The work, for string orchestra, is in one movement and its character is essentially dramatic. After a quiet introduction, the main "rowlike" theme appears. This is followed quickly by just a suggestion of the driving 16th-note "motor" figure which eventually, after other development, moves the work into its final section. It is here that the main theme joins the "motor" figure and they combine to propel the piece to its conclusion.

The Los Angeles Philharmonic, under the direction of Zubin Mehta, gave the West Coast premiere on May 24, 1967 at the University of Southern California, as part of a Rockefeller Grant-sponsored concert of modern music; the program was repeated on succeeding nights at UCLA, Occidental College and Cal State Long Beach. Williams took part in a panel discussion at USC on May 25. Los Angeles Times critic Martin Bernheimer wrote that the Essay "revealed some interesting exploitation of the instrumental resource involved, and some arresting melodic and rhythmic detail. But it lacked the linear tension to give it proper cumulative impact. And it lacked a distinctive flavor."

Williams himself conducted the work on a subscription program with the Houston Symphony, April 4-6, 1987, and more recently has begun to perform the work with other orchestras, including the Boston Symphony at Tanglewood.  It has also been performed by San Francisco's New Century Strings (in January of 1995) and by the Minnesota Orchestra under the direction of music director Eji Oue in April of 1996. The Minnesota performance was broadcast live in the Twin Cities area and later across the country as part of the orchestra's syndicated series of broadcast concerts. Williams has said of the Essay, "It's not a strict 12-tone work, but it has many gestures of that style."