The re-discovery of Middle Age’s hexacords by 12-tone music composers like Schoenberg and Webern, but also Joseph Mathias Hauer, Stefan Wolpe or Milton Babbitt, fueled a number of compositions using the 6 tones of an original hexacord and its transposition, retrograde, inversion and retrograde inversion. The use of hexacords for this purpose is described in Schoenberg’s Harmonielehre, or Theory of Music, 1922. In particular, Schoenberg based some of his piano music (like op. 33, 1931), the Moses und Aron oratorio (1928) and Ode to Napoleon Bonaparte (1942) on hexacords. There’s even a “Schoenberg hexachord” which he used as his signature. Hexacords are only one constituent of the twelve-tone technique, yet their use in 20th century music contributed in no small part to the much scorned “dissonance” effect.
Belonging to Igor Stravinsky’s serial period (1951–1966), the sacred cantata A Sermon, a Narrative, and a Prayer, composed in 1961, is based on a strict series of hexacords. The sound excerpt above is from the first movement, while the table sums up all hexacords used in the score. According to U.S. musicologist Robert Sivy (An Explanation of Anomalous Hexachords in Four Serial Works by Igor Stravinsky, 2011, see PDF), Stravinsky arranged hexacords into “rotational arrays” prior to composing, and then distributed subsequent series of notes between several instruments/voices.