All-interval twelve-tone row

All-interval row from Alban Berg's Lyric Suite
Elliott Carter often based his all-interval sets on the list generated by Bauer-Mendelberg and Ferentz and uses them as a "tonic" sonority[1]
All-interval series from Luigi Nono's Il canto sospeso[2] (Equivalent to Nicolas Slonimsky's "Grandmother Chord".)[3]
[3]

In music, an all-interval twelve-tone row, series, or chord, is a twelve-tone tone row arranged so that it contains one instance of each interval within the octave, 1 through 11 (an ordering of every interval, 0 through 11, that contains each (ordered) pitch-interval class, 0 through 11). A "twelve-note spatial set made up of the eleven intervals [between consecutive pitches]."[1] There are 1,928 distinct all-interval twelve-tone rows.[4] These sets may be ordered in time or in register. "Distinct" in this context means in transpositionally and rotationally normal form (yielding 3856 such series), and disregarding inversionally related forms.[5] These 1,928 tone rows have been independently rediscovered several times, their first computation probably was by Andre Riotte in 1961.[6]

Since the sum of numbers 1 through 11 equals 66, an all-interval row must contain a tritone between its first and last notes,[7] as well as in their middle.

  1. ^ a b Schiff, David (1998). The Music of Elliott Carter, second edition (Ithaca: Cornell University Press), pp. 34–36. ISBN 0-8014-3612-5. Labels added to image.
  2. ^ Leeuw, Ton de (2005). Music of the Twentieth Century: A Study of Its Elements and Structure , translated from the Dutch by Stephen Taylor (Amsterdam: Amsterdam University Press), p. 177. ISBN 90-5356-765-8. Translation of Muziek van de twintigste eeuw: een onderzoek naar haar elementen en structuur. Utrecht: Oosthoek, 1964. Third impression, Utrecht: Bohn, Scheltema & Holkema, 1977. ISBN 90-313-0244-9.
  3. ^ a b Slonimsky, Nicolas (1975). Thesaurus of Scales and Melodic Patterns Archived 2017-01-09 at the Wayback Machine, p. 185. ISBN 0-8256-1449-X.
  4. ^ Carter, Elliott (2002). Harmony Book, p. 15. Nicholas Hopkins and John F. Link, eds. ISBN 9780825845949.
  5. ^ Robert Morris and Daniel Starr (1974). "The Structure of All-Interval Series", Journal of Music Theory 18/2: pp. 364–389, citation on p. 366.
  6. ^ André Riotte (1963) Génération des cycles équilibrés, Rapport interne n°353 Euratom. Ispra.
  7. ^ Slonimsky (1975), p. iv.