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Syncopation: Unifying Music Theory and Perception

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Syncopation: Unifying Music Theory and Perception Syncopation: Unifying Music Theory and Perception Thesis submitted in partial fulfilment of the requirements of the University of London for the Degree of Doctor of Philosophy Chunyang Song June 2014 Department of Electronic Engineering, Queen Mary, University of London I, Chunyang Song, confirm that the research included within this thesis is my own work or that where it has been carried out in collaboration with, or supported by others, that this is duly acknowledged below and my con- tribution indicated. Previously published material is also acknowledged below. I attest that I have exercised reasonable care to ensure that the work is original, and does not to the best of my knowledge break any UK law, infringe any third party's copyright or other Intellectual Property Right, or contain any confidential material. I accept that the College has the right to use plagiarism detection software to check the electronic version of the thesis. I confirm that this thesis has not been previously submitted for the award of a degree by this or any other university. The copyright of this thesis rests with the author and no quotation from it or information derived from it may be published without the prior written consent of the author. Signature: Date: Details of collaboration and publications: • Song C, Simpson AJR, Harte CA, Pearce MT, Sandler MB (2013) Syncopation and the Score. PLoS ONE 8(9): e74692. This work is covered in Chapter 4. • Song C, Harte CA, Simpson AJR, Sandler MB, Syncopation models: do they measure up? Submitted to Music Perception in May, 2014. This work is covered in Chapters 3 and 5. 2 Abstract Syncopation is a fundamental feature of rhythm in music. However, the relationship between theory and perception is currently not well under- stood. This thesis is concerned with characterising this relationship and identifying areas where the theory is incomplete. We start with a review of relevant musicological background and theory. Next, we use psychophysi- cal data to characterise the perception of syncopation for simple rhythms. We then analyse the predictions of current theory using this data and iden- tify strengths and weaknesses in the theory. We then introduce further psychophysical data which characterises the perception of syncopation for simple rhythms at different tempi. This leads to revised theory and a new model of syncopation that is tempo-dependent. 3 Acknowledgements I would like to thank my supervisors Mark Sandler and Marcus Pearce for their guidance and support. I would also like to acknowledge the Joint Programme College Scholarship that funded my studies and especially Yue Chen for extending the funding to support my writing up. Special thanks to Mark Plumbley for always making time to talk and for helping me several times with my travel to conferences and research visits. Many thanks to Tanya Gold for proof-reading my thesis and to Michael Tautschnig for advice on mathematical notation. I would like to give my biggest thanks to Chris Harte, not only for always making the time to discuss research with me and giving me good advice, but also for being my greatest support and mentor. Without his enduring encouragement I could not possibly have the confidence and persistence to drive myself to the finish line. I also owe a great deal of thanks to Andy Simpson, the sweetest unan- ticipated surprise along my Ph.D journey, for pointing me in the right direction and helping me find so much insight and passion in my work. His help really put a rocket under my research in my final year and for this I will always be very grateful. I must also thank all the people who participated in my listening tests (in alphabetical order): Alice, Alo, Andy, Bogdan, Boris, Brecht, Chris, Dan, Dimitrios, Daniele, Elio, Emmanouil, George, Han, Holger, Jordan, Katerina, Magda, Mike, Steve and Sonia. Many thanks also to my friends in Georgia Tech who helped me so much during my three-month research visit: Qingfen, Jiechao, Weibin, Ruofeng, Aron and Mason; and Yi for taking care of me during my trip to SMPC in Toronto. Special thanks to my dear \104 gang", especially Siying, Tian and Yading for their huge support and great company. I will always remember 4 the times when we worked together till late, and when we said we would work hard but ended up nut-chatting the whole night. I appreciate that you guys tried all sorts to help me with writing up, such as hiding my phone and working in shift to watch over me. Thanks particularly to Sonia for being my writing-up buddy and cheering every step of my progress with me. Finally, I am very grateful to my parents and entire family members in China, and also my family in UK: grandma, grandpa, ma, pa, and all my awesome Leavening branch, for their everlasting support and love. 5 Contents Abstract :::::::::::::::::::::::::::::::: 3 1 Introduction :::::::::::::::::::::::::::: 17 1.1 Motivations . 18 1.2 Methodology . 21 1.3 Goals and objectives . 23 1.4 Thesis outline . 24 2 Syncopation in music theory ::::::::::::::::: 27 2.1 Fundamentals of rhythm . 27 2.1.1 Rhythm . 27 2.1.2 Beat . 31 2.1.3 Meter . 31 2.1.4 Tempo . 35 2.2 Definitions for syncopation . 37 2.2.1 Violation of the regular beat salience . 37 2.2.2 Off-beat . 38 2.2.3 Transformation of meter . 40 2.2.4 Polyrhythm . 41 2.3 Overview of syncopation models . 42 2.3.1 Categories of models . 43 2.3.2 Capabilities of models . 44 2.4 Summary . 45 3 Review of syncopation models :::::::::::::::: 46 3.1 Background . 46 3.1.1 Sequences . 46 3.1.2 Rhythm in continuous time . 48 3.1.3 Discrete time representation . 49 3.1.4 Metrical hierarchy . 52 6 3.2 Syncopation models . 55 3.2.1 Longuet-Higgins and Lee 1984 (LHL) . 55 3.2.2 Pressing 1997 (PRS) . 58 3.2.3 Toussaint 2002 `Metric Complexity' (TMC) . 61 3.2.4 Sioros and Guedes 2011 (SG) . 62 3.2.5 Keith 1991 (KTH) . 65 3.2.6 Toussaint 2005 ‘Off-Beatness’ (TOB) . 66 3.2.7 G´omez2005 `Weighted Note-to-Beat Distance' (WNBD) 67 3.3 Summary . 68 4 Syncopation and the score ::::::::::::::::::: 70 4.1 Experiment 1: Score . 70 4.1.1 Participants . 71 4.1.2 Stimuli . 71 4.1.3 Procedure . 74 4.2 Results . 75 4.2.1 6/8 is more syncopated than 4/4 . 75 4.2.2 Polyrhythms are more syncopated . 75 4.2.3 Missing down-beats result in syncopation . 77 4.2.4 Switching component order affects syncopation . 78 4.3 Discussion . 81 4.3.1 4/4 versus 6/8 . 81 4.3.2 Missing down-beats . 82 4.3.3 Possible interpretation of 6/8 as 3/4 . 83 4.3.4 Polyrhythms . 84 4.4 Summary . 85 5 Evaluation of the models :::::::::::::::::::: 86 5.1 Dataset 1 . 86 5.2 Evaluation results . 89 5.3 Discussion: strengths and weaknesses of models . 90 5.3.1 Hierarchical models . 90 5.3.2 Off-beat models . 95 5.3.3 Classification models . 97 5.3.4 General discussion . 98 5.4 Summary . 98 7 6 Tempo affects syncopation ::::::::::::::::::: 100 6.1 Background . 101 6.1.1 Tactus perception and tempo . 101 6.1.2 Tempo limits of tactus and meter perception . 102 6.1.3 Dynamic meter perception influenced by tempo . 103 6.1.4 Hypotheses for tempo effects on syncopation . 106 6.2 Experiment 2: Tempo . 108 6.2.1 Participants . 108 6.2.2 Stimuli . 108 6.2.3 Procedure . 111 6.3 Results . 111 6.3.1 Syncopation is a function of tempo . 111 6.3.2 Quadratic function . 113 6.3.3 Polyrhythms are more resistant to tempo changes . 114 6.3.4 No evidence of an effect of time-signature . 117 6.3.5 Individual rhythms show different sensitivity to tempo120 6.4 Discussion . 126 6.4.1 The tempo effect on syncopation parallels the tempo effect on tactus . 127 6.4.2 Adjustable tactus level and syncopation . 128 6.4.3 Peak tempo of syncopation is lagged to that of tactus129 6.4.4 Polyrhythms versus monorhythms . 129 6.4.5 Possible meter induction at extremely fast tempi . 130 6.4.6 Time-signature . 130 6.5 Summary . 132 7 Improving syncopation modelling :::::::::::::: 134 7.1 Best-Single Combined models (BSC) . 134 7.1.1 The three-way BSC model (BSC3) . 135 7.1.2 The two-way BSC model (BSC2) . 135 7.2 Weighted-Multiple Combined model (WMC) . 136 7.3 Validation of combined models for Dataset 1 . 138 7.4 Tempo-dependent models . 140 7.4.1 General design . 140 7.4.2 Tempo-dependent combined models . 140 7.5 Validation of tempo-dependent combined models for Dataset 2................................ 142 8 7.6 Discussion . 145 7.7 Summary . 146 8 Conclusions :::::::::::::::::::::::::::: 147 8.1 Thesis contributions . 147 8.2 General discussion . 148 8.3 Future work . 150 Bibliography ::::::::::::::::::::::::::::: 154 9 List of Figures 1.1 Tested and untested relationships between theory and per- ception. 20 1.2 Transformation: from the music score to perception. 22 1.3 Thesis outline. 25 2.1 The equation of note-values. 29 2.2 Examples of triplets. 29 2.3 Examples of tied notes. 30 2.4 Examples of dotted notes. 30 2.5 Examples of beat groupings and the resulting beat salience. 32 2.6 Duple versus triple, simple versus compound. 33 2.7 Time-signatures and their hierarchical structures, patterns of beat groupings and beat subdivisions. 34 2.8 Metrical hierarchies projected by rhythm-patterns in a given time-signature.
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