The title refers to the division of the work into two halves, both of which last for between 8 or 9 minutes. In the first of these, concertante groupings of (usually) three instruments come and go out of the ensemble, often overlapping and being superimposed to produce somewhat hectic free jazz-like tuttis. The second part (there is no break) is dominated by amplified cello, which after a manic cadenza, is the most prominent voice (though not always the most important) in an extremely long melodic line, which slowly grows in complexity as it splits into the three separate strands, before being whisked away back to the opening sounds of the piece.
Two Part Invention was commissioned by Music Projects/London and partly funded by the Arts Council. It is dedicated to Elliot Carter in the year of his eightieth birthday.