Summary of limits in the relation of music to mathematics, language, communication and art
I would assert that music is not mathematics, or fundamentally mathematical in any special sense apart from many other disciplines or arts. It is not a language. It is not communication in any normal sense of the term. It is, perhaps, an art, but if so, it is an art which produces no objects of art, since the score is not the music. (In any case, "art" is considerably less definable than mathematics, language or communication, so any analogy to it may not help us much.) Historically, music has not been automatically considered to be an art until relatively recently in western culture, and in some other cultures not at all.
These are some things music is not. Therefore, faith integration with music will also not automatically reflect these things. If it could be conclusively shown to be primarily any of these things, the faith-integration task would be simpler, and would consist largely of borrowing approaches from other disciplines.
This is not to say that music does not share some features with mathematics, language communication and art, but none of them is an adequate metaphor for music, nor do they in combination suffice to explain or capture the essence of music. If there were any simple relationship between music and any (or all) of the foregoing, then the task of faith integration in music would reflect similar considerations to them.