The Haskell School of Music: From Signals to Symphonies

384 Pages·2018·3.76 MB·english

by  Paul Hudak

TheHaskellSchoolofMusic
Thistextbookexploresthefundamentalsofcomputermusicandfunctional
programmingthroughtheHaskellprogramminglanguage.Functionalprogrammingis
typicallyconsidereddifficulttolearn.Thisintroductioninthecontextofcreating
musicwillallowstudentsandprofessionalswithamusicalinclinationtoleveragetheir
experiencetohelpunderstandconceptsthatmightbeintimidatinginmoretraditional
computersciencesettings.Conversely,thebookopensthedoorforprogrammersto
interactwithmusicbyusingamediumthatisfamiliartothem.
ReaderswilllearnhowtousetheEuterpealibraryforHaskell(www.euterpea.com)
torepresentandcreatetheirownmusicwithcode,withouttheneedforothermusic
software.Thebookexplorescommonparadigmsusedinalgorithmicmusic
composition,suchasstochasticgeneration,musicalgrammars,self-similarity,and
real-timeinteractivesystems.Othertopicscoveredincludethebasicsofsignal-based
systemsinHaskell,soundsynthesis,andvirtualinstrumentdesign.
paul hudakwasaprofessorofcomputerscienceatYaleUniversity,Connecticut,
from1982to2015.Hewasbestknownforhiscontributionstothedevelopmentofthe
Haskellprogramminglanguage.Askilledsaxophonistandjazzmusician,Hudakhad
usedacombinationofhisenthusiasmformusicandcomputersciencetocreatethe
EuterpealibraryforrepresentingmusicinHaskell.
donya quickisResearchAssistantProfessorofMusicandComputationat
StevensInstituteofTechnology,NewJersey.Herresearchexplorestheintersectionof
artificialintelligenceandcomputationallinguisticswithmusic,andincludesworking
onanautomatedcompositionsystemcalledKulitta.Inaddition,sheisalsoinvolvedin
theMUSICAprojectforinteractiveimprovisationandcompositionbyconversion,
whichispartoftheDAPRACommunicatingwithComputersprogram.

The Haskell School of Music
From Signals to Symphonies
PAUL HUDAK
DONYA QUICK
StevensInstituteofTechnology
UniversityPrintingHouse,CambridgeCB28BS,UnitedKingdom
OneLibertyPlaza,20thFloor,NewYork,NY10006,USA
477WilliamstownRoad,PortMelbourne,VIC3207,Australia
314–321,3rdFloor,Plot3,SplendorForum,JasolaDistrictCentre,NewDelhi–110025,India
79AnsonRoad,#06–04/06,Singapore079906
CambridgeUniversityPressispartoftheUniversityofCambridge.
ItfurtherstheUniversity’smissionbydisseminatingknowledgeinthepursuitof
education,learning,andresearchatthehighestinternationallevelsofexcellence.
www.cambridge.org
Informationonthistitle:www.cambridge.org/9781108416757
DOI:10.1017/9781108241861
©PaulHudakandDonyaQuick2018
Thispublicationisincopyright.Subjecttostatutoryexception
andtotheprovisionsofrelevantcollectivelicensingagreements,
noreproductionofanypartmaytakeplacewithoutthewritten
permissionofCambridgeUniversityPress.
Firstpublished2018
PrintedintheUnitedStatesofAmericabySheridanBooks,Inc.
AcataloguerecordforthispublicationisavailablefromtheBritishLibrary.
LibraryofCongressCataloging-in-PublicationData
Names:Hudak,Paul,author.|Quick,Donya,author.
Title:TheHaskellschoolofmusic:fromsignalstosymphonies/PaulHudak,DonyaQuick.
Description:Cambridge,UnitedKingdom;NewYork,NY:
CambridgeUniversityPress,2018.|Includesbibliographicalreferencesandindex.
Identifiers:LCCN2018016879|ISBN9781108416757(hardback:alk.paper)
Subjects:LCSH:Haskell(Computerprogramlanguage)|Computermusic–Instruction
andstudy.|Functionalprogramming(Computerscience)
Classification:LCCML74.4.H37H842018|DDC781.3/45133–dc23
LCrecordavailableathttps://lccn.loc.gov/2018016879
ISBN978-1-108-41675-7Hardback
CambridgeUniversityPresshasnoresponsibilityforthepersistenceoraccuracy
ofURLsforexternalorthird-partyinternetwebsitesreferredtointhispublication
anddoesnotguaranteethatanycontentonsuchwebsitesis,orwillremain,
accurateorappropriate.
Contents
Preface pagexi
Acknowledgments xvi
1 ComputerMusic,Euterpea,andHaskell 1
1.1 TheNoteversusSignalDichotomy 2
1.2 BasicPrinciplesofProgramming 3
1.3 ComputationbyCalculation 4
1.4 ExpressionsandValues 8
1.5 Types 9
1.6 FunctionTypesandTypeSignatures 11
1.7 Abstraction,Abstraction,Abstraction 12
1.8 HaskellEqualityversusMusicalEquality 21
1.9 CodeReuseandModularity 22
1.10 [Advanced]ProgrammingwithNumbers 23
2 SimpleMusic 27
2.1 Preliminaries 27
2.2 Notes,Music,andPolymorphism 29
2.3 ConvenientAuxiliaryFunctions 34
2.4 AbsolutePitches 39
3 PolymorphicandHigher-OrderFunctions 42
3.1 PolymorphicTypes 42
3.2 AbstractionoverRecursiveDefinitions 44
3.3 Append 47
3.4 Fold 49
3.5 [Advanced]AFinalExample:Reverse 54
3.6 Currying 56
3.7 Errors 60
v
vi Contents
4 AMusicalInterlude 63
4.1 TranscribinganExistingScore 63
4.2 Modules 65
4.3 TranscribingaMoreComplexScore 67
4.4 SimpleAlgorithmicComposition 72
5 SyntacticMagic 74
5.1 Sections 74
5.2 AnonymousFunctions 75
5.3 ListComprehensions 77
5.4 FunctionComposition 80
5.5 Higher-OrderThinking 81
5.6 InfixFunctionApplication 82
6 MoreMusic 84
6.1 DelayandRepeat 84
6.2 InversionandRetrograde 85
6.3 ComputingDuration 87
6.4 Super-Retrograde 87
6.5 cutandremove 88
6.6 RemovingZeros 89
6.7 TruncatingParallelComposition 91
6.8 Trills 93
6.9 GraceNotes 95
6.10 Percussion 95
6.11 AMapforMusic 97
6.12 AFoldforMusic 99
6.13 ComplexRhythms 100
6.14 CrazyRecursion 101
7 QualifiedTypesandTypeClasses 104
7.1 Motivation 104
7.2 Equality 106
7.3 DefiningOurOwnTypeClasses 108
7.4 Haskell’sStandardTypeClasses 113
7.5 OtherDerivedInstances 118
7.6 TheTypeofplay 121
7.7 ReasoningwithTypeClasses 122
8 FromMusictoMIDI 125
8.1 AnIntroductiontoMIDI 125
Contents vii
8.2 MIDIStreams 128
8.3 Euterpea’sPlaybackFramework 129
9 InterpretationandPerformance 134
9.1 AbstractPerformance 134
9.2 Players 139
9.3 PuttingItAllTogether 144
10 Self-SimilarMusic 148
10.1 Self-SimilarMelody 148
10.2 Self-SimilarHarmony 152
10.3 OtherSelf-SimilarStructures 153
11 ProofbyInduction 156
11.1 InductionandRecursion 156
11.2 ExamplesofListInduction 157
11.3 ProvingFunctionEquivalences 159
11.4 UsefulPropertiesonLists 162
11.5 InductionontheMusicDataType 166
11.6 [Advanced]InductiononOtherDataTypes 170
12 AnAlgebraofMusic 175
12.1 MusicalEquivalence 175
12.2 SomeSimpleAxioms 177
12.3 TheFundamentalAxiomSet 180
12.4 OtherMusicalProperties 182
13 L-SystemsandGenerativeGrammars 184
13.1 ASimpleImplementation 185
13.2 AMoreGeneralImplementation 187
13.3 AnL-SystemGrammarforMusic 189
14 RandomNumbers,ProbabilityDistributions,and
MarkovChains 193
14.1 RandomNumbers 193
14.2 ProbabilityDistributions 196
14.3 MarkovChains 202
15 BasicInput/Output 205
15.1 IOinHaskell 205
15.2 doSyntax 206
15.3 ActionsAreJustValues 208
15.4 ReadingandWritingMIDIFiles 210
viii Contents
16 Higher-OrderTypesandMonads 211
16.1 TheFunctorClass 211
16.2 TheMonadClass 213
16.3 TheMonadPlusClass 221
16.4 StateMonads 222
16.5 TypeClassTypeErrors 225
17 MusicalUserInterfaces 227
17.1 Introduction 227
17.2 BasicConcepts 228
17.3 TheUISFArrow 233
17.4 Non-WidgetSignalFunctions 242
17.5 MusicalExamples 246
17.6 SpecialPurposeandCustomWidgets 251
17.7 AdvancedTopics 256
18 SoundandSignals 262
18.1 TheNatureofSound 262
18.2 DigitalAudio 273
19 Euterpea’sSignalFunctions 282
19.1 TheTypeofAudioSignals 282
19.2 GeneratingSound 289
19.3 Clipping 290
19.4 Instruments 292
20 SpectrumAnalysis 299
20.1 Fourier’sTheorem 299
20.2 TheDiscreteFourierTransform 305
20.3 TheFastFourierTransform 315
20.4 FurtherPragmatics 317
21 AdditiveandSubtractiveSynthesis 318
21.1 AdditiveSynthesis 319
21.2 SubtractiveSynthesis 326
22 AmplitudeandFrequencyModulation 331
22.1 AmplitudeModulation 331
22.2 FrequencyModulation 334
22.3 Examples 334
23 PhysicalModeling 336
23.1 Introduction 336
Contents ix
23.2 DelayLines 336
23.3 Karplus-StrongAlgorithm 340
23.4 WaveguideSynthesis 343
AppendixA ThePreludeListModule 346
AppendixB Haskell’sStandardTypeClasses 355
AppendixC Built-InTypesAreNotSpecial 365
AppendixD Pattern-MatchingDetails 367
AppendixE HaskellQuickReference 370
AppendixF EuterpeaQuickReference 373
AppendixG HSoMQuickReference 377
Bibliography 379
Index 381