1560s, "explanation of a term" (a sense now obsolete), from French notation (14c.) and directly from Latin notationem (nominative notatio) "a marking, notation, designation; etymology; shorthand; explanation," noun of action from past-participle stem of notare "to note" (see note (v.)). Meaning "a note, an annotation" is from 1580s. Meaning "system of representing numbers or quantities by signs or symbols" is attested from 1706. Related: Notational.
mid-15c., repete, in music, "a repeated passage, a passage performed a second time," from repeat (v.). By 1660s in reference to the sign in musical notation which indicates this. By 1937 of a repetition of a broadcast program.
c. 1400, "something used in tying or binding," from Late Latin ligatura "a band," from Latin ligatus, past participle of ligare "to bind" (from PIE root *leig- "to tie, bind"). In modern musical notation, "group of notes slurred together," from 1590s; of letters joined in printing or writing from 1690s.
early 14c., "small hook;" mid-15c. "a staff with a hook at the end," from Old French crochet (pronounced "crotchet") "small hook; canine tooth" (12c.), diminutive of croc "hook," from Old Norse krokr "hook," which is of obscure origin but perhaps related to the widespread group of Germanic kr- words meaning "bent, hooked."
As a curved surgical instrument with a sharp hook, from 1750. Figurative use in musical notation for "quarter note" is from mid-15c., from the shape of the notes. Also from 1670s in now-obsolete sense "one of the pair of marks now called 'brackets.'"
Meaning "whimsical fancy, singular opinion," especially one held by someone who has no competency to form a sound one, is from 1570s; the sense is uncertain, perhaps it is the same mechanical image in extended senses of crank; but other authorities link it to the musical notation one (think: "too many notes").