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It's a cute idea. I have a few notes; having a visual indicator or warning that a platform is about to fall is a good idea. Like a slight vibration or tremor animation. Also, the pacing in the level isn't super fun. It really isn't at all clear how the platforms move with the music. Having a clear base line or beat that the platforms are timed to, like a marching song would be better for making that clear.  Also, the jump doesn't feel great in terms of control nor the side to side movement. I like that the double jump is a way of correcting if you jump and realize the timing was wrong. I think the mechanics and level design of the game you have could be more fun before adding new things but I agree new things will help it.

I think the game currently lacks a fundamental core to build everything around. If you want the core to be "the the platforms move to music", then that needs to be done a lot better. I like the idea of a music platformer in general so it's not that I think that's a bad idea. Also, the lives/health mechanic isn't great. Mainly because the level doesn't feel fun to play, so forcing the player all the way back to the beginning when a lot of the level design seems to be about gotchas and failing then learning and memorizing rather than cluing the player in advance about what's coming next. Keeping the lives and health is fine if you change the level design to be either more fun or more fair. Now that all the criticism is done I do think you did a really good job for the time you have spent. The art is very polished and the game isn't buggy. The tutorial is also well done.