Muse on this.
Also, Merriam-Webster's Dictionary of English Usage says this about the matter:
Still, I think it might come down to what you're musing on or about.
For example muse on the day returned only one hit in Google books, while muse about the day returns at least four. I might be more inclined to say muse about when the object of my musing is less focused – I mused on my predicament, yet I mused about my day – but you would be foolish to regard that as a hard and fast rule.
Incidentally, if you restrict the Ngram to more recent sources, it seems to contradict the usage note in M-W, meaning about might be becoming more like upon and over, with on remaining the frontrunner. (That said, it's a silly notion to think that you should always follow what Ngram shows is most common. Muse on that advice for awhile.)