Top Qs
Timeline
Chat
Perspective
List of tone rows and series
From Wikipedia, the free encyclopedia
Remove ads
This is a list of tone rows and series. For a list of unordered collections, see set (music), Forte number, list of set classes, and trope (music).
Twelve tone rows
Summarize
Perspective
More information Row form, Integers ...
| Row form | Integers | Interval classes |
Notation | Composer: Composition | Year | Hexa- |
Hexa- |
Derivation/ |
|---|---|---|---|---|---|---|---|---|
| P: | 0 1 2 e t 9 5 4 3 6 7 8 |
1 1 3 1 1 4 1 1 3 1 1 | Anton Webern: Op. 32, later row[1] |
un- finished |
6-1 | 6-1 | — | |
| I: | 0 e t 1 2 3 7 8 9 6 5 4 | |||||||
| P: | 0 1 3 5 6 2 4 8 7 9 e t |
1 2 2 1 4 2 4 1 2 2 1 | Igor Stravinsky: Abraham & Isaac[2][3] |
1963 | 6-Z3 | 6-Z36 | — | |
| I: | 0 e 9 7 6 t 8 4 5 3 1 2 | |||||||
| P: | 0 1 3 6 7 9 8 t e 2 4 5 |
1 2 3 1 2 1 2 1 3 2 1 | Arnold Schoenberg: Serenade, op. 24, mov. 5[4] |
1920–23 | 6-30 | 6-30 | derived: 3-3 | |
| I: | 0 e 9 6 5 3 4 2 1 t 8 7 | |||||||
| P: | 0 1 3 8 4 9 t 7 6 5 e 2 |
1 2 5 4 5 1 3 1 1 6 3 |  |
Alban Berg: Kammerkonzert[5] |
1923–25 | 6-Z19 | 6-Z44 | cryptogram: |
| I: | 0 e 9 4 8 3 2 5 6 7 1 t | |||||||
| P: | 0 1 3 9 2 e 4 t 7 8 5 6 |
1 2 6 5 3 5 6 3 1 3 1 | Arnold Schoenberg: Suite for Piano, op. 25[6][7][8][9] |
1921–23 | 6-2 | 6-2 | — | |
| I: | 0 e 9 3 t 1 8 2 5 4 7 6 | |||||||
| P: | 0 1 4 2 9 5 e 3 8 t 7 6 |
1 3 2 5 4 6 4 5 2 3 1 | Pohlman Mallalieu[10][11]
Robert Morris: |
n.a.
1973 |
6-14 | 6-14 | all-interval, RT6-invariant | |
| I: | 0 e 8 t 3 7 1 9 4 2 5 6 | |||||||
| P: | 0 1 4 3 2 5 6 9 8 7 t e |
1 3 1 1 3 1 3 1 1 3 1 |  |
Anton Webern: Variations for Orchestra, Op. 30[12][3][13] |
1940 | 6-1 | 6-1 | all- combinatorial |
| I: | 0 e 8 9 t 7 6 3 4 5 2 1 | |||||||
| P: | 0 1 4 3 2 5 6 9 8 e t 7 |
1 3 1 1 3 1 3 1 3 1 3 | Igor Stravinsky: Agon, "Pas de deux", "Four trios"[2][14] |
1957 | 6-1 | 6-1 | all- combinatorial | |
| I: | 0 e 8 9 t 7 6 3 4 1 2 5 | |||||||
| P: | 0 1 4 3 7 6 e 2 t 9 5 8 |
1 3 1 4 1 5 3 4 1 4 3 | Arnold Schoenberg: Die Jakobsleiter[15] |
un- finished |
6-Z13 | 6-Z42 | — | |
| I: | 0 e 8 9 5 6 1 t 2 3 7 4 | |||||||
| P: | 0 1 4 5 8 7 6 3 2 7 e t |
1 3 1 3 1 1 3 1 5 4 1 | Walter Piston: Symphony No. 8 (first movement)[16] |
1965 | 6-Z19 | 6-Z44 | — | |
| I: | 0 e 8 7 4 5 6 9 t 5 1 2 | |||||||
| P: | 0 1 4 5 7 6 8 9 t e 2 3 |
1 3 1 2 1 2 1 1 1 3 1 | Roger Reynolds: Ambages[17] |
1965 | 6-5 | 6-5 | — | |
| I: | 0 1 4 5 7 6 8 9 t e 2 3 | |||||||
| P: | 0 1 4 6 8 t 5 7 9 e 2 3 |
1 3 2 2 2 5 2 2 2 3 1 | Ernst Krenek: Lamentatio Jeremiae Prophetae, Op. 93, row 3[18] |
1940–41 | 6-34 | 6-34 | RI- | |
| I: | 0 e 8 6 4 2 7 5 3 1 t 9 | |||||||
| P: | 0 1 4 9 5 8 3 t 2 e 6 7 |
1 3 5 4 3 5 5 4 3 5 1 | Milton Babbitt: Composition for Twelve Instruments[3][19] |
1948 | 6-20 | 6-20 | dyadic, tri-, tetra-, and hexa- chordal combina- toriality | |
| I: | 0 e 8 3 7 4 9 2 t 1 6 5 | |||||||
| P: | 0 1 5 2 6 t 3 8 9 4 7 e |
1 4 3 4 4 5 5 1 5 3 4 | Edison Denisov: Fünf Geschichten von Herrn Keuner[20] |
1966 | 6-Z43 | 6-Z17 | all-trichord | |
| I: | 0 e 7 t 6 2 9 4 3 8 5 1 | |||||||
| P: | 0 1 5 8 t 4 3 7 9 2 e 6 |
1 4 3 2 6 1 4 2 5 3 5 | Luigi Dallapiccola: Quaderno musicale di Annalibera[21] Variazioni per orchestra Canti di Liberazione[22] |
1952 1954 1951–55 |
6-31 | 6-31 | — | |
| I: | 0 e 7 4 2 8 9 5 3 t 1 6 | |||||||
| P: | 0 1 6 2 7 9 3 4 t e 5 8 |
1 5 4 5 2 6 1 6 1 6 3 | Arnold Schoenberg: Violin Concerto, op. 36[23] |
1936 | 6-Z50 | 6-Z29 | — | |
| I: | 0 e 6 t 5 3 9 8 2 1 7 4 | |||||||
| P: | 0 1 6 2 t 9 4 7 3 8 e 5 |
1 5 4 4 1 5 3 4 5 3 6 | Arnold Schoenberg: A Survivor from Warsaw[24][25] |
1947 | 6-15 | 6-15 | — | |
| I: | 0 e 6 t 2 3 8 5 9 4 1 7 | |||||||
| P: | 0 1 6 5 7 e 2 t 3 9 8 4 |
1 5 1 2 4 3 4 5 6 1 4 | Milton Babbitt: All Set[26] |
1957 | 6-7 | 6-7 | second-order combinatorial | |
| I: | 0 e 6 7 5 1 t 2 9 3 4 8 | |||||||
| P: | 0 1 7 2 3 9 t 8 6 5 e 4 |
1 6 5 1 6 1 2 2 1 6 5 | Edison Denisov: Viola concerto[27] |
1986 | 6-Z41 | 6-Z12 | — | |
| I: | 0 e 5 t 9 3 2 4 6 7 1 8 | |||||||
| P: | 0 1 7 5 6 4 t 8 9 e 2 3 |
1 6 2 1 2 6 2 1 2 3 1 |  |
Arnold Schoenberg: Moses und Aron[24] |
un- finished |
6-5 | 6-5 | inversional |
| I: | 0 e 5 7 6 8 2 4 3 1 t 9 | |||||||
| P: | 0 1 7 5 6 e 9 8 t 3 4 2 |
1 6 2 1 5 2 1 2 5 1 2 | Igor Stravinsky: Movements[2] |
1958–59 | 6-7 | 6-7 | — | |
| I: | 0 e 5 7 6 1 3 4 2 9 8 t | |||||||
| P: | 0 1 7 6 8 9 3 2 4 5 e t |
1 6 1 2 1 6 1 2 1 6 1 | Alberto Ginastera: Don Rodrigo, Act I, op. 31[28] |
1963–64 | 6-5 | 6-5 | — | |
| I: | 0 e 5 6 4 3 9 t 8 7 1 2 | |||||||
| P: | 0 1 7 9 8 6 3 t 2 5 e 4 |
1 6 2 1 2 3 5 4 3 6 5 | Karlheinz Stockhausen: Plus-Minus[29] |
1963 (rev. 1974) | 6-5 | 6-5 | — | |
| I: | 0 e 5 3 4 6 9 2 t 7 1 8 | |||||||
| P: | 0 1 7 e 8 2 6 5 t 9 3 4 |
1 6 4 3 6 4 1 5 1 6 1 |  |
Schoenberg: "Tot" ["Lifeless"], Drei Lieder, Op. 48[30] |
1933 | 6-5 | 6-5 | — |
| I: | 0 e 5 1 4 t 6 7 2 3 9 8 | |||||||
| P: | 0 1 8 e 7 3 2 5 4 t 9 6 |
1 5 3 4 4 1 3 1 6 1 3 | Karlheinz Stockhausen: Zeitmaße[31][32] |
1955–56 | 6-16 | 6-16 | — | |
| I: | 0 e 4 1 5 9 t 7 8 2 3 6 | |||||||
| P: | 0 1 9 e 3 2 6 7 t 8 4 5 |
1 4 2 4 1 4 1 3 2 4 1 | Anton Webern: Op. 32, row 1[33] |
un- finished |
6-2 | 6-2 | — | |
| I: | 0 e 3 1 9 t 6 5 2 4 8 7 | |||||||
| P: | 0 1 9 e 3 2 7 6 t 8 4 5 |
1 4 2 4 1 5 1 4 2 4 1 | Anton Webern: Op. 32, row 2[33] |
un- finished |
6-1 | 6-1 | all- combinatorial | |
| I: | 0 e 3 1 9 t 5 6 2 4 8 7 | |||||||
| P: | 0 1 9 e 8 t 4 5 6 2 3 7 |
1 4 2 3 2 6 1 1 4 1 4 |  |
Anton Webern: Variations for piano, mov. II, op. 27[34][35] |
1936 | 6-1 | 6-1 | all- combinatorial |
| I: | 0 e 3 1 4 2 8 7 6 t 9 5 | |||||||
| P: | 0 1 9 e t 7 8 3 4 6 5 2 |
1 4 2 1 3 1 5 1 2 1 3 | Igor Stravinsky: A Sermon, a Narrative and a Prayer[2] |
1961 | 6-2 | 6-2 | — | |
| I: | 0 e 3 1 2 5 4 9 8 6 7 t | |||||||
| P: | 0 1 t 2 6 4 5 3 7 e 8 9 |
1 3 4 4 2 1 2 4 4 3 1 | Luigi Dallapiccola: Dialoghi[36] |
6-21 | 6-21 | RI-invariant: P0 = RI9 | ||
| I: | 0 e 2 t 6 8 7 9 5 1 4 3 | |||||||
| P: | 0 1 t 3 4 6 8 9 e 5 7 2 |
1 3 5 1 2 2 1 2 6 2 5 | Chen Yi: Near Distance[3][37] |
1988 | 6-Z23 | 6-Z45 | — | |
| I: | 0 e 2 9 8 6 4 3 1 7 5 t | |||||||
| P: | 0 1 e 2 t 3 9 4 8 5 7 6 |
1 2 3 4 5 6 5 4 3 2 1 |  |
Luigi Nono: Canti per tredeci Il canto sospeso[15][38][39] Composizione per orchestra n. 2: Diario polacco ’58 |
1955 1955–56 1959 |
6-1 | 6-1 | symmetrical all-interval row; all- combinatorial |
| I: | 0 e 1 t 2 9 3 8 4 7 5 6 |
 |
Nicolas Slonimsky: Grandmother chord[40] | 1938 | ||||
| P: | 0 2 1 3 8 7 5 6 4 e 9 t |
2 1 2 5 1 2 1 2 5 2 1 | Joonas Kokkonen: Symphonic Sketches, mov. 3, row A[41] |
1968 | 6-Z38 | 6-Z6 | — | |
| I: | 0 t e 9 4 5 7 6 8 1 3 2 | |||||||
| P: | 0 2 1 3 4 6 7 9 8 t 5 e |
2 1 2 1 2 1 2 1 2 5 6 | Igor Stravinsky: Agon, second coda[42][43] |
1957 | 6-2 | 6-2 | — | |
| I: | 0 t e 9 8 6 5 3 4 2 7 1 |
Igor Stravinsky: coda[44] | ||||||
| P: | 0 2 1 3 4 6 7 9 8 t 5 e |
2 1 2 1 2 1 2 1 2 5 6 | Igor Stravinsky: The Flood[2] |
1962 | 6-Z12 | 6-Z41 | — | |
| I: | 0 t e 5 2 4 3 1 9 8 6 7 | |||||||
| P: | 0 2 1 3 4 6 7 9 8 t 5 e |
2 1 2 1 2 1 2 1 2 5 6 | Luigi Dallapiccola: Requiescant[36] |
6-5 | 6-5 | RI-invariant: P0 = RI5 | ||
| I: | 0 t e 5 1 4 3 6 2 8 9 7 | |||||||
| P: | 0 2 1 3 4 6 7 9 8 t 5 e |
2 1 2 1 2 1 2 1 2 5 6 | Alfred Schnittke: String Quartet No. 1[3] |
1966 | 6-1 | 6-1 | all- combinatorial | |
| I: | 0 t e 2 9 1 7 3 8 5 4 6 | |||||||
| P: | 0 2 3 1 4 5 6 7 8 9 e t |
2 1 2 3 1 1 1 1 1 2 1 | Alban Berg: Lulu, Schigolch[24][45] |
1934 | 6-1 | 6-1 | all- combinatorial, | |
| I: | 0 t 9 e 8 7 6 5 4 3 1 2 | |||||||
| P: | 0 2 3 5 4 9 7 8 t e 1 6 |
2 1 2 1 5 2 1 2 1 2 5 | Igor Stravinsky: Agon, "Bransles"[44] |
1957 | 6-Z40 | 6-Z11 | — | |
| I: | 0 t 9 7 8 3 5 4 2 1 e 6 | |||||||
| P: | 0 2 3 5 7 8 e 4 6 t 8 1 |
2 1 2 2 1 3 5 2 4 2 5 |  |
Alban Berg: "Der Wein"[46] |
1929 | 6-16 | 6-16 | D harmonic minor |
| I: | 0 t 9 7 5 4 1 8 6 2 4 e | |||||||
| P: | 0 2 3 6 8 t 5 7 9 e 1 4 |
2 1 3 2 2 5 2 2 2 2 3 | Ernst Krenek: Lamentatio Jeremiae Prophetae, Op. 93, row 2[18] |
1940–41 | 6-34 | 6-34 | RI- | |
| I: | 0 t 9 6 4 2 7 5 3 1 e 8 | |||||||
| P: | 0 2 4 5 8 t 6 7 9 e 1 3 |
2 2 1 3 2 4 1 2 2 2 2 | Ernst Krenek: Lamentatio Jeremiae Prophetae, Op. 93, row 1[18] |
1940–41 | 6-34 | 6-34 | RI- | |
| I: | 0 t 8 7 4 2 6 5 3 1 e 9 | |||||||
| P: | 0 2 4 6 7 t 5 8 9 e 1 3 |
2 2 2 1 3 5 3 1 2 2 2 | Ernst Krenek: Lamentatio Jeremiae Prophetae, Op. 93, row 6[18] |
1940–41 | 6-34 | 6-34 | RI- | |
| I: | 0 t 8 6 5 2 7 4 3 1 e 9 | |||||||
| P: | 0 2 4 6 8 9 5 7 t e 1 3 |
2 2 2 2 1 4 2 3 1 2 2 | Ernst Krenek: Lamentatio Jeremiae Prophetae, Op. 93, row 5[18] |
1940–41 | 6-34 | 6-34 | RI- | |
| I: | 0 t 8 6 4 3 7 5 2 1 e 9 | |||||||
| P: | 0 2 4 6 t 8 e 7 9 1 3 5 |
2 2 2 4 2 3 4 2 4 2 2 | Alban Berg: Lulu[24] |
1934 | 6-35 | 6-35 | — | |
| I: | 0 t 8 6 2 4 1 5 3 e 9 7 | |||||||
| P: | 0 2 5 3 t 4 6 1 e 7 8 9 |
2 3 2 5 6 2 5 2 4 1 1 | Igor Stravinsky: Variations[47][2][3][48][49][50][51][52] |
1963–64 | 6-9 | 6-9 | — | |
| I: | 0 t 7 9 2 8 6 e 1 5 4 3 | |||||||
| P: | 0 2 6 4 t 9 7 e 8 5 1 3 |
2 4 2 6 1 2 4 3 3 4 2 | Arnold Schoenberg: Piano Piece [Klavierstück], op. 33b[24] |
1931 | 6-34 | 6-34 | — | |
| I: | 0 t 6 8 2 3 5 1 4 7 e 9 | |||||||
| P: | 0 2 6 t 4 7 8 3 5 9 e 1 |
2 4 4 6 3 1 5 2 4 2 2 |  |
Alban Berg: Lulu, Schoolboy[45][53][54] |
1934 | 6-34 | 6-34 | — |
| I: | 0 t 6 2 8 5 4 9 7 3 1 e | |||||||
| P: | 0 2 9 e 8 6 5 7 t 1 4 3 |
2 5 2 3 2 1 2 3 3 3 1 | Igor Stravinsky: The Owl and the Pussy Cat[2] |
1966 | 6-Z23 | 6-Z45 | — | |
| I: | 0 t 3 1 4 6 7 5 2 e 8 9 | |||||||
| P: | 0 7 6 5 8 9 4 3 t e 2 1 |
5 1 1 3 1 5 1 5 1 3 1 | Karel Goeyvaerts: Nummer 2[55] |
1951 | 6-Z36 | 6-Z3 | — | |
| I: | 0 5 6 7 4 3 8 9 2 1 t e | |||||||
| P: | 0 2 t e 1 8 6 7 9 4 3 5 |
2 4 1 2 5 2 1 2 5 1 2 |  |
Igor Stravinsky: Requiem Canticles, 1st series[2] |
1966 | 6-2 | 6-2 | — |
| I: | 0 t 2 1 e 4 6 5 3 8 9 7 | |||||||
| P: | 0 2 e 9 t 1 3 6 4 5 7 8 |
2 3 2 1 3 2 3 2 1 2 1 | Joonas Kokkonen: Woodwind Quintet, mov. 1 & 2, row A & B[41] |
1973 | 6-1 | 6-1 | all- combinatorial | |
| I: | 0 t 1 3 2 e 9 6 8 7 5 4 | |||||||
| P: | 0 2 e 9 t 4 3 7 5 6 8 1 |
2 3 2 1 6 1 4 2 1 2 5 | Arnold Schoenberg: Dreimal Tausend Jahre, Op. 50a[3] |
1949 | 6-9 | 6-9 | — | |
| I: | 0 t 1 3 2 8 9 5 7 6 4 e | |||||||
| P: | 0 3 1 2 4 7 5 6 8 e 9 t |
3 2 1 2 3 2 1 2 3 2 1 | Arvo Pärt: Symphony No. 2[56] |
1966 | 6-Z36 | 6-Z3 | derived: 4–1 | |
| I: | 0 9 e t 8 5 7 6 4 1 3 2 | |||||||
| P: | 0 3 1 2 e t 8 9 5 7 6 4 |
3 2 1 3 1 2 1 4 2 1 2 | Milton Babbitt: Woodwind Quartet[57] |
1953 | 6-1 | 6-1 | — | |
| I: | 0 9 e t 1 2 4 3 7 5 6 8 | |||||||
| P: | 0 3 1 6 2 4 t 5 9 7 8 e |
3 2 5 4 2 6 5 4 2 1 3 | Ernst Krenek: Sechs Vermessene, Op. 168[58] |
1958 | 6-2 | 6-2 | — | |
| I: | 0 9 e 6 t 8 2 7 3 5 4 1 | |||||||
| P: | 0 3 1 6 2 t 9 8 e 7 5 4 |
3 2 5 4 4 1 1 3 4 2 1 | Ernst Krenek: Karl V[59][60] |
1938 | 6-Z39 | 6-Z10 | — | |
| I: | 0 9 e 6 t 2 3 4 1 5 7 8 | |||||||
| P: | 0 3 1 t 2 8 e 5 6 9 7 4 |
3 2 3 4 6 3 6 1 3 2 3 | Donald Martino: Fantasy Variations[61] |
1962 | 6-9 | 6-9 | — | |
| I: | 0 9 e 2 t 4 1 7 6 3 5 8 | |||||||
| P: | 0 3 2 1 4 8 e 5 t 7 6 9 |
3 1 1 3 4 3 6 5 3 1 3 | Benjamin Frankel: The Curse of the Werewolf[62] |
1961 | 6-Z37 | 6-Z4 | — | |
| I: | 0 9 t e 8 4 1 7 2 5 6 3 | |||||||
| P: | 0 3 2 9 7 8 e 6 1 5 4 t |
3 1 5 2 1 3 5 5 4 1 6 | Karlheinz Stockhausen: "Aries", from Tierkreis[63] |
1974–75 | 6-18 | 6-18 | — | |
| I: | 0 9 t 3 5 4 1 6 e 7 8 2 | |||||||
| P: | 0 3 2 1 5 4 t e 7 8 9 6 |
3 1 1 4 1 6 1 4 1 1 3 | Anton Webern: Symphony, Op. 21[4][64] |
1928 | 6-1 | 6-1 | all- combinatorial | |
| I: | 0 9 t e 7 8 2 1 5 4 3 6 | |||||||
| P: | 0 3 4 6 e 8 7 t 9 5 1 2 |
3 1 2 5 3 1 3 1 4 4 1 | Igor Stravinsky: Agon, "Mystery" (sketches only)[65] |
1957 | 6-31 | 6-31 | — | |
| I: | 0 9 8 6 1 4 5 2 3 7 e t | |||||||
| P: | 0 3 5 1 2 6 4 e 7 8 e 9 |
3 2 4 1 4 2 5 4 1 3 2 | Karlheinz Stockhausen: Klavierstück IV |
1952 | 6-Z3 | 6-Z36 | — | |
| I: | 0 9 7 e t 6 8 1 5 4 1 3 | |||||||
| P: | 0 3 5 4 e t 9 8 7 6 2 1 |
3 2 1 5 1 1 1 1 1 4 1 | Karlheinz Stockhausen: "Aquarius", from Tierkreis[63] |
1974–75 | 6-Z6 | 6-Z38 | — | |
| I: | 0 9 7 8 1 2 3 4 5 6 t e | |||||||
| P: | 0 3 5 7 9 e 6 8 t 1 2 4 |
3 2 2 2 2 5 2 2 3 1 2 | Ernst Krenek: Lamentatio Jeremiae Prophetae, Op. 93, row 4[18] |
1940–41 | 6-34 | 6-34 | RI- | |
| I: | 0 9 7 5 3 1 6 4 2 e t 8 | |||||||
| P: | 0 3 7 e 2 5 9 1 4 6 8 t |
3 4 4 3 3 4 4 3 2 2 2 |  |
Alban Berg: Violin Concerto[4][24][67] |
1935 | 6-Z24 | 6-Z46 | — |
| I: | 0 9 5 1 t 7 3 e 8 6 4 2 | |||||||
| P: | 0 3 e 2 t 1 9 5 8 4 7 6 |
3 4 3 4 3 4 4 3 4 3 1 | Anton Webern: "Erlösung" from Drei Lieder, Op. 18, No. 2[68] |
1910–13 | 6-1 | 6-1 | all- combinatorial | |
| I: | 0 9 1 t 2 e 3 7 4 8 5 6 | |||||||
| P: | 0 3 e 4 2 1 7 8 t 5 9 6 |
3 4 5 2 1 6 1 2 5 4 3 | Ernst Krenek: Quaestio temporis, Op. 170[69] |
1959 | 6-1 | 6-1 | all- combinatorial | |
| I: | 0 9 1 8 t e 5 4 2 7 3 6 | |||||||
| P: | 0 3 e t 2 9 1 5 4 8 7 6 |
3 4 1 4 5 4 4 1 4 1 1 | Anton Webern: Op. 31[12] |
1941–43 | 6-Z3 | 6-Z36 | — | |
| I: | 0 9 1 2 t 3 e 7 8 4 5 6 | |||||||
| P: | 0 4 1 8 5 9 3 e 2 7 t 6 |
4 3 5 3 4 6 4 3 5 3 4 | Milton Babbitt: Composition for Four Instruments, row iv[26] |
1948 | 6–20 | 6–20 | all- combinatorial | |
| I: | 0 8 e 4 7 3 9 1 t 5 2 6 | |||||||
| P: | 0 4 1 e 3 2 8 6 5 t 7 9 |
4 3 2 4 1 6 2 1 5 3 2 | Milton Babbitt: Composition for Four Instruments[70] |
1948 | 6–1 | 6–1 | all- combinatorial | |
| I: | 0 8 e 1 9 t 4 6 7 2 5 3 | |||||||
| P: | 0 4 2 5 7 8 t 9 e 1 6 3 |
4 2 3 2 1 2 1 2 2 5 3 | Igor Stravinsky: Anthem[2] |
1962 | 6–33 | 6–33 | — | |
| I: | 0 8 t 7 5 4 2 3 1 e 6 9 | |||||||
| P: | 0 4 3 2 5 6 t e 9 1 7 8 |
4 1 1 3 1 4 1 2 4 6 1 | Karlheinz Stockhausen: Licht, Eve formula[71][72] |
1977– 2003 |
6–2 | 6–2 | — | |
| I: | 0 8 9 t 7 6 2 1 3 e 5 4 | |||||||
| P: | 0 4 3 7 e 8 9 6 5 1 2 t |
4 1 4 4 3 1 3 1 4 1 4 | Arnold Schoenberg: Ode to Napoleon Buonaparte Suite Op. 29[73] Luigi Nono: |
1942 1926 1950 |
6–20 | 6–20 | all- combinatorial | |
| I: | 0 8 9 5 1 4 3 6 7 e t 2 | |||||||
| P: | 0 4 3 8 7 e 5 1 2 9 t 6 |
4 1 5 1 4 6 4 1 5 1 4 | Milton Babbitt: Composition for Four Instruments, row iii[26] |
1948 | 6–20 | 6–20 | all- combinatorial | |
| I: | 0 8 9 4 5 1 7 e t 3 2 6 | |||||||
| P: | 0 4 3 e 7 8 t 9 2 5 1 6 |
4 1 4 4 1 2 1 5 3 4 5 | Karlheinz Stockhausen: "Scorpio", from Tierkreis[63] |
1974–75 | 6–20 | 6–20 | — | |
| I: | 0 8 9 1 5 4 2 3 t 7 e 6 | |||||||
| P: | 0 4 3 e t 9 1 7 8 6 2 5 |
4 1 4 1 1 4 6 1 2 4 3 | Ernst Krenek: Suite, Op. 84 |
6–5 | 6–5 | — | ||
| I: | 0 8 9 1 2 3 e 5 4 6 t 7 | |||||||
| P: | 0 4 5 2 6 7 8 9 e t 3 1 |
4 1 3 4 1 1 1 2 1 5 2 | Alban Berg: Lulu[24] |
1934 | 6–9 | 6–9 | — | |
| I: | 0 8 7 t 6 5 4 3 1 2 9 e | |||||||
| P: | 0 4 5 2 7 9 6 8 e t 3 1 |
4 1 3 5 2 3 2 3 1 5 2 |  |
Alban Berg: Lulu, Basic[45][53][54] |
1934 | 6–32 | 6–32 | circle of fifths |
| I: | 0 8 7 t 5 3 6 4 1 2 9 e | |||||||
| P: | 0 4 5 e 6 t 7 3 1 2 9 8 |
4 1 6 5 4 3 4 2 1 5 1 | Milton Babbitt: All Set[76][77] |
1957 | 6–7 | 6–7 | second-order combinatorial | |
| I: | 0 8 7 1 6 2 5 9 e t 3 4 | |||||||
| P: | 0 4 5 t 7 6 1 8 e 2 9 3 |
4 1 5 3 1 5 5 3 3 5 6 | Karlheinz Stockhausen: "Gemini", from Tierkreis[63] |
1974–75 | 6-Z41 | 6-Z12 | — | |
| I: | 0 8 7 2 5 6 e 4 1 t 3 9 | |||||||
| P: | 0 4 8 9 3 2 t e 7 6 5 1 |
4 4 1 6 1 4 1 4 1 1 4 | Robert Moevs: Three Symphonic Pieces, mov. 2[78] |
1954–55 | 6-Z17 | 6-Z43 | all-trichord | |
| I: | 0 8 4 3 9 t 2 1 5 6 7 e | |||||||
| P: | 0 4 t 6 3 8 7 2 5 9 1 e |
4 6 4 3 5 1 5 3 4 4 2 | Juan Carlos Paz: Canciones y Baladas, Balada II[79] |
1936 | 6–34 | 6–34 | — | |
| I: | 0 8 2 6 9 4 5 t 7 3 e 1 | |||||||
| P: | 0 5 1 2 3 9 8 t 4 e 6 7 |
5 4 1 1 6 1 2 6 5 5 1 | Alban Berg: Lulu, Chorale[45] |
1934 | 6-Z39 | 6-Z10 | — | |
| I: | 0 7 e t 9 3 4 2 8 1 6 5 | |||||||
| P: | 0 5 1 4 2 3 9 8 t 7 e 6 |
5 4 3 2 1 6 1 2 3 4 5 | Michael Gielen: Six Songs, for bass, violin, viola, clarinet, bass clarinet, and piano[80] |
1958 | 6–1 | 6–1 | retrograde-symmetrical all-interval row, all- combinatorial hexachords | |
| I: | 0 7 e 8 t 9 3 4 2 5 1 6 | |||||||
| P: | 0 5 1 4 t 8 e 9 3 6 2 7 |
5 4 3 6 2 3 2 6 3 4 5 | Alfred Schnittke: Concerto Grosso No. 3[3] |
1985 | 6–31 | 6–31 | — | |
| I: | 0 7 e 8 2 4 1 3 9 6 t 5 | |||||||
| P: | 0 5 2 7 4 9 6 e 8 1 t 3 |
5 3 5 3 5 3 5 3 5 3 5 | Benjamin Britten: The Turn of the Screw[81] |
1954 | 6–32 | 6–32 | — | |
| I: | 0 7 t 5 8 3 6 1 4 e 2 9 | |||||||
| P: | 0 5 2 7 t 1 e 4 6 8 9 3 |
5 3 5 3 3 2 5 2 2 1 6 | Dmitri Shostakovich: Symphony No. 14, mov. III[82] |
1969 | 6-Z47 | 6-Z25 | — | |
| I: | 0 7 t 5 2 e 1 8 6 4 3 9 | |||||||
| P: | 0 5 2 t 1 7 8 6 e 4 9 3 |
5 3 4 3 6 1 2 5 5 5 6 | Alban Berg: Lulu, Countess Geschwitz[24][45][54] |
1934 | 6-Z47 | 6-Z25 | — | |
| I: | 0 7 t 2 e 5 4 6 1 8 3 9 | |||||||
| P: | 0 5 4 7 t 6 e 8 1 9 2 3 |
5 1 3 3 4 5 3 5 4 5 1 | Igor Stravinsky: Threni[2] |
1958 | 6-Z41 | 6-Z12 | — | |
| I: | 0 7 8 5 2 6 1 4 e 3 t 9 | |||||||
| P: | 0 5 7 4 2 3 9 1 8 e t 6 |
5 2 3 2 1 6 4 5 3 1 4 | Milton Babbitt: Three Compositions for Piano, no. I[83] |
1947 | 6–8 | 6–8 | — | |
| I: | 0 7 5 8 t 9 3 e 4 1 2 6 | |||||||
| P: | 0 5 7 6 e 3 4 2 9 8 t 1 |
5 2 1 5 4 1 2 5 1 2 3 | Alban Berg: Lulu, Acrobat/Athlete[24][45][54] |
1934 | 6-Z17 | 6-Z43 | all-trichord | |
| I: | 0 7 5 6 1 9 8 t 3 4 2 e | |||||||
| P: | 0 5 9 t 4 7 6 e 1 2 8 3 |
5 4 1 6 3 1 5 2 1 6 5 |  |
Alban Berg: Lulu, Dr. Schön[45][53][54] |
1934 | 6-Z25 | 6-Z47 | — |
| I: | 0 7 3 2 8 5 6 1 e t 4 9 | |||||||
| P: | 0 5 e 6 3 2 8 7 9 t 4 1 |
5 6 5 3 1 6 1 2 1 6 3 | Karlheinz Stockhausen: "Leo", from Tierkreis[63] |
1974–75 | 6Z-13 | 6-Z42 | — | |
| I: | 0 7 1 6 9 t 4 5 3 2 8 e | |||||||
| P: | 0 6 4 2 8 9 3 1 e t 7 5 |
6 2 2 6 1 6 2 2 1 3 2 | Igor Stravinsky: Elegy for J.F.K.[2] |
1964 | 6–34 | 6–34 | — | |
| I: | 0 6 8 t 4 3 9 e 1 2 5 7 | |||||||
| P: | 0 6 4 3 2 9 t 5 7 8 e 1 |
6 2 1 1 5 1 5 2 1 3 2 | Karel Husa: Mosaïques[84] |
1960 | 6-Z45 | 6-Z23 | — | |
| I: | 0 6 8 9 t 3 2 7 5 4 1 e | |||||||
| P: | 0 6 5 1 e 7 4 8 9 3 2 t |
6 1 4 2 4 3 4 1 6 1 4 | Arnold Schoenberg: "De Profundis", Op. 50b[3] |
1950 | 6–7 | 6–7 | — | |
| I: | 0 6 7 e 1 5 8 4 3 9 t 2 | |||||||
| P: | 0 6 5 2 3 4 7 8 9 t e 1 |
6 1 3 1 1 3 1 1 1 1 2 | Karlheinz Stockhausen: "Sagittarius", from Tierkreis[63] |
1974–75 | 6–2 | 6–2 | — | |
| I: | 0 6 7 t 9 8 5 4 3 2 1 e | |||||||
| P: | 0 6 5 e t 4 3 9 8 2 1 7 |
6 1 6 1 6 1 6 1 6 1 6 | Witold Lutosławski: Musique funèbre (Funeral Music)[85] |
1954–58 | 6–7 | 6–7 | — | |
| I: | 0 6 7 1 2 8 9 3 4 t e 5 | |||||||
| P: | 0 6 7 8 9 1 2 5 e 4 t 3 |
6 1 1 1 4 1 3 6 5 6 5 | Wolfgang Amadeus Mozart: String Quartet in E♭ major, K. 428 |
6–5 | 6–5 | — | ||
| I: | 0 6 5 4 3 e t 7 1 8 2 9 | |||||||
| P: | 0 6 8 5 7 e 4 3 9 t 1 2 |
6 2 3 2 4 5 1 6 1 3 1 |  |
Arnold Schoenberg: Variations, Op. 31[79][87][88] |
1926–28 | 6–5 | 6–5 | Bach motif |
| I: | 0 6 4 7 5 1 8 9 3 2 e t | |||||||
| P: | 0 6 8 t 2 4 9 5 3 e 7 1 |
6 2 2 4 2 5 4 2 4 4 6 | Arnold Schoenberg: Three Songs, Op. 48[64] |
1933 | 6–35 | 6–35 | — | |
| I: | 0 6 4 2 t 8 3 7 9 1 5 e | |||||||
| P: | 0 6 9 2 8 t 4 7 1 e 3 5 |
6 3 5 6 2 6 3 6 2 4 2 | Josef Matthias Hauer: Salambo, op. 60[89] |
1929 | 6-21 | 6-21 | — | |
| I: | 0 6 3 t 4 2 8 5 e 1 9 7 | |||||||
| P: | 0 6 t 7 9 8 3 2 4 1 5 e |
6 4 3 2 1 5 1 2 3 4 6 | Michel Fano: Sonata for Two Pianos[90] | 1951 | 6-Z3 | 6-Z36 | retrograde- | |
| I: | 0 6 2 5 3 4 9 t 8 e 7 1 | |||||||
| P: | 0 6 t 8 4 7 2 5 1 e 3 9 |
6 4 2 4 3 5 3 4 2 4 6 | Ben Johnston: String Quartet No. 7, mov. 2[91] |
1984 | 6–21 | 6–21 | just intonation: | |
| I: | 0 6 2 4 8 5 t 7 e 1 9 3 | |||||||
| P: | 0 7 1 t e 9 5 8 4 3 2 6 |
5 6 3 1 2 4 3 4 1 1 4 | Karlheinz Stockhausen: Klavierstück IV |
1952 | 6–2 | 6–2 | — | |
| I: | 0 5 e 2 1 3 7 4 8 9 t 6 | |||||||
| P: | 0 7 2 1 e 8 3 5 9 t 4 6 |
5 5 1 2 3 5 2 4 1 6 2 |  |
Arnold Schoenberg: Piano Piece, op. 33a[24][92] |
1928 | 6–5 | 6–5 | — |
| I: | 0 5 t e 1 4 9 7 3 2 8 6 | |||||||
| P: | 0 7 3 t 2 6 9 1 4 8 e 5 |
5 4 5 4 4 3 4 3 4 3 6 | Alberto Ginastera: Quintet, op. 29[28] |
1963 | 6–31 | 6–31 | — | |
| I: | 0 5 9 2 t 6 3 e 8 4 1 7 | |||||||
| P: | 0 7 4 e 6 t 3 9 1 8 5 2 |
5 3 5 5 4 5 6 4 5 3 3 | Elliott Carter: Piano Concerto, Orchestra[93] |
1964–65 | 6-Z43 | 6-Z17 | all-trichord | |
| I: | 0 5 8 1 6 2 9 3 e 4 7 t | |||||||
| P: | 0 7 6 4 5 9 8 t 3 1 e 2 |
5 1 2 1 4 1 2 5 2 2 3 | Igor Stravinsky: Requiem Canticles, 2nd series[2] |
1966 | 6-Z40 | 6-Z11 | — | |
| I: | 0 5 6 8 7 3 4 2 9 e 1 t | |||||||
| P: | 0 7 6 e 9 1 4 t 8 5 2 3 |
5 1 5 2 4 3 6 2 3 3 1 | Ernst Krenek: String Quartet No. 7, op. 96[59] |
1943–44 | 6-Z12 | 6-Z41 | — | |
| I: | 0 5 6 1 3 e 8 2 4 7 t 9 | |||||||
| P: | 0 7 e 2 1 9 3 5 t 6 8 4 |
5 4 3 1 4 6 2 5 4 2 4 | Arnold Schoenberg: Piano Concerto, Op. 42[94][95] |
1942 | 6–9 | 6–9 | inversional | |
| I: | 0 5 1 t e 3 9 7 2 6 4 8 | |||||||
| P: | 0 7 e 8 2 t 6 9 5 4 1 3 |
5 4 3 6 4 4 3 4 1 3 2 | Anton Webern: Op. 23[96] |
1933 | 6-Z10 | 6-Z39 | — | |
| I: | 0 5 1 4 t 2 6 3 7 8 e 9 | |||||||
| P: | 0 7 e t 2 9 6 1 5 4 8 3 |
5 4 1 4 5 3 5 4 1 4 5 | Ross Lee Finney: Edge of Shadow[21] |
1959 | 6–8 | 6–8 | — | |
| I: | 0 5 1 2 t 3 6 e 7 8 4 9 | |||||||
| P: | 0 7 e t 9 8 3 6 4 1 5 2 |
5 4 1 1 1 5 3 2 3 4 3 | Karlheinz Stockhausen: "Cancer", from Tierkreis[63] |
1974–75 | 6–1 | 6–1 | all- combinatorial | |
| I: | 0 5 1 2 3 4 9 6 8 e 7 t | |||||||
| P: | 0 8 1 7 2 e 9 6 4 5 3 t |
4 5 6 5 3 2 3 2 1 2 5 | Arnold Schoenberg: String Trio, Op. 45[97] |
1946 | 6–5 | 6–5 | — | |
| I: | 0 4 e 5 t 1 3 6 8 7 9 2 | |||||||
| P: | 0 8 1 t 9 e 5 3 4 7 2 6 [98][99] |
4 5 3 1 2 6 2 1 3 5 4 |  |
Karlheinz Stockhausen: Klavierstück VII Klavierstück IX Klavierstück X |
1955 1955–57 1961 1961 |
6–1 | 6–1 | all- combinatorial hexachord, retrograde-symmetrical |
| I: | 0 4 e 2 3 1 7 9 8 5 t 6 | |||||||
| P: | 0 8 1 e t 7 5 9 4 6 3 2 |
4 5 2 1 3 2 4 5 2 3 1 | Karlheinz Stockhausen: Klavierstück V (row of original 1954 version)[100] Klavierstück VIII[101] |
1954–55 1954 |
6-Z3 | 6-Z36 | — | |
| I: | 0 4 e 1 2 5 7 3 8 6 9 t | |||||||
| P: | 0 8 4 9 t 3 1 6 e 2 7 5 |
4 4 5 1 5 2 5 5 3 5 2 | Elliott Carter: Piano Concerto, Solo[ist][93] |
1964–65 | 6-Z17 | 6-Z43 | all-interval | |
| I: | 0 4 8 3 2 9 e 6 1 t 5 7 | |||||||
| P: | 0 8 5 t 7 1 6 4 e 2 3 9 |
4 3 5 3 6 5 2 5 3 1 6 |  |
Alban Berg: Lulu, Alwa[45][53][54] |
1934 | 6-Z25 | 6-Z47 | — |
| I: | 0 4 7 2 5 e 6 8 1 t 9 3 | |||||||
| P: | 0 8 7 t 4 5 2 9 e 3 1 6 |
4 1 3 6 1 3 5 2 4 2 5 | Elliott Carter: A Symphony of Three Orchestras[93] |
1976 | 6-Z24 | 6-Z46 | ordered in | |
| I: | 0 4 5 2 8 7 t 3 1 9 e 6 | |||||||
| P: | 0 8 7 e t 9 3 1 4 2 6 5 |
4 1 4 1 1 6 2 3 2 4 1 | _tone_row.png) |
Anton Webern: Variations for piano, mov. III, op. 27[102][103] |
1936 | 6–1 | 6–1 | all- combinatorial |
| I: | 0 4 5 1 2 3 9 e 8 t 6 7 | |||||||
| P: | 0 8 e t 2 1 4 3 7 6 9 5 |
4 3 1 4 1 3 1 4 1 3 4 | Anton Webern: Op. 29[104][36] |
1938 | 6–2 | 6–2 | semi- P0 = RI5 | |
| I: | 0 4 1 2 t e 8 9 5 6 3 7 | |||||||
| P: | 0 8 e t 4 6 7 1 5 3 9 2 |
4 3 1 6 2 1 6 4 2 6 5 | Ernst Krenek: Sestina, op. 161[59] |
1957 | 6–22 | 6–22 | — | |
| I: | 0 4 1 2 8 6 5 e 7 9 3 t | |||||||
| P: | 0 9 1 3 4 e 2 8 7 5 t 6 |
3 4 2 1 5 3 6 1 2 5 4 | Luigi Dallapiccola: Piccola musica notturna[105] |
1954 | 6–8 | 6–8 | — | |
| I: | 0 3 e 9 8 1 t 4 5 7 2 6 | |||||||
| P: | 0 9 1 8 4 5 7 2 3 6 t e |
3 4 5 4 1 2 5 1 3 4 1 | Milton Babbitt: Composition for Synthesizer[106] |
1961 | 6–20 | 6–20 | — | |
| I: | 0 3 e 4 8 7 5 t 9 6 2 1 | |||||||
| P: | 0 9 1 e t 2 8 7 5 4 6 3 |
3 4 2 1 4 6 1 2 1 2 3 |  |
Milton Babbitt: Composition for Four Instruments[107][108] |
1948 | 6–1 | 6–1 | all- combinatorial |
| I: | 0 3 e 1 2 t 4 5 7 8 6 9 | |||||||
| P: | 0 9 2 3 e t 5 4 1 6 7 8 |
3 5 1 4 1 5 1 3 5 1 1 | Igor Stravinsky: Epitaphium[2] |
1959 | 6-Z3 | 6-Z36 | — | |
| I: | 0 3 t 9 1 2 7 8 e 6 5 4 | |||||||
| P: | 0 9 2 8 7 5 6 1 3 4 t e |
3 5 6 1 2 1 5 2 1 6 1 | Karlheinz Stockhausen: "Capricorn", from Tierkreis[63] |
1974–75 | 6-Z47 | 6-Z25 | — | |
| I: | 0 3 t 4 5 7 6 e 9 8 2 1 | |||||||
| P: | 0 9 8 4 7 6 1 t 3 5 e 2 |
3 1 4 3 1 5 3 5 2 6 3 | David Dzubay: Di/Con[ver(gence/sions)][3] | 1988 | 6-Z39 | 6-Z10 | — | |
| I: | 0 3 4 8 5 6 e 2 9 7 1 t | |||||||
| P: | 0 9 8 e t 2 3 4 5 7 1 6 |
3 1 3 1 4 1 1 1 2 6 5 | Anton Webern: Op. 22[109] |
1929–30 | 6–2 | 6–2 | semi- | |
| I: | 0 3 4 1 2 t 9 8 7 5 e 6 | |||||||
| P: | 0 9 e 2 4 1 7 t 8 5 3 6 |
3 2 3 2 3 6 3 2 3 2 3 | Milton Babbitt: Composition for Four Instruments, row ii[26] |
1948 | 6–8 | 6–8 | — | |
| I: | 0 3 1 t 8 e 5 2 4 7 9 6 | |||||||
| P: | 0 t 1 2 5 4 6 3 7 e 8 9 |
2 3 1 3 1 2 3 4 4 3 1 | Pierre Boulez: Le marteau sans maître[3][110] |
1953–55 | 6-Z10 | 6-Z39 | — | |
| I: | 0 2 e t 7 8 6 9 5 1 4 3 | |||||||
| P: | 0 t 3 4 2 7 6 9 8 e 1 5 |
2 5 1 2 5 1 3 1 3 2 4 | Charles Ives: Tone Roads No. 1[111] |
1911 | 6-Z46 | 6-Z24 | — | |
| I: | 0 2 9 8 t 5 6 3 4 1 e 7 | |||||||
| P: | 0 t 3 e 8 7 1 2 5 9 4 6 |
2 5 4 3 1 6 1 3 4 5 2 | Elliott Carter: Night Fantasies[112] |
1982 | 6–14 | 6–14 | — | |
| I: | 0 2 9 1 4 5 e t 7 3 8 6 | |||||||
| P: | 0 t 9 8 7 5 e 1 2 3 4 6 |
2 1 1 1 2 6 2 1 1 1 2 | Milton Babbitt: Composition for Four Instruments, row i[26] |
1948 | 6–8 | 6–8 | — | |
| I: | 0 2 3 4 5 7 1 e t 9 8 6 | |||||||
| P: | 0 t 9 e 7 2 8 1 4 6 5 3 |
2 1 2 4 5 6 5 3 2 1 2 | Karlheinz Stockhausen: Kreuzspiel[113] |
1951 | 6-Z50 | 6-Z29 | — | |
| I: | 0 2 3 1 5 t 4 e 8 6 7 9 | |||||||
| P: | 0 e 1 2 9 8 t 7 5 6 4 3 |
1 2 1 5 1 2 3 2 1 2 1 | Igor Stravinsky: Agon, "Double Pas de Quatre"[2][114] |
1957 | 6-Z3 | 6-Z36 | — | |
| I: | 0 1 e t 3 4 2 5 7 6 8 9 | |||||||
| P: | 0 e 1 3 4 2 5 7 6 8 t 9 |
1 2 2 1 2 3 2 1 2 2 1 | Igor Stravinsky: Fanfare[2] |
1964 | 6–1 | 6–1 | all- combinatorial | |
| I: | 0 1 e 9 8 t 7 5 6 4 2 3 | |||||||
| P: | 0 e 1 3 4 2 7 6 9 5 8 t |
1 2 2 1 2 5 1 3 4 3 2 | Igor Stravinsky: Canticum Sacrum, II & IV[2] |
1955 | 6–1 | 6–1 | all- combinatorial | |
| I: | 0 1 e 9 8 t 5 6 3 7 4 2 | |||||||
| P: | 0 e 1 7 9 8 t 4 6 5 2 3 |
1 2 6 2 1 2 6 2 1 3 1 | Chen Yi: Woodwind Quintet[3][37] |
1987 | 6-Z4 | 6-Z37 | — | |
| I: | 0 1 e 5 3 4 2 8 6 7 t 9 | |||||||
| P: | 0 e 2 1 3 4 9 t 7 8 6 5 |
1 3 1 2 1 5 1 3 1 2 1 | Arvo Pärt: Diagrams[56] |
1964 | 6–1 | 6–1 | all- combinatorial | |
| I: | 0 1 t e 9 8 3 2 5 4 6 7 | |||||||
| P: | 0 e 2 1 5 6 3 4 8 7 t 9 |
1 3 1 4 1 3 1 4 1 3 1 |  |
Anton Webern: String Quartet, Op. 28:[104][67][102] |
1936 | 6–5 | 6–5 | derived: 4–1 (BACH motif), semi- |
| I: | 0 1 t e 7 6 9 8 4 5 2 3 | |||||||
| P: | 0 e 2 3 4 1 6 5 8 9 t 7 |
1 3 1 1 3 5 1 3 1 1 3 | Alberto Ginastera: Violin Concerto, op. 30[28] |
1963 | 6–1 | 6–1 | all- combinatorial | |
| I: | 0 1 t 9 8 e 6 7 4 3 2 5 | |||||||
| P: | 0 e 2 9 5 3 4 8 t 7 1 6 |
1 3 5 4 2 1 4 2 3 6 5 | Elliott Carter: String Quartet No. 3[115] |
1973 | 6-Z23 | 6-Z45 | — | |
| I: | 0 1 t 3 7 9 8 4 2 5 e 6 | |||||||
| P: | 0 e 3 1 7 9 6 2 t 5 8 4 |
1 4 2 6 2 3 4 4 5 3 4 | Arnold Schoenberg: Violin Phantasy, Op. 47[116][117] |
1949 | 6–21 | 6–21 | — | |
| I: | 0 1 9 e 5 3 6 t 2 7 4 8 | |||||||
| P: | 0 e 3 2 1 8 6 9 t 7 5 4 |
1 4 1 1 5 2 3 1 3 2 1 | Igor Stravinsky: Double Canon[2] |
1959 | 6-Z36 | 6-Z3 | — | |
| I: | 0 1 9 t e 4 6 3 2 5 7 8 | |||||||
| P: | 0 e 3 4 8 7 9 5 6 1 2 t |
1 4 1 4 1 2 4 1 5 1 4 |  |
Anton Webern: Concerto for Nine Instruments, Op. 24[24][68][87][92][118] |
1934 | 6–20 | 6–20 | all- combinatorial, derived: 3–3 |
| I: | 0 1 9 8 4 5 3 7 6 e t 2 | |||||||
| P: | 0 e 4 5 7 3 2 6 8 1 t 9 |
1 5 1 2 4 1 4 2 5 3 1 | David Lewin: Just a Minute, Roger[119] |
1978 | 6–16 | 6–16 | — | |
| I: | 0 1 8 7 5 9 t 6 4 e 2 3 | |||||||
| P: | 0 e 5 2 1 6 3 8 7 4 t 9 |
1 6 3 1 5 3 5 1 3 6 1 | Alfred Schnittke: Viola Concerto[3] |
1985 | 6–5 | 6–5 | — | |
| I: | 0 1 7 t e 6 9 4 5 8 2 3 | |||||||
| P: | 0 e 5 9 6 2 7 3 1 4 t 9 |
1 6 4 3 4 5 4 2 3 6 1 | Luigi Dallapiccola: Cinque Canti[36] |
6-Z50 | 6-Z29 | RI-invariant: P0 = RI9 | ||
| I: | 0 1 7 3 6 t 5 9 e 8 2 3 | |||||||
| P: | 0 e 6 5 4 3 1 t 9 7 2 8 |
1 5 1 1 1 2 3 1 2 5 6 | Pierre Boulez: Structures Ia[3][67] |
1952 | 6–5 | 6–5 | — | |
| I: | 0 1 6 7 8 9 e 2 3 5 t 4 | |||||||
| P: | 0 e 6 5 7 1 8 2 t 3 4 9 |
1 5 1 2 6 5 6 4 5 1 5 | George Perle: Three Inventions for Piano, no. 3[120] |
6–7 | 6–7 | all- combinatorial | ||
| I: | 0 1 6 7 5 e 4 t 2 9 8 3 | |||||||
| P: | 0 e 7 1 2 9 3 8 t 4 5 6 |
1 4 6 1 5 6 5 2 6 1 1 |  |
Alban Berg: Lyric Suite, mov. III[121] |
1925–26 | 6–9 | 6–9 | — |
| I: | 0 1 5 e t 3 9 4 2 8 7 6 | |||||||
| P: | 0 e 7 1 4 8 3 9 t 2 5 6 |
1 4 6 3 4 5 6 1 4 3 1 |  |
Alban Berg: Lyric Suite, mov. VI, row 1[122] |
1925–26 | 6-Z44 | 6-Z19 | — |
| I: | 0 1 5 e 8 4 9 3 2 t 7 6 | |||||||
| P: | 0 e 7 4 2 9 3 8 t 1 5 6 |
1 4 3 2 5 6 5 2 3 4 1 |  |
Fritz Heinrich Klein[123]
Alban Berg: Alberto Ginastera: |
1920– 1925–26 1976 |
6–32 | 6–32 | Mother chord (all-interval) Trichordally combinatorial: 0369[126] |
| I: | 0 1 5 8 t 3 9 4 2 e 7 6 | |||||||
| P: | 0 e 7 8 3 1 2 t 6 5 4 9 |
1 4 1 5 2 1 4 4 1 1 5 | Arnold Schoenberg: String quartet No. 4[64][116] |
1936 | 6–16 | 6–16 | — | |
| I: | 0 1 5 4 9 e t 2 6 7 8 3 | |||||||
| P: | 0 e 8 4 7 3 1 5 2 6 9 t |
1 3 4 3 4 2 4 3 4 3 1 | Arnold Schoenberg: Modern Psalm, Op. 50c[3] |
1950 | 6–20 | 6–20 | — | |
| I: | 0 1 4 8 5 9 e 7 t 6 3 2 | |||||||
| P: | 0 e 8 9 7 6 1 5 4 3 2 t |
1 3 1 2 1 5 4 1 1 1 4 |  |
Alban Berg: Lyric Suite, row 2[122] |
1925–26 | 6-Z3 | 6-Z36 | — |
| I: | 0 1 4 3 5 6 e 7 8 9 t 2 | |||||||
| P: | 0 e 9 2 t 7 1 4 8 3 5 6 |
1 2 5 4 3 6 3 4 5 2 1 | Milton Babbitt: "The Widow's Lament in Springtime"[127] |
1951 | 6–8 | 6–8 | — | |
| I: | 0 1 3 t 2 5 e 8 4 9 7 6 | |||||||
| P: | 0 e 9 4 3 t 8 7 5 6 1 2 |
1 2 5 1 5 2 1 2 1 5 1 | Dmitri Shostakovich: Symphony No. 14, mov. I[82] |
1969 | 6–5 | 6–5 | — | |
| I: | 0 1 3 8 9 2 4 5 7 6 e t | |||||||
| P: | 0 e 9 6 t 8 7 5 2 4 3 1 |
1 2 3 4 2 1 2 3 2 1 2 | Igor Stravinsky: Canticum Sacrum, II[2] |
1955 | 6–2 | 6–2 | — | |
| I: | 0 1 3 6 2 4 5 7 t 8 9 e | |||||||
| P: | 0 e t 1 3 2 4 9 8 6 5 7 |
1 1 3 2 1 2 5 1 2 1 2 | Alfred Schnittke: String Quartet No. 4, Mov. I[3] |
1989 | 6–1 | 6–1 | all- | |
| I: | 0 1 2 e 9 t 8 3 4 6 7 5 | |||||||
| P: | 0 e t 5 6 9 7 1 2 8 3 4 |
1 1 5 1 3 2 6 1 6 5 1 | Arvo Pärt: Symphony No. 1 Perpetuum Mobile[56] |
1963 1963 |
6–5 | 6–5 | — | |
| I: | 0 1 2 7 6 3 5 e t 4 9 8 |
Close
Remove ads
Other lengths
Summarize
Perspective
Fewer than twelve
- Five
More information Prime form, Interval classes ...
| Prime form | Interval classes |
Notation | Composer: Composition |
Year | Set(s) | Features |
|---|---|---|---|---|---|---|
| 0 e 8 9 t | 1 3 1 1 | Igor Stravinsky: In memoriam Dylan Thomas[128] |
1954 | 5–1 | — |
Close
- Six
More information Prime form, Interval classes ...
| Prime form | Interval classes | Notation | Composer: Composition |
Year | Set(s) | Features |
|---|---|---|---|---|---|---|
| 0 6 9 8 1 e [129][130][131][132] |
6 3 1 5 2 |  |
Pierre Boulez: Messagesquisse Dérive 1 sur Incises |
1976
1984 1984 1994 1996 |
6-Z11, (6-Z40) | Musical cryptogram: Paul Sacher |
| Conrad Beck: Für Paul Sacher: Drei Epigramme für Violoncello solo |
1976 | |||||
| Luciano Berio: Les Mots sont allés | ||||||
| Benjamin Britten: Tema "Sacher" | ||||||
| Henri Dutilleux: Trois Strophes sur le nom de Sacher | ||||||
| Wolfgang Fortner: Zum Spielen für den 70. Geburtstag: Thema und Variationen für Violoncello Solo | ||||||
| Alberto Ginastera :Puneña n° 2, op. 45 | ||||||
| Cristóbal Halffter: Variationen über das Thema eSACHERe | ||||||
| Hans Werner Henze: Capriccio per Paul Sacher | ||||||
| Heinz Holliger: Chaconne, für Violoncello Solo | ||||||
| Klaus Huber: Transpositio ad infinitum | ||||||
| Witold Lutosławski: Sacher-Variationen | ||||||
| 0 9 8 7 1 4 | 3 1 1 6 3 |  |
Arnold Schoenberg: Die glückliche Hand, Op. 18[133] |
1910–13 1913–16 |
6-Z44 (6-Z19) | Schoenberg hexachord |
Close
- Eight
More information Prime form, Interval classes ...
| Prime form | Interval classes | Notation | Composer: Composition |
Year | Set(s) | Features |
|---|---|---|---|---|---|---|
| 0 2 8 9 t 4 3 e |
2 6 1 1 6 1 4 | Alban Berg: Lyric Suite[45] |
1925–26 | 8–5 | — | |
| 0 2 9 7 t 8 e 1 |
2 5 2 3 2 3 2 | Joonas Kokkonen: Symphonic Sketches, mov. 3, row B[41] |
1968 | 8–1 | — | |
| 0 7 1 6 8 2 3 4 |
5 6 5 2 6 1 1 | Alban Berg: Lyric Suite[45] |
1925–26 | 8–5 | — | |
| 0 8 2 3 t 4 9 e |
4 6 1 5 6 5 2 | Alban Berg: Lyric Suite[45] |
1925–26 | 8–5 | — | |
| 0 t 2 4 5 7 3 1 |
2 4 2 1 2 4 2 | Igor Stravinsky: Agon, "Pas-de-Deux" refrain (b. 463–472)[134] |
1957 | 8–10 | — | |
| 0 t 3 5 2 4 1 e |
2 5 2 3 2 3 2 | Joonas Kokkonen: Symphonic Sketches, mov. 3, row C[41] |
1968 | 8–1 | — |
Close
- Nine
More information Prime form, Interval classes ...
| Prime form | Interval classes | Notation | Composer: Composition |
Year | Set(s) | Features |
|---|---|---|---|---|---|---|
| 0 2 e 4 9 7 8 6 1 |
2 3 5 5 2 1 2 5 | Joonas Kokkonen: Symphonic Sketches, mov. 3, row D[41] |
1968 | 9–8 | — |
Close
- Ten
More information Prime form, Interval classes ...
| Prime form | Interval classes | Notation | Composer: Composition |
Year | Set(s) | Features |
|---|---|---|---|---|---|---|
| 0 e 2 1 5 6 4 9 7 8 |
1 3 1 4 1 2 5 2 1 | Arvo Pärt: Collage sur B-A-C-H[56] |
1964 | — | BACH motif |
Close
- Eleven
More information Prime form, Interval classes ...
| Prime form | Interval classes | Notation | Composer: Composition |
Year | Set(s) | Features |
|---|---|---|---|---|---|---|
| 0 1 e 5 6 8 7 9 2 3 4 |
1 2 6 1 2 1 2 5 1 1 | Karel Husa: Music for Prague 1968[3] |
1968 | — | — | |
| 0 4 3 e 2 7 6 8 t 5 1 |
4 1 4 3 5 1 2 2 5 4 |  |
Aaron Copland: Inscape row 1[135] |
1967 | — | — |
| 0 7 3 9 2 4 6 t 7 e 1 |
5 4 6 5 2 2 4 3 4 2 | Aaron Copland: Inscape row 2[135] |
1967 | — | — | |
| 0 e t 4 6 2 1 9 8 5 3 |
1 1 6 2 4 1 4 1 3 2 | Karlheinz Stockhausen: Licht, Lucifer formula[71][136] |
1977– 2003 |
— | — |
Close
More than twelve
- Thirteen
More information Prime form, Interval classes ...
| Prime form | Interval classes | Notation | Composer: Composition |
Year | Set(s) | Features |
|---|---|---|---|---|---|---|
| 0 1 4 5 t 8 7 t e 6 3 2 9 |
1 3 1 5 2 1 3 1 5 3 1 7 |
Karlheinz Stockhausen: "Taurus", from Tierkreis[63] |
1974–75 | — | — | |
| 0 1 t 6 8 3 5 2 4 e 9 7 0 |
1 3 4 2 5 2 3 2 5 2 1 5 |
Karlheinz Stockhausen: Choral[137] |
1950 | — | — | |
| 0 2 e 7 8 5 t 6 4 3 1 9 0 |
2 3 4 1 3 5 4 2 1 2 4 3 |
 |
Karlheinz Stockhausen: | 1970 | — | — |
| 0 3 e 8 5 4 9 2 1 t 7 3 6 |
3 4 3 3 1 5 5 1 3 3 4 3 |
Luciano Berio: Nones[139][140] |
1953–54 | — | — | |
| 0 4 1 5 7 t 2 8 e 9 3 6 9 |
4 3 4 2 3 4 6 3 2 6 3 3 |
Karlheinz Stockhausen: "Pisces", from Tierkreis[63] |
1974–75 | — | — | |
| 0 7 8 6 e t 2 5 1 3 9 4 0 |
5 1 2 5 1 4 3 4 2 6 5 4 |
Karlheinz Stockhausen: Licht, Michael formula[71] |
1977– 2003 |
— | — | |
| 0 e 2 4 t 9 7 3 7 1 8 5 6 |
1 3 2 6 1 2 4 4 6 7 3 1 |
Karlheinz Stockhausen: "Virgo", from Tierkreis[63] |
1974–75 | — | — | |
| 0 e 4 t 9 5 8 6 2 1 6 7 3 |
1 5 6 1 4 3 2 4 1 5 1 4 |
Karlheinz Stockhausen: Klavierstück IV (first row of 48)[66] |
1952 | 6-Z38, 6-Z6 | — |
Close
- Fourteen
More information Prime form, Interval classes ...
| Prime form | Interval classes | Notation | Composer: Composition |
Year | Set(s) | Features |
|---|---|---|---|---|---|---|
| 0 1 t 3 9 4 6 7 4 5 7 3 8 e |
1 3 5 6 5 2 1 3 1 2 4 5 3 |  |
Karlheinz Stockhausen: "Libra", from Tierkreis[63] |
1974–75 | — | — |
| 0 1 t 9 2 8 e 7 3 5 6 4 0 2 |
1 3 1 5 6 3 4 4 2 1 2 4 2 | Karlheinz Stockhausen: Inori[141] |
1973–74 | — | — | |
| 0 e 2 4 1 8 t e 9 4 7 5 3 6 |
1 3 2 3 5 2 1 2 5 3 2 3 | Joonas Kokkonen: Cello Concerto, mov. 3, row A[41] |
1969 | — | — |
Close
- Seventeen
More information Prime form, Interval classes ...
| Prime form | Interval classes | Notation | Composer: Composition |
Year | Set(s) | Features |
|---|---|---|---|---|---|---|
| 0 2 1 e t 8 9 e t 0 1 e t 0 e 9 0 |
2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 3 |
Igor Stravinsky: Agon, b. 104[142] |
1957 | — | — | |
| 0 2 3 5 4 9 7 8 e 1 6 e t 0 e 9 0 |
2 1 2 1 5 2 1 3 2 5 5 1 2 1 2 3 |
Igor Stravinsky: Agon, "Bransles"[142] |
1957 | 6-Z40, 6-Z11 | — |
Close
- Twenty-two
More information Prime form, Interval classes ...
| Prime form | Interval classes | Notation | Composer: Composition |
Year | Set(s) | Features |
|---|---|---|---|---|---|---|
| 0 e 6 8 7 2 1 3 t 9 4 6 9 7 8 3 1 2 4 e t 0 |
1 5 2 1 5 1 2 5 1 5 2 3 2 1 5 2 1 2 5 1 2 |
Joonas Kokkonen: Cello Concerto, mov. 3, row B[41] |
1969 | — | — |
Close
- Twenty-four
More information Prime form, Interval classes ...
| Prime form | Interval classes | Notation | Composer: Composition |
Year | Set(s) | Features |
|---|---|---|---|---|---|---|
| 0 1 12 14 23 22 19 18 20 21 3 4 16 13 6 15 8 7 17 10 9 11 2 5 |
0.5 5.5 1 4.5 0.5 1.5 0.5 1 0.5 9 0.5 6 1.5 3.5 4.5 3.5 .5 5 3.5 0.5 5 3.5 0.5 1 4.5 1.5 | Pierre Boulez: Polyphonie X, quarter-tone series[143] |
1950–51 | — | — | |
| 0 20 1 10 9 11 17 15 16 7 2 6 23 21 22 13 8 12 18 14 19 4 3 5 |
10 9.5 4.5 0.5 1 3 1 0.5 4.5 2.5 2 8.5 1 0.5 4.5 2.5 2 3 2 2.5 7.5 0.5 1 | Karlheinz Stockhausen: Himmelfahrt, mod24 (no octave equivalency)[144] |
2004– 2005 |
— | — |
Close
Remove ads
See also
Sources
Wikiwand - on
Seamless Wikipedia browsing. On steroids.
Remove ads