At least two bands have the name Murmur, including:

1) UK Electronic artist Murmur, who say they are "possibly the most self restrained and least derivative operators in dub techno right now, and over the course of a handful of scarce twelves they've slowly gestated a frayed hybrid of minimal construction and fathomless BASS that has less in common with the hallowed Basic Channel axis then the work of most of their contemporaries."

2) Murmur, a loose acoustic drone ensemble of New Orleans who play tone/space improvisations based on a single note. Originally founded by potpie and recording on the Backporch Revolution label, the membership changes with each performance/recording and has contained anywhere from two to twelve members.

See also Murmer (note different spelling) and The Murmurs.