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early 15c., "to cover or wrap (something) to conceal or protect," perhaps from Middle French mofler "to stuff," from Old French moufle "thick glove, muff" (cf. Old French enmoufle "wrapped up"); see muff (n.). Meaning "wrap something up to deaden sound" first recorded 1761. Related: Muffled; muffling.
"thing that muffles," 1560s, from muffle (v.).