It'd be great if the mod was compatible with the mod Biome Music, as that mod plays songs pretty often.

I'm not sure I understand what needs compatibility here. If it's for the tracks the mod allows pack makers to add, that's on the pack makers to add support for. All one needs to do to add support for a track is add a line into their lang file. An example would be "sounds.musicmanager.{mod_id}.{directory to sound}": "Artist name - Track name". The sound directory will be the folder structure with each folder separated by a period, and the sound name as the last part of it.

For example, the vanilla track "Infinite Amethyst" by Lena Raine located in the folder structure sounds/music/game/infinite_amethyst.ogg would look like "sounds.musicmanager.minecraft.music.game.infinite_amethyst": "Lena Raine - Infinite Amethyst" in the lang file.

If there's something I'm missing about this mod that needs further compatibility, please let me know. The mod doesn't add any tracks of its own as far as I can tell, and the rest of the mod just customizes the sound preferences (pitch variance and disabling tracks) so I don't know what else needs to be done here.