Turns out there are nine Greek Muses, daughters of Zeus. Each involved with a different aspect of inspiration as follows: http://www.talesbeyondbelief.com/nymphs/muses.htm. I suspect the muse depicted in the painting may be Calliope or Clio, patrons of epic poetry and writing.
Here they are frolicking about as muses are wont to do.
Sit down, stay quiet and one may visit you.