All-interval Tetrachords

	All-interval Tetrachords All-interval may refer to: * All-interval hexachord All-interval tetrachord An all-interval tetrachord is a tetrachord, a collection of four pitch classes, containing all six interval classes. There are only two possible all-interval tetrachords (to within inversion), when expressed in prime form. In set theory notation, ... All-interval twelve-tone row {{Disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	All-trichord Hexachord 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 and its Forte number is 6-Z17. Its complement is 6-Z43 and they share the interval vector of . 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''.Schiff (1998), p. 41. See also * All-combinatorial hexachord All-interval tetrachord All-interval twelve-tone row References Further reading Boland, Marguerite (1999). "The All-trichord Hexachord: Compositional Strategies in Elliott Carter's ''Con leggerezza pensosa'' and ''Gra'' and a Folio of Original Compositions". MA Thesis, La Trobe University (Alegant 2010, p. 307n4). . Boland, Marguerite (2006). "'Linking' and 'Morphing': Harmonic Flow in Elliott Carter's ''Con Leggerezza Pensosa''". ''Tempo'' 60, n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	All-interval Tetrachord An all-interval tetrachord is a tetrachord, a collection of four pitch classes, containing all six interval classes. There are only two possible all-interval tetrachords (to within inversion), when expressed in prime form. In set theory notation, these are ,1,4,6(4-Z15) and ,1,3,7(4-Z29). Their inversions are ,2,5,6(4-Z15b) and ,4,6,7(4-Z29b). The interval vector for all all-interval tetrachords is ,1,1,1,1,1 Table of interval classes as relating to all-interval tetrachords In the examples below, the tetrachords ,1,4,6and ,1,3,7are built on E. Use in modern music The unique qualities of the all-interval tetrachord have made it very popular in 20th-century music. Composers including Elliott Carter ( First String Quartet) and George Perle used it extensively. See also * All-interval twelve-tone row * All-trichord hexachord Perfect ruler Serialism Trichord References External links The All-Interval Tetrachord, A Musical Application of Almost Difference Setsal ... [...More Info...] [...Related Items...] OR:* [Wikipedia] [Google] [Baidu]

	All-interval Tetrachords All-interval may refer to: * All-interval hexachord All-interval tetrachord An all-interval tetrachord is a tetrachord, a collection of four pitch classes, containing all six interval classes. There are only two possible all-interval tetrachords (to within inversion), when expressed in prime form. In set theory notation, ... All-interval twelve-tone row {{Disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	All-trichord Hexachord 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 and its Forte number is 6-Z17. Its complement is 6-Z43 and they share the interval vector of . 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''.Schiff (1998), p. 41. See also * All-combinatorial hexachord All-interval tetrachord All-interval twelve-tone row References Further reading Boland, Marguerite (1999). "The All-trichord Hexachord: Compositional Strategies in Elliott Carter's ''Con leggerezza pensosa'' and ''Gra'' and a Folio of Original Compositions". MA Thesis, La Trobe University (Alegant 2010, p. 307n4). . Boland, Marguerite (2006). "'Linking' and 'Morphing': Harmonic Flow in Elliott Carter's ''Con Leggerezza Pensosa''". ''Tempo'' 60, n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	All-interval Tetrachord An all-interval tetrachord is a tetrachord, a collection of four pitch classes, containing all six interval classes. There are only two possible all-interval tetrachords (to within inversion), when expressed in prime form. In set theory notation, these are ,1,4,6(4-Z15) and ,1,3,7(4-Z29). Their inversions are ,2,5,6(4-Z15b) and ,4,6,7(4-Z29b). The interval vector for all all-interval tetrachords is ,1,1,1,1,1 Table of interval classes as relating to all-interval tetrachords In the examples below, the tetrachords ,1,4,6and ,1,3,7are built on E. Use in modern music The unique qualities of the all-interval tetrachord have made it very popular in 20th-century music. Composers including Elliott Carter ( First String Quartet) and George Perle used it extensively. See also * All-interval twelve-tone row * All-trichord hexachord Perfect ruler Serialism Trichord References External links The All-Interval Tetrachord, A Musical Application of Almost Difference Setsal ... [...More Info...] [...Related Items...] OR:* [Wikipedia] [Google] [Baidu]