Plutarch Quaestiones Convivales 9.14.3

[3] My brother said, that the ancients celebrated but three Muses, and that to bring proofs for this assertion would be pedantic and uncivil in such a company. The reason of this number was (not as some say) the three different sorts of music, the diatonic, the chromatic, and harmonic, nor those stops that make the intervals nete, mese, and hypate; though the Delphians gave the Muses this name erroneously, in my opinion, appropriating it to one science, or rather to a part of one single science, the harmoniac part of music. But, as I think, the ancients, reducing all arts and sciences which are practised and performed by reason or discourse to three heads, philosophy, rhetoric, and mathematics, accounted them the gifts of three Gods, and named them the Muses. Afterwards, about Hesiod’s time, the sciences being better and more thoroughly looked into, men subdividing them found that each science contained three different parts. In mathematics are comprehended music, arithmetic, and geometry; in philosophy are logic, ethics, and physics. In rhetoric, they say the first part was demonstrative or encomiastic, the second deliberative, the third judicial. None of all which they believed to be without a God or a Muse or some superior power for its patron, and did not, it is probable, make the Muses equal in number to these divisions, but found them to be so. Now, as you may divide nine into threes, and each three into as many units; so there is but one rectitude of reason, which is employed about the supreme truth, and which belongs to the whole in common, while each of the three kinds of science has three Muses assigned to it, and each of these has her separate faculty assigned to her, which she disposes and orders. And I do not think the poets and astrologers will find fault with us for passing over their professions in silence, since they know, as well as we, that astrology is comprehended in geometry, and poetry in music.