The music you’re hearing is by probably the longest lasting band in San Francisco: The Golden Gate Park Band. They’ve been giving free concerts nearly ever Sunday from late April until early October... since 1882.
Few civic institutions in San Francisco pre-date the 1906 earthquake. One is the cable car, invented here in 1873. Another one is The Golden Gate Park Band. It dates from 1882, when it was a support unit of the California National Guard. Now it’s a Sunday afternoon mainstay at The Spreckles Temple of Music in Golden Gate Park.