**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.

- 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).

- 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.

- 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.

- 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.

- 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.

- 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. -
ternary.ps.gz`compressed PostScript file` -
**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. -
sevilla.long.ps.gz`compressed PostScript file` -
**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,