List of tone rows and series
This is a list of tone rows and series . For a list of unordered collections, see set (music) , Forte number , list of set classes , and trope (music) .
Twelve tone rows
Row form
Integers
Interval classes
Notation
Composer: Composition
Year
Hexa- chord I
Hexa- chord II
Derivation / Combina- toriality
P:
0 1 2 e t 9 5 4 3 6 7 8
1 1 3 1 1 4 1 1 3 1 1
Anton Webern : Op. 32, later row[ 1]
un- finished
6-1
6-1
—
I:
0 e t 1 2 3 7 8 9 6 5 4
P:
0 1 3 5 6 2 4 8 7 9 e t
1 2 2 1 4 2 4 1 2 2 1
Igor Stravinsky :Abraham & Isaac [ 2] [ 3]
1963
6-Z3
6-Z36
—
I:
0 e 9 7 6 t 8 4 5 3 1 2
P:
0 1 3 6 7 9 8 t e 2 4 5
1 2 3 1 2 1 2 1 3 2 1
Arnold Schoenberg : Serenade, op. 24, mov. 5[ 4]
1920–23
6-30
6-30
derived: 3-3
I:
0 e 9 6 5 3 4 2 1 t 8 7
P:
0 1 3 8 4 9 t 7 6 5 e 2
1 2 5 4 5 1 3 1 1 6 3
Play ⓘ
Alban Berg :Kammerkonzert [ 5]
1923–25
6-Z19
6-Z44
cryptogram : "Schoenberg"
I:
0 e 9 4 8 3 2 5 6 7 1 t
P:
0 1 3 9 2 e 4 t 7 8 5 6
1 2 6 5 3 5 6 3 1 3 1
Arnold Schoenberg :Suite for Piano , op. 25[ 7] [ 8] [ 9]
1921–23
6-2
6-2
—
I:
0 e 9 3 t 1 8 2 5 4 7 6
P:
0 1 4 2 9 5 e 3 8 t 7 6
1 3 2 5 4 6 4 5 2 3 1
Pohlman Mallalieu[ 10] [ 11]
Robert Morris :Not Lilacs [ 10]
n.a.
1973
6-14
6-14
all-interval, RT6-invariant
I:
0 e 8 t 3 7 1 9 4 2 5 6
P:
0 1 4 3 2 5 6 9 8 7 t e
1 3 1 1 3 1 3 1 1 3 1
Play ⓘ
Anton Webern : Variations for Orchestra, Op. 30[ 12] [ 3] [ 13]
1940
6-1
6-1
all- combinatorial
I:
0 e 8 9 t 7 6 3 4 5 2 1
P:
0 1 4 3 2 5 6 9 8 e t 7
1 3 1 1 3 1 3 1 3 1 3
Igor Stravinsky :Agon , "Pas de deux", "Four trios"[ 2] [ 14]
1957
6-1
6-1
all- combinatorial
I:
0 e 8 9 t 7 6 3 4 1 2 5
P:
0 1 4 3 7 6 e 2 t 9 5 8
1 3 1 4 1 5 3 4 1 4 3
Arnold Schoenberg :Die Jakobsleiter [ 15]
un- finished
6-Z13
6-Z42
—
I:
0 e 8 9 5 6 1 t 2 3 7 4
P:
0 1 4 5 8 7 6 3 2 7 e t
1 3 1 3 1 1 3 1 5 4 1
Walter Piston :Symphony No. 8 (first movement)[ 16]
1965
6-Z19
6-Z44
—
I:
0 e 8 7 4 5 6 9 t 5 1 2
P:
0 1 4 5 7 6 8 9 t e 2 3
1 3 1 2 1 2 1 1 1 3 1
Roger Reynolds :Ambages [ 17]
1965
6-5
6-5
—
I:
0 1 4 5 7 6 8 9 t e 2 3
P:
0 1 4 6 8 t 5 7 9 e 2 3
1 3 2 2 2 5 2 2 2 3 1
Ernst Krenek :Lamentatio Jeremiae Prophetae , Op. 93, row 3[ 18]
1940–41
6-34
6-34
RI- symmetry
I:
0 e 8 6 4 2 7 5 3 1 t 9
P:
0 1 4 9 5 8 3 t 2 e 6 7
1 3 5 4 3 5 5 4 3 5 1
Milton Babbitt :Composition for Twelve Instruments [ 3] [ 19]
1948
6-20
6-20
dyadic, tri-, tetra-, and hexa- chordal combina- toriality
I:
0 e 8 3 7 4 9 2 t 1 6 5
P:
0 1 5 2 6 t 3 8 9 4 7 e
1 4 3 4 4 5 5 1 5 3 4
Edison Denisov :Fünf Geschichten von Herrn Keuner [ 20]
1966
6-Z43
6-Z17
all-trichord hexachord
I:
0 e 7 t 6 2 9 4 3 8 5 1
P:
0 1 5 8 t 4 3 7 9 2 e 6
1 4 3 2 6 1 4 2 5 3 5
Luigi Dallapiccola :Quaderno musicale di Annalibera [ 21] Variazioni per orchestra Canti di Liberazione [ 22]
1952 1954 1951–55
6-31
6-31
—
I:
0 e 7 4 2 8 9 5 3 t 1 6
P:
0 1 6 2 7 9 3 4 t e 5 8
1 5 4 5 2 6 1 6 1 6 3
Arnold Schoenberg :Violin Concerto , op. 36[ 23]
1936
6-Z50
6-Z29
—
I:
0 e 6 t 5 3 9 8 2 1 7 4
P:
0 1 6 2 t 9 4 7 3 8 e 5
1 5 4 4 1 5 3 4 5 3 6
Arnold Schoenberg :A Survivor from Warsaw [ 24] [ 25]
1947
6-15
6-15
—
I:
0 e 6 t 2 3 8 5 9 4 1 7
P:
0 1 6 5 7 e 2 t 3 9 8 4
1 5 1 2 4 3 4 5 6 1 4
Milton Babbitt :All Set [ 26]
1957
6-7
6-7
second-order all- combinatorial hexachord
I:
0 e 6 7 5 1 t 2 9 3 4 8
P:
0 1 7 2 3 9 t 8 6 5 e 4
1 6 5 1 6 1 2 2 1 6 5
Edison Denisov : Viola concerto
1986
6-Z41
6-Z12
—
I:
0 e 5 t 9 3 2 4 6 7 1 8
P:
0 1 7 5 6 4 t 8 9 e 2 3
1 6 2 1 2 6 2 1 2 3 1
Play ⓘ
Arnold Schoenberg :Moses und Aron [ 24]
un- finished
6-5
6-5
inversional
I:
0 e 5 7 6 8 2 4 3 1 t 9
P:
0 1 7 5 6 e 9 8 t 3 4 2
1 6 2 1 5 2 1 2 5 1 2
Igor Stravinsky :Movements [ 2]
1958–59
6-7
6-7
—
I:
0 e 5 7 6 1 3 4 2 9 8 t
P:
0 1 7 6 8 9 3 2 4 5 e t
1 6 1 2 1 6 1 2 1 6 1
Alberto Ginastera :Don Rodrigo , Act I, op. 31[ 28]
1963–64
6-5
6-5
—
I:
0 e 5 6 4 3 9 t 8 7 1 2
P:
0 1 7 9 8 6 3 t 2 5 e 4
1 6 2 1 2 3 5 4 3 6 5
Karlheinz Stockhausen :Plus-Minus [ 29]
1963 (rev. 1974)
6-5
6-5
—
I:
0 e 5 3 4 6 9 2 t 7 1 8
P:
0 1 7 e 8 2 6 5 t 9 3 4
1 6 4 3 6 4 1 5 1 6 1
Play ⓘ
Schoenberg: "Tot" ["Lifeless"], Drei Lieder , Op. 48[ 30]
1933
6-5
6-5
—
I:
0 e 5 1 4 t 6 7 2 3 9 8
P:
0 1 8 e 7 3 2 5 4 t 9 6
1 5 3 4 4 1 3 1 6 1 3
Karlheinz Stockhausen :Zeitmaße [ 31] [ 32]
1955–56
6-16
6-16
—
I:
0 e 4 1 5 9 t 7 8 2 3 6
P:
0 1 9 e 3 2 6 7 t 8 4 5
1 4 2 4 1 4 1 3 2 4 1
Anton Webern : Op. 32, row 1[ 33]
un- finished
6-2
6-2
—
I:
0 e 3 1 9 t 6 5 2 4 8 7
P:
0 1 9 e 3 2 7 6 t 8 4 5
1 4 2 4 1 5 1 4 2 4 1
Anton Webern : Op. 32, row 2[ 33]
un- finished
6-1
6-1
all- combinatorial
I:
0 e 3 1 9 t 5 6 2 4 8 7
P:
0 1 9 e 8 t 4 5 6 2 3 7
1 4 2 3 2 6 1 1 4 1 4
Play ⓘ
Anton Webern :Variations for piano , mov. II, op. 27[ 35]
1936
6-1
6-1
all- combinatorial
I:
0 e 3 1 4 2 8 7 6 t 9 5
P:
0 1 9 e t 7 8 3 4 6 5 2
1 4 2 1 3 1 5 1 2 1 3
Igor Stravinsky :A Sermon, a Narrative and a Prayer [ 2]
1961
6-2
6-2
—
I:
0 e 3 1 2 5 4 9 8 6 7 t
P:
0 1 t 2 6 4 5 3 7 e 8 9
1 3 4 4 2 1 2 4 4 3 1
Luigi Dallapiccola :Dialoghi [ 36]
6-21
6-21
RI-invariant: P0 = RI9
I:
0 e 2 t 6 8 7 9 5 1 4 3
P:
0 1 t 3 4 6 8 9 e 5 7 2
1 3 5 1 2 2 1 2 6 2 5
Chen Yi :Near Distance [ 3] [ 37]
1988
6-Z23
6-Z45
—
I:
0 e 2 9 8 6 4 3 1 7 5 t
P:
0 1 e 2 t 3 9 4 8 5 7 6
1 2 3 4 5 6 5 4 3 2 1
Play ⓘ
Luigi Nono :Canti per tredeci Il canto sospeso [ 15] [ 39] Composizione per orchestra n. 2: Diario polacco ’58
1955 1955–56 1959
6-1
6-1
symmetrical all-interval row ; all- combinatorial
I:
0 e 1 t 2 9 3 8 4 7 5 6
Play ⓘ
Nicolas Slonimsky : Grandmother chord[ 40]
1938
P:
0 2 1 3 8 7 5 6 4 e 9 t
2 1 2 5 1 2 1 2 5 2 1
Joonas Kokkonen : Symphonic Sketches, mov. 3, row A[ 41]
1968
6-Z38
6-Z6
—
I:
0 t e 9 4 5 7 6 8 1 3 2
P:
0 2 1 3 4 6 7 9 8 t 5 e
2 1 2 1 2 1 2 1 2 5 6
Igor Stravinsky :Agon , second coda[ 43]
1957
6-2
6-2
—
I:
0 t e 9 8 6 5 3 4 2 7 1
Igor Stravinsky : coda[ 44]
P:
0 2 1 3 4 6 7 9 8 t 5 e
2 1 2 1 2 1 2 1 2 5 6
Igor Stravinsky :The Flood [ 2]
1962
6-Z12
6-Z41
—
I:
0 t e 5 2 4 3 1 9 8 6 7
P:
0 2 1 3 4 6 7 9 8 t 5 e
2 1 2 1 2 1 2 1 2 5 6
Luigi Dallapiccola :Requiescant [ 36]
6-5
6-5
RI-invariant: P0 = RI5
I:
0 t e 5 1 4 3 6 2 8 9 7
P:
0 2 1 3 4 6 7 9 8 t 5 e
2 1 2 1 2 1 2 1 2 5 6
Alfred Schnittke : String Quartet No. 1[ 3]
1966
6-1
6-1
all- combinatorial
I:
0 t e 2 9 1 7 3 8 5 4 6
P:
0 2 3 1 4 5 6 7 8 9 e t
2 1 2 3 1 1 1 1 1 2 1
Alban Berg :Lulu , Schigolch[ 24] [ 45]
1934
6-1
6-1
all- combinatorial , derived: 4–1
I:
0 t 9 e 8 7 6 5 4 3 1 2
P:
0 2 3 5 4 9 7 8 t e 1 6
2 1 2 1 5 2 1 2 1 2 5
Igor Stravinsky :Agon , "Bransles"[ 44]
1957
6-Z40
6-Z11
—
I:
0 t 9 7 8 3 5 4 2 1 e 6
P:
0 2 3 5 7 8 e 4 6 t 8 1
2 1 2 2 1 3 5 2 4 2 5
Play ⓘ
Alban Berg : "Der Wein "[ 46]
1929
6-16
6-16
D harmonic minor & in the inverted row-form added-sixth chord with both major and minor third
I:
0 t 9 7 5 4 1 8 6 2 4 e
P:
0 2 3 6 8 t 5 7 9 e 1 4
2 1 3 2 2 5 2 2 2 2 3
Ernst Krenek :Lamentatio Jeremiae Prophetae , Op. 93, row 2[ 18]
1940–41
6-34
6-34
RI- symmetry
I:
0 t 9 6 4 2 7 5 3 1 e 8
P:
0 2 4 5 8 t 6 7 9 e 1 3
2 2 1 3 2 4 1 2 2 2 2
Ernst Krenek :Lamentatio Jeremiae Prophetae , Op. 93, row 1[ 18]
1940–41
6-34
6-34
RI- symmetry
I:
0 t 8 7 4 2 6 5 3 1 e 9
P:
0 2 4 6 7 t 5 8 9 e 1 3
2 2 2 1 3 5 3 1 2 2 2
Ernst Krenek :Lamentatio Jeremiae Prophetae , Op. 93, row 6[ 18]
1940–41
6-34
6-34
RI- symmetry
I:
0 t 8 6 5 2 7 4 3 1 e 9
P:
0 2 4 6 8 9 5 7 t e 1 3
2 2 2 2 1 4 2 3 1 2 2
Ernst Krenek :Lamentatio Jeremiae Prophetae , Op. 93, row 5[ 18]
1940–41
6-34
6-34
RI- symmetry
I:
0 t 8 6 4 3 7 5 2 1 e 9
P:
0 2 4 6 t 8 e 7 9 1 3 5
2 2 2 4 2 3 4 2 4 2 2
Alban Berg :Lulu [ 24]
1934
6-35
6-35
—
I:
0 t 8 6 2 4 1 5 3 e 9 7
P:
0 2 5 3 t 4 6 1 e 7 8 9
2 3 2 5 6 2 5 2 4 1 1
Igor Stravinsky :Variations [ 47] [ 2] [ 3] [ 48] [ 49] [ 50] [ 51]
1963–64
6-9
6-9
—
I:
0 t 7 9 2 8 6 e 1 5 4 3
P:
0 2 6 4 t 9 7 e 8 5 1 3
2 4 2 6 1 2 4 3 3 4 2
Arnold Schoenberg : Piano Piece [Klavierstück], op. 33b[ 24]
1931
6-34
6-34
—
I:
0 t 6 8 2 3 5 1 4 7 e 9
P:
0 2 6 t 4 7 8 3 5 9 e 1
2 4 4 6 3 1 5 2 4 2 2
Play ⓘ
Alban Berg :Lulu , Schoolboy[ 45] [ 53] [ 54]
1934
6-34
6-34
—
I:
0 t 6 2 8 5 4 9 7 3 1 e
P:
0 2 9 e 8 6 5 7 t 1 4 3
2 5 2 3 2 1 2 3 3 3 1
Igor Stravinsky :The Owl and the Pussy Cat [ 2]
1966
6-Z23
6-Z45
—
I:
0 t 3 1 4 6 7 5 2 e 8 9
P:
0 7 6 5 8 9 4 3 t e 2 1
5 1 1 3 1 5 1 5 1 3 1
Karel Goeyvaerts :Nummer 2 [ 55]
1951
6-Z36
6-Z3
—
I:
0 5 6 7 4 3 8 9 2 1 t e
P:
0 2 t e 1 8 6 7 9 4 3 5
2 4 1 2 5 2 1 2 5 1 2
Play P ⓘ
Igor Stravinsky :Requiem Canticles , 1st series[ 2]
1966
6-2
6-2
—
I:
0 t 2 1 e 4 6 5 3 8 9 7
P:
0 2 e 9 t 1 3 6 4 5 7 8
2 3 2 1 3 2 3 2 1 2 1
Joonas Kokkonen : Woodwind Quintet, mov. 1 & 2, row A & B[ 41]
1973
6-1
6-1
all- combinatorial
I:
0 t 1 3 2 e 9 6 8 7 5 4
P:
0 2 e 9 t 4 3 7 5 6 8 1
2 3 2 1 6 1 4 2 1 2 5
Arnold Schoenberg : Dreimal Tausend Jahre, Op. 50a[ 3]
1949
6-9
6-9
—
I:
0 t 1 3 2 8 9 5 7 6 4 e
P:
0 3 1 2 4 7 5 6 8 e 9 t
3 2 1 2 3 2 1 2 3 2 1
Arvo Pärt : Symphony No. 2[ 56]
1966
6-Z36
6-Z3
derived: 4–1
I:
0 9 e t 8 5 7 6 4 1 3 2
P:
0 3 1 2 e t 8 9 5 7 6 4
3 2 1 3 1 2 1 4 2 1 2
Milton Babbitt : Woodwind Quartet
1953
6-1
6-1
—
I:
0 9 e t 1 2 4 3 7 5 6 8
P:
0 3 1 6 2 4 t 5 9 7 8 e
3 2 5 4 2 6 5 4 2 1 3
Ernst Krenek :Sechs Vermessene , Op. 168
1958
6-2
6-2
—
I:
0 9 e 6 t 8 2 7 3 5 4 1
P:
0 3 1 6 2 t 9 8 e 7 5 4
3 2 5 4 4 1 1 3 4 2 1
Ernst Krenek :Karl V [ 59] [ 60]
1938
6-Z39
6-Z10
—
I:
0 9 e 6 t 2 3 4 1 5 7 8
P:
0 3 1 t 2 8 e 5 6 9 7 4
3 2 3 4 6 3 6 1 3 2 3
Donald Martino :Fantasy Variations [ 61]
1962
6-9
6-9
—
I:
0 9 e 2 t 4 1 7 6 3 5 8
P:
0 3 2 1 4 8 e 5 t 7 6 9
3 1 1 3 4 3 6 5 3 1 3
Benjamin Frankel :The Curse of the Werewolf [ 62]
1961
6-Z37
6-Z4
—
I:
0 9 t e 8 4 1 7 2 5 6 3
P:
0 3 2 9 7 8 e 6 1 5 4 t
3 1 5 2 1 3 5 5 4 1 6
Karlheinz Stockhausen : "Aries", from Tierkreis [ 63]
1974–75
6-18
6-18
—
I:
0 9 t 3 5 4 1 6 e 7 8 2
P:
0 3 2 1 5 4 t e 7 8 9 6
3 1 1 4 1 6 1 4 1 1 3
Anton Webern : Symphony, Op. 21[ 4] [ 64]
1928
6-1
6-1
all- combinatorial
I:
0 9 t e 7 8 2 1 5 4 3 6
P:
0 3 4 6 e 8 7 t 9 5 1 2
3 1 2 5 3 1 3 1 4 4 1
Igor Stravinsky :Agon , "Mystery" (sketches only)
1957
6-31
6-31
—
I:
0 9 8 6 1 4 5 2 3 7 e t
P:
0 3 5 1 2 6 4 e 7 8 e 9
3 2 4 1 4 2 5 4 1 3 2
Karlheinz Stockhausen :Klavierstück IV (second row of 48)[ 66]
1952
6-Z3
6-Z36
—
I:
0 9 7 e t 6 8 1 5 4 1 3
P:
0 3 5 4 e t 9 8 7 6 2 1
3 2 1 5 1 1 1 1 1 4 1
Karlheinz Stockhausen : "Aquarius", from Tierkreis [ 63]
1974–75
6-Z6
6-Z38
—
I:
0 9 7 8 1 2 3 4 5 6 t e
P:
0 3 5 7 9 e 6 8 t 1 2 4
3 2 2 2 2 5 2 2 3 1 2
Ernst Krenek :Lamentatio Jeremiae Prophetae , Op. 93, row 4[ 18]
1940–41
6-34
6-34
RI- symmetry
I:
0 9 7 5 3 1 6 4 2 e t 8
P:
0 3 7 e 2 5 9 1 4 6 8 t
3 4 4 3 3 4 4 3 2 2 2
Play ⓘ
Alban Berg :Violin Concerto [ 4] [ 24] [ 67]
1935
6-Z24
6-Z46
—
I:
0 9 5 1 t 7 3 e 8 6 4 2
P:
0 3 e 2 t 1 9 5 8 4 7 6
3 4 3 4 3 4 4 3 4 3 1
Anton Webern : "Erlösung" from Drei Lieder , Op. 18, No. 2[ 68]
1910–13
6-1
6-1
all- combinatorial
I:
0 9 1 t 2 e 3 7 4 8 5 6
P:
0 3 e 4 2 1 7 8 t 5 9 6
3 4 5 2 1 6 1 2 5 4 3
Ernst Krenek :Quaestio temporis , Op. 170
1959
6-1
6-1
all- combinatorial retrograde- symmetry
I:
0 9 1 8 t e 5 4 2 7 3 6
P:
0 3 e t 2 9 1 5 4 8 7 6
3 4 1 4 5 4 4 1 4 1 1
Anton Webern : Op. 31[ 12]
1941–43
6-Z3
6-Z36
—
I:
0 9 1 2 t 3 e 7 8 4 5 6
P:
0 4 1 8 5 9 3 e 2 7 t 6
4 3 5 3 4 6 4 3 5 3 4
Milton Babbitt :Composition for Four Instruments , row iv[ 26]
1948
6–20
6–20
all- combinatorial hexachord
I:
0 8 e 4 7 3 9 1 t 5 2 6
P:
0 4 1 e 3 2 8 6 5 t 7 9
4 3 2 4 1 6 2 1 5 3 2
Milton Babbitt :Composition for Four Instruments [ 70]
1948
6–1
6–1
all- combinatorial hexachord
I:
0 8 e 1 9 t 4 6 7 2 5 3
P:
0 4 2 5 7 8 t 9 e 1 6 3
4 2 3 2 1 2 1 2 2 5 3
Igor Stravinsky :Anthem [ 2]
1962
6–33
6–33
—
I:
0 8 t 7 5 4 2 3 1 e 6 9
P:
0 4 3 2 5 6 t e 9 1 7 8
4 1 1 3 1 4 1 2 4 6 1
Karlheinz Stockhausen :Licht , Eve formula[ 71] [ 72]
1977– 2003
6–2
6–2
—
I:
0 8 9 t 7 6 2 1 3 e 5 4
P:
0 4 3 7 e 8 9 6 5 1 2 t
4 1 4 4 3 1 3 1 4 1 4
Arnold Schoenberg :Ode to Napoleon Buonaparte Suite Op. 29[ 73]
Luigi Nono :Variazioni canoniche sulla serie dell'op. 41 di Arnold Schönberg [ 74]
1942 1926
1950
6–20
6–20
all- combinatorial
I:
0 8 9 5 1 4 3 6 7 e t 2
P:
0 4 3 8 7 e 5 1 2 9 t 6
4 1 5 1 4 6 4 1 5 1 4
Milton Babbitt :Composition for Four Instruments , row iii[ 26]
1948
6–20
6–20
all- combinatorial hexachord
I:
0 8 9 4 5 1 7 e t 3 2 6
P:
0 4 3 e 7 8 t 9 2 5 1 6
4 1 4 4 1 2 1 5 3 4 5
Karlheinz Stockhausen : "Scorpio", from Tierkreis [ 63]
1974–75
6–20
6–20
—
I:
0 8 9 1 5 4 2 3 t 7 e 6
P:
0 4 3 e t 9 1 7 8 6 2 5
4 1 4 1 1 4 6 1 2 4 3
Ernst Krenek : Suite, Op. 84 for solo cello[ 75]
6–5
6–5
—
I:
0 8 9 1 2 3 e 5 4 6 t 7
P:
0 4 5 2 6 7 8 9 e t 3 1
4 1 3 4 1 1 1 2 1 5 2
Alban Berg :Lulu [ 24]
1934
6–9
6–9
—
I:
0 8 7 t 6 5 4 3 1 2 9 e
P:
0 4 5 2 7 9 6 8 e t 3 1
4 1 3 5 2 3 2 3 1 5 2
Play ⓘ
Alban Berg :Lulu , Basic[ 45] [ 53] [ 54]
1934
6–32
6–32
circle of fifths
I:
0 8 7 t 5 3 6 4 1 2 9 e
P:
0 4 5 e 6 t 7 3 1 2 9 8
4 1 6 5 4 3 4 2 1 5 1
Milton Babbitt :All Set [ 76] [ 77]
1957
6–7
6–7
second-order all- combinatorial hexachord
I:
0 8 7 1 6 2 5 9 e t 3 4
P:
0 4 5 t 7 6 1 8 e 2 9 3
4 1 5 3 1 5 5 3 3 5 6
Karlheinz Stockhausen : "Gemini", from Tierkreis [ 63]
1974–75
6-Z41
6-Z12
—
I:
0 8 7 2 5 6 e 4 1 t 3 9
P:
0 4 8 9 3 2 t e 7 6 5 1
4 4 1 6 1 4 1 4 1 1 4
Robert Moevs :Three Symphonic Pieces , mov. 2[ 78]
1954–55
6-Z17
6-Z43
all-trichord hexachord
I:
0 8 4 3 9 t 2 1 5 6 7 e
P:
0 4 t 6 3 8 7 2 5 9 1 e
4 6 4 3 5 1 5 3 4 4 2
Juan Carlos Paz :Canciones y Baladas , Balada II[ 79]
1936
6–34
6–34
—
I:
0 8 2 6 9 4 5 t 7 3 e 1
P:
0 5 1 2 3 9 8 t 4 e 6 7
5 4 1 1 6 1 2 6 5 5 1
Alban Berg :Lulu , Chorale[ 45]
1934
6-Z39
6-Z10
—
I:
0 7 e t 9 3 4 2 8 1 6 5
P:
0 5 1 4 2 3 9 8 t 7 e 6
5 4 3 2 1 6 1 2 3 4 5
Michael Gielen : Six Songs, for bass, violin, viola, clarinet, bass clarinet, and piano[ 80]
1958
6–1
6–1
retrograde-symmetrical all-interval row , all- combinatorial hexachords
I:
0 7 e 8 t 9 3 4 2 5 1 6
P:
0 5 1 4 t 8 e 9 3 6 2 7
5 4 3 6 2 3 2 6 3 4 5
Alfred Schnittke : Concerto Grosso No. 3[ 3]
1985
6–31
6–31
—
I:
0 7 e 8 2 4 1 3 9 6 t 5
P:
0 5 2 7 4 9 6 e 8 1 t 3
5 3 5 3 5 3 5 3 5 3 5
Benjamin Britten :The Turn of the Screw [ 81]
1954
6–32
6–32
—
I:
0 7 t 5 8 3 6 1 4 e 2 9
P:
0 5 2 7 t 1 e 4 6 8 9 3
5 3 5 3 3 2 5 2 2 1 6
Dmitri Shostakovich :Symphony No. 14 , mov. III[ 82]
1969
6-Z47
6-Z25
—
I:
0 7 t 5 2 e 1 8 6 4 3 9
P:
0 5 2 t 1 7 8 6 e 4 9 3
5 3 4 3 6 1 2 5 5 5 6
Alban Berg :Lulu , Countess Geschwitz[ 24] [ 45] [ 54]
1934
6-Z47
6-Z25
—
I:
0 7 t 2 e 5 4 6 1 8 3 9
P:
0 5 4 7 t 6 e 8 1 9 2 3
5 1 3 3 4 5 3 5 4 5 1
Igor Stravinsky :Threni [ 2]
1958
6-Z41
6-Z12
—
I:
0 7 8 5 2 6 1 4 e 3 t 9
P:
0 5 7 4 2 3 9 1 8 e t 6
5 2 3 2 1 6 4 5 3 1 4
Milton Babbitt :Three Compositions for Piano , no. I[ 83]
1947
6–8
6–8
—
I:
0 7 5 8 t 9 3 e 4 1 2 6
P:
0 5 7 6 e 3 4 2 9 8 t 1
5 2 1 5 4 1 2 5 1 2 3
Alban Berg :Lulu , Acrobat/Athlete[ 24] [ 45] [ 54]
1934
6-Z17
6-Z43
all-trichord hexachord
I:
0 7 5 6 1 9 8 t 3 4 2 e
P:
0 5 9 t 4 7 6 e 1 2 8 3
5 4 1 6 3 1 5 2 1 6 5
Play ⓘ
Alban Berg :Lulu , Dr. Schön[ 45] [ 53] [ 54]
1934
6-Z25
6-Z47
—
I:
0 7 3 2 8 5 6 1 e t 4 9
P:
0 5 e 6 3 2 8 7 9 t 4 1
5 6 5 3 1 6 1 2 1 6 3
Karlheinz Stockhausen : "Leo", from Tierkreis [ 63]
1974–75
6Z-13
6-Z42
—
I:
0 7 1 6 9 t 4 5 3 2 8 e
P:
0 6 4 2 8 9 3 1 e t 7 5
6 2 2 6 1 6 2 2 1 3 2
Igor Stravinsky :Elegy for J.F.K. [ 2]
1964
6–34
6–34
—
I:
0 6 8 t 4 3 9 e 1 2 5 7
P:
0 6 4 3 2 9 t 5 7 8 e 1
6 2 1 1 5 1 5 2 1 3 2
Karel Husa :Mosaïques [ 84]
1960
6-Z45
6-Z23
—
I:
0 6 8 9 t 3 2 7 5 4 1 e
P:
0 6 5 1 e 7 4 8 9 3 2 t
6 1 4 2 4 3 4 1 6 1 4
Arnold Schoenberg : "De Profundis", Op. 50b[ 3]
1950
6–7
6–7
—
I:
0 6 7 e 1 5 8 4 3 9 t 2
P:
0 6 5 2 3 4 7 8 9 t e 1
6 1 3 1 1 3 1 1 1 1 2
Karlheinz Stockhausen : "Sagittarius", from Tierkreis [ 63]
1974–75
6–2
6–2
—
I:
0 6 7 t 9 8 5 4 3 2 1 e
P:
0 6 5 e t 4 3 9 8 2 1 7
6 1 6 1 6 1 6 1 6 1 6
Witold Lutosławski :Musique funèbre (Funeral Music)[ 85]
1954–58
6–7
6–7
—
I:
0 6 7 1 2 8 9 3 4 t e 5
P:
0 6 7 8 9 1 2 5 e 4 t 3
6 1 1 1 4 1 3 6 5 6 5
Wolfgang Amadeus Mozart :String Quartet in E♭ major, K. 428 first movement, opening of development section[ 86]
6–5
6–5
—
I:
0 6 5 4 3 e t 7 1 8 2 9
P:
0 6 8 5 7 e 4 3 9 t 1 2
6 2 3 2 4 5 1 6 1 3 1
Play ⓘ
Arnold Schoenberg :Variations , Op. 31[ 79] [ 87]
1926–28
6–5
6–5
Bach motif
I:
0 6 4 7 5 1 8 9 3 2 e t
P:
0 6 8 t 2 4 9 5 3 e 7 1
6 2 2 4 2 5 4 2 4 4 6
Arnold Schoenberg : Three Songs, Op. 48[ 64]
1933
6–35
6–35
—
I:
0 6 4 2 t 8 3 7 9 1 5 e
P:
0 6 9 2 8 t 4 7 1 e 3 5
6 3 5 6 2 6 3 6 2 4 2
Josef Matthias Hauer :Salambo , op. 60[ 89]
1929
6-21
6-21
—
I:
0 6 3 t 4 2 8 5 e 1 9 7
P:
0 6 t 7 9 8 3 2 4 1 5 e
6 4 3 2 1 5 1 2 3 4 6
Michel Fano : Sonata for Two Pianos[ 90]
1951
6-Z3
6-Z36
retrograde- symmetry
I:
0 6 2 5 3 4 9 t 8 e 7 1
P:
0 6 t 8 4 7 2 5 1 e 3 9
6 4 2 4 3 5 3 4 2 4 6
Ben Johnston : String Quartet No. 7, mov. 2[ 91]
1984
6–21
6–21
just intonation : otonality & utonality
I:
0 6 2 4 8 5 t 7 e 1 9 3
P:
0 7 1 t e 9 5 8 4 3 2 6
5 6 3 1 2 4 3 4 1 1 4
Karlheinz Stockhausen :Klavierstück IV (third row of 48)[ 66]
1952
6–2
6–2
—
I:
0 5 e 2 1 3 7 4 8 9 t 6
P:
0 7 2 1 e 8 3 5 9 t 4 6
5 5 1 2 3 5 2 4 1 6 2
Play ⓘ
Arnold Schoenberg : Piano Piece, op. 33a[ 24] [ 92]
1928
6–5
6–5
—
I:
0 5 t e 1 4 9 7 3 2 8 6
P:
0 7 3 t 2 6 9 1 4 8 e 5
5 4 5 4 4 3 4 3 4 3 6
Alberto Ginastera : Quintet, op. 29[ 28]
1963
6–31
6–31
—
I:
0 5 9 2 t 6 3 e 8 4 1 7
P:
0 7 4 e 6 t 3 9 1 8 5 2
5 3 5 5 4 5 6 4 5 3 3
Elliott Carter : Piano Concerto, Orchestra[ 93]
1964–65
6-Z43
6-Z17
all-trichord hexachord ; ordered in register
I:
0 5 8 1 6 2 9 3 e 4 7 t
P:
0 7 6 4 5 9 8 t 3 1 e 2
5 1 2 1 4 1 2 5 2 2 3
Igor Stravinsky :Requiem Canticles , 2nd series[ 2]
1966
6-Z40
6-Z11
—
I:
0 5 6 8 7 3 4 2 9 e 1 t
P:
0 7 6 e 9 1 4 t 8 5 2 3
5 1 5 2 4 3 6 2 3 3 1
Ernst Krenek : String Quartet No. 7, op. 96[ 59]
1943–44
6-Z12
6-Z41
—
I:
0 5 6 1 3 e 8 2 4 7 t 9
P:
0 7 e 2 1 9 3 5 t 6 8 4
5 4 3 1 4 6 2 5 4 2 4
Arnold Schoenberg :Piano Concerto , Op. 42[ 94] [ 95]
1942
6–9
6–9
inversional
I:
0 5 1 t e 3 9 7 2 6 4 8
P:
0 7 e 8 2 t 6 9 5 4 1 3
5 4 3 6 4 4 3 4 1 3 2
Anton Webern : Op. 23[ 96]
1933
6-Z10
6-Z39
—
I:
0 5 1 4 t 2 6 3 7 8 e 9
P:
0 7 e t 2 9 6 1 5 4 8 3
5 4 1 4 5 3 5 4 1 4 5
Ross Lee Finney :Edge of Shadow [ 21]
1959
6–8
6–8
—
I:
0 5 1 2 t 3 6 e 7 8 4 9
P:
0 7 e t 9 8 3 6 4 1 5 2
5 4 1 1 1 5 3 2 3 4 3
Karlheinz Stockhausen : "Cancer", from Tierkreis [ 63]
1974–75
6–1
6–1
all- combinatorial
I:
0 5 1 2 3 4 9 6 8 e 7 t
P:
0 8 1 7 2 e 9 6 4 5 3 t
4 5 6 5 3 2 3 2 1 2 5
Arnold Schoenberg : String Trio, Op. 45[ 97]
1946
6–5
6–5
—
I:
0 4 e 5 t 1 3 6 8 7 9 2
P:
0 8 1 t 9 e 5 3 4 7 2 6 [ 98] [ 99]
4 5 3 1 2 6 2 1 3 5 4
Play ⓘ
Karlheinz Stockhausen :Klavierstück VII Gruppen Klavierstück IX Klavierstück X
1955 1955–57 1961 1961
6–1
6–1
all- combinatorial hexachord, retrograde-symmetrical all-interval
I:
0 4 e 2 3 1 7 9 8 5 t 6
P:
0 8 1 e t 7 5 9 4 6 3 2
4 5 2 1 3 2 4 5 2 3 1
Karlheinz Stockhausen :Klavierstück V (row of original 1954 version)[ 100] Klavierstück VIII [ 101]
1954–55 1954
6-Z3
6-Z36
—
I:
0 4 e 1 2 5 7 3 8 6 9 t
P:
0 8 4 9 t 3 1 6 e 2 7 5
4 4 5 1 5 2 5 5 3 5 2
Elliott Carter : Piano Concerto, Solo[ist][ 93]
1964–65
6-Z17
6-Z43
all-interval hexachord ; ordered in register
I:
0 4 8 3 2 9 e 6 1 t 5 7
P:
0 8 5 t 7 1 6 4 e 2 3 9
4 3 5 3 6 5 2 5 3 1 6
Play ⓘ
Alban Berg :Lulu , Alwa[ 45] [ 53] [ 54]
1934
6-Z25
6-Z47
—
I:
0 4 7 2 5 e 6 8 1 t 9 3
P:
0 8 7 t 4 5 2 9 e 3 1 6
4 1 3 6 1 3 5 2 4 2 5
Elliott Carter :A Symphony of Three Orchestras [ 93]
1976
6-Z24
6-Z46
ordered in register
I:
0 4 5 2 8 7 t 3 1 9 e 6
P:
0 8 7 e t 9 3 1 4 2 6 5
4 1 4 1 1 6 2 3 2 4 1
Play ⓘ
Anton Webern :Variations for piano , mov. III, op. 27[ 102] [ 103]
1936
6–1
6–1
all- combinatorial
I:
0 4 5 1 2 3 9 e 8 t 6 7
P:
0 8 e t 2 1 4 3 7 6 9 5
4 3 1 4 1 3 1 4 1 3 4
Anton Webern : Op. 29[ 104] [ 36]
1938
6–2
6–2
semi- combinatorial , RI-invariant: P0 = RI5
I:
0 4 1 2 t e 8 9 5 6 3 7
P:
0 8 e t 4 6 7 1 5 3 9 2
4 3 1 6 2 1 6 4 2 6 5
Ernst Krenek :Sestina , op. 161[ 59]
1957
6–22
6–22
—
I:
0 4 1 2 8 6 5 e 7 9 3 t
P:
0 9 1 3 4 e 2 8 7 5 t 6
3 4 2 1 5 3 6 1 2 5 4
Luigi Dallapiccola :Piccola musica notturna
1954
6–8
6–8
—
I:
0 3 e 9 8 1 t 4 5 7 2 6
P:
0 9 1 8 4 5 7 2 3 6 t e
3 4 5 4 1 2 5 1 3 4 1
Milton Babbitt :Composition for Synthesizer [ 106]
1961
6–20
6–20
—
I:
0 3 e 4 8 7 5 t 9 6 2 1
P:
0 9 1 e t 2 8 7 5 4 6 3
3 4 2 1 4 6 1 2 1 2 3
Play ⓘ
Milton Babbitt :Composition for Four Instruments [ 107] [ 108]
1948
6–1
6–1
all- combinatorial
I:
0 3 e 1 2 t 4 5 7 8 6 9
P:
0 9 2 3 e t 5 4 1 6 7 8
3 5 1 4 1 5 1 3 5 1 1
Igor Stravinsky :Epitaphium [ 2]
1959
6-Z3
6-Z36
—
I:
0 3 t 9 1 2 7 8 e 6 5 4
P:
0 9 2 8 7 5 6 1 3 4 t e
3 5 6 1 2 1 5 2 1 6 1
Karlheinz Stockhausen : "Capricorn", from Tierkreis [ 63]
1974–75
6-Z47
6-Z25
—
I:
0 3 t 4 5 7 6 e 9 8 2 1
P:
0 9 8 4 7 6 1 t 3 5 e 2
3 1 4 3 1 5 3 5 2 6 3
David Dzubay: Di/Con[ver(gence/sions)] [ 3]
1988
6-Z39
6-Z10
—
I:
0 3 4 8 5 6 e 2 9 7 1 t
P:
0 9 8 e t 2 3 4 5 7 1 6
3 1 3 1 4 1 1 1 2 6 5
Anton Webern : Op. 22[ 109]
1929–30
6–2
6–2
semi- combinatorial
I:
0 3 4 1 2 t 9 8 7 5 e 6
P:
0 9 e 2 4 1 7 t 8 5 3 6
3 2 3 2 3 6 3 2 3 2 3
Milton Babbitt :Composition for Four Instruments , row ii[ 26]
1948
6–8
6–8
—
I:
0 3 1 t 8 e 5 2 4 7 9 6
P:
0 t 1 2 5 4 6 3 7 e 8 9
2 3 1 3 1 2 3 4 4 3 1
Pierre Boulez :Le marteau sans maître [ 3] [ 110]
1953–55
6-Z10
6-Z39
—
I:
0 2 e t 7 8 6 9 5 1 4 3
P:
0 t 3 4 2 7 6 9 8 e 1 5
2 5 1 2 5 1 3 1 3 2 4
Charles Ives :Tone Roads No. 1 [ 111]
1911
6-Z46
6-Z24
—
I:
0 2 9 8 t 5 6 3 4 1 e 7
P:
0 t 3 e 8 7 1 2 5 9 4 6
2 5 4 3 1 6 1 3 4 5 2
Elliott Carter :Night Fantasies [ 112]
1982
6–14
6–14
—
I:
0 2 9 1 4 5 e t 7 3 8 6
P:
0 t 9 8 7 5 e 1 2 3 4 6
2 1 1 1 2 6 2 1 1 1 2
Milton Babbitt :Composition for Four Instruments , row i[ 26]
1948
6–8
6–8
—
I:
0 2 3 4 5 7 1 e t 9 8 6
P:
0 t 9 e 7 2 8 1 4 6 5 3
2 1 2 4 5 6 5 3 2 1 2
Karlheinz Stockhausen :Kreuzspiel [ 113]
1951
6-Z50
6-Z29
—
I:
0 2 3 1 5 t 4 e 8 6 7 9
P:
0 e 1 2 9 8 t 7 5 6 4 3
1 2 1 5 1 2 3 2 1 2 1
Igor Stravinsky :Agon , "Double Pas de Quatre"[ 2] [ 114]
1957
6-Z3
6-Z36
—
I:
0 1 e t 3 4 2 5 7 6 8 9
P:
0 e 1 3 4 2 5 7 6 8 t 9
1 2 2 1 2 3 2 1 2 2 1
Igor Stravinsky :Fanfare [ 2]
1964
6–1
6–1
all- combinatorial
I:
0 1 e 9 8 t 7 5 6 4 2 3
P:
0 e 1 3 4 2 7 6 9 5 8 t
1 2 2 1 2 5 1 3 4 3 2
Igor Stravinsky :Canticum Sacrum , II & IV[ 2]
1955
6–1
6–1
all- combinatorial
I:
0 1 e 9 8 t 5 6 3 7 4 2
P:
0 e 1 7 9 8 t 4 6 5 2 3
1 2 6 2 1 2 6 2 1 3 1
Chen Yi : Woodwind Quintet[ 3] [ 37]
1987
6-Z4
6-Z37
—
I:
0 1 e 5 3 4 2 8 6 7 t 9
P:
0 e 2 1 3 4 9 t 7 8 6 5
1 3 1 2 1 5 1 3 1 2 1
Arvo Pärt :Diagrams [ 56]
1964
6–1
6–1
all- combinatorial
I:
0 1 t e 9 8 3 2 5 4 6 7
P:
0 e 2 1 5 6 3 4 8 7 t 9
1 3 1 4 1 3 1 4 1 3 1
Play ⓘ
Anton Webern :String Quartet , Op. 28:[ 104] [ 67] [ 102]
1936
6–5
6–5
derived: 4–1 (BACH motif ), semi- combinatorial
I:
0 1 t e 7 6 9 8 4 5 2 3
P:
0 e 2 3 4 1 6 5 8 9 t 7
1 3 1 1 3 5 1 3 1 1 3
Alberto Ginastera : Violin Concerto, op. 30[ 28]
1963
6–1
6–1
all- combinatorial
I:
0 1 t 9 8 e 6 7 4 3 2 5
P:
0 e 2 9 5 3 4 8 t 7 1 6
1 3 5 4 2 1 4 2 3 6 5
Elliott Carter : String Quartet No. 3[ 115]
1973
6-Z23
6-Z45
—
I:
0 1 t 3 7 9 8 4 2 5 e 6
P:
0 e 3 1 7 9 6 2 t 5 8 4
1 4 2 6 2 3 4 4 5 3 4
Arnold Schoenberg : Violin Phantasy, Op. 47[ 116] [ 117]
1949
6–21
6–21
—
I:
0 1 9 e 5 3 6 t 2 7 4 8
P:
0 e 3 2 1 8 6 9 t 7 5 4
1 4 1 1 5 2 3 1 3 2 1
Igor Stravinsky :Double Canon [ 2]
1959
6-Z36
6-Z3
—
I:
0 1 9 t e 4 6 3 2 5 7 8
P:
0 e 3 4 8 7 9 5 6 1 2 t
1 4 1 4 1 2 4 1 5 1 4
Play ⓘ
Anton Webern :Concerto for Nine Instruments , Op. 24[ 24] [ 68] [ 87] [ 92] [ 118]
1934
6–20
6–20
all- combinatorial , derived: 3–3
I:
0 1 9 8 4 5 3 7 6 e t 2
P:
0 e 4 5 7 3 2 6 8 1 t 9
1 5 1 2 4 1 4 2 5 3 1
David Lewin :Just a Minute, Roger [ 119]
1978
6–16
6–16
—
I:
0 1 8 7 5 9 t 6 4 e 2 3
P:
0 e 5 2 1 6 3 8 7 4 t 9
1 6 3 1 5 3 5 1 3 6 1
Alfred Schnittke : Viola Concerto[ 3]
1985
6–5
6–5
—
I:
0 1 7 t e 6 9 4 5 8 2 3
P:
0 e 5 9 6 2 7 3 1 4 t 9
1 6 4 3 4 5 4 2 3 6 1
Luigi Dallapiccola :Cinque Canti [ 36]
6-Z50
6-Z29
RI-invariant: P0 = RI9
I:
0 1 7 3 6 t 5 9 e 8 2 3
P:
0 e 6 5 4 3 1 t 9 7 2 8
1 5 1 1 1 2 3 1 2 5 6
Pierre Boulez :Structures Ia[ 3] [ 67]
1952
6–5
6–5
—
I:
0 1 6 7 8 9 e 2 3 5 t 4
P:
0 e 6 5 7 1 8 2 t 3 4 9
1 5 1 2 6 5 6 4 5 1 5
George Perle :Three Inventions for Piano , no. 3[ 120]
6–7
6–7
all- combinatorial
I:
0 1 6 7 5 e 4 t 2 9 8 3
P:
0 e 7 1 2 9 3 8 t 4 5 6
1 4 6 1 5 6 5 2 6 1 1
Play ⓘ
Alban Berg :Lyric Suite , mov. III[ 121]
1925–26
6–9
6–9
—
I:
0 1 5 e t 3 9 4 2 8 7 6
P:
0 e 7 1 4 8 3 9 t 2 5 6
1 4 6 3 4 5 6 1 4 3 1
Play ⓘ
Alban Berg :Lyric Suite , mov. VI, row 1[ 122]
1925–26
6-Z44
6-Z19
—
I:
0 1 5 e 8 4 9 3 2 t 7 6
P:
0 e 7 4 2 9 3 8 t 1 5 6
1 4 3 2 5 6 5 2 3 4 1
Play ⓘ
Fritz Heinrich Klein
Alban Berg :Lyric Suite , mov. I[ 46] [ 124]
Alberto Ginastera : Sonata for Guitar, mvt. III, op. 47[ 28]
1920– 22[ 125]
1925–26
1976
6–32
6–32
Mother chord (all-interval ) Trichordally combinatorial: 0369[ 126]
I:
0 1 5 8 t 3 9 4 2 e 7 6
P:
0 e 7 8 3 1 2 t 6 5 4 9
1 4 1 5 2 1 4 4 1 1 5
Arnold Schoenberg :String quartet No. 4 [ 64] [ 116]
1936
6–16
6–16
—
I:
0 1 5 4 9 e t 2 6 7 8 3
P:
0 e 8 4 7 3 1 5 2 6 9 t
1 3 4 3 4 2 4 3 4 3 1
Arnold Schoenberg : Modern Psalm, Op. 50c[ 3]
1950
6–20
6–20
—
I:
0 1 4 8 5 9 e 7 t 6 3 2
P:
0 e 8 9 7 6 1 5 4 3 2 t
1 3 1 2 1 5 4 1 1 1 4
Play ⓘ
Alban Berg :Lyric Suite , row 2[ 122]
1925–26
6-Z3
6-Z36
—
I:
0 1 4 3 5 6 e 7 8 9 t 2
P:
0 e 9 2 t 7 1 4 8 3 5 6
1 2 5 4 3 6 3 4 5 2 1
Milton Babbitt : "The Widow's Lament in Springtime"
1951
6–8
6–8
—
I:
0 1 3 t 2 5 e 8 4 9 7 6
P:
0 e 9 4 3 t 8 7 5 6 1 2
1 2 5 1 5 2 1 2 1 5 1
Dmitri Shostakovich :Symphony No. 14 , mov. I[ 82]
1969
6–5
6–5
—
I:
0 1 3 8 9 2 4 5 7 6 e t
P:
0 e 9 6 t 8 7 5 2 4 3 1
1 2 3 4 2 1 2 3 2 1 2
Igor Stravinsky :Canticum Sacrum , II[ 2]
1955
6–2
6–2
—
I:
0 1 3 6 2 4 5 7 t 8 9 e
P:
0 e t 1 3 2 4 9 8 6 5 7
1 1 3 2 1 2 5 1 2 1 2
Alfred Schnittke : String Quartet No. 4, Mov. I[ 3]
1989
6–1
6–1
all- combinatorial
I:
0 1 2 e 9 t 8 3 4 6 7 5
P:
0 e t 5 6 9 7 1 2 8 3 4
1 1 5 1 3 2 6 1 6 5 1
Arvo Pärt : Symphony No. 1Perpetuum Mobile [ 56]
1963 1963
6–5
6–5
—
I:
0 1 2 7 6 3 5 e t 4 9 8
Other lengths
Fewer than twelve
Five
Prime form
Interval classes
Notation
Composer: Composition
Year
Set(s)
Features
0 e 8 9 t
1 3 1 1
Igor Stravinsky :In memoriam Dylan Thomas
1954
5–1
—
Six
Eight
Nine
Prime form
Interval classes
Notation
Composer: Composition
Year
Set(s)
Features
0 2 e 4 9 7 8 6 1
2 3 5 5 2 1 2 5
Joonas Kokkonen : Symphonic Sketches, mov. 3, row D[ 41]
1968
9–8
—
Ten
Eleven
More than twelve
Thirteen
Fourteen
Seventeen
Prime form
Interval classes
Notation
Composer: Composition
Year
Set(s)
Features
0 2 1 e t 8 9 e t 0 1 e t 0 e 9 0
2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 3
Igor Stravinsky :Agon , b. 104[ 141]
1957
—
—
0 2 3 5 4 9 7 8 e 1 6 e t 0 e 9 0
2 1 2 1 5 2 1 3 2 5 5 1 2 1 2 3
Igor Stravinsky :Agon , "Bransles"[ 141]
1957
6-Z40, 6-Z11
—
Twenty-two
Prime form
Interval classes
Notation
Composer: Composition
Year
Set(s)
Features
0 e 6 8 7 2 1 3 t 9 4 6 9 7 8 3 1 2 4 e t 0
1 5 2 1 5 1 2 5 1 5 2 3 2 1 5 2 1 2 5 1 2
Joonas Kokkonen : Cello Concerto, mov. 3, row B[ 41]
1969
—
—
Twenty-four
See also
Sources
^ Bailey, Kathryn (1991). The Twelve-Note Music of Anton Webern: Old Forms in a New Language . Cambridge University Press. p. 28. ISBN 9780521547963 .
^ a b c d e f g h i j k l m n o p q r 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.
^ a b c d e f g h i j k l m n o p q Dunker, Amy. "Twelve Tone Rows Used by Various Composers ". AmyDunker.com : 3. Retrieved 4 November 2013.
^ a b c 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.
^ 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 .
^ Dunker, Amy. "Twelve Tone Rows Used by Various Composers ". AmyDunker.com : 1. Retrieved 4 November 2013.
^ 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 .
^ Mayfield, Connie (2013). Theory Essentials . p. 549. ISBN 9781133713807 .
^ a b Morris, Robert (2010). The Whistling Blackbird: Essays and Talks on New Music . University Rochester. p. 188. ISBN 9781580463492 .
^ 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
^ a b Bailey 1991 , p. 26
^ 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 .
^ 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 .
^ a b Pearsall, Edward (2012). Twentieth-Century Music Theory and Practice . Routledge. p. 217. ISBN 9780415888950 .
^ 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.
^ "An Interview with Roger Reynolds ", Performance Arts Encyclopedia . Accessed May 27, 2015.
^ a b c d e f 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.
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