Anybody have any other information they'd like to see?

How about this...

Allow the user to set the total number of songs on the player (default about 3600), how many songs per album (default about 12), and how many albums per band (default about 4).

Then, graph the results, allowing you to quickly scroll through a list of band1, band2, band3, etc., and as you scroll, show the dots on the graph. Each album within a band could be a different color, so you could see if there's any clustering effect of band X along with the album effect. You could also scroll through individual albums (band 7, album 3) and show only that album on the graph, like in my illustration.

Then we'd have a very clear picture of just how clustered a truly random distribution should look.