Old English clænlic "morally pure, innocent," from clæne (see clean (adj.)). Of persons, "habitually clean," from c. 1500.
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Old English clæne "free from dirt or filth, unmixed with foreign or extraneous matter; morally pure, chaste, innocent; open, in the open," of beasts, "not forbidden by ceremonial law to eat," from West Germanic *klainja- "clear, pure" (source also of Old Saxon kleni "dainty, delicate," Old Frisian klene "small," Old High German kleini "delicate, fine, small," German klein "small;" English preserves the original Germanic sense), perhaps from PIE root *gel- "bright, gleaming" (source also of Greek glene "eyeball," Old Irish gel "bright"). But Boutkan doubts the IE etymology and that the "clean" word and the "small" word are the same.
"Largely replaced by clear, pure in the higher senses" [Weekley], but as a verb (mid-15c.) it has largely usurped what once belonged to cleanse. Meaning "whole, entire" is from c. 1300 (clean sweep in the figurative sense is from 1821). Sense of "not lewd" (as in good, clean fun) is from 1867; that of "not carrying anything forbidden" is from 1938; that of "free of drug addiction" is from 1950s. To come clean "confess" is from 1919, American English.
common adverbial suffix, forming from adjectives adverbs signifying "in a manner denoted by" the adjective, Middle English, from Old English -lice, from Proto-Germanic *-liko- (cognates: Old Frisian -like, Old Saxon -liko, Dutch -lijk, Old High German -licho, German -lich, Old Norse -liga, Gothic -leiko); see -ly (1). Cognate with lich, and identical with like (adj.).
Weekley notes as "curious" that Germanic uses a word essentially meaning "body" for the adverbial formation, while Romanic uses one meaning "mind" (as in French constamment from Latin constanti mente). The modern English form emerged in late Middle English, probably from influence of Old Norse -liga.
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she played the piano accompaniment cleanly
he bounced it cleanly off the wall
the motor burns cleanly
cleanly in their persons and habitations