Elliott Carter's Brass Quintet was composed in 1974 for a commission from the American Brass Quintet. It was completed rather quickly, over the course of the summer months of that year, mostly during the period in which both Carter and the Quintet were artists in residence in Aspen. Presumably, then, the group was on hand during the composition process to test the innovative instrumental combinations and virtuosic figures that comprised the work. It was premiered by the dedicatees the following October at a Charles Ives Festival in London, and the following month received its domestic debut.

Though no outside narrative is made explicit in connection with the Brass Quintet, the work seems to suggest a kind of extramusical depiction: a world of sonic commerce, made up of every conceivable kind of encounter between the instruments used, and demonstrating an ingenious system of musical transactions that broaden the expressive possibilities for all involved. The procedures the Carter employs to create this system inform every level of the composition, from the specific intervals that appear in each instrumental part at each phase of the work, to the overall form that the piece takes.

The work is built upon a loose recurring pattern in which tutti sections, referred to as quodlibets, are separated by a duo and a trio, not necessarily in that order. This pattern is disrupted only three times: during an extended horn solo beginning just after the midpoint of the work; in a slow, calm section near the end; and at the final coda. Carter's method for combining these nineteen individual sections is to carefully control the economy of musical resources so that the level of variety and character of the instrumental combinations can be made to contribute to the overall dramatic trajectory of the work. In this economy, each duo or trio becomes a transaction point, at which a specific interval and an associated character enter into musical circulation. Thus, after an opening quodlibet that presages the slow movement near the end of the piece, Carter writes a trio for two trumpets and first trombone. Bearing the score indication "lightly," the trio emphasizes the interval of the minor sixth. The subsequent duo between horn and first trombone, to be played "vigorously," repeatedly outlines perfect fourths. In the quodlibet that follows the instruments part ways, each assuming an individual voice by appropriating the materials with which it has thus far come into contact. This instrumentational procedure exploits the color possibilities within the ensemble by comprehensively involving every possible duo or trio combination before the piece ends.

The first interruption of the formal pattern occurs as the horn, who demonstrates a wider arrays of intervalic material than the rest of the instruments, breaks free from the musical economy and "menacingly" (as indicated in the score) celebrates its secession with a long cadenza which utilizes the still-foreign interval of the tritone. The others finally interject with "angry" octaves, at which point the trumpets, still "furious" about the horn's rebellion, converse in major sevenths. The trombones get a few licks in as well when they confront the horn in an "angry" episode on the minor ninth. Finally, after the subsequent quodlibet, unity and communion are restored as the entire ensemble returns to an extended version of the slow, calm material that began the work. A final duo takes place between the first trombone and a muted second trumpet; the coda then revisits several earlier moments before closing the work.

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