Measurement of String Instruments

JoãoMartinsHUT, Laboratoryof AcousticsandAudio SignalProcessing

jmartin s@acoustics.hut .fi

Abstract

The aim of this article is to show an overview of the methods for analysisof string instruments’ acoustical and mechanical properties. Some physi-cally meaningful quantities such as the mechanical admittance of the bridge,sound radiated and modal analysis are discussed. The measurement of thesequantities is not a straightforward process, all methods having their advan-tages and drawbacks. Problems concerning the holding of the instrument, theexcitation process and excitation signals, and the recording of the responseare shown. Finally we use the Portuguese guitar and the Turkish saz as casestudy.

Introduction

Themeasurementof musicalinstrumentpropertieshasa very long historybehindit. In-strumentmakersusedthemto evaluatethequality of theinstrumentduringtheconstruc-tion process.Stringinstrumentssopopularastheviolin or theguitarwerecarefullymea-suredandstudied(Cremer1985)but still have many unknown properties.Somepopularinstruments presentnonlineareffectswhich makestheir analysismoredifficult (Huang2000). Fromthesciencepoint of view themeasurementsarevery importantin buildingscientificmodelsfor instrumentsandthetestingof themodels.

Thefirst difficulty comesfrom thechoiceof theparameters(Jansson,Bork & Meyer1986). Which parametersarebelieved to reflectthesoundcharacteristicsandquality ofan instrument,andto what gradeof accuracy they canbe evaluated.Soundradiatedorradiativity capturedfrom a microphoneis relevant from the hearingpoint of view, butdoesn’t give very detailedknowledgeaboutthemechanicalpropertiesof theinstrument,whichareimportantfor instrumentmakersandfor modelsusedin recentmusic synthesis.A discussionaboutthemeasurementof theadmittanceor impedanceof thebridgeisbasedon (Boutillon & Weinreich1999).

Theresonantpeaksmeasuredin theadmittancemethodarecalledmodesof vibration.Eachmodegeneratesapatternof vibrationonthesurfaceof theinstrumentwith amplitudepointsthatrangefrom zero(nodallines)to pointsof localmaximum(peaksor valleys).

The holding methodof an instrument can be chosenwith two principles: Simulatetheholdingduringnormalplayingor to have aslittle externalinfluenceaspossible.Dif-ferentholdingshave beenexperimented,theuseof flexible rubberbandswith very lowmodefrequenciesapproximatestheno-holdingstate(Elejabarrieta,Ezcurra& Santamaría2000).

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Thereare differentways for exciting the instrument. Constructorsstill usetappingof the instrumentto evaluatea coarseresponseof the body, exciting the edgeof plateswith a violin bow was a commonprocedure. For scientific purposesit is commontohave an impulsegeneratedwith a hammercontaininga transducerto registerthe force.Soft andhardtip arecompared,see(Huang2000). A small magnetgluedto the bodyandexcitedwith a coil or a shaker aremethodsthatrequireanexternalexcitationsignal.The excitation can be generatedwith MLS (maximum length sequence)or sinusoidalsignalssweptin frequency (Müller & Massarani2001). Advantagesanddrawbacksofthemethodsarediscussed.

Soundradiationis recordedwith microphonein ananechoicroom.Theanechoicroomprovidesa clearview of the radiationminima. Themainproblemwith this recordingisthat it is necessaryto have a strongexcitation signaland it is highly dependentof theradiationpatternof theinstrument. To overcome theseproblemswe cantake theaverageof signalsfrom severaldirections.(Janssonet al. 1986).

Recordingthetransferfunctionsmustbecarriedoutwith aslitt le influenceaspossibletrying not to add extra resonancesor drift in the existing ones. We can evaluatethemodalpatternsby measurementof thetransferfunctionfrom thebridgeto severalpointsof thesurface(Janssonet al. 1986)usinganaccelerometeror usingopticalmethodsforvibrationanalysis(Runnemalm,Molin & Jansson2000). Thelatteroneis in principleagoodmethodbecauseit doesnot interferewith thevibrationof theinstrument.

Finally, oneof the studiedmethodsis chosento perform the analysisof the Saz,along-necklute from Turkey, andthePortugueseguitar.

1. PHYSICAL PARAMETERS AND MODAL ANALYSIS

1.1. Mechanical Admittance

Impedanceis a widely usedconceptamongengineers.Introducedin 1890by OlivierHeavisidein electricalengineering(Beyer1998)it wassoonextendedto otherdisciplines.Impedanceis aparameterthatrelatestwo quantitieslinearly, andusuallyhelpsto simplifytheanalysisof complex systems. In mechanicsit is definedby

���� �� �� � ��� ���where��

is theoutputforce�� is theinputvelocityMechanicaladmittancemeasuresthegeneralizedvelocitiesof asystemundergeneral-

izedforces(Boutillon & Weinreich1999).If werestrictouranalysisto aone-dimensionalsystem,asin electricalcircuit theory, therelationshipbetweentheconceptsis very sim-ple, the admittancebeing the mathematical inversefunction of the impedance.For asystemwith threedegreesof freedomthegeneralizationis notsoeasyto accomplish.Theimpedanceis a3x3matrixwhichmapsthevelocity vectorof apointdecomposedinto itsthreecomponentsontotheforceappliedto thepoint.�� ���������

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��(1)

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Theadmittancematrix canbededucedfrom theinverseof the impedancematrix. If oneis expectingto extract theimpedancefrom letting a surfacevibrateonly in onedirectionandrecordingtheforcein thesamedirection,hemustknow thatheis only computing oneelementof the diagonalof thematrix. It mayhappenthat forcesin otherdirectionsareinvolvedandthereciprocalof this diagonalelementdoesn’t producea physicallymean-ingful resultfor the velocity. Anotherpracticalproblemis the impossibility of excitinga singlepoint. Thereforethreeadditionaldegreesof freedomhave to be introducedtoproperlyrepresentthedynamicof arigid body. In thiscase,theadmittancedeterminationbecomes: ())))))

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with1

beingtherotationtermsandT thetorques.In practicethereis arequirementfor measurementof theimpedanceof zerovelocityin

all otherports.Thusif ahammeris usedin thistaskit shouldbeveryheavy or constrainedto moveonly in onedirection,which is animpossiblecondition to meet.Thatis why it iseasierto measuretheadmittance.

1.2. Radiated Sound

Radiatedsoundis obtainedby measurementof the total radiatedsoundpressurewhena given excitation is appliedto the instrument. It is fundamentalto do the recordingsin ananechoicchamberin orderto have a high signal-to-noiseratio (SNR)andto haveameasurementfreeof contaminatingreflections.Radiatedsoundis veryimportantfrom thesynthesisandrecordingpoint of view. In physicalmodeling of instrumentstherecordedsoundis ofteninversefilteredto extractthemodel’sexcitationsignals.Moreover its studyhelpssoundrecordingtechniciansto placethemicrophonesin themostsuitableposition.

1.3. Modal Analysis

Structuralpartsof musicalinstrumentscanbeseenascomplex mass-springsystemsthatvibrate with a patternwhen stimulated at resonancefrequencies. In the 18th centuryChladniregisteredpatternsof vibrationin platesby clampingsomepointsof thesurfaceandexciting theplatewith aviolin bow. Thisprocedureis similar to theexcitationof thehighermodesof a stringthatarealsocalledovertones:onepoint is clamped(node)andoneof thefreepointsis pluckedor bowed. In a surfacethepatternwill becomposedofnodallines(pointsof novibration) andcorrespondingpeaksof vibration.

Thenameof themodes( MONQP ) is relatedto thenumberM of verticalnodallinesand Pof horizontallines.

HutchinsandJanssonhave mappedcarefully the patternsof many differentkinds ofviolins andnowadayssomeconstructorstuneviolin platesapplyingthis techniquebeforeassemblingtheinstrument. A veryinterestingstudyof thepatternsduringtheconstructionprocessof thetopplateandbracingof theclassicalguitaris presentedin (Elejabarrietaetal. 2000).

Modalanalysisis usuallyperformedaimingacertainpartof theinstrument.Thebodyis a preferredpart, but also the bridge,which hasa major role in the transmittanceof

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Figure1: Rectangularplateandviolin backexcitedin themode(0,2)

thesound,andneckaresubjectto analysis(Boullosa2001).Modalanalysiscanbedoneby recordingthetransferfunctionsfrom theexcitedbridgeto anaccelerometerplacedinmany differentpoints in the instrument.As this transferfunction is a linearsystem,onecaninterchangethe inputsandoutputs andrecordthebridgeaccelerationwhenexcitingthe body at specificpoints. An alternative that is becomingmorefrequentis the useofholographicinterferometryor TV holography. Therearemany advantagesin thismethodsthatwill bediscussedfurtheron.

2. MEASUREMENT PROCEDURES

2.1. Holding of the instrument

Theholdingof the instrumentis anaspectthatcaninfluenceits vibration. For measure-ment proceduresit is commonto searchfor a methodthat lets the instrumentvibratefreely. Janssonat theKTH (Royal Institute of Technologyof Stockholm) andHutchins(Hutchins1997)whohasbeenmeasuringtheviolin family for many years,useveryflex-ible rubberbandsin thesupportof theinstrument.Therubberbandshavevery low reso-nancefrequenciesthatdonot interferewith therangeof frequency desired(Elejabarrietaet al. 2000). The problemwith this methodis thesteadinessof the instrument,becauseif it moves,thereproducibility of theexperienceis affected(Janssonet al. 1986)andthesteadinessis critical in theopticalexperiments.

Anotherpossibility is to softly clampthe instrumentin theheadwith a sticky rubber,asin theDünwald method(Dünwald 1982)or clampat theheadandhold thebodyon aplasticspongein PTB method(Lottermoser& Jenkner1971).Theclampingis necessaryfor the lasermeasurementsbut it changesthe level andfrequency of theresonancesandmayeveneliminatesomeof them,asis thecaseof theC3resonancein theviolin measuredwith theDünwaldmethod.Althoughnoneof thesemethodsinfluencesasmuchashavingtheinstrumentheldin aplayingposition.

2.2. Excitation

Theexcitationprocessfor measurementof loudspeaker’s impulseresponsesis somehowaneasyprocedurebecausethesignalcanbefedelectricallyto thedeviceundertest(DUT)thatconvertsit to acousticalwaves. String instrumentscanbeexcitedby a loudspeaker,but this processis not so closely relatedto what happensin playing conditions. Themotionof thestringdoesnot radiatemuchto theair, andthesoundheardcomesmainlyfrom the vibration of the soundboardand air motion inside the cavity. The string is

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coupledto the sound-boardthroughthe bridge,being the excitation signal transmittedthroughthispartof theinstrument.

Wecanevaluatethephysicalproperties,likesoundradiationormechanicaladmittance,by playingthe instrument, with a plectrum,finger, or bow, or usingmechanicalsystemsto convey severalsignalpossibilities to thebridge.

2.2.1. Signals

Most of the methodsaim to computethe impulse responseor frequency responseof aparticularpart of the instrument. One possibility is to usea signal, rich in frequencycomponents,asinput ROSUT V to computeits FFT andtheoutput’s, andthendivide:W SYX3V!Z\[ SYX3V] SYX3V (3)

For mostof thecasestwo FFTshave to becalculatedin eachexperiment.An impulseis the naturalsignalto useto computethe impulseresponse(IR). If the

impulse is notproducedin a deterministic way, asin themajority of thecases,theexper-imentshouldberepeatedmany timesandthesignalssynchronouslyaveragedto increasetheSNR,correspondingto a 3 dB reductionof uncorrelatednoiseeachtime thenumberof averagesis doubled.A problemwith thesemeasuresis thattypical transducersarenotableto provide impulsiveexcitation with therequiredpower, speciallyin soundradiationmeasures.

Many othersignalscanbeusedfor thispurpose.For instance,signalswith whitespec-trum allow theuseof crosscorrelationto computethespectrumof thesignal(Müller &Massarani2001).Maximum LengthSequence(MLS) isveryeasytogeneratein hardwareandconsistsof a signalwith ^`_badc valuesthat arerepeatedperiodicallyasan impulsetrain. As a resultat all frequenciestheMLS hassimilar amplitude,which meansthat itsspectrumis white. This canalsobeseenin theautocorrelationfunctionof theMLS thatis closeto a Dirac pulse.Comparingto theimpulse,asanexcitation,muchmoreenergycanbe fed to the systemin the time domainasthe signalis stretchedout over the holemeasurementperiod. MLS benefitsof analgorithmin thetime domain(Hadamard)thatenablesthecomputationof theIR veryquickly.

Anotherpossibility is to usearbitrary ^fe sequences.They have an advantagein re-lation to thegeneraltwo-channelFFT techniquebecausethey arepseudo-randomnoise,meaningthatthesignalis known in advance.Theconsequenceis thatweneedto computeits FFTonly onceandthemethodis deterministic, nothaving thenecessityof reproducingit many timeswhich is commonin thedual-channelcase(Müller & Massarani2001).

Althoughnoisebasedexcitationstendto savememoryandprocessingtimethey donothave sogoodresolution, thesoundlevel is low, andunavoidablyleadto thedistribuitionof distortion productsover theperiodof measurement.Sweptsinewavesovercomesthisproblems,anddo not consumeso much time as the old stepedsinewavesmethod,inwhich the signalhad to remainabsolutelyperiodic for one FFT block. With sweeps,harmonicdistortion nonlinearitiesareeasyto isolatefrom the impulse responseof theDUT. A detailedexplanation is presentedin (Müller & Massarani2001).

2.2.2. Impact hammer

The impact hammeris a widely usedmethodof excitation in the literaturesinceit issimple to useanddoesnot producea massload to the system. However it hasmany

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Figure2: Exampleof a sweptsinefunction

drawbacks,for instancethereproducibilityof theexcitationisquitedifficult andtheattackangleis notprecise.A pendulum maybeusedfor attainingmoreaccurateresults,in-spiteof the rotationterm that should be taken into account.Also frequency rangeis limitedandthe energy in the high frequenciesis low. The big advantageof the hammerariseswhenwehave to performmodalanalysisandrecord50or morepointsalongthebodyoftheinstrument,asit is easyto changethehitting point.

In measurementsperformedat theLaboratoryof AcousticsandAudio andSignalPro-cessingof Helsinki University of Technology(HUT) anddescribedin (Huang2000),anICP R

gImpulse-ForceTestHammerwasusedtoexcitetheKantele,aFinnishstringinstru-

mentthatexistedfor a few thousandyears,from thefamily of theBaltic psaltery(Peekna& Rossing2001). Two differenttips wereusedin thehammer. Theresponseof thesoftvinyl tip presentedpoorerfrequency rangethanthemetalone(rangesandgraphs).How-ever thevinyl tip hastheadvantageof avoidingdamagesto theinstrumentandof excitingonesingletime thebody. With thehardtip a broadrangein frequency canbeproducedbut sometimesthehammerhits twice the instrumentcausinga notchfilter effect cuttingsomefrequencies.

2.2.3. Shaker

Thefollowing methodsareparticularlyinterestingif onechoosesto compute thetransferfunctionwith signalsotherthanimpulses.

The excitation with shaker is basedon a driven point with contactfrom a vibratingdevice. JanssonandMeyer (Janssonet al. 1986)do ananalysisof thesystemusedin thePhysiskalish-TechnischeBundesanstalt,Braunschweig,referred to asPTB.TheLing 100vibratorfrom thissystemhasa ratherhighdynamicmass(7g)andaresonancefrequencyin therangeof 80 Hz. Thepositive aspectis that it providesa high soundpressurelevel(SPL),whichmakesit asuitablemethodfor recordingit.

2.2.4. Magnet driven by coil

ThismethodwasdevelopedattheKTH laboratoryin Stockholmandis describedin (Jans-sonet al. 1986). It is intendedto excite vertically thebridgeof a violin andconsistsof acoil thatproducesa magneticfield that interactswith a smallmagnetfastenedwith waxneartheG string. Themainadvantageof this schemeis that it is a very light device (thecobalt-sasamariummagnetweights0.24g)thatdoesnot addany resonancesto thebody.

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The measuringschemeis speciallysensitive to distanceand requiresvery low drivingforceswhich resultsin low soundlevels.

2.3. Recording

2.3.1. Accelerometer

Accelerometersaretransducersthatconvert acceleration into anelectricsignal.They aremadefrom piezoelectricmaterialsandarewidely usedto measurevibrations.Therearemany differentkindsof accelerometersavailablein themarket. They arechosenaccordingto their weightandflatnessin the response.Usually, lighter accelerometershave worseresponsein thelow frequencies.If theaccelerometeris heavy, theresponseimproves butthebodyof themusicalinstrumentis loadedwith amassthatcanchangetheplaceof theresonancesof theinstrument.

2.3.2. Microphone

From the synthesispoint of view it is very important to measure,not only the bridgeparametersandtransferfunction to the restof thebody, but thesoundpressureradiatedwhena string is pluckedor bowed. Themicrophoneshouldbeplacedat 1 meterasthischoicerepresentsa compromisebetweenthemeasurementof the far field (which is notreally possible becausethe wavelength h shouldbe at leastten timessmallerthan thedistancei ), andobtainingenoughsignalto noiseratio.

2.3.3. Laser Vibrometer

In evaluatingthevibrationcharacteristics,lasermeasurementsarepreferredto any othersschemes.Thereis no load on the instrument while it is vibrating, which makes it analmostperfectmeasurementsystem. Nevertheless, the sensibility of the laserrequiresa rigid holding for obtaining precisemeasurements.The laservibrometermeasuresthedisplacementof a reflectingsurface(silver stickersaregluedto theplatesor pegsof theinstrument). Far from Chladni’s first experimentsin modalanalysis,a techniquecalledholographicinterferometrywasdevelopedandenablesvisualizationof amplitudesaswellasnodal lines asis shown in Fig. 3. Two beamsof light proceedfrom a laser: oneiscalledthereferencebeamandis directedto theholographicplateby a reflectingmirror;theotherbeamis reflectedfrom thevibratingobjectbeforegoingto theplate.Thedelayin thesecondbeamcausedby thedisplacementof theinstrument’s surfacecausessignalcancellationor addingbetweenthetwo beamsresultingin thehologram(Cremer1985).

3. THE PORTUGUESE GUITAR AND THE TURKISH SAZ

3.1. The Portuguese Guitar

The Portugueseguitar is an instrument consideredby CaldeiraCabral(V. de Oliveira2001)asbeinga fusionbetweenthewesternEuropeancithernfrom the17jlk centuryandtheEnglishguitar. It has12stringsdividedin setsof two thatareplayedat a time. Threesetsaretunedin unisonandtheremainingthreearetunedin octaves.

Theinstrumenthasamovablebridgelike theonesof its family andtheneckhasmetalfrets. Theplayingtechniqueof the left handis similar to instrumentslike theguitarandtheright handtechniqueconsistsof theusageof thethumbin theold “figeta” stylewhile

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LASER

HOLOGRAM PLATE

Figure3: Arrangementfor time-averageholography

String Pitch Frequency [Hz] Gauge Type1mon A4 440 0.011 plainsteel2pGq A4 440 0.011 plainsteel3r"q G4 392.00 0.012 plainsteel4nls G4 392.00 0.012 plainsteel5nls D4 293.66 0.015 plainsteel6nls D4 293.66 0.015 plainsteel7nls A3 220 0.022 woundsteel8nls A4 440 0.011 plainsteel9nls G3 196 0.024 woundsteel10nls G4 392.00 0.012 plainsteel11nls C2 130.81 0.038 woundsteel12nls C2 261.63(130.81) 0.018(0.022) plainsteel(orwoundsteel)

Table1: 12steelstrings- pitchandstringgaugefor Coimbra’sPortugueseguitar

theindex fingerplucksthestringbackandforth. Theleft handthumbis usedfor frettingthe6thcourseof stringsbeinganessentialpartof theharmony.

Mostof theplayersuseanartificial fingernail madeof turtleshellor celluloid.

To gain familiarity with the measurementprocedurewe chosesomepoints of thesoundboardto computethe impulse responseswith a simplehammer(pencil)anda mi-crophoneB&K, type4191with preamplifiertype2669.Is wasvery importantto preparethesetupbeforeenteringtheanechoicroom,andspecialconcernaboutsmallobjectsisnecessary, in ordernot to dropanythingontothelowerwedges.All thecableconnectionsmustbeisolatedfrom thesteelgrid.

Thegraphicsarein appendixin Fig. 6, andevenwith suchacoarseexperimentwecanseetheresonancescaracteristicof stringinstruments.

Thereis alsoa graphin Fig.(9) with the frequency responseof a pluck in the lowerpitchedG stringsrecordedin anormalfurnishedroomwith a“Shure”microphone,modeltGuwv`x at 30cm distantfrom thesoundboard.

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H

A

C

B

D

F

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G

Figure4: Pictureof aPortugueseguitarandpoints hit duringtheexperiment

Figure5: Two setupsfor measurementsof thesazin anechoicchamber

3.2. The Turkish Saz

TheSazis aninstrumentfrom thefamily of thelong-necklutes,which includetheGreek(andIrish) Bouzouki,IndianSitar, AfghanTumbur, DamburaandDutar, andthePersianSetar.

It’ s ancestor, thekopuz,is first referred in writings of the8y{z centuryandis differentfrom thesazfamily in thesensethatit hadthebodycoveredwith leather, thestringsweremadeoutof horsehair andit hadno frets.

Sazmeansmusicalinstrument in Persian.It is a traditional instrument from Turkeyandtherearemany differentsizesfor it, but all havecommoncharacteristicssuchas:Thebody of the instrument is almond-shaped,typically madeof a singlepieceof mulberrywood, with or without sound-hole. The instrumenthasthin neck with tied, movable,nylon frets,andasmallbridgemadeof wood.Most instrumentshave3 doublecoursesofmetalstringswith the3rdcoursedoubledin octaves.Thebaglamamodelhasanadditionalthird stringin thefirst course,oneoctave lower thantheothers.

The mostcommontuning schemeis G D A, startingfrom the 3rd course,but othertuningsareused,suchas:E D A, G D G, A D A, A E A, A D G, andmany others.The

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String Pitch Frequency [Hz] Type1|o} A3 220 plainsteel2~G� A3 220 plainsteel3�"� A2 110 woundsteel4}l� D3 146.83 plainsteel5}l� D3 146.83 plainsteel6}l� G3 196 plainsteel7}l� G2 98 woundsteel

Table2: 7 steelstrings- pitch for theSaz

playing techniqueincludesthe usea soft plectrum,in backand forth movement. Theright handfingershit the soundboardin a rhythmic way, andleft handthumbalsofretsthestringsasin thePortugueseguitar.

Nowadays,constructorsstart to make the body of the instrumentin lute-typestavedjuniperwood. Spruceis usedfor thesoundboard,which is no longercurved, like in thepast,andkelebekwoodfor thefingerboard.

Websourcesaboutthesazcanbefoundat:� http:// www-perso nal.umic h.edu/˜mh uey/instr uments.ht m#saz� http:// home3.swi pnet.se/ %7Ew-35053/sazandb .htm

The measurementsof the sazwereperformedwith an excitationsignalgeneratedbythe impulse-forcehammer, recording,simultaneously, the soundradiatedto the B&Kmicrophone,theaccelerationin a point nearto thebridge,andthe forcesignalfrom thehammer. All measurementdevicesaredescribedin Table3. Themicrophonewasagainplacedat 1 meterfrom thetopand4 experiments werecarriedout. Bothhardandsoft tipfor thehammerwereusedandtheholdingmethodvariedbetweentheuseof rubberbandsor layingit onablanket in theanechoicroom,asshown in Fig. 5. Therubberbandswerequite stretchedandonecould easilyhearthat therewassomecoupling to the body oftheinstrument, sopossibly wecanfind somedifferencesspeciallyin thelow frequencies.Although, for thehammerexcitationJanssonsaysthat thereareno specialrequirementsfor theholding.

Themeasurementof theadmittanceof thebridgeimpliesthattheaccelerometeris hitby thehammer. Evento fastentheaccelerometerin thebridgeis problematic. Insteadwefastenit in thesoundboard,nearbythebridge,andthuscalculatea transferfunctionthatis closeto theadmittance.

Oneevidenceshown in Figs. 7, 8, 9, and10 is the pro-eminenceof the peaksandvalleys for theaccelerometerresults.Anothernoticeablefact is thedifficulty of analysisathighfrequencies.Thehigherthespectrum,themorestrictbecometherequirementsfortheattackanglesandreproducibilityof theexperiment.A deeperanalysisof thegraphicsandexperiments shouldbecarriedout in thefuture.

Acknowledgments

I would like to thankMr. Paulo EsquefandMr. CumhurErkut for the help with themeasurementprocedures,andfor all the discussion aroundthe subject. I would like tothankalsoto ProfessorMatti KarjalainenandMr. PauloEsquefandfor all thesugestions,

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Equipment Manufacturer Type ObservationCondenserMicrophone Brüel&Kjær 4179 highSNRandsensibilityMicrophonePreamplifier Brüel&Kjær 2660MicrophonePowerSupply Brüel&Kjær 2804 usesabatteryof 9VICP R

�Accelerometer PCBR

�Piezotronics 309A 1.1gweight

ICP R�

Impulse Hammer PCB R�

Piezotronics 086C01 100gweightComputerMainframe Hewlett Packard HP E1421B Soft FrontPanelRubberBands hold theinstrumentElectricCables with BNC connectors

Table3: Equipmentandmaterialsusedin themeasurementprocedureof theSaz

comments,and patiencein reviewing the text, and to Mr. Poju Antsalo for teachingme how to usethe anechoicroom. A specialthanksto the MM fund for suportingthisresearch.

4. BIBLIOGRAPHY

Beyer, R. (1998),Sound of Our Times, Springer-VerlagNew York Inc.

Boullosa,R. (2001),Admittancemeasurementsin theneckof a classicalguitar, in D. G.Davide Bonsi & D. Stanzial,eds,‘ISMA 2001Procedings’,The Musical andAr-chitecturalAcousticsLaboratoryFondazioneScuoladi SanGiorgio-CNR,Venezia,Italy, pp.425–429.

Boutillon, X. & Weinreich,G. (1999),‘Three-dimensionaladmittance:Theoryandnewmeasurementmethodappliedto theviolin bridge’,J. Acoust. Soc. Am. 105(6),3524–3533.

Cremer, L. (1985),The physics of the violin, MIT press,CambridgeMassachusetts.transl.J.S.Allen.

Dünwald,H. (1982),‘Messungvongeigenfrequenzgängen’,Acustica.

Elejabarrieta,M. J., Ezcurra,A. & Santamaría,C. (2000),‘Evolution of the vibrationalbehaviour of aguitarsoundboardalongsuccessiveconstructionphasesby meansofthemodalanalysistechnique’,J. Acoust. Soc. Am. 108(1), 369–378.

Huang,P. (2000),Measurementof the kanteleand isolation of bridgebar, tuning peg,andbody resonancesin threeorthogonal polarizations, Technicalreport,HelsinkiUniversity of Technology, Laboratoryof AcousticsandAudio SignalProcessing.

Hutchins, C. (1997), ‘The air and wood modesof the violin’, J. Audio Eng. Soc.46(9), 751–765.

Jansson,E., Bork, I. & Meyer, J. (1986),‘Investigationsinto theacousticalpropertiesoftheviolin’, Acustica, Europhysics Journal 62(1), 1–15.

Lottermoser, W. & Jenkner, E. (1971),‘Vergleishsuchungenandviolinen in denusaundderbrd.’, Instrumentenbauzeitschrift.

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Müller, S. & Massarani,P. (2001), ‘Transfer-function measurementswith sweeps’,J.Audio Eng. Soc. 49(6), 443–471.

Peekna,A. & Rossing,T. D. (2001), The acousticsof baltic psaltery, in D. G. Da-videBonsi& D. Stanzial,eds,‘ISMA 2001Procedings’,TheMusicalandArchitec-tural AcousticsLaboratoryFondazioneScuoladi SanGiorgio-CNR,Venezia,Italy,pp.437–442.

Runnemalm,A., Molin, N.-E. & Jansson,E. (2000),‘On operatingdeflectionshapesoftheviolin bodyincludingin-planemotions’, J. Acoust. Soc. Am. 107(6),3452–3459.

V. deOliveira,E.(2001),Intrumentos Musicais Populares Portugueses, 3rdedn,Bertrand,chapterGuitarraPortuguesa,pp.194–199.

A. GRAPHICS

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Figure7: Frequency responseof thebodyof thesazdueto onehit with hardtip on thebridge,usingrubberbandsasholdingmethod

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103

104

−150

−100

−50

Mag

nitu

de (

db)

Velocity of accelerometer

102

103

104

−60−40−20

020

Mag

nitu

de (

db)

Impulse hammer response

102

103

104

−120

−100

−80

−60

−40

Frequency [Hz]

Mag

nitu

de (

db)

Transfer function from the bridge to acc.

Figure8: Frequency responseof the body of the sazdueto onehit with soft tip on thebridge,usingrubberbandsasholdingmethod

13

102

103

104

−50

0

50M

agni

tude

(db

)

Frequency response with hard tipMicrophone response

102

103

104

−150

−100

−50

Mag

nitu

de (

db)

Velocity of accelerometer

102

103

104

−80−60−40−20

020

Mag

nitu

de (

db)

Impulse hammer response

102

103

104

−140−120−100−80−60−40

Frequency [Hz]

Mag

nitu

de (

db)

Transfer function from the bridge to acc.

Figure9: Frequency responseof thebodyof thesazdueto onehit with hardtip on thebridge,laying theinstrumenton theground

102

103

104

−50

0

50

Mag

nitu

de (

db)

Frequency response with soft tipMicrophone response

102

103

104

−150

−100

−50

Mag

nitu

de (

db)

Velocity of accelerometer

102

103

104

−60−40−20

020

Mag

nitu

de (

db)

Impulse hammer response

102

103

104

−120−100−80−60−40

Frequency [Hz]

Mag

nitu

de (

db)

Transfer function from the bridge to acc.

Figure10: Frequency responseof thebodyof thesazdueto onehit with soft tip on thebridge,laying theinstrumenton theground

14