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 pitch class sets, and trope (music).

Twelve tone rows

Row form Integers 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]		 later row Anton Webern:
Op. 32		 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
[2][3]		 Igor Stravinsky:
Abraham & Isaac		 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
[4]		 Arnold Schoenberg:
Serenade, op. 24, mov. 5		 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
[5]
Alban Berg:
Kammerkonzert		 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
[6][7][8][9]		 Arnold Schoenberg:
Suite for Piano, op. 25		 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
[10][11]		 Pohlman Mallalieu

Robert Morris:
Not Lilacs

 n.a.

1973

 6–14 6–14 —
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
[12][3][13]
 Play 
 Anton Webern:
Variations for Orchestra, Op. 30		 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
[2][14]		 Igor Stravinsky:
Agon, "Pas de deux", "Four trios"		 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
[15]		 Arnold Schoenberg:
Die Jakobsleiter		 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
[16]		 Walter Piston:
Symphony No. 8 (first movement)		 1965 6-Z19 6-Z44 —
I: 0 e 8 7 4 5
6 9 t 5 1 2
P: 0 1 4 6 8 t
5 7 9 e 2 3
[17]		 row 3 Ernst Krenek:
Lamentatio Jeremiae Prophetae, Op. 93		 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
[3][18]		 Milton Babbitt:
Composition for Twelve Instruments		 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
[19]		 Edison Denisov:
Fünf Geschichten von Herrn Keuner		 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
[20][21]		 Luigi Dallapiccola:
Quaderno musicale di Annalibera
Variazioni per orchestra
Canti di Liberazione		 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
[22]		 Arnold Schoenberg:
Violin Concerto, op. 36		 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
[23][24]		 Arnold Schoenberg:
A Survivor from Warsaw		 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
[25]		 Milton Babbitt:
All Set		 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
[26]		 Edison Denisov:
Viola concerto		 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
[23]
Arnold Schoenberg:
Moses und Aron		 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
[2]		 Igor Stravinsky:
Movements		 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
[27]		 Alberto Ginastera:
Don Rodrigo, Act I, op. 31		 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
[28]		 Karlheinz Stockhausen:
Plus-Minus		 1963 (rev. 1974) 6–5 6–5 —
I: 0 e 5 3 4 6
9 2 t 7 1 8
P: 0 1 8 e 7 3
2 5 4 t 9 6
[29][30]		 Karlheinz Stockhausen:
Zeitmaße		 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
[31]		 row 1 Anton Webern:
Op. 32		 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
[31]		 row 2 Anton Webern:
Op. 32		 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
[32][33]
 Play 
 Anton Webern:
Variations for piano, mov. II, op. 27		 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
[2]		 Igor Stravinsky:
A Sermon, a Narrative and a Prayer		 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
[34]		 Luigi Dallapiccola:
Dialoghi		 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
[3][35]		 Chen Yi:
Near Distance		 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
[15][36][37]
 Play 
 Luigi Nono:
Canti per tredeci
Il canto sospeso
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
[38]
Grandmother chord  Play 
 Nicolas Slonimsky 1938
P: 0 2 1 3 8 7
5 6 4 e 9 t
[39]		 row A Joonas Kokkonen:
Symphonic Sketches, mov. 3		 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
[40][41]		 Igor Stravinsky:
Agon, second coda		 1957 6–2 6–2 —
I: 0 t e 9 8 6
5 3 4 2 7 1		 Igor Stravinsky:
coda[42]
P: 0 2 1 7 t 8
9 e 3 4 6 5
[2]		 Igor Stravinsky:
The Flood		 1962 6-Z12 6-Z41 —
I: 0 t e 5 2 4
3 1 9 8 6 7
P: 0 2 1 7 e 8
9 6 t 4 3 5
[34]		 Luigi Dallapiccola:
Requiescant		 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 t 3 e
5 9 4 7 8 6
[3]		 Alfred Schnittke:
String Quartet No. 1		 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
[23][43]		 Schigolch Alban Berg:
Lulu		 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
[42]		 Igor Stravinsky:
Agon, "Bransles"		 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
[44]
 Play 
 Alban Berg:
"Der Wein"		 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
[17]		 row 2 Ernst Krenek:
Lamentatio Jeremiae Prophetae, Op. 93		 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
[17]		 row 1 Ernst Krenek:
Lamentatio Jeremiae Prophetae, Op. 93		 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
[17]		 row 6 Ernst Krenek:
Lamentatio Jeremiae Prophetae, Op. 93		 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
[17]		 row 5 Ernst Krenek:
Lamentatio Jeremiae Prophetae, Op. 93		 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
[23]		 Alban Berg:
Lulu		 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
[45]		 Igor Stravinsky:
Variations		 1963–64 6–9 6–9 —
I: 0 t 7 9 2 8
6 e 1 5 4 3
[2][3][46][47][48][49][50]
P: 0 2 6 4 t 9
7 e 8 5 1 3
[23]		 Arnold Schoenberg:
Piano Piece [Klavierstück], op. 33b		 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
[43][51][52]
Schoolboy
 Alban Berg:
Lulu		 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]		 Igor Stravinsky:
The Owl and the Pussy Cat		 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
[53]		 Karel Goeyvaerts:
Nummer 2		 1951 6Z36 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]
1st series
 Igor Stravinsky:
Requiem Canticles		 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
[39]		 row A & B Joonas Kokkonen:
Woodwind Quintet, mov. 1 & 2		 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
[3]		 Arnold Schoenberg:
Dreimal Tausend Jahre, Op. 50a		 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
[54]		 Arvo Pärt:
Symphony No. 2		 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
[55]		 Milton Babbitt:
Woodwind Quartet		 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
[56]		 Ernst Krenek:
Sechs Vermessene, Op. 168		 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
[57][58]		 Ernst Krenek:
Karl V		 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
[59]		 Donald Martino:
Fantasy Variations		 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
[60]		 Benjamin Frankel:
The Curse of the Werewolf		 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
[61]		 Karlheinz Stockhausen:
"Aries", from Tierkreis		 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
[4][62]		 Anton Webern:
Symphony, Op. 21		 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
[63]		 Igor Stravinsky:
Agon, "Mystery" (sketches only)		 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
[64]		 Karlheinz Stockhausen:
Klavierstück IV (second row of 48)		 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
[61]		 Karlheinz Stockhausen:
"Aquarius", from Tierkreis		 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
[17]		 row 4 Ernst Krenek:
Lamentatio Jeremiae Prophetae, Op. 93		 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
[4][23][65]
 Play 
 Alban Berg:
Violin Concerto		 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
[66]		 Anton Webern:
"Erlösung" from Drei Lieder, Op. 18, No. 2		 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
[67]		 Ernst Krenek:
Quaestio temporis, Op. 170		 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
[12]		 Anton Webern:
Op. 31		 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
[25]		 "row iv" Milton Babbitt:
Composition for Four Instruments		 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
[68]		 Milton Babbitt:
Composition for Four Instruments		 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
[2]		 Igor Stravinsky:
Anthem		 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
[69][70]		 Karlheinz Stockhausen:
Licht, Eve formula		 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
[71][72]		 Arnold Schoenberg:
Ode to Napoleon Buonaparte
Suite Op. 29

Luigi Nono:
Variazioni canoniche sulla serie dell'op. 41 di Arnold Schönberg

 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
[25]		 "row iii" Milton Babbitt:
Composition for Four Instruments		 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
[61]		 Karlheinz Stockhausen:
"Scorpio", from Tierkreis		 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
[73]		 Ernst Krenek:
Suite, Op. 84 for solo cello		 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
[23]		 Alban Berg:
Lulu		 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
[43][51][52]
Basic
 Alban Berg:
Lulu		 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
[74][75]		 Milton Babbitt:
All Set		 1957 6–7 6–7 all-interval row
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
[61]		 Karlheinz Stockhausen:
"Gemini", from Tierkreis		 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
[76]		 Robert Moevs:
Three Symphonic Pieces, mov. 2		 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
[77]		 Juan Carlos Paz:
Canciones y Baladas, Balada II		 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
[43]		 Chorale Alban Berg:
Lulu		 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
[78]		 Michael Gielen:
Six Songs, for bass, violin, viola, clarinet, bass clarinet, and piano		 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
[3]		 Alfred Schnittke:
Concerto Grosso No. 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
[79]		 Benjamin Britten:
The Turn of the Screw		 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
[80]		 Dmitri Shostakovich:
Symphony No. 14, mov. III		 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
[23][43][52]		 Countess Geschwitz Alban Berg:
Lulu		 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
[2]		 Igor Stravinsky:
Threni		 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
[81]		 Milton Babbitt:
Three Compositions for Piano, no. I		 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
[23][43][52]		 Acrobat/Athlete Alban Berg:
Lulu		 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
[43][51][52]
Dr. Schön
 Alban Berg:
Lulu		 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
[61]		 Karlheinz Stockhausen:
"Leo", from Tierkreis		 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
[2]		 Igor Stravinsky:
Elegy for J.F.K.		 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
[82]		 Karel Husa:
Mosaïques		 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
[3]		 Arnold Schoenberg:
"De Profundis", Op. 50b		 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
[61]		 Karlheinz Stockhausen:
"Sagittarius", from Tierkreis		 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
[83]		 Witold Lutosławski:
Musique funèbre (Funeral Music) 		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
[84]		 Wolfgang Amadeus Mozart:
String Quartet in E♭ major, K. 428 first movement, opening of development section		 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
[77][85][86]
 Play 
 Arnold Schoenberg:
Variations, Op. 31		 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
[62]		 Arnold Schoenberg:
Three Songs, Op. 48		 1933 6–35 6–35 —
I: 0 6 4 2 t 8
3 7 9 1 5 e
P: 0 6 t 7 9 8
3 2 4 1 5 e
[87]		 Michel Fano: Sonata for Two Pianos 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
[88]		 Ben Johnston:
String Quartet No. 7, mov. 2		 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
[64]		 Karlheinz Stockhausen:
Klavierstück IV (third row of 48)		 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
[23][89]
 Play 
 Arnold Schoenberg:
Piano Piece, op. 33a		 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
[27]		 Alberto Ginastera:
Quintet, op. 29		 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
[90]		 Orchestra Elliott Carter:
Piano Concerto		 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
[2]		 2nd series Igor Stravinsky:
Requiem Canticles		 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
[57]		 Ernst Krenek:
String Quartet No. 7, op. 96		 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
[91]		 Arnold Schoenberg:
Piano Concerto, Op. 42		 1942 6–9 6–9 —
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
[92]		 Anton Webern:
Op. 23		 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
[21]		 Ross Lee Finney:
Edge of Shadow		 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
[61]		 Karlheinz Stockhausen:
"Cancer", from Tierkreis		 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
[93]		 Arnold Schoenberg:
String Trio, Op. 45		 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
[94][95]
 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
[96][97]		 Karlheinz Stockhausen:
Klavierstück V (row of original 1954 version)
Klavierstück VIII		 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
[90]		 Solo[ist] Elliott Carter:
Piano Concerto		 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
[43][51][52]
Alwa
 Alban Berg:
Lulu		 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
[90]		 Elliott Carter:
A Symphony of Three Orchestras		 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
[98][99]
 Play 
 Anton Webern:
Variations for piano, mov. III, op. 27		 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
[100][34]		 Anton Webern:
Op. 29		 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
[57]		 Ernst Krenek:
Sestina, op. 161		 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
[101]		 Luigi Dallapiccola:
Piccola musica notturna		 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
[102]		 Milton Babbitt:
Composition for Synthesizer		 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
[103][104]
 Play 
 Milton Babbitt:
Composition for Four Instruments		 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
[2]		 Igor Stravinsky:
Epitaphium		 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
[61]		 Karlheinz Stockhausen:
"Capricorn", from Tierkreis		 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]		 David Dzubay: Di/Con[ver(gence/sions)] 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
[105]		 Anton Webern:
Op. 22		 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
[25]		 "row ii" Milton Babbitt:
Composition for Four Instruments		 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
[3][106]		 prime form ("série droit") Pierre Boulez:
Le marteau sans maître		 1953–55 6-Z10 6-Z39 —
I: 0 2 e t 7 8
6 9 5 1 4 3		 inverse form ("série renversée")
P: 0 t 3 4 2 7
6 9 8 e 1 5
[107]		 Charles Ives:
Tone Roads No. 1		 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
[108]		 Elliott Carter:
Night Fantasies		 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
[25]		 "row i" Milton Babbitt:
Composition for Four Instruments		 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
[109]		 Karlheinz Stockhausen:
Kreuzspiel		 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
[2][110]		 Igor Stravinsky:
Agon, "Double Pas de Quatre"		 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
[2]		 Igor Stravinsky:
Fanfare		 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
[2]		 Igor Stravinsky:
Canticum Sacrum, II & IV		 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
[3][35]		 Chen Yi:
Woodwind Quintet		 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
[54]		 Arvo Pärt:
Diagrams		 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
 Play 
 Anton Webern:
String Quartet, Op. 28:[100][65][98]		 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
[27]		 Alberto Ginastera:
Violin Concerto, op. 30		 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
[111]		 Elliott Carter:
String Quartet No. 3		 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
[112][113]		 Arnold Schoenberg:
Violin Phantasy, Op. 47		 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
[2]		 Igor Stravinsky:
Double Canon		 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
[23][114][85][89][66]
 Play 
 Anton Webern:
Concerto for Nine Instruments, Op. 24		 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
[115]		 David Lewin:
Just a Minute, Roger		 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
[3]		 Alfred Schnittke:
Viola Concerto		 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
[34]		 Luigi Dallapiccola:
Cinque Canti		 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
[3][65]		 Pierre Boulez:
Structures Ia		 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
[116]		 George Perle:
Three Inventions for Piano, no. 3		 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
[117]
Alban Berg:
Lyric Suite, mov. III		 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
[118]
row 1  Play 
 Alban Berg:
Lyric Suite, mov. VI		 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
 Play 
 Fritz Heinrich Klein[119]

Alban Berg:
Lyric Suite, mov. I[44][120]

Alberto Ginastera:
Sonata for Guitar, mvt. III, op. 47[27]

 1920–22[121]

1925–26

1976

 6–32 6–32 Mother chord (all-interval)
Trichordally combinatorial: 0369[122]
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
[62][112]		 Arnold Schoenberg:
String quartet No. 4		 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
[3]		 Arnold Schoenberg:
Modern Psalm, Op. 50c		 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
[118]
row 2  Play 
 Alban Berg:
Lyric Suite		 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
[123]		 Milton Babbitt:
"The Widow's Lament in Springtime"		 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
[80]		 Dmitri Shostakovich:
Symphony No. 14, mov. I		 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
[2]		 Igor Stravinsky:
Canticum Sacrum, II		 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
[3]		 Alfred Schnittke:
String Quartet No. 4, Mov. I		 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
[54]		 Arvo Pärt:
Symphony No. 1
Perpetuum Mobile		 1963
1963		 6–5 6–5 —
I: 0 1 2 7 6 3
5 e t 4 9 8

Other lengths

Less than twelve

Five
Prime form Notation Composer:
Composition		 Year Set(s) Features
0 e 8 9 t
[124]		 Igor Stravinsky:
In memoriam Dylan Thomas		 1954 5–1 —
Six
Prime form Notation Composer:
Composition		 Year Set(s) Features
0 6 9 8 1 e
[125][126][127][128]
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
[129]
 Play 
 Arnold Schoenberg:
Die glückliche Hand, Op. 18

"Seraphita", op. 22, no. 1

1910–13

1913–16

 6-Z44 (6-Z19) Schoenberg hexachord
Eight
Prime form Notation Composer:
Composition		 Year Set(s) Features
0 2 8 9
t 4 3 e
[43]		 Alban Berg:
Lyric Suite		 1925–26 8–5 —
0 2 9 7
t 8 e 1
[39]		 row B Joonas Kokkonen:
Symphonic Sketches, mov. 3		 1968 8–1 —
0 7 1 6
8 2 3 4
[43]		 Alban Berg:
Lyric Suite		 1925–26 8–5 —
0 8 2 3
t 4 9 e
[43]		 Alban Berg:
Lyric Suite		 1925–26 8–5 —
0 t 2 4
5 7 3 1
[130]		 Igor Stravinsky:
Agon, "Pas-de-Deux" refrain
(b. 463–72)		 1957 8–10 —
0 t 3 5
2 4 1 e
[39]		 row C Joonas Kokkonen:
Symphonic Sketches, mov. 3		 1968 8–1 —
Nine
Prime form Notation Composer:
Composition		 Year Set(s) Features
0 2 e 4 9
7 8 6 1
[39]		 row D Joonas Kokkonen:
Symphonic Sketches, mov. 3		 1968 9–8 —
Ten
Prime form Notation Composer:
Composition		 Year Set(s) Features
0 e 2 1 5
6 4 9 7 8
[54]		 Arvo Pärt:
Collage sur B-A-C-H		 1964 — BACH motif
Eleven
Prime form Notation Composer:
Composition		 Year Set(s) Features
0 1 e 5 6 8
7 9 2 3 4
[3]		 Karel Husa:
Music for Prague 1968		 1968 — —
0 e t 4 6 2
1 9 8 5 3
[69][131]		 Karlheinz Stockhausen:
Licht, Lucifer formula		 1977–
2003		 — —

More than twelve

Thirteen
Prime form Notation Composer:
Composition		 Year Set(s) Features
0 1 4 5 t 8 7
t e 6 3 2 9
[61]		 Karlheinz Stockhausen:
"Taurus", from Tierkreis		 1974–75 — —
0 1 t 6 8 3 5
2 4 e 9 7 0
[132]		 Karlheinz Stockhausen:
Choral		 1950 — —
0 3 e 8 5 4
9 2 1 t 7 3 6
[133][134]		 Luciano Berio:
Nones		 1953–54 — —
0 4 1 5 7 t 2
8 e 9 3 6 9
[61]		 Karlheinz Stockhausen:
"Pisces", from Tierkreis		 1974–75 — —
0 7 8 6 e t 2
5 1 3 9 4 0
[69]		 Karlheinz Stockhausen:
Licht, Michael formula		 1977–
2003		 — —
0 e 2 4 t 9
7 3 7 1 8 5 6
[61]		 Karlheinz Stockhausen:
"Virgo", from Tierkreis		 1974–75 — —
0 e 4 t 9 5
8 6 2 1 6 7 3
[64]		 Karlheinz Stockhausen:
Klavierstück IV
(first row of 48)		 1952 6-Z38, 6-Z6 —
Fourteen
Prime form Notation Composer:
Composition		 Year Set(s) Features
0 1 t 3 9 4 6
7 4 5 7 3 8 e
[61]
Karlheinz Stockhausen:
"Libra", from Tierkreis		 1974–75 — —
0 1 t 9 2 8 e
7 3 5 6 4 0 2
[135]		 Karlheinz Stockhausen:
Inori		 1973–74 — —
0 e 2 4 1 8 t
e 9 4 7 5 3 6
[39]		 row A Joonas Kokkonen:
Cello Concerto, mov. 3		 1969 — —
Seventeen
Prime form Notation Composer:
Composition		 Year Set(s) Features
0 2 1 e t 8
9 e t 0 1 e
t 0 e 9 0
[136]		 Igor Stravinsky:
Agon, b. 104		 1957 — —
0 2 3 5 4 9
7 8 e 1 6 e
t 0 e 9 0
[136]		 Igor Stravinsky:
Agon, "Bransles"		 1957 6-Z40, 6-Z11 —
Twenty-two
Prime form 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
[39]		 row B Joonas Kokkonen:
Cello Concerto, mov. 3		 1969 — —
Twenty-four
Prime form 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
[137]		 quarter-tone series Pierre Boulez:
Polyphonie X		 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
[138]		 mod24 (no octave equivalency) Karlheinz Stockhausen:
Himmelfahrt		 2004–
2005		 — —

See also

Sources

  1. ↑ Bailey, Kathryn (1991). The Twelve-Note Music of Anton Webern: Old Forms in a New Language, p.28. ISBN 9780521547963.
  2. ↑ 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.11 2.12 2.13 2.14 2.15 2.16 2.17 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". D.M.A. diss. (University of Colorado). Retrieved 4 November 2013.
  3. ↑ 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 3.11 3.12 3.13 3.14 3.15 3.16 Dunker, Amy. "Twelve Tone Rows Used by Various Composers". AmyDunker.com: 3. Retrieved 4 November 2013.
  4. ↑ 4.0 4.1 4.2 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. Retrieved 11 November 2013. Citation on p.93.
  9. ↑ Mayfield, Connie (2013). Theory Essentials. p. 549. ISBN 9781133713807.
  10. ↑ Morris (2010), 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): 233–72. Citation on pp. 235–37.
  12. ↑ 12.0 12.1 Bailey, Kathryn (1991), p. 26.
  13. ↑ Leeuw, Ton de (2005). Music of the Twentieth Century: A Study of Its Elements and Structure. Amsterdam: Amsterdam University Press. p. 161. ISBN 90-5356-765-8. Translated from the Dutch by Stephen Taylor. 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. 1999. "Stravinsky's Second Crisis: Reading the Early Serial Sketches". Perspectives of New Music 37, no. 2 (Summer): 117–46. Citation on pp. 126–27, 134, 142.
  15. ↑ 15.0 15.1 Pearsall, Edward (2012). Twentieth-Century Music Theory and Practice, 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. 263–68.
  17. ↑ 17.0 17.1 17.2 17.3 17.4 17.5 Ernst Krenek, "Extents and Limits of Serial Techniques", The Musical Quarterly 46, no. 2, Special Issue: Problems of Modern Music. The Princeton Seminar in Advanced Musical Studies (April 1960): pp. 210–32. Citation on p. 212.
  18. ↑ Babbitt, Milton (2011). The Collected Essays of Milton Babbitt. p. 94. ISBN 9780691089669.
  19. ↑ Kholopov, Yuri; Tsenova, Valeria (1997). Edison Denisov. p. 81. ISBN 9780203479599.
  20. ↑ Luigi Dallapiccola, "Notes for an Analysis of the Canti di Liberazione", translated by Chloe Stodt. Perspectives of New Music 38, no. 1 (Winter 2000): 2–24. Citation on p. 10. Accessed 16 November 2013.
  21. ↑ 21.0 21.1 Cooper, Paul (1975). Perspectives in Music Theory, p.266. ISBN 0-396-06752-2.
  22. ↑ Lewin (1962), pp. 113–15.
  23. ↑ 23.0 23.1 23.2 23.3 23.4 23.5 23.6 23.7 23.8 23.9 23.10 Dunker, Amy. "Twelve Tone Rows Used by Various Composers". AmyDunker.com: 2. Retrieved 4 November 2013.
  24. ↑ "A Survivor from Warsaw: the twelve-note row". AEIOU.at. Retrieved 13 November 2013. ( (German))
  25. ↑ 25.0 25.1 25.2 25.3 25.4 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): 155–86. Citation on p. 159.
  26. ↑ Kholopov & Tsenova (1997), p.103. ISBN 9780203479599.
  27. ↑ 27.0 27.1 27.2 27.3 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. 152–4 & 161.-->
  28. ↑ Jonathan Harvey, The Music of Stockhausen: An Introduction (Berkeley and Los Angeles: University of California Press, 1975): p. 93. ISBN 0-520-02311-0.
  29. ↑ Genevieve Marcus, "Stockhausen's Zeitmasse", The Music Review 29, no. 2 (May 1968): 142–56. Citation on p. 144.
  30. ↑ Rigoni, Michel (1998). Stockhausen: ... un vaisseau lancé vers le ciel (second edition, revised, corrected, and enlarged ed.). Lillebonne: Millénaire III Editions. pp. 141–42. ISBN 978-2911906022.
  31. ↑ 31.0 31.1 Bailey (1991), p.27.
  32. ↑ Leeuw. 2005. p. 158. ISBN 90-5356-765-8.
  33. ↑ 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. Retrieved 8 November 2013.
  34. ↑ 34.0 34.1 34.2 34.3 Alegent, Brian (2010). The Twelve-tone Music of Luigi Dallapiccola, p.48. ISBN 9781580463256.
  35. ↑ 35.0 35.1 Guo, Xin (2003-01-01). "Chinese Musical Language Interpreted by Western Idioms: Fusion Process in the Instrumental Works by Chen Yi". Dissertation. Retrieved 8 November 2013.
  36. ↑ Leeuw. 2005. p. 177. ISBN 90-5356-765-8.
  37. ↑ 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.
  38. ↑ Slonimsky, Nicolas (1975). Thesaurus of Scales and Melodic Patterns, p. 243. ISBN 0-8256-1449-X.
  39. ↑ 39.0 39.1 39.2 39.3 39.4 39.5 39.6 Jurkowski, Edward (2004). The Music of Joonas Kokkonen, pp.78, 84, & 184. ISBN 9780754607892.
  40. ↑ Smyth (Summer 1999), pp. 126–27, 142.
  41. ↑ Wiens, Carl Kristian (1997). Igor Stravinsky and Agon, p.168. University of Michigan.
  42. ↑ 42.0 42.1 Jacobi, Bonnie S. (2000). "The Bransles of Stravinsky's Agon: A Transition to Serial Composition", Moores School of Music.
  43. ↑ 43.0 43.1 43.2 43.3 43.4 43.5 43.6 43.7 43.8 43.9 43.10 Headlam, David John (1996). The Music of Alban Berg, pp.265, 304, & 306. ISBN 9780300064001.
  44. ↑ 44.0 44.1 Pople, Anthony (1991). Berg: Violin Concerto. pp. 18 & 21. ISBN 0-521-39976-9.
  45. ↑ Eric Walter White, "Two New Memorial Works by Stravinsky", Tempo, new series, no. 74 (Autumn 1965), pp. 18–21.
  46. ↑ Claudio Spies, "Notes on Stravinsky's Variations", Perspectives of New Music 4, no. 1 (Autumn-Winter 1965): pp. 62–74. Citation on p. 66.
  47. ↑ Igor Stravinsky and Robert Craft, Themes and Episodes (NewYork: Alfred A. Knopf,1967): p. 60.
  48. ↑ 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. 391–92.
  49. ↑ 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.
  50. ↑ Smyth (Summer 1999), pp. 139–40, 142.
  51. ↑ 51.0 51.1 51.2 51.3 Whittall (2008), p.81.
  52. ↑ 52.0 52.1 52.2 52.3 52.4 52.5 Hailey, Christopher, ed. (2010). Alban Berg and His World. p. 215. ISBN 9781400836475.
  53. ↑ Herman Sabbe, 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.
  54. ↑ 54.0 54.1 54.2 54.3 Hillier, Paul (1997). Arvo Pärt. pp. 40, 47, & 50. ISBN 9780191590481.
  55. ↑ Babbitt (2011). p.350. ISBN 9781400841226.
  56. ↑ Krenek (April 1960), p. 229.
  57. ↑ 57.0 57.1 57.2 Stewart, John Lincoln (1991). Ernst Krenek: The Man and His Music. pp. 169, 250, & 290. ISBN 9780520070141.
  58. ↑ Tregear, Peter John (Mar., 2001). "Musical Style and Political Allegory in Krenek's Karl V", Cambridge Opera Journal, Vol. 13, No. 1, pp.55–80. Citation on 73.
  59. ↑ Boros, James (Summer 1991). "Donald Martino's Fantasy Variations: The First Three Measures". Perspectives of New Music 29 (2): 280–93. Retrieved 11 November 2013.
  60. ↑ Huckvale, David (2008). Hammer Film Scores and the Musical Avant-Garde. p. 43. ISBN 9780786451661.
  61. ↑ 61.0 61.1 61.2 61.3 61.4 61.5 61.6 61.7 61.8 61.9 61.10 61.11 Jerome Kohl, "The Evolution of Macro- and Micro-Time Relations in Stockhausen's Recent Music", Perspectives of New Music 22, nos. 1 & 2 (Fall-Winter 1983/ Spring-Summer 1984): 147–85. ISSN 0031-6016. Retrieved November 2013. Citation on p. 151 (subscription required).
  62. ↑ 62.0 62.1 62.2 Hurry, Pam; Phillips, Mark; Richards, Mark (2001). Heinemann Advanced Music. pp. 100, 122, & 303. ISBN 9780435812584.
  63. ↑ Smyth (Summer 1999), pp. 136–37, 142.
  64. ↑ 64.0 64.1 64.2 Rudolf Frisius,.. Karlheinz Stockhausen II: Die Werke|1950–1977; Gespräch mit Karlheinz Stockhausen, "Es geht aufwärts" (Mainz, London, Berlin, Madrid, New York, Paris, Prague, Tokyo, Toronto: Schott Musik International, 2008): p. 73. ISBN 978-3-7957-0249-6.
  65. ↑ 65.0 65.1 65.2 Cooper (1975). p.265. ISBN 0-396-06752-2.
  66. ↑ 66.0 66.1 Lewin (1962), p. 94.
  67. ↑ Krenek (April 1960), p. 230.
  68. ↑ 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.
  69. ↑ 69.0 69.1 69.2 Karlheinz Stockhausen and Rudolph Frisius, "Die Tonhöhen der Superformel für LICHT", in Karlheinz Stockhausen, Texte zur Musik 9, edited by Christoph von Blumröder, 13–33 (Kürten: Stockhausen-Verlag, 1998): 13. ISBN 978-3-00-002131-0.
  70. ↑ Karlheinz Stockhausen and Rudolph Frisius, "Es geht aufwärts", in Karlheinz Stockhausen, Texte zur Musik 9, edited by Christoph von Blumröder, 391–512 (Kürten: Stockhausen-Verlag, 1998): 396. ISBN 978-3-00-002131-0.
  71. ↑ Van den Toorn, Pieter C. (1996). Music, Politics, and the Academy, p.128-29. ISBN 0-520-20116-7.
  72. ↑ Lewin, David (1959). "Re: Intervallic Relations Between Two Collections of Notes". Journal of Music Theory 3, no. 2 (November 1959): 298–301. p.300.
  73. ↑ 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.
  74. ↑ Babbitt, Milton. 1987. Words about Music, p.115-17. Edited by Stephen Dembski and Joseph N. Straus. The Madison Lectures. Madison: University of Wisconsin Press. ISBN 0299107906 (cloth); ISBN 0299107949.
  75. ↑ 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.
  76. ↑ Boros, James (Winter, 1990). "The Evolution of Robert Moevs's Compositional Methodology". American Music 8 (4): 383–404. Retrieved 11 November 2013.
  77. ↑ 77.0 77.1 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.
  78. ↑ Friedrich Saathen, "Current Chronicle: Austria", The Musical Quarterly 44, no. 4 (October 1958): 515–19. Citation on p. 517.
  79. ↑ Burton, Ian (2004). Listening Tests for Students. p. 26. ISBN 9781904226345.
  80. ↑ 80.0 80.1 Fairclough, Pauline (2010). Shostakovich Studies 2, Volume 2. p. 202. ISBN 9780521111188.
  81. ↑ Taruskin, Richard (2009). Music in the Late Twentieth Century: The Oxford History of Western Music 5. p. 137. ISBN 9780199796007.
  82. ↑ Craig Cummings. "Compositional Techniques in Karel Husa's Early Serial Works Poème and Mosaïques". Ex-tempore.org. Retrieved 11 November 2013.
  83. ↑ Peck, Robert W. (August 2003). "Klein-Bottle Tonnetze". Music Theory Online (Society for Music Theory) 9 (3). Retrieved 8 November 2013. [See: Tonnetz]
  84. ↑ Hans Keller, "Strict Serial Technique in Classical Music", Tempo, new series, no. 37 (Autumn 1955): 12–24. Citation on p. 16.
  85. ↑ 85.0 85.1 Hoffer, Charles (2010). Cengage Advantage Books: Music Listening Today. pp. 271 & 273. ISBN 9780495916147.
  86. ↑ Pearsall (2012). p.212. ISBN 9780415888950.
  87. ↑ Richard Toop, "Messiaen/ Goeyvaerts, Fano/ Stockhausen, Boulez", Perspectives of New Music 13, no. 1 (Autumn -Winter,1974): 141–69. Citation on p. 164
  88. ↑ Fonville, John (Summer, 1991). "Ben Johnston's Extended Just Intonation: A Guide for Interpreters". Perspectives of New Music 29 (2): 106–137. Retrieved 11 November 2013.
  89. ↑ 89.0 89.1 Randel, Don Michael; ed. (2003). The Harvard Dictionary of Music, p.928. ISBN 9780674011632.
  90. ↑ 90.0 90.1 90.2 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.]
  91. ↑ Roeder, Michael Thomas (1994). A History of the Concerto. p. 367. ISBN 9780931340611.
  92. ↑ Bailey (1991), p.20.
  93. ↑ Cherlin, Michael (Autumn, 1998). "Memory and Rhetorical Trope in Schoenberg's String Trio". Journal of the American Musicological Society 51 (3): 559–602. Retrieved 8 November 2013.
  94. ↑ Harvey, Jonathan (1975). The Music of Stockhausen: An Introduction. pp. 42, 56–58. ISBN 0-520-02311-0.
  95. ↑ Robin Maconie, Other Planets: The Music Of Karlheinz Stockhausen (Lanham, Maryland; Toronto; Oxford: Scarecrow Press, 2005): 215. ISBN 0-8108-5356-6.
  96. ↑ Richard Toop, "Stockhausen's Klavierstück VIII", Miscellanea Musicologica (Adelaide) 10 (1979): 93–130. Citation on p. 99.
  97. ↑ Richard Toop, "Stockhausen's Other Piano Pieces." The Musical Times 124 no. 1684 (June 1983): 348–52. Citation on p. 350.
  98. ↑ 98.0 98.1 Lewin (1962), p. 95.
  99. ↑ Wason, Robert W. (1987). "Webern's 'Variations for Piano', Op. 27: Musical Structure and the Performance Score". Intégral 1: 74. Retrieved 11 November 2013.
  100. ↑ 100.0 100.1 Bailey, Kathryn (1991), p. 25.
  101. ↑ Dallapiccola (Winter 2000), p. 7.
  102. ↑ Morris, Robert (Summer, 1997). "Listening to Milton Babbitt's Electronic Music: The Medium and the Message". Perspectives of New Music 35 (2): 85–99. Retrieved 11 November 2013.
  103. ↑ 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.
  104. ↑ Taruskin (2009), p.143. ISBN 9780195384857.
  105. ↑ Bailey (1991), p.19.
  106. ↑ Ulrich Mosch, Musikalisches Hören serieller Musik: Untersuchungen am Beispiel von Pierre Boulez' 'Le Marteau sans maître' (Saarbrücken: Pfau-Verlag, 2004): pp. 51, 71–72. ISBN 3-89727-253-9.
  107. ↑ Schoffman, Nachum; Ives, Charles (Sep., 1981). "Serialism in the Works of Charles Ives". Tempo (138): 21–32. Retrieved 11 November 2013.
  108. ↑ Marvin & Hermann, eds. (2002). p.88. ISBN 9781580460965.
  109. ↑ Pearsall (2012). p.206. ISBN 9780415888950.
  110. ↑ Vlad, Roman (1967). Stravinsky, p.199. Oxford University Press, London. Cited in Jacobi (2000).
  111. ↑ Marvin & Hermann, eds. (2002). p.74. ISBN 9781580460965.
  112. ↑ 112.0 112.1 Lewin (1962), p. 91.
  113. ↑ Lewin, David (Autumn-Winter, 1967). "A Study of Hexachord Levels in Schoenberg's Violin Fantasy". Perspectives of New Music 6 (1): 18–32. Retrieved 11 November 2013.
  114. ↑ Bailey (1991), p.21.
  115. ↑ 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. 209–13.
  116. ↑ 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.
  117. ↑ Stroh, Wolfgang Martin (Fall-Winter 1968). "Alban Berg's 'Constructive Rhythm'". Perspectives of New Music 7 (1): 18–31. Retrieved 11 November 2013.
  118. ↑ 118.0 118.1 Antokoletz, Elliott (1992). Twentieth-Century Music, p.70. ISBN 9780139341267.
  119. ↑ Whittall (2008), p.68.
  120. ↑ Perle, George (1996). Twelve-Tone Tonality, pp.12, 14, & 20. ISBN 0-520-20142-6.
  121. ↑ Pople, Anthony, ed. (1997). The Cambridge Companion to Berg, p.288-9, no.27. ISBN 9780521564892.
  122. ↑ Headlam, David John (1996). The Music of Alban Berg, p.202. Yale University. ISBN 9780300064001.
  123. ↑ Morris (2010), p.45. ISBN 9781580463492.
  124. ↑ Whittall (2008), p.127.
  125. ↑ Whittall (2008), 206.
  126. ↑ Steven Stucky, Lutosławski and His Music (Cambridge and New York: Cambridge University Press, 1981): 97. ISBN 9780521227995.
  127. ↑ Robin Stowell, The Cambridge Companion to the Cello (Cambridge and New York: Cambridge University Press, 1999): 144. ISBN 9780521629287.
  128. ↑ Edward Campbell, Boulez, Music and Philosophy, . (Oxford and New York: Oxford University Press, 2010): 206. ISBN 978-0-521-86242-4.
  129. ↑ Simms, Bryan R. (2000). The Atonal Music of Arnold Schoenberg, 1908–1923, p.145. ISBN 0-19-512826-5.
  130. ↑ Smyth (Summer 1999), pp. 135.
  131. ↑ Karlheinz Stockhausen and Rudolph Frisius, "Es geht aufwärts", in Karlheinz Stockhausen, Texte zur Musik 9, edited by Christoph von Blumröder, 391–512 (Kürten: Stockhausen-Verlag, 1998): pp. 396, 446. ISBN 978-3-00-002131-0.
  132. ↑ Frisius, Rudolf. 2008. Karlheinz Stockhausen II: Die Werke 1950–1977; Gespräch mit Karlheinz Stockhausen, "Es geht aufwärts", p.29. Mainz, London, Berlin, Madrid, New York, Paris, Prague, Tokyo, Toronto: Schott Musik International. ISBN 978-3-7957-0249-6.
  133. ↑ Michael Hicks, "Exorcism and Epiphany: Luciano Berio's Nones", Perspectives of New Music 27, no. 2 (Summer 1989): pp. 252–68. Citation on p. 254.
  134. ↑ Christoph Neidhöfer, "Inside Luciano Berio's Serialism", Music Analysis 28, nos. 2–3 (2009): pp. 301–48. Citation on p. 306.
  135. ↑ Karlheinz Stockhausen and Rudolph Frisius, "Es geht aufwärts", in Karlheinz Stockhausen, Texte zur Musik 9, edited by Christoph von Blumröder, 391–512 (Kürten: Stockhausen-Verlag, 1998): p. 394. ISBN 978-3-00-002131-0.
  136. ↑ 136.0 136.1 Smyth (Summer 1999), p. 142.
  137. ↑ Pierre Boulez, "The System Exposed" in Orientations: Collected Writings by Pierre Boulez, edited by Jean-Jacques Nattiez, translated by Martin Cooper, 129–42 (Cambridge: Harvard University Press, 1986): p. 129. ISBN 0-674-64375-5.
  138. ↑ 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.