In Greek mythology, the Muses are nine goddesses who personify fields of artistic endeavor. They are used in modern times to refer to inspiration, often with creators half-jokingly referring to their own personal artistic muse, as if they were a form of quirky guardian angel with endless numbers but unpredictable demands. In addition, the word amuse has its roots in their name.
The number of Muses began as three, quickly expanded to four and finally, still in ancient Greek times, to nine. The Muses were not assigned standardized divisions of poetry/song until late Hellenistic times. The assignments themselves were not completely hard and fast even then. Apparently, in the 19th century, that age of grand systemizing, various "duties" and forms of art were assigned to them, with which they are now identified, although there are several versions of the system.
Likewise, traditionally, there is a numbered list of the Arts. The number itself has varied widely, from five to nine, generally. Originally they were all versions of poetry and literature, with the addition of dance, comedy (theatre), tragedy, and usually history and astronomy. To the ancient Greek, all forms of literature were forms of poetry, and therefore of music, as poetry was sung. Ricciotto Canudo, an Italian film theoretician living in France, claimed in 1911 that film was the sixth art. Later, Canudo renumbered his list, in the article Reflections on the Seventh Art, making film the seventh. Then, in 1964 Claude Beylie, a leading French film academic, said that comics were the ninth art, as Beylie felt that television was the eighth.
As I said above, the Muses, usually nine, were often assigned art forms, especially in the 19th century. This activity began to cross with that of numbering the arts to produce various strange and enchanting lists. One common one was the following:
Calliope was the muse of epic poetry. Clio was the muse of history. Erato was the muse of love poetry. Euterpe was the muse of music. Melpomene was the muse of tragedy. Polymnia was the muse of sacred poetry. Terpsichore was the muse of dance. Thalia was the muse of comedy. Urania was the muse of astronomy.
However, nowadays it is usually different — we see history and astronomy as sciences, so Clio and Urania have to get other jobs. Additionally, we see all poetry as one art form, so Calliope, Erato and Polymnia have overlapping functions. We also think theatre is one thing, not comedy and tragedy as separate, so Thalia and Melpomene have to work together.
Taking into account current divisions, utilizing Clemens' vast knowledge (he is also a scholar of ancient Greek), thus considering the meanings of the Greek names of the Muses, here is Clemens' and my list, for our Postmodern times:
The Nine Arts and Nine Muses
1) painting (including drawing and photography) — Polymnia
2) sculpture (including installation) — Clio
3) theatre — Melpomene
4) architecture — Urania
5) music — Euterpe
6) dance — Terpsichore
7) literature — Calliope
8) cinema ("moving images" in whatever technological format,
so also TV, video, etc.) — Erato
9) comics (now universally called the ninth art, the only really fixed
"number term" nowadays, and the most recent) — Thalia
Polymnia, all painting is somehow sacred, celebrates vision; her name means "many hymns," but is not exclusively sacred, it also means "many songs of praise," "many paeans," "many expressions of joy." That's painting to me. Drawing as an aspect of painting is clear, but also photography is, I believe, indeed photo-graph-y, i.e. "drawing with light," thus a form of painting.
Clio, sculpture was originally born of works of commemoration, seeking "monumental presence." A solid remembrance, related to Mneme, the unnamed precursor of the Muses, the Muse/goddess of memory. Clio's name is from the root meaning "recount" or "make famous".
Melpomene, because tragedy is clearly now the queen of drama. There is an enduring tradition of paintings of famous actresses posed as Melpomene.
Urania, " heavenly measure," mathematics embodied, is now more architecture than astronomy.
Euterpe, she keeps her original job, which was one of the few rather fixed points, and her name means rejoicing/singing well, singing with delight, to please well.
Terpsichore, she too keeps her traditional assignment, and her name fits it well ("delight of dancing").
Calliope, because literature, whose queen is nowadays the novel, was all born of epic poetry; "beautiful-voiced," "beautiful speaking.".
Erato, well, you know --- love stories, eroticism, reigns in movies; even the fact that "eros" implies a more superficial form of love seems appropriate; one of her sites was a pilgrimage place for star-crossed lovers in ancient times; her name means something close to "lovely."
Thalia, (meaning “blooming,” "flourishing," the amused muse), because the term for comics in most languages (incl. comics, funnies, manga, etc.) is a form of "comic story" or "amusing art."
Image: The Dance of Apollo with the Muses, by Baldassare Tommaso Peruzzi, early 1500s