Conchord: An Application for Generating Musical Harmony by Navigating in a Perceptually Motivated Tonal Interval Space

We present Conchord, a system for real-time automatic generation of musical harmony through navigation in a novel 12-dimensional Tonal Interval Space. In this tonal space, Euclidean distances among multi-level pitch configurations equate with their perceptual proximity, and Euclidean distances of pitch configurations from the center of the space acts as an indicator of consonance. Building upon these attributes, users can intuitively and dynamically define a collection of chords based on their relation to a tonal center (or key) and their consonance level. Furthermore, two algorithmic strategies grounded in principles from function and root-motion harmonic theories generate chord progressions characteristic of Western tonal music.

[1]  Massimiliano Lucchesi,et al.  The Numerical Method , 2008 .

[2]  Robert Rowe,et al.  Machine Musicianship , 2001 .

[3]  François Pachet,et al.  Formulating Constraint Satisfaction Problems on Part-Whole Relations : The Case of Automatic Musical Harmonization , 1998 .

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

[5]  C. Krumhansl,et al.  Tracing the dynamic changes in perceived tonal organization in a spatial representation of musical keys. , 1982 .

[6]  Somnuk Phon-Amnuaisuk,et al.  Evolving Musical Harmonisation , 1999, ICANNGA.

[7]  Elaine Chew,et al.  A Hybrid System for Automatic Generation of Style-Specific A ccompaniment , 2007 .

[8]  Eytan Agmon,et al.  Functional Harmony Revisited: A Prototype-Theoretic Approach , 1995 .

[9]  Wendy E. Mackay,et al.  PaperTonnetz: Music Composition with Interactive Paper , 2012 .

[10]  Constantine Frithiof Malmberg,et al.  The perception of consonance and dissonance , 1918 .

[11]  A. Schoenberg,et al.  Structural functions of harmony , 1954 .

[12]  Jean Philippe Rameau,et al.  Traité de l'harmonie , 1992 .

[13]  Gabriel Gatzsche,et al.  Interaction with Tonal Pitch Spaces , 2008, NIME.

[14]  E. Chew Towards a mathematical model of tonality , 2000 .

[15]  Nicolas Meeùs Toward a Post-Schoenbergian Grammar of Tonal and Pre-tonal Harmonic Progressions , 2000 .

[16]  M. Rohrmeier A generative grammar approach to diatonic harmonic structure , 2007 .

[17]  Daniel Lehmann,et al.  Harmonizing Melodies in Real-Time: the Connectionist Approach , 1997, ICMC.

[18]  C. Harte,et al.  Detecting harmonic change in musical audio , 2006, AMCMM '06.

[19]  A. Kameoka,et al.  Consonance theory part I: consonance of dyads. , 1969, The Journal of the Acoustical Society of America.

[20]  Norman D. Cook,et al.  Harmony, Perspective, and Triadic Cognition , 2011 .

[21]  David Huron,et al.  Interval-Class Content in Equally Tempered Pitch-Class Sets: Common Scales Exhibit Optimum Tonal Consonance , 1994 .

[22]  J. Kruskal Nonmetric multidimensional scaling: A numerical method , 1964 .

[23]  Francois Pachet,et al.  The MusES system: an environment for experimenting with knowledge representation techniques in tonal harmony , 2007 .