music is a nice/neat/natural way to approach some very advanced CS algorithms/applications etc. and there has been a large burst of innovation and crosspollination between the two areas in the last decade especially in computer music software.
one important area involves attempting to separate different channels from a mixed sound. in other words suppose separate tracks are mixed together into a single track (separate instruments, vocals, etc). its actually a very advanced statistical/AI problem of separating out the original tracks from the mixed track. another basic application is attempting to remove vocals only from music; there are devices advertised to do this, some of them highly engineered and expensive, called vocal removers. this same problem arises in other guises in statistics. my understanding is that ICA, independent component analysis can be used to solve this problem.
another interesting area of application of CS to music related to vocals, enjoying a massive surge in use in the last decade: pitch correctors or so-called autotune which adjust vocal pitch to discrete, on-key increments. Autotune has an origination in scientific/statistical/mathematical analysis; from wikipedia:
Auto-Tune was initially created by Andy Hildebrand, an engineer working for Exxon. Hildebrand developed methods for interpreting seismic data and subsequently realized that the technology could be used to detect, analyze, and modify the pitch in audio files.
also, audio plugins for effects, or "effects boxes", often involve many highly advanced CS/signal processing concepts, closely connected to algorithmic and mathematical theory, such as Fourier Transforms, etcetera. another common effect with some algorithmic theory/complexity is reverb which has roots in mathematical convolution.
ref  from wikipedia with more on autotune & Hildebrand: The Gerbils Revenge / Auto-Tune corrects a singer’s pitch. It also distorts—a grand tradition in pop., Sasha Frere-Jones, New Yorker 6/9/2008