Rhythm and Melody

Rhythm, Melody, and Voice Leading
- a sample of my work -

"Music and rhythm find their way into the secret places of the soul." - Plato

"There is geometry in the humming of strings." - Pythagoras

"The mathematics of rhythm are universal. They don't belong to any particular culture." - John McLaughlin

"I am in favor of mathematizing everything you can." - Mario Bunge

Godfried T. Toussaint, "Computational geometric aspects of rhythm, melody, and voice-leading," Computational Geometry: Theory and Applications, Vol. 43, Issue 1, January 2010, pp. 2-22.

PDF file: rhythm-melody-voice-leading.pdf

Godfried T. Toussaint, "Interlocking rhythms, duration interval content, cyclotomic sets, and the haxachordal theorem," Fourth International Workshop on Computational Music Theory, Universidad Politecnica de Madrid, Escuela Universitaria de Informatica, July 24-28, 2006 (Abstract only).

PDF file: interlocking-rhythms.pdf

Godfried T. Toussaint, "The Euclidean algorithm generates traditional musical rhythms," Proceedings of BRIDGES: Mathematical Connections in Art, Music, and Science, Banff, Alberta, Canada, July 31 to August 3, 2005, pp. 47-56.

Godfried Toussaint, "The geometry of musical rhythm," Proceedings of the Japan Conference on Discrete and Computational Geometry, J. Akiyama et al. (Eds.), LNCS 3742, Springer-Verlag, Berlin, Heidelberg, 2005, pp. 198-212.

PDF file: geometry-of-rhythm.pdf

Godfried Toussaint, "Mathematical features for recognizing preference in Sub-Saharan African traditional rhythm timelines," Proceedings of the 3rd International Conference on Advances in Pattern Recognition, University of Bath, Bath, United Kingdom, August 22-25, 2005, pp. 18-27.

PDF file: off-beatness.pdf

Godfried T. Toussaint, "Computational geometric aspects of musical rhythm," Abstracts of the 14th Annual Fall Workshop on Computational Geometry, Massachussetts Institute of Technology, November 19-20, 2004, pp. 47-48.

PDF file

Godfried T. Toussaint, "A comparison of rhythmic similarity measures," Proceedings of ISMIR 2004: 5th International Conference on Music Information Retrieval, Universitat Pompeu Fabra, Barcelona, Spain, October 10-14, 2004, pp. 242-245. A longer version also appeared in: FORMA, Vol. 21, No. 2, 2006, pp. 129-149, and in: School of Computer Science, McGill University, Technical Report SOCS-TR-2004.6, August 2004.

PDF file (long version)

Godfried T. Toussaint, "Classification and phylogenetic analysis of African ternary rhythm timelines," Extended version of paper that appeared in: Proceedings of BRIDGES: Mathematical Connections in Art, Music, and Science, University of Granada, Granada, Spain July 23-27, 2003, pp. 25-36.

compressed PostScript file ternary.ps.gz
PDF file
Conference proceedings version - PDF file

Godfried T. Toussaint, "Algorithmic, geometric, and combinatorial problems in computational music theory," Extended version of paper that appeared in: Proceedings of X Encuentros de Geometria Computacional, University of Sevilla, Sevilla, Spain June 16-17, 2003, pp. 101-107.

compressed PostScript file sevilla.long.ps.gz
PDF file (long)
Conference proceedings version - PDF file

Godfried T. Toussaint, "A mathematical analysis of African, Brazilian, and Cuban clave rhythms," Proceedings of BRIDGES: Mathematical Connections in Art, Music and Science, Townson University, Towson, MD, July 27-29, 2002, pp. 157-168. Also the long version is Technical Report SOCS-02.2, May 2002.

long version clave.pdf
proceedings version PDF file