An Explanation of Anomalous Hexachords in Four Serial Works by Igor Stravinsky

Igor Stravinsky's precompositional process was so methodical that his move to serialism is no surprise. After becoming acquainted with the music of Schoenberg and Webern, Stravinsky was moved to experiment with serial techniques. He rejected many of the conventional approaches developed by the serial architects, only to adopt the technique at its basic form—the use of a series of pitches—and cultivate it into his own compositional style. Stravinsky continued to refine his style throughout his serial period (1951–1966) as each composition grew increasingly more serial than the last. For each work composed after 1960, Stravinsky constructed rotation arrays, a serial technique he adopted from Ernst Krenek. These arrays consisted of a twelve-tone row partitioned into hexachords, with each hexachord rotated to create five additional permutations per hexachord. These permutations were then transposed so that the first pitch of the original hexachord was retained for each permutation. This operation was performed on four series forms: prime, inversion, retrograde, and inversion of the retrograde (favored by Stravinsky over the traditional retrograde inversion form). It is from his rotational arrays that Stravinsky systematically chose hexachords to compose A Sermon, a Narrative, and a Prayer (1961); The Flood (1962); Abraham and Isaac (1963); and Requiem Canticles (1966). Though his precompositional charts are very specific in determining pitch application, it is difficult to account for the use of some hexachords that are found in these works but not found in Stravinsky's charts, as the hexachords do not explicitly appear in the charts. Many analysts have glossed over these incongruities. For instance, Joseph Straus mentions very little about these “anomalous hexachords” in Stravinsky's Late Music (2001); and Claudio Spies completely ignores the hexachords in question. In this paper I will identify these anomalous hexachords and attempt to explain their derivation from Stravinsky's charts.