Sometimes the music doesn't play in stages, boss fights and even the music room! It just happens at random and it really sucked on my first playthrough having no music during the fight with Gates and Vivit.
UPDATE: Get VirtualMIDISynth. Get MS GS Wavetable Synth soundfont from the link in the description here:
https://youtu.be/VgkoLQMzuhw. Open VirtualMIDISynth, go to soundfonts, click the + sign, find and open your soundfont. Go to MIDI mapper, change default MIDI out device to VirtualMIDISynth. Boom, you got the music working, you can use different soundfonts and VirtualMIDISynth should open upon opening Shuusou. Sorry I took too long to update this post. Any questions?