I often consult a website called Thesaurus Musicarum Latinarum of Latin writings on music theory and practice. Note that the web address changes every couple of years.
Why "musicarum latinarum" in the first declension? Why not "musicorum latinorum"?
In the masculine, it would read "thesaurus of Latin musicians" (music theorists really), but in the feminine it appears to read "thesaurus of Latin musics", which makes no sense to me.
Simply, it's because musica is a feminine noun.
As to why it might be plural, which is a separate question really, it seems here to mean something more akin to "musical arts." This isn't really a Classical development, but was probably what the founders of the TML had in mind when they founded it, especially given it's mission:
The Thesaurus Musicarum Latinarum (TML) was created in 1990 by the initiative of a group of scholars from around the world, under the direction of Thomas Mathiesen at Indiana University, with the ambition to collect in electronic format the entire corpus of Latin music theory written during the Middle Ages and the Renaissance.
These texts are literary works that discuss general principles (e.g. the origin and nature of music, its role within human activities) or technical issues (e.g. the construction of musical instruments); or describe or define procedures (composition, notation and performance), and genres or styles (within liturgical, secular, and instrumental repertories, in monody and polyphony).
So it's not about musicians or even songs per se, but the multitude of theories and arts that go into the creation of Latin music.
Thesaurus Musicorum Latinorum could be understood to mean "A treasury of Latin musicians", where the noun is not the feminine mūsica ('music') but the masculine mūsicus ('musician'). I suppose it's the masculine thēsaurus that's throwing you off: gender signals agreement inside the noun phrase (or with a relative pronoun etc.), assigned by the head noun; the head of one noun phrase (thēsaurus) cannot change the gender of another noun phrase (mūsicae Latīnae).
That said, there also exists the neuter plural mūsica Latīna, whose genitive is precisely mūsicōrum Latīnōrum, so that too would be a valid if somewhat ambiguous phrasing.
The feminine noun is in the plural because it's countable; but somewhat counter-intuitively, the neuter noun is plural because it's a mass noun "the stuff of the Muses". You're being confused by the fact that "music" isn't normally countable in English, but it can be treated as countable, as the numerous google results for "musics" testify.
Musica can be feminine singular, or neuter plural; both mean "music" and both are good classical Latin. In the former case the genitive is musicae; in the latter it is musicorum (sic). "musicarum latinarum" could mean "of female Latin musicians", or "of Latin musics" (genitive plural of musicae). This is not classical, but it has its logic.
