early 15c., quaveren, "to vibrate, tremble, have a tremulous motion," probably a frequentative of cwavien "to tremble, shake, be afraid" (early 13c.), which probably is related to Low German quabbeln "tremble," and possibly of imitative origin. Meaning "sing in trills or quavers, sing with a tremulous tone" is recorded by 1530s. Related: Quavered; quavering.
1560s, in music, "an eighth-note," from quaver (v.). Sense of "a shake or trill in singing" is from 1610s; meaning "a tremble in the voice" is by 1748.