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-chord I	Hexa-chord II	Derivation/ Combina-toriality
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	Play	Alban Berg: Kammerkonzert [5]	1923–25	6-Z19	6-Z44	cryptogram: "Schoenberg"
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: Not Lilacs [10]	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	Play	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-symmetry
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 hexachord
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 all- combinatorial hexachord
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	Play	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	Play	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	Play	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	Play	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		Play	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, derived: 4–1
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	Play	Alban Berg: "Der Wein" [46]	1929	6-16	6-16	D harmonic minor & in the inverted row-form added-sixth chord with both major and minor third
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-symmetry
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-symmetry
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-symmetry
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-symmetry
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	Play	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	Play P	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 (second row of 48) [66]	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-symmetry
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	Play	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 retrograde-symmetry
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 hexachord
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 hexachord
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: Variazioni canoniche sulla serie dell'op. 41 di Arnold Schönberg [74]	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 hexachord
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 for solo cello [75]		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	Play	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 all- combinatorial hexachord
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 hexachord
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 hexachord
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	Play	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 first movement, opening of development section [86]		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	Play	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-symmetry
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: otonality & utonality
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 (third row of 48) [66]	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	Play	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 hexachord; ordered in register
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	Play	Karlheinz Stockhausen: Klavierstück VII Gruppen Klavierstück IX Klavierstück X	1955 1955–57 1961 1961	6–1	6–1	all- combinatorial hexachord, retrograde-symmetrical all-interval
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 hexachord; ordered in register
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	Play	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 register
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	Play	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-combinatorial, RI-invariant: 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	Play	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-combinatorial
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	Play	Anton Webern: String Quartet, Op. 28: [104] [67] [102]	1936	6–5	6–5	derived: 4–1 (BACH motif), semi-combinatorial
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	Play	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	Play	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	Play	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	Play	Fritz Heinrich Klein [123] Alban Berg: Lyric Suite , mov. I [46] [124] Alberto Ginastera: Sonata for Guitar, mvt. III, op. 47 [28]	1920–22 [125] 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	Play	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-combinatorial
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	Sacher hexachord Play	Pierre Boulez: Messagesquisse Répons Dérive 1 Incises 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	Play	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	Spacing, orchestration not shown	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	Play	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

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