If you can get the music in isolation from other sources, REMIXAVIER may be of use:
The Remixavier ("remix savior") project is concerned with recovering the "difference" between different mixes of the same track. For instance, given a full mix and an instrumental, we can try to recover the vocals, or given the full mix and an a cappella version, we can try to produce an instrumental version. In the process, we can identify the precise temporal alignment between the two versions, which may be useful in its own right.
http://www.ee.columbia.edu/~dpwe/resources/matlab/remixavier/
http://labrosa.ee.columbia.edu/hamr2013/proceedings/doku.php/remixavier
Example 1: Significant time skew and channel difference
This example consists of an original instrumental track, digitized from a vinyl LP release, and a rap that uses the track as backing, taken directly from a CD. Thus, the different signal paths mean that the timing is significantly different (clock drift of 0.1%), and the overall spectrum is very different too.