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<ul><li><p>Analysis of Motifs in Carnatic Music: AComputational Perspective</p><p>A THESIS</p><p>submitted by</p><p>SHREY DUTTA</p><p>for the award of the degree</p><p>of</p><p>MASTER OF SCIENCE(by Research)</p><p>DEPARTMENT OF COMPUTER SCIENCE ANDENGINEERING</p><p>INDIAN INSTITUTE OF TECHNOLOGY, MADRAS.October 2015</p></li><li><p>THESIS CERTIFICATE</p><p>This is to certify that the thesis entitled Analysis of Motifs in Carnatic Music:</p><p>A Computational Perspective, submitted by Shrey Dutta, to the Indian Institute</p><p>of Technology, Madras, for the award of the degree of Master of Science (by</p><p>Research), is a bona fide record of the research work carried out by him under my</p><p>supervision. The contents of this thesis, in full or in parts, have not been submitted</p><p>to any other Institute or University for the award of any degree or diploma.</p><p>Dr. Hema A. MurthyResearch GuideProfessorDept. of Computer Science and EngineeringIIT-Madras, 600 036</p><p>Place: Chennai</p><p>Date:</p></li><li><p>ACKNOWLEDGEMENTS</p><p>I joined IIT Madras with the intention of mastering the techniques used in machine</p><p>learning. There is so much data available in digital form and I used to think that</p><p>machine learning techniques help in making sense of this data just as human brain</p><p>makes sense of the raw data received from different senses. As I started gaining</p><p>deep understanding in machine learning techniques, I realized that these tech-</p><p>niques are not mature enough to mimic the human brain and thus, should not be</p><p>used blindly. I understood that the data needs to be represented in a sensible form</p><p>which depends on the task under consideration. These techniques are designed to</p><p>use this representation in achieving the desired task. After understanding this, I</p><p>was able to use the existing techniques efficiently as well as design new techniques</p><p>when required. This level of understanding was not possible without the immense</p><p>knowledge and experience shared by my adviser, Prof. Hema A. Murthy, through</p><p>endless captivating discussions.</p><p>I would like to express my sincere gratitude to her for the excellent guidance,</p><p>patience and providing me with an excellent atmosphere for doing research. She</p><p>helped me to develop my background in signal processing and machine learning</p><p>and to experience the practical issues beyond the textbooks. She has not only</p><p>helped in improving my perspective towards research but also towards life.</p><p>I would like to thank my collaborators Vignesh Ishwar, Krishnaraj Sekhar</p><p>and Ashwin Bellur. The completion of this thesis would not have been possible</p><p>without their contribution. They helped me in building datasets, carrying out the</p><p>i</p></li><li><p>experiments, analyzing results and in writing research papers.</p><p>I am grateful to the members of my General Test Committee, Prof. C. Chandra</p><p>Sekhar and Prof. C. S. Ramalingam, for their suggestions and criticisms with</p><p>respect to the presentation of my work. I am also grateful for being a part of the</p><p>CompMusic project. It was a great learning experience working with the members</p><p>of this consortium.</p><p>I would like to thank my music teachers Prof. M.V.N. Murthy and Niveditha</p><p>Bharath. Prof. M.V.N. Murthy patiently taught me to play the instrument,</p><p>Saraswati Veena, in his unique and excellent style. He always encouraged me</p><p>to explore the music beyond what he used to teach in classes which certainly</p><p>manifested my creativity. Madam Nivedita Bharath taught me to sing Carnatic</p><p>music. She is an excellent and a very friendly teacher. Her classes were full of fun</p><p>and excitement. Learning music from these wonderful teachers also helped me to</p><p>better understand the work with respect to this thesis.</p><p>I would like to thank Aashish, Anusha, Asha, Jom, Karthik, Manish, Padma,</p><p>Praveen, Raghav, Rajeev, Sarala, Saranya, Sridharan, Srikanth and other members</p><p>of Donlab for their help and unconditional support over the years. It would have</p><p>been a lonely lab without them. I am also grateful to Alastair, Ajay and Sankalp</p><p>from MTG Barcelona for always clearing my doubts and helping in my research. I</p><p>would also like to acknowledge the help of Kaustuv from IIT Bombay. He always</p><p>found time to answer my questions regarding Hindustani music.</p><p>I am also obliged to the European Research Council for funding the research un-</p><p>der the European Unions Seventh Framework Program, as part of the CompMusic</p><p>project (ERC grant agreement 267583).</p><p>I would like to thank all my friends at IIT Madras without whom the life at IIT</p><p>ii</p></li><li><p>campus would have been dry and boring. If not for them, I would have finished</p><p>my thesis much earlier. They have always been a source of refreshment during</p><p>stressful times.</p><p>I would like to thank my parents who have made many sacrifices so that I can</p><p>get a good education and a good life. They have always tolerated my stubborn</p><p>and rebellious nature which I am constantly trying to change. I wish to make them</p><p>proud one day.</p><p>Lastly, I would like to thank my loving brother Anubhav for always being</p><p>an anchor of my life. It was he who has taken the responsibility of financially</p><p>supporting our family at an early age and motivated me to pursue any path I wish</p><p>to choose. I will always be grateful to him and I wish him all the happiness in life.</p><p>iii</p></li><li><p>ABSTRACT</p><p>KEYWORDS: Carnatic Music, Pattern Discovery, Motif Spotting, Motif Dis-</p><p>covery, Raga Verification, Stationary Points, Rough Longest</p><p>Common Subsquence, Longest Common Segment Set</p><p>In Carnatic music, a collective expression of melodies that consists of svaras</p><p>(ornamented notes) in a well defined order and phrases (aesthetic threads of or-</p><p>namented notes) that have been formed through the ages defines a raga. Melodic</p><p>motifs are those unique phrases of a raga that collectively give a raga its identity.</p><p>These motifs are rendered repeatedly in every rendition of the raga, either compo-</p><p>sitional or improvisational, so that the identity of a raga is established. Different</p><p>renditions of a motif makes it challenging for a time-series matching algorithm to</p><p>match them as they differ slightly from each other. In this thesis, we design al-</p><p>gorithmic techniques to automatically find these motifs, their different renditions</p><p>and, then use the regions rich in these motifs to perform raga verification.</p><p>The initial focus of the thesis is on finding different renditions of melodic</p><p>motifs in an improvisational form of the raga called the alapana. Then we make</p><p>an attempt to automatically discover these motifs from the composition lines. The</p><p>results suggest that composition lines are indeed replete with melodic motifs.</p><p>Using these composition lines, raga verification is performed. In raga verification,</p><p>a melody (a single phrase or an aesthetic concatenation of many such phrases)</p><p>along with a raga claim is supplied to the system. The system confirms or rejects</p><p>the claim.</p><p>iv</p></li><li><p>Two algorithms for time-series matching are proposed in this work. One is</p><p>a modification of the existing algorithm, Rough Longest Common Subsequence</p><p>(RLCS). Another proposed algorithm, Longest Common Segment Set (LCSS), is</p><p>completely novel and uses in between matched segments to give a holistic score.</p><p>Using the proposed algorithm LCSS, an error rate of 12% is obtained for raga</p><p>verification on a database consisting of 17 ragas.</p><p>v</p></li><li><p>TABLE OF CONTENTS</p><p>ACKNOWLEDGEMENTS i</p><p>ABSTRACT iv</p><p>LIST OF TABLES x</p><p>LIST OF FIGURES xi</p><p>ABBREVIATIONS xii</p><p>NOTATION xiii</p><p>1 Introduction 1</p><p>1.1 Overview of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . 1</p><p>1.2 Contribution of the thesis . . . . . . . . . . . . . . . . . . . . . . . 3</p><p>1.3 Organization of the thesis . . . . . . . . . . . . . . . . . . . . . . . 3</p><p>2 Literature Survey 5</p><p>3 Motif Spotting 20</p><p>3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20</p><p>3.2 Stationary Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21</p><p>3.2.1 Method of obtaining Stationary Points . . . . . . . . . . . . 23</p><p>3.3 Rough Longest Common Subsequence Algorithm . . . . . . . . . 25</p><p>3.3.1 Rough match . . . . . . . . . . . . . . . . . . . . . . . . . . 25</p><p>3.3.2 WAR and WAQ for local similarity . . . . . . . . . . . . . . 26</p><p>3.3.3 Score matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . 27</p><p>3.4 Modified-Rough Longest Common Subsequence . . . . . . . . . . 27</p><p>3.4.1 Rough and actual length of RLCS . . . . . . . . . . . . . . 28</p><p>vi</p></li><li><p>3.4.2 RWAR and RWAQ . . . . . . . . . . . . . . . . . . . . . . . 28</p><p>3.4.3 Matched rate on the query sequence . . . . . . . . . . . . . 30</p><p>3.5 A Two-Pass Dynamic Programming Search . . . . . . . . . . . . . 30</p><p>3.5.1 First Pass: Determining Candidate Motif Regions using RLCS 31</p><p>3.5.2 Second Pass: Determining Motifs from the Groups . . . . 32</p><p>3.6 Dataset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32</p><p>3.7 Experiments and Results . . . . . . . . . . . . . . . . . . . . . . . . 33</p><p>3.7.1 Querying motifs in the alapanas . . . . . . . . . . . . . . . . 33</p><p>3.7.2 Comparison between RLCS and Modified-RLCS using longermotifs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36</p><p>3.8 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38</p><p>3.8.1 Importance of VAD in motif spotting . . . . . . . . . . . . 39</p><p>3.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40</p><p>4 Motif Discovery 41</p><p>4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41</p><p>4.2 Lines from the compositions . . . . . . . . . . . . . . . . . . . . . . 44</p><p>4.3 Optimization criteria to find Rough Longest Common Subsequence 44</p><p>4.3.1 Density of the match . . . . . . . . . . . . . . . . . . . . . . 45</p><p>4.3.2 Normalized weighted length . . . . . . . . . . . . . . . . . 46</p><p>4.3.3 Linear trend in stationary points . . . . . . . . . . . . . . . 46</p><p>4.4 Discovering typical motifs of ragas . . . . . . . . . . . . . . . . . . 49</p><p>4.4.1 Filtering to get typical motifs of a raga . . . . . . . . . . . . 49</p><p>4.5 Dataset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50</p><p>4.6 Experiments and results . . . . . . . . . . . . . . . . . . . . . . . . 52</p><p>4.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55</p><p>5 Raga Verification 56</p><p>5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56</p><p>5.2 Dataset used . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57</p><p>5.2.1 Extraction of pallavi lines . . . . . . . . . . . . . . . . . . . . 58</p><p>vii</p></li><li><p>5.2.2 Selection of cohorts . . . . . . . . . . . . . . . . . . . . . . . 58</p><p>5.3 Longest Common Segment Set Algorithm . . . . . . . . . . . . . . 59</p><p>5.3.1 Common segments . . . . . . . . . . . . . . . . . . . . . . . 60</p><p>5.3.2 Common segment set . . . . . . . . . . . . . . . . . . . . . 62</p><p>5.3.3 Longest Common Segment Set . . . . . . . . . . . . . . . . 62</p><p>5.4 Raga Verification . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64</p><p>5.4.1 Score Normalization . . . . . . . . . . . . . . . . . . . . . . 65</p><p>5.5 Performance evaluation . . . . . . . . . . . . . . . . . . . . . . . . 66</p><p>5.5.1 Experimental configuration . . . . . . . . . . . . . . . . . . 66</p><p>5.5.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67</p><p>5.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68</p><p>5.6.1 Combining hard-LCSS and soft-LCSS . . . . . . . . . . . . 69</p><p>5.6.2 Reduction of overlap in score distribution by T-norm . . . 69</p><p>5.6.3 Scalability of raga verification . . . . . . . . . . . . . . . . . 70</p><p>5.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70</p><p>6 Conclusion 71</p><p>6.1 Salient Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71</p><p>6.2 Criticism of the work . . . . . . . . . . . . . . . . . . . . . . . . . . 72</p><p>6.3 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73</p></li><li><p>LIST OF TABLES</p><p>2.1 Svaras and their respective ratios to the base pitch S. . . . . . . . 6</p><p>3.1 Dataset of alapanas . . . . . . . . . . . . . . . . . . . . . . . . . . . 33</p><p>3.2 Short Motifs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33</p><p>3.3 Long Motifs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33</p><p>3.4 Short Motifs: Retrieved regions after the first pass . . . . . . . . . 34</p><p>3.5 Long Motifs: Retrieved regions after the first pass . . . . . . . . . 35</p><p>3.6 Short Motifs: Top 10 retrieved motifs after the second pass . . . . 35</p><p>3.7 Long Motifs: Top 10 retrieved motifs after the second pass . . . . 35</p><p>3.8 Long Motifs: Retrieved regions after the first pass . . . . . . . . . 37</p><p>3.9 Long Motifs: Retrieved regions after the second pass . . . . . . . 38</p><p>3.10 Retrieved Groups after both the passes for modified-RLCS withoutVAD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39</p><p>4.1 D1: Dataset of composition lines . . . . . . . . . . . . . . . . . . . 50</p><p>4.2 D1: Dataset for filtering . . . . . . . . . . . . . . . . . . . . . . . . 50</p><p>4.3 D2: Dataset of composition lines . . . . . . . . . . . . . . . . . . . 51</p><p>4.4 D2: Dataset for filtering . . . . . . . . . . . . . . . . . . . . . . . . 51</p><p>4.5 D1:Similar motifs retrieved from composition lines . . . . . . . . . 52</p><p>4.6 D1:Percentage of motifs preserved after filtering . . . . . . . . . . 53</p><p>4.7 D2:Similar motifs retrieved from composition lines . . . . . . . . . 53</p><p>4.8 D2:Percentage of motifs preserved after filtering . . . . . . . . . . 54</p><p>5.1 Details of the database used. Durations are given in approximatehours (h), minutes (m) or seconds (s). . . . . . . . . . . . . . . . . 58</p><p>5.2 EER(%) for different algorithms using different normalizations ondifferent datasets. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67</p><p>ix</p></li><li><p>5.3 Number of claims correctly verified by hard-LCSS only, by soft-LCSS only, by both and by neither of them for D1 and D2 usingT-norm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69</p><p>x</p></li><li><p>LIST OF FIGURES</p><p>2.1 Comparing Pitch Histogram of Raga Sankarabharanam with itsHindustani and Western classical counterparts. . . . . . . . . . . . 7</p><p>2.2 Comparing a phrase in raga Sankarabaranam with gamakas and with-out gamakas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8</p><p>2.3 The gamakas in their true form are marked in a pitch contour of amelody . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9</p><p>2.4 Tonic normalization of two similar phrases in raga sankarabha-ranam rendered at different tonics. . . . . . . . . . . . . . . . . . . 10</p><p>2.5 Different renditions of a melodic motif in raga Kalyani and ragaKamboji. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11</p><p>2.6 Different instances of a melodic motif in an alapana marked in red. 12</p><p>2.7 Extraction of stationary points and their interpolation to get a smoothpitch contour. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14</p><p>3.1 A Phrase with Stationary Points . . . . . . . . . . . . . . . . . . . . 22</p><p>3.2 The Pitch and Stationary Point Histograms of the raga Kamboji . 23</p><p>3.3 Original and Cubic Interpolated pitch contours . . . . . . . . . . . 24</p><p>3.4 a) True positive groups and false alarm groups score distributionfor RLCS. b) True positive groups and false alarm groups sc...</p></li></ul>

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