Although invented in the early 1840s, the saxophone was still fairly new and unfamiliar in Glazunov's day; it remained untouched for a long time as it was considered "middle class".
He hounded Glazunov for a saxophone concerto, so much so that the composer wrote to a colleague that he had started the piece in March "under the influences of attacks rather than requests from the Danish (sic) saxophonist named Sigurd Rascher".
According to French saxophonist Marcel Mule, Glazunov had a reading of the piece with him prior to its publication, the composer playing the piano part.
However, in 1936, the publishing company made an addition to the piano reduction: they added A. Petiot as a second composer, probably for copyright purpose as it was common for Soviet Union artists.
[1] This is the structural breakdown according to Glazunov himself, taken from a letter he wrote to Maximilian Steinberg: Above forms occur again before leading to the coda (E flat major).
Some well-known saxophonists have made recordings of this piece, including John-Edward Kelly, Arno Bornkamp, Gary Louie Joe Lulloff, Christopher Creviston, Jean-Yves Fourmeau, Lawrence Gwozdz, John Harle, Theodore Kerkezos, Robert Eason, Karel Krautgartner, Jean-Marie Londeix, Marcel Mule, Kenneth Radnofsky, Debra Richtmeyer, and Eugene Rousseau.