By the late 1920s, Webern had developed an extraordinary application of Arnold Schoenberg's twelve-tone technique in works like String Trio (1927), Symphony (1928), and Quartet (1932).

In early February, Webern began attempting to create a melodic equivalent of a sator square.

In addition to writing "tenet" in his first sketch for the Concerto, he ended his lectures about new music by quoting it to his audience.

[2][3]: 431  The essentially meaningless square arranges all the letters contained in the phrase "a[lpha] pater noster o[mega]" in highly palindromic configurations that read both horizontally and vertically.

[4] Webern ended up relying on a three-note musical germ (C♯–C–E) he had used in his 1905 String Quartet to generate the row.

There are no soloists, but each instrument is playing miniature solos of 2–3 notes apiece which aggregate into the "gathering" implied by the title.

Webern's tone row is played a trichord at a time by the oboe, flute, trumpet, and clarinet.

Webern chooses a transposition of the retrograde inversion that also precisely reverses each trichord of the original row.

[10] The concerto is based on a derived row, "often cited [such as by Milton Babbitt (1972)[full citation needed]] as a paragon of symmetrical construction".

[15] "Webern takes full advantage of this property [its fourfold degree of symmetry] in the Concerto," that under four appropriate transformations (T0T6I5IB), the tone row maintains its unordered trichords (j=019,091,etc., k=2te, l=367, and m=458).

[16] According to Brian Alegant, "[t]he Latin square... clearly shows the built in redundancy of [the] partition," four, and, "needless to say, Webern takes full advantage of this property in the Concerto":[13] For example, I5 = 548, 376, 2et, 109.