Some High, Some Low, Some Places to Go

While setting puzzles, I sometimes have a song running through my mind, but when it comes to naming, often I find that I’ve misremembered lyrics or entirely invented songs. This puzzle’s title goes with a tune, but none that’s ever been heard by anyone but me.

Rules:
Normal Sudoku rules apply.
Colored cells contain digits which are greater than (red, arrowheads pointing out) or less than (pink, arrowheads pointing in) the digits in the uncolored or different-colored cells with which they share an edge.

Estimated difficulty: 1.5 out of 5