The music forcibly turning on/off your movement is in interesting concept. I personally think having to deal with this kind of movement is rather sluggish and limits player expression. Though I supposed it has its appeal as force jumping isn't an untapped design space(the music part is new).
However, having an air dash make up for it.
So does the level design. The branching paths of every set piece requires different combinations of jumps, timing, and air dashes. Effectively Solving the limitation I've mentioned above.
Maybe aside the graphics being kinda one note and how players can engage with the on/off theme, this game is an excellent argument for this kind of mechanic. 10/10