All-interval twelve-tone row

All-interval twelve-tone row

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

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] There are 1,928 distinct all-interval twelve-tone rows.[4] "Distinct" in this context means in transpositionally and rotationally normal form (yielding 3856 such series), and disregarding inversionally related forms.[5]

For example, the first all-interval row, devised by Fritz Heinrich Klein: F, E, C, A, G, D, A, D, E, G, B, C.[6]

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).

Chromatic scale    .

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.

Grandmother chord

Grandmother chord[7] About this sound   

The Grandmother chord is an eleven-interval, twelve-note, invertible chord with all of the properties of the Mother chord. Additionally, the intervals are so arranged that they alternate odd and even intervals (counted by semitones) and that the odd intervals successively decrease by one while the even intervals successively increase by one.[8] It was invented by Nicolas Slonimsky on February 13, 1938.[9] The sum of numbers 1 through 11 = 66 and thus the chord contains a tritone between its outer notes[10] and as its sixth (middle) interval, and between the two notes directly outside of those, etc.

See also


  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. ^ Slonimsky, Nicolas (1975). Thesaurus of Scales and Melodic Patterns, 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. 364-89, citation on p. 366.
  6. ^ Whittall, Arnold (2008). The Cambridge Introduction to Serialism, p. 271 and 68–69. ISBN 978-0-521-68200-8.
  7. ^ Slonimsky (1975), p.243.
  8. ^ Slonimsky (1975), p.iii.
  9. ^ Slonimsky (1975), p.vii.
  10. ^ Slonimsky (1975), p.iv.

Further reading

  • Bauer-Mendelberg, Stefan, and Melvin Ferentz (1965). "On Eleven-Interval Twelve-Tone Rows", Perspectives of New Music 3/2: 93–103.
  • Cohen, David (1972–73). "A Re-examination of All-Interval Rows", Proceedings of the American Society of University Composers 7/8: 73–74.

External links

  • List of all all-interval rows