All-interval twelve-tone chord
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In music
Music
Music is an art form whose medium is sound and silence. Its common elements are pitch , rhythm , dynamics, and the sonic qualities of timbre and texture...
, an all-interval twelve-tone row is a twelve-tone
Twelve-tone technique
Twelve-tone technique is a method of musical composition devised by Arnold Schoenberg...
tone row
Tone row
In music, a tone row or note row , also series and set, refers to a non-repetitive ordering of a set of pitch-classes, typically of the twelve notes in musical set theory of the chromatic scale, though both larger and smaller sets are sometimes found.-History and usage:Tone rows are the basis of...
arranged so that it contains one instance of each interval
Interval (music)
In music theory, an interval is a combination of two notes, or the ratio between their frequencies. Two-note combinations are also called dyads...
within the octave, 1 through 11. A, "twelve-note spatial set made up of the eleven intervals [between consecutive pitches]." 3856 distinct all-interval twelve-tone rows exist.
For example, the first all-interval row, devised by Fritz Heinrich Klein
Fritz Heinrich Klein
Fritz Heinrich Klein was an Austrian composer. He was a student of Alban Berg and the inventor of the all-interval row....
: F, E, C, A, G, D, A, D, E, G, B, C.
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
Alban Berg
Alban Maria Johannes Berg was an Austrian composer. He was a member of the Second Viennese School with Arnold Schoenberg and Anton Webern, and produced compositions that combined Mahlerian Romanticism with a personal adaptation of Schoenberg's twelve-tone technique.-Early life:Berg was born in...
in his Lyric Suite (1926).
Chromatic scale
The chromatic scale is a musical scale with twelve pitches, each a semitone apart. On a modern piano or other equal-tempered instrument, all the half steps are the same size...
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.
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: 73-4.
- Morris, Robert, and Daniel Starr (1974). "The Structure of All-Interval Series", Journal of Music Theory 18/2: 364-89.