List of tone rows and series

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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[edit]

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]
Berg - Chamber Concerto twelve-tone material.png
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]
About this sound 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]
About this sound 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]
About this sound 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 About this sound 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]
About this sound 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]
About this sound 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:
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]
About this sound 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]
About this sound 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]
About this sound 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]
About this sound 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]
About this sound 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
About this sound 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]
About this sound 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]
Lyric Suite Movement III tone row.svg
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 About this sound 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
About this sound 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)
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 About this sound 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

[122]
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[edit]

Less than twelve[edit]

Five
Prime form Notation Composer:
Composition
Year Set(s) Features
0 e 8 9 t
[123]
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
[124][125][126][127]
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
[128]
About this sound 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
[129]
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][130]
Karlheinz Stockhausen:
Licht, Lucifer formula
1977–
2003

More than twelve[edit]

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
[131]
Karlheinz Stockhausen:
Choral
1950
0 3 e 8 5 4
9 2 1 t 7 3 6
[132][133]
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]
Stockhausen Tierkreis Libra.png
Karlheinz Stockhausen:
"Libra", from Tierkreis
1974–75
0 1 t 9 2 8 e
7 3 5 6 4 0 2
[134]
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
[135]
Igor Stravinsky:
Agon, b. 104
1957
0 2 3 5 4 9
7 8 e 1 6 e
t 0 e 9 0
[135]
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
[136]
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
[137]
mod24 (no octave equivalency) Karlheinz Stockhausen:
Himmelfahrt
2004–
2005

See also[edit]

Sources[edit]

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