Musical Knots
The following recordings were made by Thomas Stauffer (PSU '28) and represent the specified torus knot as a path along a generalized version of Waller's torus, a torus obtained by identifying edges of a periodic region of the Douthett-Steinbach graph which is dual to the Tonnetz, first introduced by Euler, and a popular visualization in neo-Riemannian music theory. For more on this topic, see here.
(4,3)-Torus Knot
When played in a loop, this song is also equivalent to an infinite sequence of additional torus knots made up of the boxed elements in the image on the right.
(3,2)-Torus Knot
When played in a loop, this song is also equivalent to an infinite sequence of additional torus knots made up of the boxed elements in the image on the right.
Trefoil Knot
An alternative version of the trefoil knot (which is a (3,2)-torus knot) arranged for the piano.
