What were the nine goddess of the arts?

The Muses of Greek mythology were goddesses of art:

Calliope - epic poetry

Clio - history

Erato - lyrical poetry

Euterpe - music

Melpomene - tragedic theatre

Polyhymnia - hymnal/choral poetry

Terpsichore - dance/choreography

Thalia - comedic theatre

Urania - astronomy

Muses. Sometimes referred to as Water Nymphs.