A Computer Model for the Schillinger System of Musical Composition

137 Pages·2012·1.568 MB·English

by  Matthew Rankin

A Computer Model for the
Schillinger System of Musical
Composition
Matthew Rankin
A thesis submitted in partial fulfillment of the degree of
Bachelor of Science (Honours) at
The Department of Computer Science
Australian National University
August 2012
(cid:13)c MatthewRankin
Exceptwhereotherwiseindicated,thisthesisismyownoriginalwork.
MatthewRankin
28August2012

Acknowledgements
The author wishes to sincerely thank Dr. Henry Gardner for his extremely valuable
assistance, insight and encouragement; Dr. Ben Swift also for his continuous encour-
agement and academic mentorship; Jim Cotter for igniting what was a smouldering
interest in algorithmic composition and more recently providing participants for the
listeningexperiment;andMiaforherunyielding,belligerentoptimism.
v

Abstract
A system for the automated composition of music utilising the procedures of Joseph
Schillinger has been constructed. Schillinger was a well-known music theorist and
composition teacher in New York between the first and second World Wars who de-
veloped a formalism later published as The Schillinger System of Musical Composition
[Schillinger1978]. Inthepastthetheoriescontainedinthesevolumeshavegenerally
not been treated in a sufficiently rigorous fashion to enable the automatic genera-
tion of music, partly because they contain mathematical errors, notational inconsis-
tencies and elements of ‘pseudo-science’ [Backus 1960]. This thesis presents ways of
resolvingtheseissuesandacomputersystemwhichcangeneratecompositionsusing
Schillinger’s formalism. By means of the analysis of data gathered from a rigorous
listening survey and the results from an automatic genre classifier, the output of the
systemhasbeenvalidatedaspossessingintrinsicmusicalmeritandcontainingarea-
sonable degree of stylistic diversity within the broad categories of Jazz and Western
Classical music. These results are encouraging, and warrant further development of
thesoftwareintoaflexibletoolforcomposersandcontentcreators.
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viii
Contents
Acknowledgements v
Abstract vii
1 Background 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 IntroductiontotheSchillingerSystem . . . . . . . . . . . . . . . . . . . . 2
1.2.1 SchillingerinComputer-aidedCompositionLiterature . . . . . . 3
1.2.2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2.3 Criticism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 SummaryofthisThesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2 OverviewofComputer-aidedComposition 7
2.1 DominantParadigmsinComputer-aidedComposition . . . . . . . . . . 9
2.1.1 StyleImitationversusGenuineComposition . . . . . . . . . . . . 9
2.1.2 Push-buttonversusInteractive . . . . . . . . . . . . . . . . . . . . 10
2.1.3 Data-drivenversusKnowledge-engineered . . . . . . . . . . . . . 11
2.1.4 MusicalDomainKnowledgeversusEmergentBehaviour . . . . . 12
2.2 FormalComputationalApproaches . . . . . . . . . . . . . . . . . . . . . 12
2.2.1 MarkovModels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2.2 ArtificialNeuralNetworks . . . . . . . . . . . . . . . . . . . . . . 15
2.2.3 GenerativeGrammarsandFiniteStateAutomata . . . . . . . . . 16
2.2.4 Case-basedReasoningandFuzzyLogic . . . . . . . . . . . . . . . 18
2.2.5 EvolutionaryAlgorithms . . . . . . . . . . . . . . . . . . . . . . . 20
2.2.6 ChaosandFractals . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.2.7 CellularAutomata . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.2.8 SwarmAlgorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.3 TheAutomatedSchillingerSysteminContext . . . . . . . . . . . . . . . 27
3 ImplementationoftheSchillingerSystem 29
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.1.1 ABriefRefresher . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.1.2 TheImpromptuEnvironment . . . . . . . . . . . . . . . . . . . . . 31
3.2 TheoryofRhythm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.2.1 RhythmsfromInterferencePatterns . . . . . . . . . . . . . . . . . 32
3.2.2 SynchronisationofMultiplePatterns. . . . . . . . . . . . . . . . . 34
3.2.3 ExtendingRhythmicMaterialUsingPermutations . . . . . . . . . 34
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3.2.4 RhythmsfromAlgebraicExpansion . . . . . . . . . . . . . . . . . 35
3.3 TheoryofPitchScales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.3.1 FlatandSymmetricScales . . . . . . . . . . . . . . . . . . . . . . . 36
3.3.2 TonalExpansions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.3.3 Nearest-Tonevoice-leading . . . . . . . . . . . . . . . . . . . . . . 38
3.3.4 DerivingSimpleHarmonicProgressionsFromSymmetricScales 40
3.4 VariationsofMusicbyMeansofGeometricalProgression . . . . . . . . . 41
3.4.1 GeometricInversionandExpansion . . . . . . . . . . . . . . . . . 41
3.4.2 SplicingHarmoniesUsingInversion . . . . . . . . . . . . . . . . . 43
3.5 TheoryofMelody . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.5.1 TheAxesofMelody . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.5.2 SuperimpositionofRhythmandPitchonAxes . . . . . . . . . . . 46
3.5.3 TypesofMotionAroundtheAxes . . . . . . . . . . . . . . . . . . 48
3.5.4 BuildingMelodicCompositions . . . . . . . . . . . . . . . . . . . 52
3.6 StructureoftheAutomatedSchillingerSystem . . . . . . . . . . . . . . . 54
3.6.1 RhythmGenerators. . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.6.2 HarmonicandMelodicModules . . . . . . . . . . . . . . . . . . . 58
3.6.3 ParameterSettings . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.7 PartsofSchillinger’sTheoriesNotUtilised . . . . . . . . . . . . . . . . . 62
3.8 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4 ResultsandEvaluation 67
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.2 CommonMethodsofEvaluation . . . . . . . . . . . . . . . . . . . . . . . 67
4.3 AutomatedSchillingerSystemOutput . . . . . . . . . . . . . . . . . . . . 68
4.4 AssessingStylisticDiversity . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.4.1 OverviewofAutomatedGenreClassification . . . . . . . . . . . . 71
4.4.2 ChoiceofSoftware . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.4.3 ClassificationExperiment . . . . . . . . . . . . . . . . . . . . . . . 73
4.4.4 PreparationofMIDIfiles . . . . . . . . . . . . . . . . . . . . . . . 74
4.4.5 ClassifierConfiguration . . . . . . . . . . . . . . . . . . . . . . . . 75
4.4.6 ClassificationResults . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.5 AssessingMusicalMerit . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.5.1 ListeningSurveyDesign . . . . . . . . . . . . . . . . . . . . . . . . 78
4.5.2 ListeningExperiment . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.5.3 QuantitativeAnalysisandResults . . . . . . . . . . . . . . . . . . 81
4.5.4 QualitativeAnalysis . . . . . . . . . . . . . . . . . . . . . . . . . . 86
4.5.4.1 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . 86
4.5.4.2 AnalysisandResults . . . . . . . . . . . . . . . . . . . . 87
4.5.4.3 GenreandStyle . . . . . . . . . . . . . . . . . . . . . . . 91
4.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92