In reply to:

Mk1 owners don't have a clock, but it'll keep track of the number of times a song has been played, so they can at least hear the songs that have been played a fewer number of times than the others (similar, but different).

Theoriticially the MK1 could still keep track of the number of hours since the song was last herd though, since it does keep time when it's powered. And from my experiences with my MK1, the time started from where it was left off when it gets power back, and not reset.