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研究生:史盟
研究生(外文):ALEKSANDR SIMAK
論文名稱:音樂的旋律和節奏結構的複雜評估
論文名稱(外文):Structural Complexity Assessments on Musical Melody and Rhythm
指導教授:劉長遠
指導教授(外文):Cheng-Yuan Liou
口試委員:呂育道趙坤茂林軒田林智仁吳建銘
口試委員(外文):Yuh-Dauh LyuuKun-Mao ChaoHsuan-Tien LinChih-Jen LinJiann-Ming Wu
口試日期:2015-01-09
學位類別:博士
校院名稱:國立臺灣大學
系所名稱:資訊工程學研究所
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2015
畢業學年度:103
語文別:英文
論文頁數:76
中文關鍵詞:音樂的複雜性結構複雜
外文關鍵詞:music complexitystructural complexitybarlow dictionary
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There is no definite meaning for music complexity. Current work studied it in terms of complexity of music structure, extending previous research on the complexity of rhythmic structure only. Melody and rhythm this time both encoded within binary tree and the assessment on structural properties of the tree performed. This is the key difference with other studies where complexity assessments performed on music components independently. The concepts of rewriting and L-Systems used to extract repeatable patterns from the tree and form tree generating context-sensitive grammar. Elementary notes transition represented as grammar’s rewriting rules. Rewriting rules classification transforms context-sensitive grammars to context-free stochastic variant. More complex tree has more complex generating grammar, the final assessment score is well-known complexity (or entropy) of context-free grammar.
Current work updated the method with new binary tree. Redefined tree is capable to store arbitrary content inside the nodes, thus encoding dissimilar features such as melody and rhythm within its structure and nodes simultaneously. Notions of similarity for rewriting rules were updated accordingly. Better algorithm for rewriting rules classification was proposed and approbated during the study. Finally, minor theoretical conform issues of notations were accurately justified.
Updated method was approbated with two datasets: drums exercises and Barlow dictionary of 10,000 classical themes. Empirical results revealed enough method sensitivity to detect atypical samples within the corpus, discriminate samples by their relative complexity and score the comprehensiveness of particular musical or personal style.

1 Abstract ................................................. ii
2 Contents .................................................iii
3 List of Figures ...........................................vi
4 List of Tables ..........................................viii
5 Introduction .............................................. 1
5.1 Complexity .............................................. 1
5.2 Music Origins............................................ 3
5.3 Structural Complexity ................................... 5
5.4 Rewriting................................................ 7
5.4.1 Formal grammar ........................................ 7
5.4.2 Lindenmayer System .................................... 8
6 Literature Review ........................................ 10
6.1 Music Complexity Perspectives .......................... 10
6.2 Melody Complexity ...................................... 11
6.3 Rhythm Complexity ...................................... 12
6.3.1 Structural Complexity of Musical Rhythm .............. 13
6.4 Structural Complexity of DNA-sequence .................. 15
6.5 Syntactic sensitive complexity for symbol-free sequence 17
7 Problem .................................................. 19
7.1 Context ................................................ 19
7.2 Statement............................................... 19
7.3 Contribution ........................................... 20
8 Methods .................................................. 21
8.1 Representation.......................................... 21
8.1.1 Binary Tree L-System ................................. 22
8.2 Rewriting Rules ........................................ 24
8.2.1 Homomorphism and Isomorphism ......................... 26
8.3 Classification.......................................... 28
8.4 Complexity Assessment .................................. 31
8.5 Numeric Estimation ..................................... 32
9 Assessments .............................................. 33
9.1 Assessment 1 ........................................... 33
9.2 Assessment 2 ........................................... 33
9.3 Assessment 3 ........................................... 34
9.4 Future perspectives .................................... 34
9.4.1 Assessment 4 ......................................... 34
9.4.2 Formula modification ................................. 35
10 Datasets ................................................ 36
10.1 Dataset-1 ............................................. 36
10.2 Dataset-2 ............................................. 37
10.2.1 Dataset Bias ........................................ 38
11 Empirical Results ....................................... 39
11.1 Preprocessing ......................................... 39
11.2 Dataset-1 ............................................. 40
11.2.1 Assessment 1 ........................................ 40
11.2.2 Assessment 2 ........................................ 46
11.2.3 Assessment 3 ........................................ 48
11.3 Dataset-2 ............................................. 54
11.3.1 Assessment 1 ........................................ 55
11.3.2 Assessment 2 ........................................ 55
11.3.3 Assessment 3 ........................................ 62
12 Implementation .......................................... 67
13 Discussion .............................................. 70
14 References .............................................. 71

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