rap (n.) Look up rap at Dictionary.com
c.1300, "a quick, light blow, stroke," also "a fart" (late 15c.), native or borrowed from a Scandinavian source (compare Danish rap, Swedish rapp "light blow"); either way probably of imitative origin (compare slap, clap).

Slang meaning "rebuke, blame, responsibility" is from 1777; specific meaning "criminal indictment" (as in rap sheet, 1960) is from 1903. To beat the rap is from 1927. Meaning "music with improvised words" first in New York City slang, 1979 (see rap (v.2)).
rap (v.1) Look up rap at Dictionary.com
mid-14c., "strike, smite, knock," from rap (n.). Related: Rapped; rapping. To rap (someone's) knuckles "give light punishment" is from 1749. Related: Rapped; rapping.
rap (v.2) Look up rap at Dictionary.com
"talk informally, chat," 1929, popularized c.1965 in Black English, possibly first in Caribbean English and from British slang meaning "say, utter" (1879), originally "to utter a sudden oath" (1540s), ultimately from rap (n.). As a noun in this sense from 1898. Meaning "to perform rap music" is recorded by 1979. Related: Rapped; rapping.