Analyzing Temporal Dynamics in Music

THIS ARTICLE INTRODUCES THEORETICAL and analytical tools for research involving musical emotion or musical change. We describe techniques for visualizing and analyzing data drawn from timevarying processes, such as continuous tension judgments, movement tracking, and performance tempo curves. Functional Data Analysis tools are demonstrated with real-time judgments of musical tension (a proxy for musical affect) to reveal patterns of tension and resolution in a listener’s experience. The derivatives of tension judgment curves are shown to change with cycles of expectation and release in music, indexing the dynamics of musical tension. We explore notions of potential energy and kinetic energy in music and propose that affective energy is stored or released in the listener as musical tension increases and decreases. Differential calculus (and related concepts) are introduced as tools for the analysis of temporal dynamics in musical performances, and phase-plane plots are described as a means to quantify and to visualize musical change.

[1]  James O. Ramsay,et al.  Applied Functional Data Analysis: Methods and Case Studies , 2002 .

[2]  Fred Lerdahl,et al.  Calculating Tonal Tension , 1996 .

[3]  A. Lehmann,et al.  Tracking Performance Correlates of Changes in Perceived Intensity of Emotion During Different Interpretations of a Chopin Piano Prelude , 2001 .

[4]  C. Krumhansl.  A Perceptual Analysis of Mozart's Piano Sonata K. 282: Segmentation, Tension, and Musical Ideas , 1996 .

[5]  W. Thompson,et al.  A Cross-Cultural Investigation of the Perception of Emotion in Music: Psychophysical and Cultural Cues , 1999 .

[6]  B. Repp.  Diversity and commonality in music performance: an analysis of timing microstructure in Schumann's "Träumerei". , 1992, The Journal of the Acoustical Society of America.

[7]  C. Krumhansl,et al.  Can Dance Reflect the Structural and Expressive Qualities of Music? A Perceptual Experiment on Balanchine's Choreography of Mozart's Divertimento No. 15 , 1997 .

[8]  I. Peretz,et al.  The Cognitive Neuroscience of Music , 2003 .

[9]  C. R. Deboor,et al.  A practical guide to splines , 1978 .

[10]  I. Newton.  Philosophiæ naturalis principia mathematica , 1973 .

[11]  William E. Fredrickson.  Effect of Musical Performance on Perception of Tension in Gustav Hoist's First Suite in E-flat , 1999 .

[12]  Emery Schubert.  Correlation analysis of continuous emotional response to music: Correcting for the effects of serial correlation , 2001 .

[13]  C. Krumhansl.  An exploratory study of musical emotions and psychophysiology. , 1997, Canadian journal of experimental psychology = Revue canadienne de psychologie experimentale.

[14]  W. E. Fredrickson,et al.  A Comparison of Perceived Musical Tension and Aesthetic Response , 1995 .

[15]  Manfred Clynes,et al.  THE LIVING QUALITY OF MUSIC Neurobiologic Patterns of Communicating Feeling , 1982 .

[16]  Marcelo M. Wanderley,et al.  Performance Gestures of Musicians: What Structural and Emotional Information Do They Convey? , 2003, Gesture Workshop.

[17]  B. Repp.  Patterns of note onset asynchronies in expressive piano performance. , 1996, The Journal of the Acoustical Society of America.

[18]  Michael Unser,et al.  Splines: a perfect fit for signal and image processing , 1999, IEEE Signal Process. Mag..

[19]  R. Shepard.  Ecological constraints on internal representation: resonant kinematics of perceiving, imagining, thinking, and dreaming. , 1984, Psychological review.

[20]  Steve L Arson.  Musical Forces and Melodic Expectations: Comparing Computer Models and Experimental Results , 2004 .

[21]  S. Kuwano,et al.  Continuous judgment of level-fluctuating sounds and the relationship between overall loudness and instantaneous loudness , 1985, Psychological research.

[22]  B. Repp.  Expressive Timing in a Debussy Prelude: A Comparison of Student and Expert Pianists , 1997 .

[23]  C. Krumhansl,et al.  Cross-modal interactions in the perception of musical performance , 2006, Cognition.

[24]  C. Krumhansl.  Music as Cognition. , 1987 .

[25]  K. Scherer,et al.  Emotional states generated by music: An exploratory study of music experts , 2001 .

[26]  Eric Clarke,et al.  Rhythm and Timing in Music , 1999 .

[27]  C. Krumhansl.  Music: A Link Between Cognition and Emotion , 2002 .

[28]  Nicholas A. Smith,et al.  Perceptions of Musical Dimensions in Beethoven's Waldsiein Sonata: An Application of Tonal Pitch Space Theory , 2003 .

[29]  J. Russell.  Affective space is bipolar. , 1979 .

[30]  Diego Vega.  A Perceptual Experiment on Harmonic Tension and Melodic Attraction in Lerdahl's Tonal Pitch Space , 2003 .

[31]  E. Bigand,et al.  Perceiving musical tension in long chord sequences , 1999, Psychological research.

[32]  Clifford K. Madsen,et al.  The Experience of Musical Tension: A Replication of Nielsen's Research Using the Continuous Response Digital Interface , 1993 .

[33]  Yoshitaka Nakajima,et al.  Auditory Scene Analysis: The Perceptual Organization of Sound Albert S. Bregman , 1992 .

[34]  Aniruddh D. Patel,et al.  Language, music, syntax and the brain , 2003, Nature Neuroscience.

[35]  M. Kenward,et al.  An Introduction to the Bootstrap , 2007 .

[36]  Jenny R. Saffran.  Mechanisms of Musical Memory in Infancy , 2003 .

[37]  Keith J. Worsley,et al.  Rotation space random fields with an application to fMRI data , 2003 .

[38]  William E. Fredrickson,et al.  Perception of tension in music: musicians versus nonmusicians. , 2000, Journal of music therapy.

[39]  Stephen McAdams,et al.  Influences of Large-Scale Form on Continuous Ratings in Response to a Contemporary Piece in a Live Concert Setting , 2004 .

[40]  Siobhan Chapman.  Logic and Conversation , 2005 .

[41]  J. Sundberg,et al.  Does music performance allude to locomotion? A model of final ritardandi derived from measurements of stopping , 1999 .

[42]  J. Sloboda,et al.  Music and emotion: Theory and research , 2001 .

[43]  W. E. Fredrickson,et al.  Elementary, Middle, and High School Student Perceptions of Tension in Music , 1997 .

[44]  Laurel J. Trainor,et al.  Memory for melody: infants use a relative pitch code , 2005, Cognition.

[45]  K. Scherer,et al.  EMOTIONAL EFFECTS OF MUSIC: PRODUCTION RULES , 2001 .

[46]  W. Jay Dowling,et al.  The Development of Music Perception and Cognition , 1999 .

[47]  S. Trehub.  Musical Predispositions in Infancy , 2001, Annals of the New York Academy of Sciences.

[48]  J. Ramsay,et al.  Introduction to Functional Data Analysis , 2007 .

[49]  James O. Ramsay,et al.  Functional Components of Variation in Handwriting , 2000 .

[50]  John R. Clark.  The dynamics of creation , 1979, Journal of Religion and Health.

[51]  Neil P. McAngus Todd,et al.  Motion in Music: A Neurobiological Perspective , 1999 .

[52]  Thomas P. Rohrer.  The science and psychology of music performance: creative strategies for teaching and learning , 2004 .

[53]  Marcelo M. Wanderley,et al.  Quantitative Analysis of Non-obvious Performer Gestures , 2001, Gesture Workshop.

[54]  Robert O. Gjerdingen,et al.  The Cognition of Basic Musical Structures , 2004 .

[55]  R. Shepard,et al.  Toward a universal law of generalization for psychological science. , 1987, Science.

[56]  R. Jackendoff,et al.  A Generative Theory of Tonal Music , 1985 .