Rio Nido is based on the bossa nova groove, which originated in Brazil. The feel is relaxed throughout, and played in a very "unhurried" manner. The song has an AABA form, with the melody being passed between the brass and woodwind sections every eight bars before a short interlude into the solo section. Following the solos, a brief shout chorus is heard before the song recaps at the bridge. The piece concludes with a tag of the last four bars of the song, ending on a unison pitch.
