Consider that with a linear regulator (ie - LM317) the current input and output are equal, and the entire voltage difference is across the regulator. P = V * I, and thus the power it dissipates is equal to the voltage difference, and the output current. Because of this, a linear regulator would be a TERRIBLE solution for this application, unless your mp3 player uses VERY little current and you don't care at ALL about how long the battery lasts on a charge.
18v - 1.5v = 16.5v. 1.5v/16.5v = 9%. That means that only 9% of the power coming from the battery will make it to the MP3 player, and the other 91% will be dissipated as heat by the regulator. A linear regulator like this, even with a heatsink attached, can't deal with very high power dissipation, and with a 16.5v drop across it, that's not much current to make it heat up a lot. If your mp3 player needs more than a fraction of an amp, I would steer clear of linear regulators.
A switching regulator is a much better solution; they can offer efficiencies of 75% or more. Based on your question I'm going to assume you probably don't want to try to build one just yet, because they can be rather complicated, but you might be able to find something commercially.