Among the shouts and chants from a picket line on the Upper East Side on a recent evening were a few sounds of a less discordant nature: the thump of a bass drum, the toot of a trombone, the melodious drone of a clarinet.

For nearly a decade, members of a collective called the Rude Mechanical Orchestra have provided the unlikely musical accompaniment to various rebellious street events in New York City and beyond.

The group, which is named in part after characters in “A Midsummer Night’s Dream,” was formed in 2004 to take part in a march in Washington organized by the National Organization for Women. Since then, it has performed during antiwar demonstrations, rallies protesting gentrification and parades celebrating the community gardens of the Lower East Side.

The band, whose 30-odd revolving members dress in green and black, usually donates its services. One exception came in 2008 when it accompanied the indie-rockers Matt and Kim at the McCarren Park Pool in Brooklyn. The proceeds enabled them to buy a biofuel bus that transported the musicians and their instruments to St. Paul, Minn., where they joined protests during the Republican National Convention.