Hexachordal Combinatoriality

Definition

Hexachordal combinatoriality refers to a compositional technique where hexachords, which are six-note aggregates, are combined and permuted to create new musical material. This method allows composers to explore different organizational possibilities within a limited pitch set, often resulting in complex textures and relationships between musical lines. In atonality and serialism, hexachordal combinatoriality becomes an essential tool for generating themes and developing motifs while avoiding traditional tonal constraints.

5 Must Know Facts For Your Next Test

1. Hexachords can be derived from larger pitch collections and used to construct melodies and harmonies without relying on traditional tonal relationships.
2. Combinatoriality allows composers to rearrange hexachords in various ways, generating new musical ideas and maintaining coherence within atonal music.
3. The concept is closely linked to the twelve-tone technique, where hexachords can serve as subsets of the larger twelve-tone row.
4. Hexachordal combinatoriality promotes innovation in music composition, enabling the exploration of both vertical (harmonic) and horizontal (melodic) relationships.
5. This technique was notably utilized by composers such as Anton Webern and Milton Babbitt, who sought to expand the boundaries of pitch organization in their works.

Review Questions

• How does hexachordal combinatoriality enhance the compositional process in atonal music?
  • Hexachordal combinatoriality enhances the compositional process in atonal music by allowing composers to combine and rearrange hexachords to create new material. This flexibility enables the exploration of diverse textures and relationships without relying on traditional tonal structures. As composers manipulate these six-note aggregates, they can maintain coherence while inventing innovative themes and motifs that reflect the principles of atonality.
• In what ways does hexachordal combinatoriality relate to other techniques such as the twelve-tone method?
  • Hexachordal combinatoriality relates closely to the twelve-tone method by serving as a means to manipulate subsets of the twelve-tone row. Since hexachords can be derived from this larger set, they allow composers to explore different arrangements while adhering to the serialist principle of avoiding repetition of pitches until all have been used. This relationship showcases how hexachordal techniques can contribute to the overall structural organization of a piece within the framework of serialism.
• Evaluate the significance of hexachordal combinatoriality in expanding the boundaries of modern music composition.
  • Hexachordal combinatoriality significantly expands the boundaries of modern music composition by introducing novel methods for organizing pitch material beyond conventional tonal frameworks. Through this technique, composers can explore intricate relationships among pitches, resulting in complex harmonic and melodic structures that challenge listeners' expectations. This innovation fosters creativity and encourages experimentation in music, ultimately contributing to the evolution of contemporary styles and forms.

Related terms

Hexachord: A hexachord is a group of six different pitches that can be used as a building block for composition, often serving as a basis for various manipulations and transformations.

Serialism: A method of composition that uses a series of values to manipulate various musical elements, including pitch, rhythm, and dynamics, aiming for a systematic approach to atonality.

Twelve-tone technique: A specific form of serialism developed by Arnold Schoenberg, which involves using all twelve pitches of the chromatic scale in a predetermined order (the tone row) before any pitch can be repeated.