String Quartet No. 1 is a predominantly serial work. The first movement (in
sonata-allegro form) is based on a row [A-Bb-F-C#-D-E-G-Ab-Eb-B-C-G#] given horizontally at the
outset by the viola and then vertically in the form of four tri-chords. The second movement utilizes quartal harmonies, and in form is a tonal
chaconne wherein each successive statement of the
chaconne takes place at a transposition beginning with each subsequent chord in the
chaconne. The finale is a tonal triple fugue within a
rondo form, with each return of the A section serving as a new fugue exposition. The B sections recaptiulate and further develop material from the previous movements.
Hagen first completed the quartet on 27 January 1985 in New York City. It was first performed at the Juilliard Opera Theater at Lincoln Center in New York as Hagen's second
quartet (the first has since been withdrawn) on a concert of the Focus! Festival. Hagen presented the work on concerts of his Perpetuum Mobile ensemble in Philadelphia and New York before withdrawing it for revisions. During the summer of 1985, Hagen developed a close relationship with Louis Krasner; working with Krasner, he revised the piece substantially before it's premiere there. Hagen dedicated the work to Krasner in appreciation. Nevertheless, Hagen again withdrew the work in early 1986.
In 2002, Hagen made final revisions to the quartet and retitled it String Quartet No. 1 prior to including it in his catalogue of recognized works.
— Neil Erickson, 2006