Creston began composition by June: it was completed by the end of August and slated for publication in 1940, although this was postponed to 1945 due to World War II.

A slower middle movement with song-like melodies follows, before the sonata ends with a rhythmically complex rondo featuring polymeters.

No critics were present at the premiere, but the sonata's 1955 debut recording by Vincent Abato and Creston obtained a mixed response.

Paul Creston believed that composition was a spiritual act, "just as vital ... as prayer and good deeds", and thought it should not be restricted to career composers.

[1] He was a recipient of a 1938 Guggenheim Fellowship for composition, and part of his wide-ranging output was dedicated to advancing the classical repertoire of instruments little-used within the tradition, like the saxophone.

"[7] He credited Leeson for inspiring his love of the saxophone—which he previously thought of as "ugly ... with an irritatingly buzzy tone"[8][9]—as well as the success of his compositions for the instrument.

[11] The instrument suffered from a dearth of original concert repertoire: aside from Glazunov's Concerto, Debussy's Rhapsodie and Creston's own Suite, Leesons's recitals of the time were dominated by transcriptions of vocal and string music.

"Opus 19, which you have so greatly crusaded for, seems to be buried midst the archives of one Maxwell Weaner and will not see the light of publication until this planetary conflict instigated by one rat with a toothbrush mustache shall have expended itself."

Later, realizing its popularity after attending the 1978 Marcel Mule International Saxophone Competition, Creston wrote to Shawnee's president to suggest that the publishers should consider opening a French branch.

[24] The sonata was given its official premiere by Creston and Leeson at a New Music Group concert at the Carnegie Chamber Hall on February 15, 1940.

[26] No reviews exist of the sonata's premiere performance as Weill Recital Hall concerts were not frequented by New York critics.

[28] In a review for the Library Journal, Mark Melson agreed with Ellsworth on the sonata's structure, finding it traditional and ably written.

[29] The composer and musicologist Dika Newlin reviewed the sonata in Sigma Alpha Iota's Pan Pipes, finding it enjoyable with "disarmingly catchy rhythms", but also found it to lack depth.

[31] American Record Guide's editor James Lyons criticized the sonata's styling as incompatible with the "awfully note-heavy" writing (particularly the accompaniment).

[32] In The New York Times, its later chief music critic Harold Schonberg wrote that he found the melodic content enjoyable, but saw it as using a "near-salon approach".

[34] Tim Page of The New York Times wrote in 1983 that he considered the sonata underrated, complimenting its authentic and "distinctly American sound".

In a conversation with Eugene Rousseau, Marcel Mule stated he considered the sonata "one of the definitive works for saxophone and piano" along with Claude Pascal's Sonatine.

[2] Stephen Cottrell—professor of music at City, University of London—expressed a similar sentiment, saying it is "probably now the single most frequently performed recital work in the saxophone repertoire".

[5] Along with his other works, the success of Creston's sonata contributed to the development of the saxophone's repertory by inspiring other American composers—including Edvard Moritz, Bernhard Heiden and Burnet Tuthill—to compose for the instrument.

[20] The opening movement is in common time and is written in a modified sonata form without a full recapitulation, comprising an exposition where two themes are stated, a development section and a coda.

[40][41] The movement's harmony mainly uses seventh chords containing tritones[42] and features pantonality: temporary tonal centers occasionally emerge,[43] the principal of which is E major.

Creston uses scalic runs and the heights of the saxophones range (up to altissimo G6) to create a climax,[40] before using a coda based on the first theme to end the movement.

[66] The principal theme returns after a transition (the saxophone melody and piano countermelody are now switched)[69] but is abruptly diverted into another episode after seven bars.

[73] Contrary to traditional practice, Creston eschews Italian tempi and expression markings, using English throughout the sonata (e.g. increase instead of crescendo).

He requested that performers of the sonata change the tempi at the 1978 Marcel Mule International Saxophone Competition in Gap, France.

Londeix considered these alterations beneficial, giving a better balance of tempi and "[allowing] a more clearly defined chamber music character to emerge".

According to Mauk, Creston self-deprecatingly exclaimed that "the person who put the tempo markings on this piece was a fool", suggesting slower tempi of = 52–56 and = 144 for movements II and III instead.

[82] By 1978, the sonata had appeared on eight records, including those made by Marcel Mule, Sigurd Raschèr, François Daneels and Jean-Marie Londeix;[2] two years later that number increased to fourteen.