Flute acoustics: measurement, modelling and - School of Physics

353 Pages·2007·17.32 MB·English

Flute acoustics: measurement, modelling and design
by
Paul A. Dickens
BSc(Hons),Syd
Infulfillment
oftherequirementsforthedegree
DoctorofPhilosophy
SchoolofPhysics
UniversityofNewSouthWales
November2007
Copyright©2007byPaulA.Dickens
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Iherebydeclarethatthissubmissionismyownworkandtothebestofmyknowledgeit
containsnomaterialspreviouslypublishedorwrittenbyanotherperson, orsubstantialpro-
portionsofmaterialwhichhavebeenacceptedfortheawardofanyotherdegreeordiploma
at UNSW or any other educational institution, except where due acknowledgement is made
in the thesis. Any contribution made to the researchby others, with whom I have worked at
UNSWorelsewhere,isexplicitlyacknowledgedinthethesis.Ialsodeclarethattheintellectual
contentofthisthesisistheproductofmyownwork,excepttotheextentthatassistancefrom
othersintheproject’sdesignandconceptionorinstyle,presentationandlinguisticexpression
isacknowledged.
IherebygranttheUniversityofNewSouthWalesoritsagentstherighttoarchiveandto
makeavailablemythesisordissertationinwholeorpartintheUniversitylibrariesinallforms
ofmedia,noworhereafterknown,subjecttotheprovisionsoftheCopyrightAct1968.Iretain
allproprietaryrights,suchaspatentrights.Ialsoretaintherighttouseinfutureworks(suchas
articlesorbooks)allorpartofthisthesisordissertation.IalsoauthoriseUniversityMicrofilms
tousethe350wordabstractofmythesisinDissertationAbstractInternational(thisisapplica-
bletodoctoralthesesonly). Ihaveeitherusednosubstantialportionsofcopyrightmaterialin
mythesisorIhaveobtainedpermissiontousecopyrightmaterial; wherepermissionhasnot
beengrantedIhaveapplied/willapplyforapartialrestrictionofthedigitalcopyofmythesis
ordissertation.
IcertifythattheLibrarydepositdigitalcopyisadirectequivalentofthefinalofficiallyap-
provedversionofmythesis.Noemendationofcontenthasoccurredandifthereareanyminor
variationsinformatting,theyaretheresultoftheconversiontodigitalformat.
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ToRenée
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Acknowledgements
Thisthesiswouldnotbepossiblewithoutthecollaborationandassistanceofmanypeople.
Firstly, many thanks to my supervisor Joe Wolfe, for well-timed encouragement, motiva-
tionandunderstandingthroughoutmycandidature,especiallyregardingthevarieddemands
ofhavingayoungfamily.Joe’scommitmenttointegrityinresearchisapowerfulexample,sup-
portedbyhiswillingcomradeshipthroughmanylaboriouslate-nightsexperiments. Joe(with
Andrew Botros) also conducted the flute tuning measurements of Chapter 7 in my absence.
Thankstomyco-supervisorJohnSmithforhismanyhelpfulinsightsandforsharinghisideas
astheprojectprogressed.JoeandJohncollaboratedwithmeonthewritingofpapersthatpub-
lishedthematerialreportedinChapters3and5. Theircommentsonearlydraftsofthethesis
aremuchappreciated.
ThankstoJohnTannforinvaluableandvariedtechnicalassistance,forapositive,‘can-do’
approachtothemanyproblemsIbroughttohim,andforthemanyilluminatingdiscussions
resultingfrommysometimeserraticandill-formedquestions.
MuchofthesoftwarecodefortheflutemodelisderivedfromtheexcellentworkofAndrew
Botros. Andrewgaveuphisowntimetohelpwithissuesofsoftwaredesignandhisgenerosity
inthisisappreciated.
ThankstoTerryMcGeeandMarkO’Connerforgraciouslyimpartingtheirpracticalknowl-
edgeintheartandscienceofflutemaking, toTerryfortakingmeonasapprenticeforaday
and for being a guinea-pig in the development of the flute design software. Terry’s insights
aboutclassicalflutetuningformpartofthediscussioninChapter9.ThankstothePowerhouse
Museum, Sydney and the museum’s curator of musical instruments, Michael Lee, for access
totheircollectionofinstrumentsaswellasfinancialsupportoftheproject. Thecollaboration
withTerryandMichaelwasmadepossiblethroughanAustralianPostgraduateAward(Indus-
try)grantedbytheAustralianResearchCouncil.
FlutistsJaneCavanagh,CécilevanderBurgh,CaoimheMcMillanandclarinettistCatherine
Youngaddedamuch-neededhumandimensiontowoodwindmodelling.Iamgratefulforthe
wayinwhicheachonecheerfullycooperatedwithuncomfortableandrepetitiveexperiments.
MythankstofellowstudentsintheAcousticslab,particularlyClaudiaFritzandRaInta,for
helpingtokeepmyspiritsupandformanyfascinatingdiscussions(someofwhichwereabout
acoustics).
Ken Jackson and Pritipal Baweja in the Physics workshop turned my hasty sketches into
beautifulcreationsinbrassandaluminium—theiringenuityandcraftsmanshipisappreciated.
IamsupportedbyadiversecommunityofpeoplewithwhomIamlinkedbyourcommon
Christianfaith. IparticularlywishtothankIan,GinaandAmandafortheirhopeful,frequent
andsincereencouragementinthisendeavour, andforhelpingprovideperspectivewhenthe
treesgotinthewayoftheforest.
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Iamgratefultomyparents,RossandValerie,andtomysiblingsandsiblings-in-lawforthe
giftofconstantlove,whichfrequentlytooktheformofweeknightdinners.
Finally,myhumblethankstomywifeRenée. Hersupportandtrustthroughmycandida-
turehasbeenagreatblessingandsourceofstrength. AndtomysonOliver,forhisone-year-
old’ssenseoffun.
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Abstract
A well-made flute is always a compromise and the job of flute makers is to achieve a
musicallyandaestheticallysatisfyingcompromise; ataskthatinvolvesmuchtrial-and-error.
Thepracticalaimofthisthesisistodevelopamathematicalmodelofthefluteandacomputer
programthatassistsintheflutedesignprocess.
Manymusicalqualitiesofawoodwindinstrumentmaybecalculatedfromtheacousticim-
pedancespectrumoftheinstrument. Atechniqueforfastandaccuratemeasurementofthis
quantity is developed. The technique is based on the multiple-microphone technique, and
usesresonance-freeimpedanceloadstocalibratethesystemandspectralshapingtoimprove
theprecisionatimpedanceextrema.Theimpedancespectraofthefluteandclarinetaremea-
sured over a wide range of fingerings, yielding a comprehensive and accurate database. The
impedance properties of single finger holes are measured using a related technique, and fit-
formulaearederivedforthelengthcorrectionsofclosedfingerholesforatypicalrangeofhole
sizesandlengths.
Theboresurfaceofwoodeninstrumentscanchangeovertimewithplayingandthiscan
affecttheacousticimpedance,andthereforetheplayingquality.Suchchangesinacousticim-
pedanceareexploredusingwoodentestpipes. Toaccountfortheeffectofatypicalplayeron
flutetuning,anempiricalcorrectionisdeterminedfromthemeasuredtuningofbothmodern
andclassicalflutesasplayedbyseveralprofessionalandsemi-professionalplayers. Bycom-
biningthemeasuredimpedancedatabasewiththeplayereffectsandvariousresultsinthelit-
eratureamathematicalmodeloftheinputimpedanceofflutesisdevelopedandimplemented
incommand-lineprogramswritteninthesoftwarelanguageC.
Auser-friendlygraphicalinterfaceiscreatedusingthefluteimpedancemodelforthepur-
poses of flute acoustical design and analysis. The program calculates the tuning and other
acousticalpropertiesforanygivengeometry. Theprogramisappliedtoamodernfluteanda
classicalflute. Thecapabilitiesandlimitationsofthesoftwarearetherebyillustratedandpos-
siblecontributionsoftheprogramtocontemporaryflutedesignareexplored.
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Contents
Dedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
Acknowledgements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
CHAPTERS
I Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Introductiontofluteacoustics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Theflutemaker,thecuratorandthesoftwareengineer . . . . . . . . . . . . . . . . . . 2
1.3 ‘FluteCAD’:takingtheguessworkoutofflutedesign . . . . . . . . . . . . . . . . . . . . 3
1.4 Howfluteswork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.5 Acousticimpedance: predictingtheplayingqualitiesofaflute . . . . . . . . . . . . . . 6
1.6 Tuning,traditionandthe‘standardflutist’ . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.7 Softwareimplementation: goalsandlimitations. . . . . . . . . . . . . . . . . . . . . . . 8
1.8 Guidetothethesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
II Theoryandliteraturereview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.1 Flutesandflutemaking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2 Acousticsofwoodwindinstruments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3 Computermodels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
III Measuringacousticimpedance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2 Reviewofmeasurementtechniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.3 Theoryofacousticimpedancemeasurements . . . . . . . . . . . . . . . . . . . . . . . 32
3.4 Calibrationofimpedanceheads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.5 Errors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.6 Optimisationoftheoutputsignal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.7 Materialsandmethods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.8 Resultsanddiscussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
IV Fingerholeimpedancespectraandlengthcorrections . . . . . . . . . . . . . . . . . . 53
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.2 Materialsandmethods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.3 Resultsanddiscussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
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4.4 Conclusionsandfurtherdirections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
V Impedancespectraofthefluteandclarinet . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.2 Materialsandmethods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.3 Resultsanddiscussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
VI Materialandsurfaceeffects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
6.2 Materialsandmethods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
6.3 Resultsanddiscussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
6.4 Furtherinvestigations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .102
VII Theembouchureholeandplayercorrections . . . . . . . . . . . . . . . . . . . . . . . . 103
7.1 Playerimpedancecorrections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .103
7.2 Modernflutetuning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .104
7.3 Correctionfactor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .106
7.4 Applicationtotheclassicalflute . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .107
7.5 Conclusionsandfurtherdirections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .108
VIII Softwareimplementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
8.1 Theimpedancemodel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .111
8.2 Theuserinterface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .119
IX Applicationsandfurtherdirections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
9.1 Addinganewholetothemodernflute . . . . . . . . . . . . . . . . . . . . . . . . . . .127
9.2 Eight-keyflutebyRudall&Rose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .132
9.3 Conclusionsandfurtherdirections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .138
AppendixA—Impedancespectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
AppendixB—Programlistings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
AppendixC—Quantifyingmusic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339