Asymmetric Rhythms and Tiling Canons
Audio Examples

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

Jump to Audio Example 1 2 3 4 5 6 7 8 9 10 11 12 13

NOTE: Except where noted, sound examples were created by Rachel Hall. You are welcome to download them. If you use them for any purpose, please give her credit.

• Audio Example 1: ZZ Top, “Sharp Dressed Man,” ZZ Top - Greatest Hits, Warner Brothers, 1992.
• Audio Example 2: Hansel Martinez Y La Orquestra Calle Ocho, “Quitate la Mascara,” Salsa Fresca! Dance Hits of the '90s, Rhino Records, 1996.
• Audio Example 3: The rhythm cycle

|: x..x..x. :|.

All the shifts of the cycle sound the same if the beginning of a measure is not marked.

• Audio Example 4: The non-asymmetric rhythm

|: x.x...x. :|.

Again, all possible shifts of the rhythm are juxtaposed with the duple meter accompaniment. Compare with the asymmetric rhythm

|: x..x..x. :|,

also with duple meter accompaniment. You can hear an asymmetric rhythm in the song “Bobangi” (Aka Pygmies, “Bobangi,” African Rhythms, Warner Classics, 2003.)

• Audio Example 5: The 3-asymmetric cycle

|: x.....x..x.x :|,

with shifts against an accompaniment in triple meter.  

• Audio Example 6: The 5-asymmetric rhythm

|: x..x..|....x.|.x....|..x..x|...... :|,

against an accompaniment in quintuple meter.

· Audio Example 7: Rhythm cycles of length 12 which are 3-asymmetric and have four note onsets:

• Pattern 1, |: xxxx........ :| with an accompaniment in triple meter.
• Pattern 2, |: xxx....x.... :|
• Pattern 3, |: xx....xx.... :|
• Pattern 4, |: xx.x......x. :|
• Pattern 5, |: xx.x..x..... :|
• Pattern 6, |: x.....x..x.x :|
• Pattern 7, |: x.x..x.x.... :|
• Pattern 8, |: x..x..x..x.. :|
• Audio Example 8: Messiaen's canon, rhythm only.  The inner rhythm is

x..x....x.......x....x..x...x..x......x..x...x.x.x..x....x..x.x.

and the outer rhythm is e.e.e

• Audio Example 9: The canon generated by |: x.....x..x.x :| and |: e...e...e... :|

· Audio Example 10: The 12-periodic tiling canons of three equally spaced voices:

• Canon 1, generated by |: xxxx........ :|.  Each voice plays through two cycles before the next voice enters.
• Canon 2, generated by |: xxx....x.... :|
• Canon 3, generated by |: xx....xx.... :|
• Canon 4, generated by |: xx.x......x. :|
• Canon 5, generated by |: xx.x..x..... :|
• Canon 6, generated by |: x.....x..x.x :|
• Canon 7, generated by |: x.x..x.x.... :|
• Canon 8, generated by |: x..x..x..x.. :|
• Audio Example 11: Tiling canon with unequally-spaced voices generated by the inner rhythm

|: x.x..... :|

and outer rhythm |: ee..ee.. :|.

• Audio Example 12: Tiling canon of maximal category with period 72, generated by inner rhythm

xx...xx.....x............x...x......x.....x.....xx...x..................

with outer rhythm

e.......e.........e.......e.............e.................e.............

Voice onsets are marked by whistles about halfway through the track.

• Bonus Example 13: Beethoven’s canon with inversion. “Allegretto” from Beethoven string quartet Op. 59, no. 2, Shanghai String Quartet, Delos Records, 2004.