The Muses Euterpe and Urania (a detail from Pompeo Battoni (1708-1787), "Apollo and the Two Muses") [Source]
The Muse Euterpe (Ευτέρπη ) ("rejoicing well" or "delight"), in Greek mythology, was one of the Muses, the daughters of Mnemosyne, fathered by Zeus. Called the "Giver of Pleasure", when later poets assigned roles to each of the Muses, she was the muse of music. In late Classical times she was named muse of lyric poetry and depicted holding a flute. A few say she invented the aulos or double-flute, though most mythographers credit Marsyas with its invention. The river Strymon impregnated Euterpe; her son Rhesus led a band of Thracians and was killed by Diomedes at Troy, according to Homer's Iliad.
Euterpe, 1842, Camiile Roqueplanartist (1803 - 1855)
The Muses Clio, Euterpe and Thalia, Eustache Le Sueur
Her name is from Greek eu (good, well) and τέρπ-εω (to please)
There is also an asteroid 27 Euterpe.
A genus of Brazilian palms called Euterpe.
Euterpe were a 'spin-off' group from the rock band Gong.