Anacrustic

prosody. an unstressed syllable or syllable group that begins a line of verse but is not counted as part of the first foot.
music. the note or notes preceding a downbeat; upbeat.
noun (pl) -ses (-siːz)
(prosody) one or more unstressed syllables at the beginning of a line of verse
(music)

an unstressed note or group of notes immediately preceding the strong first beat of the first bar
another word for upbeat

n.

“unstressed syllable at the beginning of a verse,” 1833, latinized from greek anakrousis “a pushing back,” of a ship, “backing water,” from anakrouein “to push back, stop short, check,” from ana- “back” (see ana-) + krouein “to strike,” from pie -kreue- (2) “to push, strike” (cf. russian krusit, lithuanian krusu “to smash, shatter,” old church slavonic kruchu “piece, bit of food,” old english hreowian “feel pain or sorrow,” old norse hryggja “make sad”).