Surface topology in the canons of J. S. Bach

To make your own canonical Möbius strip.

Steady state of the top two voices in Canon 5, BWV 1087.

Print this image on a sheet of transparent material.
Cut out the two 2-bar segments, leaving about 1cm of extra space at each end.
Tape the two together to form the entire 4-bar steady state of (the upper two voices of) Canon 5.
Wrap this 4-bar segment twice around itself with a twist, to form a Möbius strip; tape to hold coil.

Here's what it sounds like:

For more information: The sound of topology: two-dimensional manifolds in Bach (with Eric L. Altschuler), The Musical Times, Winter 2015, 57-64

Updated, 7/1/25.