The Harmonic Musical Surface and Two Novel Chord Representation Schemes

Selecting an appropriate representation for chords is important for encoding pertinent harmonic aspects of the musical surface, and, at the same time, is crucial for building effective computational models for music analysis. This chapter, initially, addresses musicological, perceptual and computational aspects of the harmonic musical surface. Then, two novel general chord representations are presented: the first, the General Chord Type (GCT) representation, is inspired by the standard Roman numeral chord type labelling, but is more general and flexible so as to be applicable to any idiom; the second, the Directed Interval Class (DIC) vector, captures the intervallic content of a transition between two chords in a transposition-invariant idiom-independent manner. Musical examples and preliminary evaluations of both encoding schemes are given, illustrating their potential to form a basis for harmonic processing in the domain of computational musicology.

[1]  David Lewin,et al.  Re: Intervallic Relations between Two Collections of Notes , 1959 .

[2]  Maxime Crochemore,et al.  Algorithms For Computing Approximate Repetitions In Musical Sequences , 2002, Int. J. Comput. Math..

[3]  P. Vernon.  AUDITORY PERCEPTION: I. THE GESTALT APPROACH , 1934 .

[4]  William Hutchinson,et al.  The acoustic component of western consonance , 1978 .

[5]  David Temperley,et al.  Computational Models of Music Cognition , 2013 .

[6]  E. Cambouropoulos.  The Musical Surface: Challenging Basic Assumptions , 2010 .

[7]  S. Jeong.  Harmony , 2012, SIGGRAPH '12.

[8]  Emilios Cambouropoulos.  A Directional Interval Class Representation of Chord Transitions. , 2012 .

[9]  Maximos A. Kaliakatsos-Papakostas,et al.  HARMONY IN THE POLYPHONIC SONGS OF EPIRUS : REPRESENTATION , STATISTICAL ANALYSIS AND GENERATION , 2014 .

[10]  G. Kramer.  Auditory Scene Analysis: The Perceptual Organization of Sound by Albert Bregman (review) , 2016 .

[11]  T L Hubbard,et al.  Recognizing the component tones of a major chord. , 2001, The American journal of psychology.

[12]  Richard Parncutt.  A Model of the Perceptual Root(s) of a Chord Accounting for Voicing and Prevailing Tonality , 1996, Joint International Conference on Cognitive and Systematic Musicology.

[13]  Fred Lerdahl,et al.  Tonal Pitch Space , 2001 .

[14]  Albert S. Bregman,et al.  The Auditory Scene. (Book Reviews: Auditory Scene Analysis. The Perceptual Organization of Sound.) , 1990 .

[15]  Maximos A. Kaliakatsos-Papakostas,et al.  Probabilistic harmonization with fixed intermediate chord constraints , 2014, ICMC.

[16]  Richard Parncutt.  Template‐matching models of musical pitch and rhythm perception , 1994 .

[17]  R. Jackendoff,et al.  The capacity for music: What is it, and what’s special about it? , 2006, Cognition.

[18]  Dirk-Jan Povel,et al.  Perceptual Mechanisms in Music Processing , 2001 .

[19]  C. Chuan.  Tone and Voice: A Derivation of the Rules of Voice-Leading from Perceptual Principles , 2001 .

[20]  E. Cambouropoulos.  Voice And Stream: Perceptual And Computational Modeling Of Voice Separation , 2008 .

[21]  A. Forte.  The Structure of Atonal Music , 1973 .

[22]  Anna Jordanous.  Voice separation in Polyphonic Music: a Data-Driven Approach , 2008, ICMC.

[23]  David Lewin,et al.  Generalized Musical Intervals and Transformations , 1987 .

[24]  Dmitri Tymoczko.  A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice , 2011 .

[25]  Costas Tsougras,et al.  IDIOM-INDEPENDENT HARMONIC PATTERN RECOGNITION BASED ON A NOVEL CHORD TRANSITION REPRESENTATION , 2013 .

[26]  Remco C. Veltkamp,et al.  Tonal Pitch Step Distance: a Similarity Measure for Chord Progressions , 2008, ISMIR.

[27]  Diana Deutsch,et al.  THE PROCESSING OF PITCH COMBINATIONS , 1999 .

[28]  S. Locke,et al.  Categorical perception in a non-linguistic mode. , 1973, Cortex; a journal devoted to the study of the nervous system and behavior.

[29]  Diana Deutsch,et al.  7 – The Processing of Pitch Combinations , 2013 .

[30]  D. Temperley.  The Cognition of Basic Musical Structures , 2001 .

[31]  Remco C. Veltkamp,et al.  A geometrical distance measure for determining the similarity of musical harmony , 2013, International Journal of Multimedia Information Retrieval.

[32]  E. M. Burns.  Intervals, Scales, and Tuning , 1999 .

[33]  R. Jackendoff.  Consciousness and the Computational Mind , 1987 .

[34]  Kai-Uwe Kühnberger,et al.  COINVENT: Towards a Computational Concept Invention Theory , 2014, ICCC.

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

[36]  Anssi Klapuri,et al.  Automatic Transcription of Melody, Bass Line, and Chords in Polyphonic Music , 2008, Computer Music Journal.

[37]  Steven G. Laitz,et al.  The Complete Musician: An Integrated Approach to Tonal Theory, Analysis, and Listening , 2003 .

[38]  David Lewin.  Special Cases of the Interval Function between Pitch-Class Sets X and Y , 2001 .

[39]  S. Handel,et al.  Listening: An Introduction to the Perception of Auditory Events , 1993 .

[40]  John A. Sloboda,et al.  The musical mind , 1986 .

[41]  R. Parncutt.  Harmony: A Psychoacoustical Approach , 1989 .

[42]  J. D. Smith,et al.  What child is this? What interval was that? Familiar tunes and music perception in novice listeners , 1994, Cognition.

[43]  Maximos A. Kaliakatsos-Papakostas,et al.  Evaluating the General Chord Type Representation in Tonal Music and Organising GCT Chord Labels in Functional Chord Categories , 2015, ISMIR.

[44]  Anne Sullivan,et al.  Auditory perception. , 1973, British medical journal.

[45]  Mark B. Sandler,et al.  Symbolic Representation of Musical Chords: A Proposed Syntax for Text Annotations , 2005, ISMIR.

[46]  David Barber,et al.  A generative model for music transcription , 2006, IEEE Transactions on Audio, Speech, and Language Processing.

[47]  Maximos A. Kaliakatsos-Papakostas,et al.  An Idiom-independent Representation of Chords for Computational Music Analysis and Generation , 2014, ICMC.