedtodrivethephysicalmodel,whichproducedwaveformsthatwerealsorecorded.Thissetupwassimpleenoughtoallowfastandeasyrecordingandtesting,andwasusedtoreproducesomeofthebowstrokesthatarefundamentaltotherighthandtechniqueofanaccom-plishedbowedstringplayer,suchaslegato,detach«e,andbalzato.Thewaveformsoftheviolinwerethenqualitativelycomparedtothoseproducedbythemodelusingbothtimeandspectraldo-mainevaluationandperceptualevaluation.TheexperimentalsetupusedisshowninFigure4. Figure4:Setupusedfortheexperiments.4.1.PlayingwithDownwardForceWebegantheintegrationofthebowcontrollerhardwarewiththesoftwaremodelbyaddressingoneinputparameteratatime.IntheÞrsttrialweusedthedownwardstrainsensortocontrolthedownwardforceparameterforthebowedstringmodel.Withthemodelparametersofbow-bridgedistance,bowveloc-ity,bowwidth,andfrequencyheldconstant,wevariedthedown-wardforcebetween0and5N.Otherthansettingathresholdappropriateforthesensorrange,itwasunnecessarytoperformanyadjustmentstothismapping.Usingthebowcontrollertoplayasinglestringonthetestviolin,wewereabletocomparethesoundproducedbythemodelwiththatofthetestviolin.Wewereabletoquicklyproducesonoritiesfromthemodelthatsoundedappropriatefortheamountofpres-sureweappliedtothebow.Interestingly,themodelproducedsoundsthatseemedpercep-tuallycorrectforlongsustainedstrokesaswellasforshortstrokeswithsharpattacksanddecays.4.2.AddingVelocityandBow-BridgeDistanceNextweaddedthebowvelocityandbow-bridgedistancecontrolsbyusingthedatafromthebowpositionsensor.Bytakingthedatavaluescorrespondingtothetipandthefrog,thetransversebowpositionwasdetermined,andfromthisthevelocityvaluewasderived.Thebow-bridgedistancewastakenasthesumofthetipandthefrogvalues.Wewereabletochangethesoundofthetonesproducedbythemodelbyadjustingbowpressure,speed,bow-bridgedistance,andbysimplychangingthebowdirection.Asthesoundofthetestvi-olinofferedaneasycomparisontothemodel,weexperimentedbyplayingtwoopenstrings(ofthetestviolin)whilecontrollingasin-gletoneofthemodeltunedtodifferentintervalsaboveandbelowthehigherstring.Playingthesmallduetbetweenrealandvirtualviolinswewereabletomakesmalladjustmentsinthemappingssothatthetimberssoundedasthoughtheywereallthreeemanatingfromthetestviolin.5.COMPLETEMAPPINGInordertobuildanexpressivevirtualmusicalinstrument,thecap-tureofthegestureoftheperformanceisasimportantasthemannerinwhichthemappingofgesturaldataontosynthesisparametersisdone.Inthecaseofphysicalmodelingsynthesis,aone-to-onemappingapproachofcontrolvaluestosynthesisparametersmakessenseduetothefactthattherelationbetweengestureinputandsoundproductionisoftenhard-codedinsidethesynthesismodelodel?].Becauseboththephysicalmodelandthebowcontrolleraredevelopedaccordingtophysicalinputandoutputparameters,thecompletemappingbetweenthetwoisstraightforward.Figure5showshowallthedatasentbythebowcontrollerweremappedtotheinputparametersofthephysicalmodel.Downwardbowforceofthecontrollerisdirectlymappedintobowforceinthephysi-calmodel.Bowvelocityandbow-bridgedistancewerecapturedbymeasuringthehorizontalandverticalpositionofthebowre-spectively.Moreover,lateralstrainsensorsweremappedontotheamountofbowhairincontactwiththebow.5.1.BowstrokesAsmentionedinthepreviousparagraph,theevaluationofthebowstrokesusingtheexperimentalsetupwasdonebycomparingtheoutputoftheelectricviolintotheoutputofthephysicalmodel,usingthesameinputparameters.ThisevaluationwasÞrstper-formedbycomparingtheshapeofthetimedomainandfrequencydomainwaveformsproducedbythetwoinstruments.Thisevalua-tion,however,didnotseemveryeffective:notsurprisingly,wave-formswithquitedifferentshapesinsomecasesturnedouttosoundsimilar.InspectionofwaveformsalonewasnotsufÞcienttodeterminethesimilaritybetweensounds.Wethereforestartedperforming ProceedingsoftheStockholmMusicAcousticsConference,August6-9,2003(SMAC03),Stockholm,Sweden Figure5:Finalmappingsofthebowcontrollertothebowedstringphysicalmodel.listeningteststoevaluatetheaccuratenessoftheoverallsetup.6.CONCLUSIONSWeproposedthecombinationofabowedstringphysicalmodelandabowcontrollertoexaminehowdifferentbowstrokescanbeachievedinavirtualbowedstringinstruments.Preliminaryexper-imentsshowthatthebowstrokesthatabeginnerÕsviolinplayerlearnsafterfewyearsofpracticeareeasilyreproduced.Moreac-curatelisteningtestsandcomparisonsbetweenallthevariationsofinputparametersandbowstrokesneedtobetestedinordertofullyvalidatetheplayabilityofourinstrument.7.REFERENCES[1]JamesWoodhouse,ÒOntheplayabilityofviolins.PartI:Reßectionfunctions.PartII:Minimumbowforceandtran-sients,ÓAcustica,vol.78,pp.125Ð136,137Ð153,1993.[2]JohnC.Schelleng,ÒThebowedstringandtheplayer,ÓJour-naloftheAcousticalSocietyofAmerica,vol.53,no.1,pp.26Ð41,Jan.1973.[3]StefaniaSeraÞn,JuliusO.Smith,III,andJimWoodhouse,ÒAninvestigationoftheimpactoftorsionwavesandfrictioncharacteristicsontheplayabilityofvirtualbowedstrings,ÓNewYork,Oct.1999,IEEEPress.[4]AndersAskenfelt,ÒMeasurementofthebowingparametersinviolinplaying,ÓJournaloftheAcousticalSocietyofAmer-ica,vol.86,no.2,pp.503Ð516,August1989.[5]DavidJaffeandJuliusSmith,ÒPerformanceexpressionincommutedwaveguidesynthesisofbowedstrings,ÓinProc.InternationalComputerMusicConference.ICMA,1995,pp.[6]D.YoungandS.SeraÞn,ÒPlayabilityevaluationofavirtualbowedstringinstrument,ÓinProc.NIME,Montreal,CA,[7]JuliusO.Smith,ÒPhysicalmodelingusingdigitalwave-guides,ÓComputerMusicJournal,vol.16,no.4,pp.74Ð91,Winter1992.[8]R.Pitteroff,ÒMechanicsofthecontactareabetweenavi-olinbowandastring.parti:reßectionandtransmissionbe-haviour.partii:Simulatingthebowedstring.partiii:Pa-rameterdependance,ÓinAcustica-ActaAcustica,1998,pp.[9]JonathanH.SmithandJamesWoodhouse,ÒThetribologyofrosin.,ÓJ.MechPhys.Solids,vol.48,pp.1633Ð1681.[10]DianaYoung,ÒThehyperbowcontroller:Real-timedynam-icsmeasurementofviolinperformance,ÓinProc.NIME