This is a generalized lesson on how to achieve C6 sounds on the E9 tuning. The chords in the song Heart of a Clown lend themselves well to C6 style jazz chord structures. You will find that in order to achieve a desired chord the root note and sometimes the fifth tone of the chord can be left out leaving the thirds, sevenths, ninths, etc that can be played to define the chord. The piano, bass, and/or guitar will be playing the full chords leaving you the freedom to play the notes that only define the chord.
Sample: