List of tone rows and series

From Wikipedia, the free encyclopedia

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

More information Row form, Integers ...

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	1 1 3 1 1 4 1 1 3 1 1		Anton Webern: Op. 32, later row^[1]	un- finished	6-1	6-1	—
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	1 2 2 1 4 2 4 1 2 2 1		Igor Stravinsky: Abraham & Isaac^[2]^[3]	1963	6-Z3	6-Z36	—
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	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
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	1 2 5 4 5 1 3 1 1 6 3	Play^ⓘ	Alban Berg: Kammerkonzert^[5]	1923–25	6-Z19	6-Z44	cryptogram: "Schoenberg"
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	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	—
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	1 3 2 5 4 6 4 5 2 3 1			n.a. 1973	6-14	6-14	all-interval, RT6-invariant
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	1 3 1 1 3 1 3 1 1 3 1	Play^ⓘ		1940	6-1	6-1	all- combinatorial
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	1 3 1 1 3 1 3 1 3 1 3			1957	6-1	6-1	all- combinatorial
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	1 3 1 4 1 5 3 4 1 4 3		Arnold Schoenberg: Die Jakobsleiter^[15]	un- finished	6-Z13	6-Z42	—
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	1 3 1 3 1 1 3 1 5 4 1		Walter Piston: Symphony No. 8 (first movement)^[16]	1965	6-Z19	6-Z44	—
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	1 3 1 2 1 2 1 1 1 3 1		Roger Reynolds: Ambages^[17]	1965	6-5	6-5	—
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	1 3 2 2 2 5 2 2 2 3 1			1940–41	6-34	6-34	RI-symmetry
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	1 3 5 4 3 5 5 4 3 5 1			1948	6-20	6-20	dyadic, tri-, tetra-, and hexa- chordal combina- toriality
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	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
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	1 4 3 2 6 1 4 2 5 3 5			1952 1954 1951–55	6-31	6-31	—
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	1 5 4 5 2 6 1 6 1 6 3		Arnold Schoenberg: Violin Concerto, op. 36^[23]	1936	6-Z50	6-Z29	—
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	1 5 4 4 1 5 3 4 5 3 6		Arnold Schoenberg: A Survivor from Warsaw^[24]^[25]	1947	6-15	6-15	—
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	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
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	1 6 5 1 6 1 2 2 1 6 5		Edison Denisov: Viola concerto^[27]	1986	6-Z41	6-Z12	—
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	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
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	1 6 2 1 5 2 1 2 5 1 2		Igor Stravinsky: Movements^[2]	1958–59	6-7	6-7	—
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	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	—
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	1 6 2 1 2 3 5 4 3 6 5		Karlheinz Stockhausen: Plus-Minus^[29]	1963 (rev. 1974)	6-5	6-5	—
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	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	—
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	1 5 3 4 4 1 3 1 6 1 3		Karlheinz Stockhausen: Zeitmaße^[31]^[32]	1955–56	6-16	6-16	—
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	1 4 2 4 1 4 1 3 2 4 1		Anton Webern: Op. 32, row 1^[33]	un- finished	6-2	6-2	—
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	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
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	1 4 2 3 2 6 1 1 4 1 4	Play^ⓘ		1936	6-1	6-1	all- combinatorial
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	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	—
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	1 3 4 4 2 1 2 4 4 3 1		Luigi Dallapiccola: Dialoghi^[36]		6-21	6-21	RI-invariant: P0 = RI9
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	1 3 5 1 2 2 1 2 6 2 5		Chen Yi: Near Distance^[3]^[37]	1988	6-Z23	6-Z45	—
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	1 2 3 4 5 6 5 4 3 2 1	Play^ⓘ	Nicolas Slonimsky: Grandmother chord^[40]	1938	6-1	6-1	symmetrical all-interval row; all- combinatorial
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	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	—
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	2 1 2 1 2 1 2 1 2 5 6		Igor Stravinsky: coda^[44]	1957	6-2	6-2	—
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: The Flood^[2]	1962	6-Z12	6-Z41	—
I:	0 t e 5 2 4 3 1 9 8 6 7	2 1 2 1 2 1 2 1 2 5 6		Igor Stravinsky: The Flood^[2]	1962	6-Z12	6-Z41	—
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	2 1 2 1 2 1 2 1 2 5 6		Luigi Dallapiccola: Requiescant^[36]		6-5	6-5	RI-invariant: P0 = RI5
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	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
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	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
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	2 1 2 1 5 2 1 2 1 2 5		Igor Stravinsky: Agon, "Bransles"^[44]	1957	6-Z40	6-Z11	—
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	2 1 2 2 1 3 5 2 4 2 5	Play^ⓘ	Alban Berg: "Der Wein"^[46]	1929	6-16	6-16
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	2 1 3 2 2 5 2 2 2 2 3			1940–41	6-34	6-34	RI-symmetry
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	2 2 1 3 2 4 1 2 2 2 2			1940–41	6-34	6-34	RI-symmetry
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	2 2 2 1 3 5 3 1 2 2 2			1940–41	6-34	6-34	RI-symmetry
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	2 2 2 2 1 4 2 3 1 2 2			1940–41	6-34	6-34	RI-symmetry
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	2 2 2 4 2 3 4 2 4 2 2		Alban Berg: Lulu^[24]	1934	6-35	6-35	—
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	2 3 2 5 6 2 5 2 4 1 1			1963–64	6-9	6-9	—
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	2 4 2 6 1 2 4 3 3 4 2		Arnold Schoenberg: Piano Piece [Klavierstück], op. 33b^[24]	1931	6-34	6-34	—
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	2 4 4 6 3 1 5 2 4 2 2	Play^ⓘ	Alban Berg: Lulu, Schoolboy^[45]^[53]^[54]	1934	6-34	6-34	—
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	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	—
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	5 1 1 3 1 5 1 5 1 3 1		Karel Goeyvaerts: Nummer 2^[55]	1951	6-Z36	6-Z3	—
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	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	—
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	2 3 2 1 3 2 3 2 1 2 1			1973	6-1	6-1	all- combinatorial
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	2 3 2 1 6 1 4 2 1 2 5		Arnold Schoenberg: Dreimal Tausend Jahre, Op. 50a^[3]	1949	6-9	6-9	—
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	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
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	3 2 1 3 1 2 1 4 2 1 2		Milton Babbitt: Woodwind Quartet^[57]	1953	6-1	6-1	—
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	3 2 5 4 2 6 5 4 2 1 3		Ernst Krenek: Sechs Vermessene, Op. 168^[58]	1958	6-2	6-2	—
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	3 2 5 4 4 1 1 3 4 2 1		Ernst Krenek: Karl V^[59]^[60]	1938	6-Z39	6-Z10	—
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	3 2 3 4 6 3 6 1 3 2 3		Donald Martino: Fantasy Variations^[61]	1962	6-9	6-9	—
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	3 1 1 3 4 3 6 5 3 1 3		Benjamin Frankel: The Curse of the Werewolf^[62]	1961	6-Z37	6-Z4	—
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	3 1 5 2 1 3 5 5 4 1 6		Karlheinz Stockhausen: "Aries", from Tierkreis^[63]	1974–75	6-18	6-18	—
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	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
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	3 1 2 5 3 1 3 1 4 4 1		Igor Stravinsky: Agon, "Mystery" (sketches only)^[65]	1957	6-31	6-31	—
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	3 2 4 1 4 2 5 4 1 3 2			1952	6-Z3	6-Z36	—
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	3 2 1 5 1 1 1 1 1 4 1		Karlheinz Stockhausen: "Aquarius", from Tierkreis^[63]	1974–75	6-Z6	6-Z38	—
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	3 2 2 2 2 5 2 2 3 1 2			1940–41	6-34	6-34	RI-symmetry
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	3 4 4 3 3 4 4 3 2 2 2	Play^ⓘ	Alban Berg: Violin Concerto^[4]^[24]^[67]	1935	6-Z24	6-Z46	—
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	3 4 3 4 3 4 4 3 4 3 1			1910–13	6-1	6-1	all- combinatorial
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	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
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	3 4 1 4 5 4 4 1 4 1 1		Anton Webern: Op. 31^[12]	1941–43	6-Z3	6-Z36	—
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	4 3 5 3 4 6 4 3 5 3 4			1948	6–20	6–20	all- combinatorial hexachord
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	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
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	4 2 3 2 1 2 1 2 2 5 3		Igor Stravinsky: Anthem^[2]	1962	6–33	6–33	—
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	4 1 1 3 1 4 1 2 4 6 1		Karlheinz Stockhausen: Licht, Eve formula^[71]^[72]	1977– 2003	6–2	6–2	—
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	4 1 4 4 3 1 3 1 4 1 4			1942 1926 1950	6–20	6–20	all- combinatorial
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	4 1 5 1 4 6 4 1 5 1 4			1948	6–20	6–20	all- combinatorial hexachord
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	4 1 4 4 1 2 1 5 3 4 5		Karlheinz Stockhausen: "Scorpio", from Tierkreis^[63]	1974–75	6–20	6–20	—
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	4 1 4 1 1 4 6 1 2 4 3		Ernst Krenek: Suite, Op. 84 for solo cello^[75]		6–5	6–5	—
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	4 1 3 4 1 1 1 2 1 5 2		Alban Berg: Lulu^[24]	1934	6–9	6–9	—
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	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
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	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
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	4 1 5 3 1 5 5 3 3 5 6		Karlheinz Stockhausen: "Gemini", from Tierkreis^[63]	1974–75	6-Z41	6-Z12	—
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	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
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	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	—
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	5 4 1 1 6 1 2 6 5 5 1		Alban Berg: Lulu, Chorale^[45]	1934	6-Z39	6-Z10	—
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	5 4 3 2 1 6 1 2 3 4 5			1958	6–1	6–1
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	5 4 3 6 2 3 2 6 3 4 5		Alfred Schnittke: Concerto Grosso No. 3^[3]	1985	6–31	6–31	—
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	5 3 5 3 5 3 5 3 5 3 5		Benjamin Britten: The Turn of the Screw^[81]	1954	6–32	6–32	—
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	5 3 5 3 3 2 5 2 2 1 6		Dmitri Shostakovich: Symphony No. 14, mov. III^[82]	1969	6-Z47	6-Z25	—
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	5 3 4 3 6 1 2 5 5 5 6		Alban Berg: Lulu, Countess Geschwitz^[24]^[45]^[54]	1934	6-Z47	6-Z25	—
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	5 1 3 3 4 5 3 5 4 5 1		Igor Stravinsky: Threni^[2]	1958	6-Z41	6-Z12	—
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	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	—
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	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
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	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	—
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	5 6 5 3 1 6 1 2 1 6 3		Karlheinz Stockhausen: "Leo", from Tierkreis^[63]	1974–75	6Z-13	6-Z42	—
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	6 2 2 6 1 6 2 2 1 3 2		Igor Stravinsky: Elegy for J.F.K.^[2]	1964	6–34	6–34	—
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	6 2 1 1 5 1 5 2 1 3 2		Karel Husa: Mosaïques^[84]	1960	6-Z45	6-Z23	—
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	6 1 4 2 4 3 4 1 6 1 4		Arnold Schoenberg: "De Profundis", Op. 50b^[3]	1950	6–7	6–7	—
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	6 1 3 1 1 3 1 1 1 1 2		Karlheinz Stockhausen: "Sagittarius", from Tierkreis^[63]	1974–75	6–2	6–2	—
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	6 1 6 1 6 1 6 1 6 1 6		Witold Lutosławski: Musique funèbre (Funeral Music)^[85]	1954–58	6–7	6–7	—
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	6 1 1 1 4 1 3 6 5 6 5				6–5	6–5	—
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	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
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	6 2 2 4 2 5 4 2 4 4 6		Arnold Schoenberg: Three Songs, Op. 48^[64]	1933	6–35	6–35	—
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	6 3 5 6 2 6 3 6 2 4 2		Josef Matthias Hauer: Salambo, op. 60^[89]	1929	6-21	6-21	—
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	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
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	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
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	5 6 3 1 2 4 3 4 1 1 4			1952	6–2	6–2	—
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	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	—
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	5 4 5 4 4 3 4 3 4 3 6		Alberto Ginastera: Quintet, op. 29^[28]	1963	6–31	6–31	—
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	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
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	5 1 2 1 4 1 2 5 2 2 3		Igor Stravinsky: Requiem Canticles, 2nd series^[2]	1966	6-Z40	6-Z11	—
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	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	—
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	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
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	5 4 3 6 4 4 3 4 1 3 2		Anton Webern: Op. 23^[96]	1933	6-Z10	6-Z39	—
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	5 4 1 4 5 3 5 4 1 4 5		Ross Lee Finney: Edge of Shadow^[21]	1959	6–8	6–8	—
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	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
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	4 5 6 5 3 2 3 2 1 2 5		Arnold Schoenberg: String Trio, Op. 45^[97]	1946	6–5	6–5	—
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	4 5 3 1 2 6 2 1 3 5 4	Play^ⓘ		1955 1955–57 1961 1961	6–1	6–1
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	4 5 2 1 3 2 4 5 2 3 1			1954–55 1954	6-Z3	6-Z36	—
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	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
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	4 3 5 3 6 5 2 5 3 1 6	Play^ⓘ	Alban Berg: Lulu, Alwa^[45]^[53]^[54]	1934	6-Z25	6-Z47	—
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	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
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	4 1 4 1 1 6 2 3 2 4 1	Play^ⓘ		1936	6–1	6–1	all- combinatorial
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	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
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	4 3 1 6 2 1 6 4 2 6 5		Ernst Krenek: Sestina, op. 161^[59]	1957	6–22	6–22	—
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	3 4 2 1 5 3 6 1 2 5 4		Luigi Dallapiccola: Piccola musica notturna^[105]	1954	6–8	6–8	—
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	3 4 5 4 1 2 5 1 3 4 1		Milton Babbitt: Composition for Synthesizer^[106]	1961	6–20	6–20	—
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	3 4 2 1 4 6 1 2 1 2 3	Play^ⓘ		1948	6–1	6–1	all- combinatorial
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	3 5 1 4 1 5 1 3 5 1 1		Igor Stravinsky: Epitaphium^[2]	1959	6-Z3	6-Z36	—
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	3 5 6 1 2 1 5 2 1 6 1		Karlheinz Stockhausen: "Capricorn", from Tierkreis^[63]	1974–75	6-Z47	6-Z25	—
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	3 1 4 3 1 5 3 5 2 6 3		David Dzubay: Di/Con[ver(gence/sions)]^[3]	1988	6-Z39	6-Z10	—
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	3 1 3 1 4 1 1 1 2 6 5		Anton Webern: Op. 22^[109]	1929–30	6–2	6–2	semi-combinatorial
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	3 2 3 2 3 6 3 2 3 2 3			1948	6–8	6–8	—
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	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	—
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	2 5 1 2 5 1 3 1 3 2 4		Charles Ives: Tone Roads No. 1^[111]	1911	6-Z46	6-Z24	—
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	2 5 4 3 1 6 1 3 4 5 2		Elliott Carter: Night Fantasies^[112]	1982	6–14	6–14	—
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	2 1 1 1 2 6 2 1 1 1 2			1948	6–8	6–8	—
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	2 1 2 4 5 6 5 3 2 1 2		Karlheinz Stockhausen: Kreuzspiel^[113]	1951	6-Z50	6-Z29	—
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	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	—
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	1 2 2 1 2 3 2 1 2 2 1		Igor Stravinsky: Fanfare^[2]	1964	6–1	6–1	all- combinatorial
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	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
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	1 2 6 2 1 2 6 2 1 3 1		Chen Yi: Woodwind Quintet^[3]^[37]	1987	6-Z4	6-Z37	—
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	1 3 1 2 1 5 1 3 1 2 1		Arvo Pärt: Diagrams^[56]	1964	6–1	6–1	all- combinatorial
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	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
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	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
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	1 3 5 4 2 1 4 2 3 6 5		Elliott Carter: String Quartet No. 3^[115]	1973	6-Z23	6-Z45	—
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	1 4 2 6 2 3 4 4 5 3 4		Arnold Schoenberg: Violin Phantasy, Op. 47^[116]^[117]	1949	6–21	6–21	—
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	1 4 1 1 5 2 3 1 3 2 1		Igor Stravinsky: Double Canon^[2]	1959	6-Z36	6-Z3	—
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	1 4 1 4 1 2 4 1 5 1 4	Play^ⓘ		1934	6–20	6–20	all- combinatorial, derived: 3–3
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	1 5 1 2 4 1 4 2 5 3 1		David Lewin: Just a Minute, Roger^[119]	1978	6–16	6–16	—
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	1 6 3 1 5 3 5 1 3 6 1		Alfred Schnittke: Viola Concerto^[3]	1985	6–5	6–5	—
P:	0 e 5 9 6 2 7 3 1 4 t 8	1 6 4 3 4 5 4 2 3 6 2		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	1 6 4 3 4 5 4 2 3 6 2		Luigi Dallapiccola: Cinque Canti^[36]		6-Z50	6-Z29	RI-invariant: P0 = RI9
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	1 5 1 1 1 2 3 1 2 5 6		Pierre Boulez: Structures Ia^[3]^[67]	1952	6–5	6–5	—
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	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
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	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	—
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	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	—
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	1 4 3 2 5 6 5 2 3 4 1	Play^ⓘ		1920–22^[125] 1925–26 1976	6–32	6–32
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	1 4 1 5 2 1 4 4 1 1 5		Arnold Schoenberg: String quartet No. 4^[64]^[116]	1936	6–16	6–16	—
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	1 3 4 3 4 2 4 3 4 3 1		Arnold Schoenberg: Modern Psalm, Op. 50c^[3]	1950	6–20	6–20	—
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	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	—
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	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	—
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	1 2 5 1 5 2 1 2 1 5 1		Dmitri Shostakovich: Symphony No. 14, mov. I^[82]	1969	6–5	6–5	—
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	1 2 3 4 2 1 2 3 2 1 2		Igor Stravinsky: Canticum Sacrum, II^[2]	1955	6–2	6–2	—
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	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
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	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	—

Other lengths

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	—

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	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

More information Prime form, Interval classes ...

Prime form	Interval classes	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

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	—

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

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	Spacing,^[135] 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

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	Play^ⓘ	Karlheinz Stockhausen: Mantra^[138]	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	—

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	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^[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	—	—

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	—

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	—	—

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	—	—

Sources

[1]
Bailey, Kathryn (1991). The Twelve-Note Music of Anton Webern: Old Forms in a New Language. Cambridge University Press. p. 28. ISBN 9780521547963.
[2]
Kuster, Andrew (2000). "Stravinsky's Topology: An Examination of his Twelve-Tone Works through Object-Oriented Analysis of Structural and Poetic-Expressive Relationships with Special Attention to his Choral Works and Threni Archived 2013-12-03 at the Wayback Machine". D.M.A. diss. (University of Colorado). Retrieved 4 November 2013.
[3]
Dunker, Amy. "Twelve Tone Rows Used by Various Composers". AmyDunker.com: 3. Retrieved 4 November 2013.
[4]
Hunter, David J.; von Hippel, Paul T. (Feb., 2003). "How Rare Is Symmetry in Musical 12-Tone Rows?". The American Mathematical Monthly (Mathematical Association of America) 110 (2): 124–132. Retrieved 4 November 2013.
[5]
Whittall, Arnold (2008). The Cambridge Introduction to Serialism. Cambridge Introductions to Music. New York: Cambridge University Press. p. 71. ISBN 978-0-521-68200-8.
[6]
Whittall 2008, p. 2.
[7]
Dunker, Amy. "Twelve Tone Rows Used by Various Composers". AmyDunker.com: 1. Retrieved 4 November 2013.
[8]
Lewin, David (Autumn 1962). "A Theory of Segmental Association in Twelve-Tone Music". Perspectives of New Music. 1 (1): 89–116 (93). doi:10.2307/832181. JSTOR 832181.
[9]
Mayfield, Connie (2013). Theory Essentials. p. 549. ISBN 9781133713807.
[10]
Morris, Robert (2010). The Whistling Blackbird: Essays and Talks on New Music. University Rochester. p. 188. ISBN 9781580463492.
[11]
Brian Alegant and Martin Lofthouse, "Having Your Cake and Eating It, Too: The Property of Reflection in Twelve-Tone Rows (Or, Further Extensions on the Mallelieu Complex)", Perspectives of New Music 40, no. 2 (Summer 2002): 233–272. Citation on pp. 235–237. JSTOR 25164497
[12]
Bailey 1991, p. 26
[13]
Leeuw, Ton de (2005). Music of the Twentieth Century: A Study of Its Elements and Structure. Translated by Stephen Taylor. Amsterdam: Amsterdam University Press. p. 161. ISBN 90-5356-765-8. Translation of Muziek van de twintigste eeuw: een onderzoek naar haar elementen en structuur. Utrecht: Oosthoek, 1964. Third impression, Utrecht: Bohn, Scheltema & Holkema, 1977. ISBN 90-313-0244-9.
[14]
Smyth, David (Summer 1999). "Stravinsky's Second Crisis: Reading the Early Serial Sketches". Perspectives of New Music. 37 (2): 117–146 (126–127, 134, 142. doi:10.2307/833512. JSTOR 833512.
[15]
Pearsall, Edward (2012). Twentieth-Century Music Theory and Practice. Routledge. p. 217. ISBN 9780415888950.
[16]
Archibald, Bruce (1978). "Reviews of Records: Walter Piston: Symphony No. 7, Symphony No. 8, Louisville Orchestra, Jorge Mester; Walter Piston: Symphony No. 5, Louisville Orchestra, Robert Whitney; Walter Piston: Concerto for Viola and Orchestra, Paul Doktor, viola, Louisville Orchestra, Robert Whitney; Walter Piston: The Incredible Flutist, Louisville Orchestra, Jorge Mester". The Musical Quarterly 64 (2): 267. pp. 263–268.
[17]
"An Interview with Roger Reynolds", Performance Arts Encyclopedia. Accessed May 27, 2015.
[18]
Krenek, Ernst (April 1960). "Extents and Limits of Serial Techniques". The Musical Quarterly. 46 (2): 210–232 (212). doi:10.1093/mq/XLVI.2.210.. Special Issue: Problems of Modern Music. The Princeton Seminar in Advanced Musical Studies.
[19]
Babbitt, Milton (2011). The Collected Essays of Milton Babbitt. Princeton University Press. p. 94. ISBN 9780691089669.
[20]
Kholopov, Yuri; Tsenova, Valeria (1997). Edison Denisov. p. 81. ISBN 9780203479599.
[21]
Cooper, Paul (1975). Perspectives in Music Theory, p.266. ISBN 0-396-06752-2.
[22]
Dallapiccola, Luigi (Winter 2000). "Notes for an Analysis of the Canti di Liberazione". Perspectives of New Music. 38 (1). Translated by Chloe Stodt: 2–24 (10). doi:10.2307/833586. JSTOR 833586.
[23]
Lewin 1962, pp. 113–115
[24]
Dunker, Amy. "Twelve Tone Rows Used by Various Composers". AmyDunker.com: 2. Retrieved 4 November 2013.
[25]
"A Survivor from Warsaw: the twelve-note row". AEIOU.at. Retrieved 13 November 2013. ( (in German))
[26]
Stephen Arnold and Graham Hair, "An Introduction and a Study: String Quartet No. 3", Perspectives of New Music 14, no. 2 and 15, no. 1 (Spring-Summer/Fall-Winter 1976): 155–186. Citation on p. 159.
[27]
Kholopov & Tsenova 1997, p. 103.
[28]
Fobes, Christopher Anderson (2006). "A Theoretical Investigation of Twelve-tone Rows, Harmonic Aggregates, and Non-twelve-tone Materials in the Late Music of Alberto Ginastera", PhD diss. (Buffalo: State University of New York at Buffalo, 2006): pp. 152–154 & 161.
[29]
Jonathan Harvey, The Music of Stockhausen: An Introduction (Berkeley and Los Angeles: University of California Press, 1975): p. 93. ISBN 0-520-02311-0.
[30]
Berry, Wallace (1976/1987). Structural Functions in Music, p.175. Dover. ISBN 0-486-25384-8.
[31]
Genevieve Marcus, "Stockhausen's Zeitmasse", The Music Review 29, no. 2 (May 1968): 142–156. Citation on p. 144.
[32]
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.
[33]
Bailey 1991, p. 27
[34]
Leeuw 2005, p. 158.
[35]
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.
[36]
Alegent, Brian (2010). The Twelve-tone Music of Luigi Dallapiccola, p.48. ISBN 9781580463256.
[37]
Guo, Xin (2002). Chinese Musical Language Interpreted by Western Idioms: Fusion Process in the Instrumental Works by Chen Yi (PhD dissertation). Florida State University.
[38]
Leeuw 2005, p. 177.
[39]
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.
[40]
Slonimsky, Nicolas (1975). Thesaurus of Scales and Melodic Patterns, p. 243. ISBN 0-8256-1449-X.
[41]
Jurkowski, Edward (2004). The Music of Joonas Kokkonen, pp.78, 84, 184. ISBN 9780754607892.
[42]
Smyth 1999, pp. 126–127, 142.
[43]
Wiens, Carl Kristian (1997). Igor Stravinsky and Agon, p. 168. University of Michigan.
[44]
Jacobi, Bonnie S. (2000). "The Bransles of Stravinsky's Agon: A Transition to Serial Composition", Moores School of Music.
[45]
Headlam, David John (1996). The Music of Alban Berg, pp.265, 304, & 306. ISBN 9780300064001.
[46]
Pople, Anthony (1991). Berg: Violin Concerto. pp. 18 & 21. ISBN 0-521-39976-9.
[47]
Eric Walter White, "Two New Memorial Works by Stravinsky", Tempo, new series, no. 74 (Autumn 1965), pp. 18–21.
[48]
Claudio Spies, "Notes on Stravinsky's Variations", Perspectives of New Music 4, no. 1 (Autumn-Winter 1965): pp. 62–74. Citation on p. 66.
[49]
Igor Stravinsky and Robert Craft, Themes and Episodes (New York: Alfred A. Knopf,1967): p. 60.
[50]
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.
[51]
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.
[52]
Smyth 1999, pp. 139–140, 142.
[53]
Whittall 2008, p. 81
[54]
Hailey, Christopher, ed. (2010). Alban Berg and His World. p. 215. ISBN 9781400836475.
[55]
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.
[56]
Hillier, Paul (1997). Arvo Pärt. pp. 40, 47, & 50. ISBN 9780191590481.
[57]
Babbitt 2011, p. 350.
[58]
Krenek 1960, p. 229.
[59]
Stewart, John Lincoln (1991). Ernst Krenek: The Man and His Music. pp. 169, 250, 290. ISBN 9780520070141.
[60]
Tregear, Peter John (March 2001). "Musical Style and Political Allegory in Krenek's Karl V", Cambridge Opera Journal, vol. 13, no. 1, pp. 55–80. Citation on 73.
[61]
Boros, James (Summer 1991). "Donald Martino's Fantasy Variations: The First Three Measures". Perspectives of New Music 29 (2): 280–293. JSTOR 833442 Retrieved 11 November 2013.
[62]
Huckvale, David (2008). Hammer Film Scores and the Musical Avant-Garde. p. 43. ISBN 9780786451661.
[63]
Kohl, Jerome (Autumn 1983 – Summer 1984). "The Evolution of Macro- and Micro-Time Relations in Stockhausen's Recent Music". Perspectives of New Music. 22 (1–2): 147–185 (151). doi:10.2307/832939. JSTOR 832939. (subscription required).
[64]
Hurry, Pam; Phillips, Mark; Richards, Mark (2001). Heinemann Advanced Music. pp. 100, 122, & 303. ISBN 9780435812584.
[65]
Smyth 1999, pp. 136–137, 142.
[66]
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.
[67]
Cooper (1975). p.265. ISBN 0-396-06752-2.
[68]
Lewin 1962, p. 94
[69]
Krenek 1960, p. 230.
[70]
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.
[71]
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.
[72]
Frisius; Stockhausen (1998). "Es geht aufwärts", p. 396. Blumröder, ed. ISBN 978-3-00-002131-2.^{[full citation needed]}
[73]
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.
[74]
Lewin, David (1959). "Re: Intervallic Relations Between Two Collections of Notes". Journal of Music Theory 3, no. 2 (November 1959): 298–301. p. 300.
[75]
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.
[76]
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.
[77]
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.
[78]
Boros, James (Winter, 1990). "The Evolution of Robert Moevs's Compositional Methodology". American Music 8 (4): 383–404. Retrieved 11 November 2013.
[79]
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.
[80]
Friedrich Saathen, "Current Chronicle: Austria", The Musical Quarterly 44, no. 4 (October 1958): 515–519. Citation on p. 517.
[81]
Burton, Ian (2004). Listening Tests for Students. p. 26. ISBN 9781904226345.
[82]
Fairclough, Pauline (2010). Shostakovich Studies 2, Volume 2. p. 202. ISBN 9780521111188.
[83]
Taruskin, Richard (2009). Music in the Late Twentieth Century: The Oxford History of Western Music 5. p. 137. ISBN 9780199796007.
[84]
Craig Cummings. "Compositional Techniques in Karel Husa's Early Serial Works Poème and Mosaïques". Ex-tempore.org. Retrieved 11 November 2013.
[85]
Peck, Robert W. (August 2003). "Klein-Bottle Tonnetze". Music Theory Online (Society for Music Theory) 9 (3). Retrieved 8 November 2013. [See: Tonnetz]
[86]
Hans Keller, "Strict Serial Technique in Classical Music", Tempo, new series, no. 37 (Autumn 1955): 12–24. Citation on p. 16.
[87]
Hoffer, Charles (2010). Cengage Advantage Books: Music Listening Today. pp. 271 & 273. ISBN 9780495916147.
[88]
Pearsall 2012, p. 212.
[89]
Shaw-Miller, Simon (2004). Visible Deeds of Music: Art and Music from Wagner to Cage, p.270, n.28. Yale. ISBN 9780300107531.
[90]
Richard Toop, "Messiaen/ Goeyvaerts, Fano/ Stockhausen, Boulez", Perspectives of New Music 13, no. 1 (Autumn–Winter 1974): 141–169. Citation on p. 164
[91]
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.
[92]
Randel, Don Michael; ed. (2003). The Harvard Dictionary of Music, p. 928. ISBN 9780674011632.
[93]
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.]
[94]
Roeder, Michael Thomas (1994). A History of the Concerto. p. 367. ISBN 9780931340611.
[95]
Walter Boyce Bailey, ed. (1998). The Arnold Schoenberg Companion, p. 166. Greenwood. ISBN 9780313287794.
[96]
Bailey 1991, p. 20
[97]
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.
[98]
Harvey, Jonathan (1975). The Music of Stockhausen: An Introduction. pp. 42, 56–58. ISBN 0-520-02311-0.
[99]
Robin Maconie, Other Planets: The Music Of Karlheinz Stockhausen (Lanham, Maryland; Toronto; Oxford: Scarecrow Press, 2005): 215. ISBN 0-8108-5356-6.
[100]
Richard Toop, "Stockhausen's Other Piano Pieces." The Musical Times 124, no. 1684 (June 1983): 348–352. Citation on p. 350.
[101]
Richard Toop, "Stockhausen's Klavierstück VIII", Miscellanea Musicologica (Adelaide) 10 (1979): 93–130. Citation on p. 99.
[102]
Lewin 1962, p. 95
[103]
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.
[104]
Bailey 1991, p. 25
[105]
Dallapiccola 2000, p. 7.
[106]
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.
[107]
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.
[108]
Taruskin (2009), p.143. ISBN 9780195384857.
[109]
Bailey 1991, p. 19
[110]
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.
[111]
Schoffman, Nachum; Ives, Charles (September 1981). "Serialism in the Works of Charles Ives". Tempo (138): 21–32. JSTOR 946249 Retrieved 11 November 2013.
[112]
Marvin & Hermann, eds. (2002). p.88. ISBN 9781580460965.
[113]
Pearsall 2012, p. 206
[114]
Vlad, Roman (1967). Stravinsky, p.199. Oxford University Press, London. Cited in Jacobi (2000).
[115]
Marvin & Hermann, eds. (2002). p.74. ISBN 9781580460965.
[116]
Lewin 1962, p. 91
[117]
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.
[118]
Bailey 1991, p. 21
[119]
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.
[120]
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.
[121]
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.
[122]
Antokoletz, Elliott (1992). Twentieth-Century Music, p.70. ISBN 9780139341267.
[123]
Whittall 2008, p. 68.
[124]
Perle, George (1996). Twelve-Tone Tonality, pp.12, 14, & 20. ISBN 0-520-20142-6.
[125]
Pople, Anthony, ed. (1997). The Cambridge Companion to Berg, p.288-9, no.27. ISBN 9780521564892.
[126]
Headlam, David John (1996). The Music of Alban Berg, p.202. Yale University. ISBN 9780300064001.
[127]
Morris 2010, p. 45.
[128]
Whittall 2008, p. 127.
[129]
Whittall 2008, p. 206.
[130]
Steven Stucky, Lutosławski and His Music (Cambridge and New York: Cambridge University Press, 1981): 97. ISBN 9780521227995.
[131]
Robin Stowell, The Cambridge Companion to the Cello (Cambridge and New York: Cambridge University Press, 1999): 144. ISBN 9780521629287.
[132]
Edward Campbell, Boulez, Music and Philosophy, . (Oxford and New York: Oxford University Press, 2010): 206. ISBN 978-0-521-86242-4.
[133]
Simms, Bryan R. (2000). The Atonal Music of Arnold Schoenberg, 1908–1923, p.145. ISBN 0-19-512826-5.
[134]
Smyth 1999, p. 135.
[135]
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.
[136]
Frisius and Stockhausen (1998). "Es geht aufwärts", pp. 396, 446. ISBN 978-3-00-002131-2.^{[full citation needed]}
[137]
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.
[138]
Chang, Ed. "Stockhausen: Sounds in Space - MANTRA". Retrieved 18 April 2025.
[139]
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.
[140]
Christoph Neidhöfer, "Inside Luciano Berio's Serialism", Music Analysis 28, nos. 2–3 (2009): pp. 301–348. Citation on p. 306.
[141]
Frisius and Stockhausen (1998). "Es geht aufwärts", p. 394. ISBN 978-3-00-002131-2.^{[full citation needed]}
[142]
Smyth 1999, p. 142
[143]
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.
[144]
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.

List of tone rows and series

Twelve tone rows

Other lengths

Fewer than twelve

More than twelve

See also

Sources

Related Articles

Timelines

Top Qs

Fact Checks