late 14c., "make a low continuous noise; grumble, complain," from Old French murmurer "murmur, grouse, grumble" (12c.), from murmur "rumbling noise" (see murmur (n.)). Transitive sense of "say indistinctly" is from 1530s. Related: Murmured; murmuring.
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Definitions of murmuring from WordNet
a low continuous indistinct sound; often accompanied by movement of the lips without the production of articulate speech;
Synonyms: mutter / muttering / murmur / murmuration / mussitation