The Mathematics of Rhythm

Rachel W. Hall
Associate Professor
Department of Mathematics and Computer Science
Saint Joseph's University, 5600 City Avenue, Philadelphia, PA 19131
rhall@sju.edu

Audio examples for “Asymmetric Rhythms and Tiling Canons,”
Rachel W. Hall and Paul Klingsberg, American Mathematical Monthly 113 (2006), no.10, 887-896.

Publications on the mathematics of rhythm

• Rachel W. Hall and Paul Klingsberg. Asymmetric rhythms and tiling canons. American Mathematical Monthly 113 (2006), no.10, 887-896.
• Article (PDF)
• Audio files
• New results (Summer 2005)
• The number of asymmetric rhythm cycles modulo inversion
• The number of r-note asymmetric cycles modulo inversion
• Rachel W. Hall.  Math for poets and drummers.  Accepted by Math Horizons, 2006.  Intended for undergraduate math students and their teachers.
• Article (PDF)
• Rachel W. Hall. Playing musical tiles. In Bridges: Mathematical Connections in Art, Music, and Science. R. Sarhanghi and J. Sharp, eds., London, 2006. Includes some discussion of rhythmic tiling.
• Article (PDF)
• Joseph E. Flannick, Rachel W. Hall, and Robert Kelly. Detecting meter in recorded music. In Bridges: Mathematical Connections in Art, Music, and Science. R. Sarhanghi and C. Sequin, eds., Banff, Canada, 2005.
• Article (PDF)
• Rachel W. Hall and Paul Klingsberg.  Asymmetric rhythms, tiling canons, and Burnside's lemma.  In Bridges: Mathematical Connections in Art, Music, and Science. R. Sarhanghi and C. Sequin, eds., pp. 189-194.  Winfield, Kansas, 2004.
• Article (PDF)
• Audio files

Presentations

• “Asymmetric rhythms and tiling canons,” invited address, MAA Eastern Pennsylvania and Delaware section meeting, October 2006.
• Presentation (PPT) with embedded audio
• QuickTime movie of presentation (MOV) with audio
• Handout (PDF)
• “Math for poets and drummers,” Arcadia University colloquium series, February 2006
• Presentation (PDF)

Undergraduate research

• Bobby Kelly.  Mathematics of musical rhythm.  Undergraduate honors thesis, Saint Joseph's University, 2002. Winner of MAA-EPADEL best student paper award, 2002.
• Thesis (PDF)
• Slides from Bobby's final presentation (PDF)
• Joseph E. Flannick.  Rhythm detection in recorded music.  Undergraduate honors thesis, Saint Joseph's University, 2003.
• Thesis (PDF)
• Audio files

Multicultural mathematics course (Math 1011)

• Article (PDF) Multicultural mathematics is a course I designed for undergraduate liberal arts majors. This article details the course goals and topics covered. In addition, I provide sample projects, exercises, and an extensive course list. The course includes a unit on the mathematics of drumming.
• Course home page
• Abcdrums is a program for writing drum compositions created by Dr. Adlai Waksman (formerly of St. Joseph’s University). I used it in the Multicultural Mathematics course. The sound examples for “Asymmetric rhythms and tiling canons” were also created using Abcdrums.
• Abcdrums tutorial

Other people in the mathematics of rhythm

• Godfried Toussaint, Professor of Computer Science at McGill University, has written numerous articles on computational analysis of world rhythms. He is particularly known for his phylogenetic analysis of flamenco rhythms.
• Bill Sethares, Professor of Electrical Engineering at University of Wisconsin—Madison wrote several articles on rhythm detection that were the inspiration for the undergraduate research projects I supervised.
• Moreno Andreatta, IRCAM, introduced me to tiling canons.
• There are many others. See references in my articles.