臺灣博碩士論文加值系統

音樂是有規則的時間序列, 其規則之一為和聲學。傳統和聲學規則 肇始於複音音樂,完備於主音音樂,在非調性音樂又趨於瓦解。若能 利用電腦輔助分析和聲學規則, 則可以幫助理解音樂, 甚至創造新的音 樂規則。
本論文將音樂行進之和聲取出, 並以圖論為模型, 企圖描述音樂背後 隱含的和聲規則。 將此模型視覺化, 可發現其與傳統和聲理論有不謀 而合之處。本文重點之一在於描述此模型與和聲學之異同。
此外, 利用社群網路分析之技巧, 得以擷取圖之若干特徵, 這些特徵 表現了不同音樂風格之特性。利用機器學習方法, 擷取之特徵作為資 料, 可以驗證這些特徵值的確能夠體現並分辨不同風格之音樂。

致謝 i
中文摘要 ii
1 Introduction 1
1.1 Motivation.................................. 1
1.2 KeyContribution .............................. 2
1.3 LiteratureSurveyandRelatedWorks.................... 3
1.4 ChapterOutline............................... 4
2 Music Theory Background 6
2.1 ChromaticScale............................... 6
2.2 MajorScaleandTriad............................ 7
2.3 TonalityandRulesofHarmony....................... 7
2.4 Harmonic Characteristic of Polyphonic, Homophonic, and Atonal Music . 8
2.5 HarmonicRhythmandNotationalRhythm................. 8
3 Social Network Analysis Background 10
3.1 GraphTheoryandSocialNetworkAnalysis . . . . . . . . . . . . . . . . 10
3.2 StatisticPropertiesofaNetwork ...................... 11
3.2.1 AveragePathLength ........................ 11
3.2.2 ClusterCoefficient ......................... 11
3.2.3 PowerLaw ............................. 12
4 Harmony Graph, the Model 13
4.1 DefinitionofHarmony ........................... 13
4.2 EncodingofHarmony............................ 13
4.3 ConstructionofHarmonyGraph ...................... 14
5 Results and Discussions 17
5.1 TheFiveCategories............................. 17
5.2 CorpusVisualization ............................ 17
5.3 SocialNetworkAnalysis .......................... 21
5.3.1 DegreeDistribution......................... 22
5.3.2 AveragePathLength ........................ 22
5.3.3 ClusteringCoefficient ....................... 26
5.3.4 Agglomeration ........................... 26
5.4 CorpusDistinguishing ........................... 28
6 Conclusion and Future Works 29
6.1 Conclution.................................. 29
6.2 FutureWorks ................................ 29
Bibliography 31
Appendix 33

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