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
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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
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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.
