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.

No description available.

Die im 16. Jahrhundert in Europa weitgehend universell eingesetzte Hexachordsolmisation stand im Laufe des 17. Jahrhunderts verstärkt in der Kritik und sollte um eine siebte Silbe ergänzt werden. Da Solmisationssilben stets mit bestimmten Klangcharakteren assoziiert wurden (u.a. bei Agricola 1533), stellt sich die Frage nach dem etwaigen Klangcharakter einer siebten Silbe. Die Klangcharaktere der Solmisationssilben definieren sich, wie auch die Solmisationssilben selbst, durch eine jeweils konkrete Position im diatonischen Raum. Da der Hexachord stets nur einen Teil des diatonischen Raumes beleuchtet, überschneiden sich die Definitionen, wie auch die Klangcharaktere von je zwei Solmisationssilben. Außerdem kommen die der Diatonik inhärenten Intervalle der übermäßigen Quarte und verminderten Quinte im Hexachord nicht vor, die siebte Silbe hingegen trägt das harmonische und melodische Potential der übermäßigen Quarte und verminderten Quinte in sich. Dies kann eine mögliche Erklärung dafür sein, warum sie in der Hexachordsolmisation ausgespart, jedoch im Zuge der Entwicklung der Musiksprache im 17. Jahrhundert als fehlend empfunden wurde. / Hexachord solmisation, which was used almost universally throughout Europe in the sixteenth century, came under increasing criticism in the seventeenth century, with theorists advocating the addition of a seventh syllable. The widespread association of specific solmisation syllables with specific sound qualities (e.g., in Agricola, 1533) raises the question of the sound quality of a seventh syllable. A solmisation syllable is defined by its unique position in the diatonic scale, which in turn leads to its inherent sound quality. As the hexachord takes into consideration only part of the diatonic scale, the definitions as well as sound qualities of some solmisation syllables overlap. Moreover, the augmented fourth and diminished fifth, though inherent in the diatonic scale, are absent from the hexachord. The seventh syllable, however, strongly connotes the augmented fourth and diminished fifth – a possible explanation for its absence in hexachordal solmisation until the evolving musical language of the seventeenth century found it missing.

No description available.

No description available.