I'd like to know what's the singular term of music, is it muse?
Music is usually used as uncountable.
But when this noun means "a distinctive type or category of music" (https://www.merriam-webster.com/dictionary/music) it is a countable noun.
So in this meaning it has both singular and plural forms (i.e., a music, some musics).
Etymologically MUSIC is connected with MUSE:
"from Greek mousikē (technē) "(art) of the Muses," from fem. of mousikos "pertaining to the Muses"" (https://www.etymonline.com/).