This web site will help get you and your students into the mood for e Day (February 7). To appreciate the site fully, you need to visit the web site in class so that the site is shown on a screen or monitor your students can see.
Basically, this e-song discusses many aspects of the number e, occasionally at the precalculus level or above. The associated web site provides links embedded in the lyrics so you can explore the mathematics involved.
If you want to hear music directly tied to the digits in the number e, you might want to listen to Kris Lennox's 'e' = C (2) (Toccata). After playing it, you should read the explanatory text for this "bilinear ikosikaitetraphonic integral hyper-serialist work." That's a mouthful!
So, where's the matha-musical genius who will write the first e-tude? It seems like a natural diversion, yet know one has apparently thought of it!