List of tone rows and series
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
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 | ![]() | 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 |
Other lengths
Fewer than twelve
- Five
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 | — |
- Six
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] "Seraphita", op. 22, no. 1[133] | 1910–13 1913–16 | 6-Z44 (6-Z19) | Schoenberg hexachord |
- Eight
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 | — |
- Nine
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 | — |
- Ten
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 |
- Eleven
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 | — | — |
More than twelve
- Thirteen
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 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[138][139] | 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 | — |
- Fourteen
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[140] | 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 | — | — |
- Seventeen
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[141] | 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"[141] | 1957 | 6-Z40, 6-Z11 | — |
- Twenty-two
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 | — | — |
- Twenty-four
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[142] | 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)[143] | 2004– 2005 | — | — |
See also
- Aggregate
- Atonality
- Complementation
- Distance model
- List of dodecaphonic and serial compositions
- Serialism
- Twelve-tone technique
Sources
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- ^ a b Bailey 1991, p. 26
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- ^ Lewin 1962, pp. 113–115
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- ^ Jonathan Harvey, The Music of Stockhausen: An Introduction (Berkeley and Los Angeles: University of California Press, 1975): p. 93. ISBN 0-520-02311-0.
- ^ Berry, Wallace (1976/1987). Structural Functions in Music, p.175. Dover. ISBN 0-486-25384-8.
- ^ Genevieve Marcus, "Stockhausen's Zeitmasse", The Music Review 29, no. 2 (May 1968): 142–156. Citation on p. 144.
- ^ Rigoni, Michel (1998). Stockhausen: ... un vaisseau lancé vers le ciel (second edition, revised, corrected, and enlarged ed.). Lillebonne: Millénaire III Editions. pp. 141–142. ISBN 978-2911906022.
- ^ a b Bailey 1991, p. 27
- ^ Leeuw 2005, p. 158.
- ^ Nolan, Catherine (1995). "Structural Levels and Twelve-Tone Music: A Revisionist Analysis of the Second Movement of Webern's 'Piano Variations Op. 27'". Journal of Music Theory 39 (1 (Spring)): 49–50. JSTOR 843898 Retrieved 8 November 2013.
- ^ a b c d Alegent, Brian (2010). The Twelve-tone Music of Luigi Dallapiccola, p.48. ISBN 9781580463256.
- ^ a b Guo, Xin (2002). Chinese Musical Language Interpreted by Western Idioms: Fusion Process in the Instrumental Works by Chen Yi (PhD dissertation). Florida State University.
- ^ Leeuw 2005, p. 177.
- ^ Carola Nielinger, "'The Song Unsung': Luigi Nono's Il canto sospeso", Journal of the Royal Musical Association 131, no. 1 (2006): 83–150. Citation on p. 97.
- ^ Slonimsky, Nicolas (1975). Thesaurus of Scales and Melodic Patterns, p. 243. ISBN 0-8256-1449-X.
- ^ a b c d e f g Jurkowski, Edward (2004). The Music of Joonas Kokkonen, pp.78, 84, 184. ISBN 9780754607892.
- ^ Smyth 1999, pp. 126–127, 142.
- ^ Wiens, Carl Kristian (1997). Igor Stravinsky and Agon, p. 168. University of Michigan.
- ^ a b Jacobi, Bonnie S. (2000). "The Bransles of Stravinsky's Agon: A Transition to Serial Composition", Moores School of Music.
- ^ a b c d e f g h i j k Headlam, David John (1996). The Music of Alban Berg, pp.265, 304, & 306. ISBN 9780300064001.
- ^ a b Pople, Anthony (1991). Berg: Violin Concerto. pp. 18 & 21. ISBN 0-521-39976-9.
- ^ Eric Walter White, "Two New Memorial Works by Stravinsky", Tempo, new series, no. 74 (Autumn 1965), pp. 18–21.
- ^ Claudio Spies, "Notes on Stravinsky's Variations", Perspectives of New Music 4, no. 1 (Autumn-Winter 1965): pp. 62–74. Citation on p. 66.
- ^ Igor Stravinsky and Robert Craft, Themes and Episodes (New York: Alfred A. Knopf,1967): p. 60.
- ^ Jerome Kohl, "Exposition in Stravinsky's Orchestral Variations", Perspectives of New Music 18, nos. 1 and 2 (Autumn 1979 – Summer 1980): pp. 391–405. Citation on pp. 391–392.
- ^ Paul Schuyler Phillips, "The Enigma of 'Variations': A Study of Stravinsky's Final Work for Orchestra", Music Analysis 3, no. 1 (March 1984): pp. 69–89. Citation on p. 69.
- ^ Smyth 1999, pp. 139–140, 142.
- ^ a b c d Whittall 2008, p. 81
- ^ a b c d e f Hailey, Christopher, ed. (2010). Alban Berg and His World. p. 215. ISBN 9781400836475.
- ^ Herman Sabbe [nl], Het muzikale serialisme als techniek en als denkmethode: Een onderzoek naar de logische en historische samenhang van de onderscheiden toepassingen van het seriërend beginsel in de muziek van de periode 1950–1975 (Ghent: Rijksuniversiteit te Gent, 1977): 55.
- ^ a b c d Hillier, Paul (1997). Arvo Pärt. pp. 40, 47, & 50. ISBN 9780191590481.
- ^ Babbitt 2011, p. 350.
- ^ Krenek 1960, p. 229.
- ^ a b c Stewart, John Lincoln (1991). Ernst Krenek: The Man and His Music. pp. 169, 250, 290. ISBN 9780520070141.
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- ^ a b c Hurry, Pam; Phillips, Mark; Richards, Mark (2001). Heinemann Advanced Music. pp. 100, 122, & 303. ISBN 9780435812584.
- ^ Smyth 1999, pp. 136–137, 142.
- ^ a b c Rudolf Frisius,.. Karlheinz Stockhausen II: Die Werke 1950–1977; Gespräch mit Karlheinz Stockhausen (Mainz, London, Berlin, Madrid, New York, Paris, Prague, Tokyo, Toronto: Schott Musik International, 2008): p. 73. ISBN 978-3-7957-0249-6.
- ^ a b c Cooper (1975). p.265. ISBN 0-396-06752-2.
- ^ a b Lewin 1962, p. 94
- ^ Krenek 1960, p. 230.
- ^ Milton Babbitt, 1976. "Responses: A First Approximation", Perspectives of New Music 14, no. 2/15, no. 1 (Spring-Summer/Fall-Winter 1976): 8–10. Citation on p. 12.
- ^ a b c Frisius, Rudolph and Stockhausen, Karlheinz (1998). "Die Tonhöhen der Superformel für LICHT", in Karlheinz Stockhausen, Texte zur Musik 9, edited by Christoph von Blumröder, 13–33 (Kürten: Stockhausen-Verlag): 13. ISBN 978-3-00-002131-2.
- ^ Frisius; Stockhausen (1998). "Es geht aufwärts", p. 396. Blumröder, ed. ISBN 978-3-00-002131-2.[full citation needed]
- ^ Van den Toorn, Pieter C. (1995). Music, Politics, and the Academy, p.128-29. University of California. ISBN 0-520-20115-9. ISBN 0-520-20116-7.
- ^ Lewin, David (1959). "Re: Intervallic Relations Between Two Collections of Notes". Journal of Music Theory 3, no. 2 (November 1959): 298–301. p. 300.
- ^ George Perle, Serial Composition and Atonality: An Introduction to the Music of Schoenberg, Berg, and Webern, fourth edition, revised (Berkeley, Los Angeles, and London: University of California Press, 1977): pp. 64–65. ISBN 0-520-03395-7.
- ^ Babbitt, Milton. 1987. Words about Music, pp. 115-117. Edited by Stephen Dembski and Joseph N. Straus. The Madison Lectures. Madison: University of Wisconsin Press. ISBN 0299107906 (cloth); ISBN 0299107949.
- ^ Stuessy, Clarence Joseph Jr. 1978. The Confluence of Jazz and Classical Music from 1950 to 1970, p. 166. PhD diss. Rochester: The University of Rochester, Eastman School of Music.
- ^ Boros, James (Winter, 1990). "The Evolution of Robert Moevs's Compositional Methodology". American Music 8 (4): 383–404. Retrieved 11 November 2013.
- ^ a b Sargent, David H. (1975). "The Twelve-Tone Row Technique of Juan Carlos Paz". Anuario Interamericano de Investigation Musical 11: 82–105. Retrieved 11 November 2013.
- ^ Friedrich Saathen, "Current Chronicle: Austria", The Musical Quarterly 44, no. 4 (October 1958): 515–519. Citation on p. 517.
- ^ Burton, Ian (2004). Listening Tests for Students. p. 26. ISBN 9781904226345.
- ^ a b Fairclough, Pauline (2010). Shostakovich Studies 2, Volume 2. p. 202. ISBN 9780521111188.
- ^ Taruskin, Richard (2009). Music in the Late Twentieth Century: The Oxford History of Western Music 5. p. 137. ISBN 9780199796007.
- ^ Craig Cummings. "Compositional Techniques in Karel Husa's Early Serial Works Poème and Mosaïques". Ex-tempore.org. Retrieved 11 November 2013.
- ^ Peck, Robert W. (August 2003). "Klein-Bottle Tonnetze". Music Theory Online (Society for Music Theory) 9 (3). Retrieved 8 November 2013. [See: Tonnetz]
- ^ Hans Keller, "Strict Serial Technique in Classical Music", Tempo, new series, no. 37 (Autumn 1955): 12–24. Citation on p. 16.
- ^ a b Hoffer, Charles (2010). Cengage Advantage Books: Music Listening Today. pp. 271 & 273. ISBN 9780495916147.
- ^ Pearsall 2012, p. 212.
- ^ Shaw-Miller, Simon (2004). Visible Deeds of Music: Art and Music from Wagner to Cage, p.270, n.28. Yale. ISBN 9780300107531.
- ^ Richard Toop, "Messiaen/ Goeyvaerts, Fano/ Stockhausen, Boulez", Perspectives of New Music 13, no. 1 (Autumn–Winter 1974): 141–169. Citation on p. 164
- ^ Fonville, John (Summer, 1991). "Ben Johnston's Extended Just Intonation: A Guide for Interpreters". Perspectives of New Music 29 (2): 106–137. JSTOR 833435 Retrieved 11 November 2013.
- ^ a b Randel, Don Michael; ed. (2003). The Harvard Dictionary of Music, p. 928. ISBN 9780674011632.
- ^ a b c Elizabeth West Marvin and Richard Hermann, eds. (2002). Concert Music, Rock, and Jazz Since|1945: Essays and Analytical Studies, pp.72 & 80. ISBN 9781580460965. [Uses absolute notation: 5 1 0 3 9 10 7 2 4 8 6 11.]
- ^ Roeder, Michael Thomas (1994). A History of the Concerto. p. 367. ISBN 9780931340611.
- ^ Walter Boyce Bailey, ed. (1998). The Arnold Schoenberg Companion, p. 166. Greenwood. ISBN 9780313287794.
- ^ Bailey 1991, p. 20
- ^ Cherlin, Michael (Autumn, 1998). "Memory and Rhetorical Trope in Schoenberg's String Trio". Journal of the American Musicological Society 51 (3): 559–602. JSTOR 832039 Retrieved 8 November 2013.
- ^ Harvey, Jonathan (1975). The Music of Stockhausen: An Introduction. pp. 42, 56–58. ISBN 0-520-02311-0.
- ^ Robin Maconie, Other Planets: The Music Of Karlheinz Stockhausen (Lanham, Maryland; Toronto; Oxford: Scarecrow Press, 2005): 215. ISBN 0-8108-5356-6.
- ^ Richard Toop, "Stockhausen's Other Piano Pieces." The Musical Times 124, no. 1684 (June 1983): 348–352. Citation on p. 350.
- ^ Richard Toop, "Stockhausen's Klavierstück VIII", Miscellanea Musicologica (Adelaide) 10 (1979): 93–130. Citation on p. 99.
- ^ a b Lewin 1962, p. 95
- ^ Wason, Robert W. (1987). "Webern's 'Variations for Piano', Op. 27: Musical Structure and the Performance Score]". Intégral 1: 74. JSTOR 40213898 Retrieved 11 November 2013.
- ^ a b Bailey 1991, p. 25
- ^ Dallapiccola 2000, p. 7.
- ^ Morris, Robert (Summer, 1997). "Listening to Milton Babbitt's Electronic Music: The Medium and the Message". Perspectives of New Music 35 (2): 85–99. JSTOR 833644 Retrieved 11 November 2013.
- ^ Perle, George (1991). Serial Composition and Atonality: An Introduction to the Music of Schoenberg, Berg, and Webern (Sixth ed.), p. 82. Berkeley and Los Angeles: University of California Press. ISBN 9780520074309.
- ^ Taruskin (2009), p.143. ISBN 9780195384857.
- ^ Bailey 1991, p. 19
- ^ Ulrich Mosch, Musikalisches Hören serieller Musik: Untersuchungen am Beispiel von Pierre Boulez' 'Le Marteau sans maître' (Saarbrücken: Pfau-Verlag, 2004): pp. 51–71. ISBN 3-89727-253-9.
- ^ Schoffman, Nachum; Ives, Charles (September 1981). "Serialism in the Works of Charles Ives". Tempo (138): 21–32. JSTOR 946249 Retrieved 11 November 2013.
- ^ Marvin & Hermann, eds. (2002). p.88. ISBN 9781580460965.
- ^ Pearsall 2012, p. 206
- ^ Vlad, Roman (1967). Stravinsky, p.199. Oxford University Press, London. Cited in Jacobi (2000).
- ^ Marvin & Hermann, eds. (2002). p.74. ISBN 9781580460965.
- ^ a b Lewin 1962, p. 91
- ^ Lewin, David (Autumn-Winter 1967). "A Study of Hexachord Levels in Schoenberg's Violin Fantasy]". Perspectives of New Music 6 (1): 18–32. JSTOR 832403 Retrieved 11 November 2013.
- ^ Bailey 1991, p. 21
- ^ Andrew Mead, "Some Implications of the Pitch-Class/Order-Number IsomorphismInherent in the Twelve-Tone System: Part Two; The Mallelieu Complex: Its Extensions and Related Rows", Perspectives of New Music 27, no. 1 (Winter 1989): 180–233. Citation on pp. 209–213.
- ^ George Perle, Serial Composition and Atonality: An Introduction to the Music of Schoenberg, Berg, and Webern, fourth edition, revised (Berkeley, Los Angeles, and London: University of California Press, 1977): p. 131. ISBN 0-520-03395-7.
- ^ Stroh, Wolfgang Martin (Fall-Winter 1968). "Alban Berg's 'Constructive Rhythm'". Perspectives of New Music 7 (1): 18–31. JSTOR 832424 Retrieved 11 November 2013.
- ^ a b Antokoletz, Elliott (1992). Twentieth-Century Music, p.70. ISBN 9780139341267.
- ^ Whittall 2008, p. 68.
- ^ Perle, George (1996). Twelve-Tone Tonality, pp.12, 14, & 20. ISBN 0-520-20142-6.
- ^ Pople, Anthony, ed. (1997). The Cambridge Companion to Berg, p.288-9, no.27. ISBN 9780521564892.
- ^ Headlam, David John (1996). The Music of Alban Berg, p.202. Yale University. ISBN 9780300064001.
- ^ Morris 2010, p. 45.
- ^ Whittall 2008, p. 127.
- ^ Whittall 2008, p. 206.
- ^ Steven Stucky, Lutosławski and His Music (Cambridge and New York: Cambridge University Press, 1981): 97. ISBN 9780521227995.
- ^ Robin Stowell, The Cambridge Companion to the Cello (Cambridge and New York: Cambridge University Press, 1999): 144. ISBN 9780521629287.
- ^ Edward Campbell, Boulez, Music and Philosophy, . (Oxford and New York: Oxford University Press, 2010): 206. ISBN 978-0-521-86242-4.
- ^ a b Simms, Bryan R. (2000). The Atonal Music of Arnold Schoenberg, 1908–1923, p.145. ISBN 0-19-512826-5.
- ^ Smyth 1999, p. 135.
- ^ a b c Ensign, Jeffrey S. From Outward Appearance to Inner Reality: A Reading of Aaron Copland's Inscape. Master of Music (Music Theory), December 2010, 72 pp.
- ^ Frisius and Stockhausen (1998). "Es geht aufwärts", pp. 396, 446. ISBN 978-3-00-002131-2.[full citation needed]
- ^ Frisius, Rudolf. 2008. Karlheinz Stockhausen II: Die Werke 1950–1977; Gespräch mit Karlheinz Stockhausen, p.29. Mainz, London, Berlin, Madrid, New York, Paris, Prague, Tokyo, Toronto: Schott Musik International. ISBN 978-3-7957-0249-6.
- ^ Michael Hicks, "Exorcism and Epiphany: Luciano Berio's Nones", Perspectives of New Music 27, no. 2 (Summer 1989): pp. 252–268. Citation on p. 254.
- ^ Christoph Neidhöfer, "Inside Luciano Berio's Serialism", Music Analysis 28, nos. 2–3 (2009): pp. 301–348. Citation on p. 306.
- ^ Frisius and Stockhausen (1998). "Es geht aufwärts", p. 394. ISBN 978-3-00-002131-2.[full citation needed]
- ^ a b Smyth 1999, p. 142
- ^ Pierre Boulez, "The System Exposed" in Orientations: Collected Writings by Pierre Boulez, edited by Jean-Jacques Nattiez, translated by Martin Cooper, 129–142 (Cambridge: Harvard University Press, 1986): p. 129. ISBN 0-674-64375-5.
- ^ Karlheinz Stockhausen, Stockhausen-Kurse Kürten 2006: Kompositions-Kurs über KLANG, Die 24 Stunden des Tages: Erste Stunde: HIMMELFAHRT für Orgel oder Synthesize, Sopran, Tenor, 2004/05/Stockhausen-Courses Kuerten 2006: Composition Course on KLANG/SOUND, the 24 Hours of the Day: First Hour: ASCENSION for Organ or Synthesizer, Soprano and Tenor, 2004/05, Work No. 81 (Kürten: Stockhausen-Verlag, 2006): p. 12.
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