Английская Википедия:Chromatic hexachord

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Шаблон:Short description Шаблон:Infobox chord

Файл:Chromatic hexachord on C.png
On C Шаблон:Audio
Файл:Dowland fantasia chromatic hexachord.png
Chromatic hexachords in John Dowland fantasia Шаблон:Harv Шаблон:Audio

In music theory, the chromatic hexachord is the hexachord consisting of a consecutive six-note segment of the chromatic scale. It is the first hexachord as ordered by Forte number, and its complement is the chromatic hexachord at the tritone. For example, zero through five and six through eleven. On C:

and

This is the first of the six hexachords identified by Milton Babbitt as all-combinatorial source sets, a "source set" being "a set considered only in terms of the content of its hexachords, and whose combinatorial characteristics are independent of the ordering imposed on this content" Шаблон:Harv. In the larger context of thirty-five source hexachords catalogued by Donald Martino, it is designated "Type A" Шаблон:Harv. Applying the circle of fifths transformation to the chromatic hexachord produces the diatonic hexachord Шаблон:Harv. As with the diatonic scale, the chromatic hexachord is, "hierarchical in interval makeup," and may also be produced by, or contains, 3-1, 3-2, 3-3, 3-6, and 3-7 Шаблон:Harv.

Serial compositions including Karlheinz Stockhausen's Kreuzspiel and Klavierstück I feature the chromatic hexachord in permuted orderings, as do certain pieces composed by Milton Babbitt, Alban Berg, Ernst Krenek, Luigi Nono, Karlheinz Stockhausen, Igor Stravinsky, and Anton Webern in various fixed-order derivations (twelve-tone rows and arrays). Babbitt's Second Quartet and Reflections for piano and tape feature the hexachord Шаблон:Harv. The retrograde-symmetrical all-interval series employed by Luigi Nono for the first time in Canti per tredeci in 1955, also used in his Il canto sospeso and nearly all subsequent works up to Composizione per orchestra n. 2: Diario polacco ’58 in 1959, is built from two chromatic hexachords Шаблон:Harv.

Файл:Webern - Piano Variations op. 27 tone row.png
Row of Webern's Piano Variations, a fixed-order series derived from the (unordered) chromatic source hexachord, displaying its combinatorial properties
Файл:Nono - Il Canto sospeso all-interval series.png
The "wedge" row, derived from the same source set, used by (amongst others) Nono in Il canto sospeso and Stockhausen in Kontakte

Stefan Wolpe's Suite in Hexachord (1936) begins with a chromatic hexachord on G, introducing the complementary hexachord in the final movement, while Elliott Carter calls his own piece, "Inner Song" for solo oboe—the second movement of Trilogy for oboe and harp (1992)—"some thoughts about Wolpe's hexachord" Шаблон:Harv.

See also

Sources

Шаблон:Pitch segments


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