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

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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.

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

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

|: 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.)

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

with shifts against an accompaniment in triple meter.  

|: 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:

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

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

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

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.