All-interval twelve-tone row

In music, an all-interval twelve-tone row is a twelve-tone tone row arranged so that it contains one instance of each interval within the octave, 1 through 11. A, "twelve-note spatial set made up of the eleven intervals [between consecutive pitches]."[1] 3856 distinct all-interval twelve-tone rows exist.

For example, the first all-interval row, devised by Fritz Heinrich Klein: F, E, C, A, G, D, A♭, D♭, E♭, G♭, B♭, C♭.[3]

0 e 7 4 2 9 3 8 t 1 5 6

with the intervals between consecutive pairs of notes being (t = 10, e = 11):

 e 8 9 t 7 6 5 2 3 4 1

This row was also used by Alban Berg in his Lyric Suite (1926).

In contrast, the chromatic scale only contains the interval 1 between each consecutive note:

0 1 2 3 4 5 6 7 8 9 t e
 1 1 1 1 1 1 1 1 1 1 1

and is thus not an all-interval row.

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See also

Sources

  1. ^ a b Schiff, David (1998). The Music of Elliott Carter, second edition (Ithaca: Cornell University Press), pp. 34–36. ISBN 0801436125. 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 9053567658. 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 9031302449.
  3. ^ Whittall, Arnold (2008). The Cambridge Introduction to Serialism, p. 271 and 68–69. ISBN 978-0-521-68200-8.

Further reading

External links