Question about the Pitch Black/Dark Rondo

After seeing La Croix also using the Rondo and very obviously being "An die Freude," it made me wonder if Kagetsumugi's Rondo is also inspired/taken from an existing song.



I've tried looking up the lyrics she sings but couldn't find anything.
Considering Kagetsumugi's very Japanese aesthetic, I was thinking maybe it's based on a Japanese song that I don't know?