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All-trichord hexachord — Wikipedia (en)

Source: Wikipedia (en)
Original: https://en.wikipedia.org/wiki/All-trichord_hexachord
License (as archived): CC-BY-SA-4.0
Archived: 2026-11-08T13:22:29.864Z
SHA-256 of the archived text: 28cbbf002c68206fa46a75fd4891a66cc92907b12d44e9a45811b239c5cb3dc6
Stable URL of this page: https://metraipolis.com/documento/dc_d8a64672d2fe

How to cite

All-trichord hexachord — Wikipedia (en) — Wikipedia (en), https://en.wikipedia.org/wiki/All-trichord_hexachord (CC-BY-SA-4.0); archived copy: https://metraipolis.com/documento/dc_d8a64672d2fe (Metraipolis archive dc_d8a64672d2fe, sha256 28cbbf002c68206fa46a75fd4891a66cc92907b12d44e9a45811b239c5cb3dc6)

BibTeX

@misc{dcd8a64672d2fe,
  title = {All-trichord hexachord — Wikipedia (en)},
  howpublished = {Wikipedia (en)},
  url = {https://en.wikipedia.org/wiki/All-trichord_hexachord},
  note = {License CC-BY-SA-4.0; archived copy https://metraipolis.com/documento/dc_d8a64672d2fe; sha256 28cbbf002c68206fa46a75fd4891a66cc92907b12d44e9a45811b239c5cb3dc6},
  year = {2026}
}

Archived text

Reproduced under CC-BY-SA-4.0. Attribution: Wikipedia (en), https://en.wikipedia.org/wiki/All-trichord_hexachord. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

In music, the all-trichord hexachord is a unique hexachord that contains all twelve trichords, or from which all twelve possible trichords may be derived. The prime form of this set class is {012478} and its Forte number is 6-Z17. The following is an example of the all-trichord hexachord. Its complement is 6-Z43 and they share the interval vector of <3,2,2,3,3,2>. It appears in pieces by Robert Morris and Elliott Carter. Carter uses all-interval twelve-tone sets consisting of all-trichord hexachords in his Symphonia: sum fluxae pretium spei. In 1992, composer and Carter scholar John Link generated a list of every all-interval twelve-tone row from which an all-trichord hexachord could be derived, and offered it to Carter to help with his work.

Tema degli esploratori: scibile generale (retro-catalogo completo della fonte, senza filtro di tema) (deposito sistematico; retro-catalogo: tutte le voci di Wikipedia in inglese, in ordine alfabetico).
Fonte: Wikipedia in inglese, voce «All-trichord hexachord» — https://en.wikipedia.org/wiki/All-trichord_hexachord
Wikidata Q4728362 (dati Wikidata in CC0 1.0) — https://www.wikidata.org/wiki/Q4728362
Autori: i contributori di Wikipedia (cronologia: https://en.wikipedia.org/wiki/All-trichord_hexachord?action=history).
Licenza: Creative Commons Attribuzione-Condividi allo stesso modo 4.0 (CC BY-SA 4.0) — https://creativecommons.org/licenses/by-sa/4.0/. Il riuso richiede attribuzione e stessa licenza.
Estratto dell'introduzione non modificato nel contenuto; revisione 1374600060, consultata il 2026-11-08T13:15:48.420Z tramite l'API ufficiale di Wikipedia. Impronta SHA-256 dell'estratto: ef74b5261288e125ff6728b5fccc78b8839fb1f4b5d0ec43f8451b2fd373d511