  A function is called quasiperiodic if its fundamental frequencies are
linearly independent over the rationals. With appropriate parameters, the
sliding window point clouds of such functions can be shown to be dense in tori
with dimension equal to the number of independent frequencies. In this paper,
we develop theoretical and computational techniques to study the persistent
homology of such sets. Specifically, we provide parameter optimization schemes
for sliding windows of quasiperiodic functions, and present theoretical lower
bounds on their Rips persistent homology. The latter leverages a recent
persistent K\"{u}nneth formula. The theory is illustrated via computational
examples and an application to dissonance detection in music audio samples.
