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  • Analysis of Motifs in Carnatic Music: AComputational Perspective

    A THESIS

    submitted by

    SHREY DUTTA

    for the award of the degree

    of

    MASTER OF SCIENCE(by Research)

    DEPARTMENT OF COMPUTER SCIENCE ANDENGINEERING

    INDIAN INSTITUTE OF TECHNOLOGY, MADRAS.October 2015

  • THESIS CERTIFICATE

    This is to certify that the thesis entitled Analysis of Motifs in Carnatic Music:

    A Computational Perspective, submitted by Shrey Dutta, to the Indian Institute

    of Technology, Madras, for the award of the degree of Master of Science (by

    Research), is a bona fide record of the research work carried out by him under my

    supervision. The contents of this thesis, in full or in parts, have not been submitted

    to any other Institute or University for the award of any degree or diploma.

    Dr. Hema A. MurthyResearch GuideProfessorDept. of Computer Science and EngineeringIIT-Madras, 600 036

    Place: Chennai

    Date:

  • ACKNOWLEDGEMENTS

    I joined IIT Madras with the intention of mastering the techniques used in machine

    learning. There is so much data available in digital form and I used to think that

    machine learning techniques help in making sense of this data just as human brain

    makes sense of the raw data received from different senses. As I started gaining

    deep understanding in machine learning techniques, I realized that these tech-

    niques are not mature enough to mimic the human brain and thus, should not be

    used blindly. I understood that the data needs to be represented in a sensible form

    which depends on the task under consideration. These techniques are designed to

    use this representation in achieving the desired task. After understanding this, I

    was able to use the existing techniques efficiently as well as design new techniques

    when required. This level of understanding was not possible without the immense

    knowledge and experience shared by my adviser, Prof. Hema A. Murthy, through

    endless captivating discussions.

    I would like to express my sincere gratitude to her for the excellent guidance,

    patience and providing me with an excellent atmosphere for doing research. She

    helped me to develop my background in signal processing and machine learning

    and to experience the practical issues beyond the textbooks. She has not only

    helped in improving my perspective towards research but also towards life.

    I would like to thank my collaborators Vignesh Ishwar, Krishnaraj Sekhar

    and Ashwin Bellur. The completion of this thesis would not have been possible

    without their contribution. They helped me in building datasets, carrying out the

    i

  • experiments, analyzing results and in writing research papers.

    I am grateful to the members of my General Test Committee, Prof. C. Chandra

    Sekhar and Prof. C. S. Ramalingam, for their suggestions and criticisms with

    respect to the presentation of my work. I am also grateful for being a part of the

    CompMusic project. It was a great learning experience working with the members

    of this consortium.

    I would like to thank my music teachers Prof. M.V.N. Murthy and Niveditha

    Bharath. Prof. M.V.N. Murthy patiently taught me to play the instrument,

    Saraswati Veena, in his unique and excellent style. He always encouraged me

    to explore the music beyond what he used to teach in classes which certainly

    manifested my creativity. Madam Nivedita Bharath taught me to sing Carnatic

    music. She is an excellent and a very friendly teacher. Her classes were full of fun

    and excitement. Learning music from these wonderful teachers also helped me to

    better understand the work with respect to this thesis.

    I would like to thank Aashish, Anusha, Asha, Jom, Karthik, Manish, Padma,

    Praveen, Raghav, Rajeev, Sarala, Saranya, Sridharan, Srikanth and other members

    of Donlab for their help and unconditional support over the years. It would have

    been a lonely lab without them. I am also grateful to Alastair, Ajay and Sankalp

    from MTG Barcelona for always clearing my doubts and helping in my research. I

    would also like to acknowledge the help of Kaustuv from IIT Bombay. He always

    found time to answer my questions regarding Hindustani music.

    I am also obliged to the European Research Council for funding the research un-

    der the European Unions Seventh Framework Program, as part of the CompMusic

    project (ERC grant agreement 267583).

    I would like to thank all my friends at IIT Madras without whom the life at IIT

    ii

  • campus would have been dry and boring. If not for them, I would have finished

    my thesis much earlier. They have always been a source of refreshment during

    stressful times.

    I would like to thank my parents who have made many sacrifices so that I can

    get a good education and a good life. They have always tolerated my stubborn

    and rebellious nature which I am constantly trying to change. I wish to make them

    proud one day.

    Lastly, I would like to thank my loving brother Anubhav for always being

    an anchor of my life. It was he who has taken the responsibility of financially

    supporting our family at an early age and motivated me to pursue any path I wish

    to choose. I will always be grateful to him and I wish him all the happiness in life.

    iii

  • ABSTRACT

    KEYWORDS: Carnatic Music, Pattern Discovery, Motif Spotting, Motif Dis-

    covery, Raga Verification, Stationary Points, Rough Longest

    Common Subsquence, Longest Common Segment Set

    In Carnatic music, a collective expression of melodies that consists of svaras

    (ornamented notes) in a well defined order and phrases (aesthetic threads of or-

    namented notes) that have been formed through the ages defines a raga. Melodic

    motifs are those unique phrases of a raga that collectively give a raga its identity.

    These motifs are rendered repeatedly in every rendition of the raga, either compo-

    sitional or improvisational, so that the identity of a raga is established. Different

    renditions of a motif makes it challenging for a time-series matching algorithm to

    match them as they differ slightly from each other. In this thesis, we design al-

    gorithmic techniques to automatically find these motifs, their different renditions

    and, then use the regions rich in these motifs to perform raga verification.

    The initial focus of the thesis is on finding different renditions of melodic

    motifs in an improvisational form of the raga called the alapana. Then we make

    an attempt to automatically discover these motifs from the composition lines. The

    results suggest that composition lines are indeed replete with melodic motifs.

    Using these composition lines, raga verification is performed. In raga verification,

    a melody (a single phrase or an aesthetic concatenation of many such phrases)

    along with a raga claim is supplied to the system. The system confirms or rejects

    the claim.

    iv

  • Two algorithms for time-series matching are proposed in this work. One is

    a modification of the existing algorithm, Rough Longest Common Subsequence

    (RLCS). Another proposed algorithm, Longest Common Segment Set (LCSS), is

    completely novel and uses in between matched segments to give a holistic score.

    Using the proposed algorithm LCSS, an error rate of 12% is obtained for raga

    verification on a database consisting of 17 ragas.

    v

  • TABLE OF CONTENTS

    ACKNOWLEDGEMENTS i

    ABSTRACT iv

    LIST OF TABLES x

    LIST OF FIGURES xi

    ABBREVIATIONS xii

    NOTATION xiii

    1 Introduction 1

    1.1 Overview of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . 1

    1.2 Contribution of the thesis . . . . . . . . . . . . . . . . . . . . . . . 3

    1.3 Organization of the thesis . . . . . . . . . . . . . . . . . . . . . . . 3

    2 Literature Survey 5

    3 Motif Spotting 20

    3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

    3.2 Stationary Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

    3.2.1 Method of obtaining Stationary Points . . . . . . . . . . . . 23

    3.3 Rough Longest Common Subsequence Algorithm . . . . . . . . . 25

    3.3.1 Rough match . . . . . . . . . . . . . . . . . . . . . . . . . . 25

    3.3.2 WAR and WAQ for local similarity . . . . . . . . . . . . . . 26

    3.3.3 Score matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

    3.4 Modified-Rough Longest Common Subsequence . . . . . . . . . . 27

    3.4.1 Rough and actual length of RLCS . . . . . . . . . . . . . . 28

    vi

  • 3.4.2 RWAR and RWAQ . . . . . . . . . . . . . . . . . . . . . . . 28

    3.4.3 Matched rate on the query sequence . . . . . . . . . . . . . 30

    3.5 A Two-Pass Dynamic Programming Search . . . . . . . . . . . . . 30

    3.5.1 First Pass: Determining Candidate Motif Regions using RLCS 31

    3.5.2 Second Pass: Determining Motifs from the Groups . . . . 32

    3.6 Dataset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

    3.7 Experiments and Results . . . . . . . . . . . . . . . . . . . . . . . . 33

    3.7.1 Querying motifs in the alapanas . . . . . . . . . . . . . . . . 33

    3.7.2 Comparison between RLCS and Modified-RLCS using longermotifs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

    3.8 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

    3.8.1 Importance of VAD in motif spotting . . . . . . . . . . . . 39

    3.9 Summary . .