"For Calvin (And His Next Two Hitch-Hikers)" was written during Frank Zappa's convalescence in 1972 and recorded for the album The Grand Wazoo. It is the only vocal song of this set. The title and the lyrics refer to a real-life story that happened to Cal Schenkel, Zappa's favorite cover artist. The story goes (as it appeared in a few interviews) that, in 1969, Schenkel picked up a hippie couple that never said a word to him, stayed in the car after he arrived at work, ate lunch there, and finally left. "Where do they go? Where did they come from?," ask the lyrics.
The main theme is a slow and somewhat disquieting melody, not unlike the one in the Mothers of Invention's 1966 song "Who Are the Brain Police?" It is followed by a section of improvised bits over a soft flooring with lots of weird percussion (like flexatones and vibraslaps). The orchestra gathers for a bouncy new theme, which is actually a quote from "The Adventures of Greggary Peccary" (the "Who is making these new brown clouds" section) -- both pieces were written at the same time. Then the orchestra attacks with some avant-garde jazz licks and creative improvisation not unlike what trombonist George Lewis was writing around the same time.
The most avant-gardist piece Zappa wrote for a large jazz ensemble, "For Calvin" was only performed during the Grand Wazoo and Petit Wazoo tours, from October to December 1972.