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List of musical works in unusual time signatures

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This is a list of musical compositions or pieces of music that have unusual time signatures. "Unusual" is here defined to be any time signature other than simple time signatures with top numerals of 2, 3, or 4 and bottom numerals of 2, 4, or 8, and compound time signatures with top numerals of 6, 9, or 12 and bottom numerals 4, 8, or 16.[1]

The conventions of musical notation typically allow for more than one written representation of a particular piece. The chosen time signature largely depends upon musical context, personal taste of the composer or transcriber, and the graphic layout on the written page. Frequently, published editions were written in a specific time signature to visually signify the tempo for slow movements in symphonies, sonatas, and concerti.

A perfectly consistent unusual metrical pattern may be notated in a more familiar time signature that does not correspond to it. For example, the Passacaglia from Britten's opera Peter Grimes consists of variations over a recurring bass line eleven beats in length but is notated in ordinary 4
4 time, with each variation lasting 2+3⁄4 bars, and therefore commencing each time one crotchet earlier in the bar than the preceding one.[2]

Upper number of 1

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1
1

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1
2

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1
4

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1
8

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  • Amor dammi quel fazzolettino by Andrew Violette, for one measure in the left hand of the second piano part.[61]
  • Black Tea by Andrew Violette.[62]
  • 20 Caprices and Rhythmic Studies, by Émile Jaques-Dalcroze, in No. 9.[63]
  • Caprice Variations by George Rochberg, in variation 19.[64]

1
16

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1
32

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1
64

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Upper number of 2

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2
1

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2
16

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2
32

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Upper number of 3

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See also: Triple meter

3
1

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3
16

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3
32

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Upper number of 4

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4
1⁄2

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4
1

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4
16

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4
32

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Upper number of 5

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Main article: Quintuple meter

Upper number of 6

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See also: Sextuple meter

6
2

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6
32

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Upper number of 7

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Main article: Septuple meter

Upper number of 8

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Note: 8
4 or 8
8 may refer to an evenly divided compound duple or quadruple meter. While this is arguably extremely common in music, the notations 8
4 and 8
8 themselves are not, so all divisions of this time signature are listed here

8
1

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8
2

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8
4

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8
8

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8
16

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Upper number of 9

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Time signatures that group nine beats into 3+3+3 are very common in music. This section only lists other groupings, such as 2+3+2+2.

9
4

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  • Agon by Igor Stravinsky, at measure 167. Although other measures of 9
    4     in the same section are subdivided 3+3+3, this measure is 3+2+2+2.[112]
  • Concertino by Igor Stravinsky, one measure after rehearsal mark 14 (subdivided 4+3+2).[127]

9
8

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9
16

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9
32

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Upper number of 10

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10
2

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  • Hyperchromatica by Kyle Gann, in bar 12 of the movement Liquid Mechanisms.[43]

10
4

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10
8

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10
16

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10
32

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  • Hyperchromatica by Kyle Gann, in bars 50 and 158 of the movement Ride the Cosmos.[43]

Upper number of 11

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See also: Undecuple meter

11
4

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11
8

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11
16

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  • 20 Caprices and Rhythmic Studies, by Émile Jaques-Dalcroze, in Nos. 3 and 16.[63]
  • Charon by Richard Barrett, in bar 65.[65]
  • Concerto for Piano, Clarinet, and String Quartet by Roy Harris.[172]
  • Custer and Sitting Bull by Kyle Gann, in some measures (m. 13, 15, 28, etc.) of parts 3 and 4.[115]
  • Earth-Preserving Chant by Kyle Gann, in measures 17, 300, and 314–315.[215]
  • How Miraculous Things Happen by Kyle Gann, in bar 136.[42]
  • Hyperchromatica by Kyle Gann, in the movements Ride the Cosmos and Spacecat.[43]

11
32

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11
64

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Upper number of 12

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12
2

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  • Concerto for Piano, Clarinet, and String Quartet by Roy Harris, in one measure of the second movement.[172]

12
32

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Upper number of 13

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13
4

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13
8

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13
16

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13
32

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  • Hyperchromatica by Kyle Gann, in several bars of the movement Ride the Cosmos.[43]

Upper number of 14

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See also: Septuple meter

14
4

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14
8

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14
16

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  • American Song Set by Andrew Violette, for two measures in one of the songs.[235]
  • 20 Caprices and Rhythmic Studies, by Émile Jaques-Dalcroze, in Nos. 3 and 16.[63]
  • Concerto for Piano, Clarinet, and String Quartet by Roy Harris.[172]
  • Hyperchromatica by Kyle Gann, in bars 4-5 and 171-172 of the movement Ride the Cosmos.[43]

Upper number of 15

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See also: Quintuple meter

15
4

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  • Hyperchromatica by Kyle Gann, in bar 41 of the movement Delta Oracle.[43]

15
8

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15
16

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15
32

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  • Custer and Sitting Bull by Kyle Gann, in measure 76 of part 3.[115]
  • Hyperchromatica by Kyle Gann, in five bars of the movement Ride the Cosmos.[43]
  • Piano Sonata No. 1 by Charles Wuorinen, at measure 163 of part 1 (written 5
     .    ).[70]

Upper number of 16

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16
4

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  • Custer and Sitting Bull by Kyle Gann, in measures 153, 157, and 162 of part 3.[115]

16
8

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16
16

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  • 20 Caprices and Rhythmic Studies, by Émile Jaques-Dalcroze, in No. 5.[63]
  • Concerto for Piano, Clarinet, and String Quartet by Roy Harris.[172]
  • Earth-Preserving Chant by Kyle Gann, in measure 210.[215]
  • Hyperchromatica by Kyle Gann, in bar 27 of the movement Ride the Cosmos.[43]

Upper number of 17

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17
4

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17
8

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17
16

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  • Concerto for Piano, Clarinet, and String Quartet by Roy Harris.[172]
  • Desert Sonata by Kyle Gann, in the first movement.[222]
  • Earth-Preserving Chant by Kyle Gann, in measures 30, 34, 51, 71, 75, 90, 115, 143, 147, 161, 201, 207, 242, 281, 285, and 309.[215]
  • Hovenweep by Kyle Gann, in bars 29 and 33.[41]
  • Hyperchromatica by Kyle Gann, in bars 2, 8, and 175 of the movement Ride the Cosmos.[43]

17
32

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  • Hyperchromatica by Kyle Gann, in bars 99, 101, and 102 of the movement Ride the Cosmos.[43]

Upper number of 18

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See also: Sextuple meter

18
8

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18
16

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18
32

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  • Hyperchromatica by Kyle Gann, in five bars of the movement Ride the Cosmos.[43]

Upper number of 19

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19
4

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  • "33 222 1 222" by Don Ellis.[265] Its title represents the subdivision: 3+3+2+2+2+1+2+2+2
    4    [266]

19
8

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19
16

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19
32

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  • Hyperchromatica by Kyle Gann, in bars 28, 29, and 111 of the movement Ride the Cosmos.[43]

Upper number between 20 and 29

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20

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21

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See also: Septuple meter
  • "The Art Of Dying" by Gojira (2008) cycles from 4
    4     to 2
    4     to 21
    16     (grouped 5+5+5+3+3) and repeats this pattern during the intro and beginning of the song.[271]
  • 3 Danses from L'Oeuvre d'orgue by Jehan Alain, for one measure in the first dance.[272]
  • Desert Sonata by Kyle Gann has 21
    16     in the second movement.[222]
  • Happy Ending (for David Garland) by Kyle Gann. Bars 63 and 124 are in 21
    8    , and bar 129 is in 21
    16    .[117]
  • Hyperchromatica by Kyle Gann. The movements Ride the Cosmos and Busted Grooves have 21
    16    , and Ride the Cosmos also has 21
    32    .[43]
  • "In Re Con Moto Et Al" by Charles Ives uses 21
    8    .[194]
  • In the Dead of the Night suite by U.K., "contains an instrumental refrain in 21
    16    ".[219]
  • "Keep It Greasy" by Frank Zappa on Joe's Garage (the second verse is in 21
    16    ).[221]
  • Master of Puppets by Metallica features measures that can be interpreted as 21
    32    .[273]

22

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23

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24

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  • American Song Set by Andrew Violette. One of the songs is in 4
    4    (24
    16    ) and two other songs have some measures in 24
    16     in the piano's right hand against 4
    4     in the piano's left hand and voice.[235]
  • Amor dammi quel fazzolettino by Andrew Violette has a passage of 24
    16     in the first piano against 6
    4     in the second piano.[61]
  • "Brobdingnagische Gigue", from Intrada, nebst burlesquer Suite, for two violins (the so-called "Gulliver Suite") by Georg Philipp Telemann is in 24
    1    .[104]
  • 20 Caprices and Rhythmic Studies, by Émile Jaques-Dalcroze has 24
    16     in Nos. 3 (as 24
         (12
         )) and 11 (as 8
     .    ).[63]
  • Carmina Burana by Carl Orff has 24
    4     (written as 8
     .    ) in the movement Veris leta facies.[14]
  • The Death of the Hired Man by Andrew Violette has 24
    16    .[35]
  • Hyperchromatica by Kyle Gann has 24
    32     in the movement Ride the Cosmos.[43]
  • Suite in E Minor, HWV 438 by George Frideric Handel uses 24
    16     for the Gigue.[277]
  • The Well-Tempered Clavier, Book 1 by Johann Sebastian Bach. The upper stave of Prelude No. 15 is in 24
    16     (The bottom stave is in  ).[278]

25

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  • Happy Ending (for David Garland) by Kyle Gann, in bars 46, 51, 55, and 60 (25
    16    ).[117]
  • How Miraculous Things Happen by Kyle Gann, in bar 152 (25
    16    ).[42]
  • Hyperchromatica by Kyle Gann has 25
    16     in the movement Busted Grooves and 25
    32     in the movement Ride the Cosmos.[43]
  • "How's This for Openers?" by Don Ellis (25
    8    ).[279]
  • "Memory Daydreams Lapses" by OSI (25
    16    ).[280]
  • "Tenemos Roads", by National Health includes "some extremely intricate passages in 25
    16    ".[219]

26

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  • Hyperchromatica by Kyle Gann has 26
    32     in the movement Ride the Cosmos.[43]

27

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  • The Death of the Hired Man by Andrew Violette has 27
    16    (3
     .+ .    ) in measures 373 and 381.[35]
  • Desert Sonata by Kyle Gann has 27
    16     in the first movement.[222]
  • "Goliath" by Karnivool (27
    4    ).[281]
  • Hyperchromatica by Kyle Gann has 27
    16     and 27
    32     in the movement Ride the Cosmos.[43]
  • Happy Ending (for David Garland) by Kyle Gann, in bars 45, 47, 50, 56, and 59 (27
    16    ).[117]

28

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  • Hyperchromatica by Kyle Gann has 28
    32     in the movement Ride the Cosmos.[43]

29

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Upper number between 30 and 39

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30

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  • American Song Set by Andrew Violette. One of the songs has 30
    16     in the piano's right hand against 5
    4     in the piano's left hand and voice.[235]
  • Bicinium by Charles Wuorinen, at bar 89 (30
    32    , written as 10
     .    ).[75]
  • Hyperchromatica by Kyle Gann has 30
    32     in bar 149 of the movement Ride the Cosmos.[43]

31

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32

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33

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35

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  • "Entertain Me" by Tigran Hamasyan contains a repeating melody in 35
    16    , overlayed on top of the main 256
    32     meter.[228]
  • "Nairian Odyssey" by Tigran Hamasyan contains a solo section in 35
    16    , divided variously as 6
    4     + 5
    16     + 3
    8     and 6+8+6+9+6
    16    .[287]

36

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  • American Song Set by Andrew Violette. One of the songs has a measure in 36
    16     in the piano's right hand against 6
    4     in the piano's left hand and voice and another has the same, but with 3
    2     instead of 6
    4    .[235]
  • Charon by Richard Barrett has 36
    8     in bar 58.[65]
  • The Death of the Hired Man by Andrew Violette has 36
    16    (4
     .+ .    ) in bar 372.[35]
  • Organbook by Andrew Violette has 36
    16    .[293]

37

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  • Hyperchromatica by Kyle Gann has 37
    32     in the movement Spacecat.[43]

Upper number between 40 and 49

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40

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41

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42

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43

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44

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47

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48

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  • American Song Set by Andrew Violette. One song has a measure of 24
    16     in the piano's right hand against 48
    32     in the piano's left hand and 4
    4     in the voice.[235]

Upper number between 50 and 59

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51

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  • Desert Sonata by Kyle Gann has 51
    16     in the first movement.[222]
  • Hyperchromatica by Kyle Gann has 51
    32     in the movement 2.7 Kelvin.[43]

53

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Upper number more than 59

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77

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86

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101

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  • Hyperchromatica by Kyle Gann has 101
    64     in the movement Spacecat.[43]

256

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  • "Entertain Me" by Tigran Hamasyan is in 256
    32    , with a repeating motif in 35
    16     laid over it.[228]

Fractional time signatures

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See also: Time signature § Variants

Irrational time signatures

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See also: Time signature § Irrational meters

Combined unusual signatures

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See also: Time signature § Mixed meters
  • Anyone Who Had a Heart, by Burt Bacharach uses 4
    4    , 5
    4    , and 7
    8    .[323]
  • "Butterflies, Hummingbirds", No. 5 from Twelve New Etudes by William Bolcom, has parenthesized time signatures of 18
    64    , 20
    64    , and 38
    64    .[324]
  • Chichester Psalms by Leonard Bernstein uses irregular 9
    2     and 9
    4    , 10
    4     notated as 5+5
    4    , and 12
    2    .[325]
  • Earth, the fifth part of Fictions by Richard Barrett, has 2
    16    , 3
    [16]    , 4
    [16]    , 5
    8    , 5
    16    , 7
    8    , 7
    16    , 11
    8    , 11
    16    , 13
    16    , 15
    8    , 15
    16    , 17
    8    , 17
    16    , 19
    8    , and 25
    16    .[326]
  • The Exterminating Angel Symphony by Thomas Adès has 1
    4    , 5
    4    , 5
    8    , 7
    4    , 7
    8    , and 8
    8    .[310]
  • "Firth of Fifth": Introduction, by Tony Banks of Genesis, mixes duple and quadruple meters with 13
    16     and 15
    16     signatures.[327]
  • Intermezzo by Andrew Violette has 3
    16    , 4
    16    , 5
    4    , 5
    8    , 5
    16    , 7
    8    , 7
    16    , 8
    16    , 10
    16    , 11
    16    , and 20
    16    .[328]
  • I Open and Close, the sixth part of Fictions by Richard Barrett, has 1
    8    , 2
    16    , 3
    16    , 3
    2    , 5
    8    , 5
    16    , 7
    8    , 7
    16    , 7
    32    , 8
    8    , 11
    16    , 13
    16    , 15
    16    , 15
    32    , and 24
    8    .[315]
  • "I Say a Little Prayer" by Dionne Warwick uses two measures of 4
    4    , one measure of 10
    4     and two measures of 4
    4     for verses and 11
    4     for its chorus.[329]
  • Klavierstück IX (1954–55/61) by Karlheinz Stockhausen uses 21
    8    , 34
    8    , 42
    8    , 87
    8    , and 142
    8    .[330]
  • Lemma-Icon-Epigram by Brian Ferneyhough has 1
    8    , 1
    16    , 1
    32    , 1
    64     (in an additive time signature), 3
    16    , 5
    8    , 5
    16    , 5
    32    , 7
    8    , 7
    16    , 8
    8    , 9
    16     (in various groupings such as 3+2+2+2), and 11
    16    .[316]
  • Lieder vom Wasser, the tenth part of Fictions by Richard Barrett, has 1
    8    , 1
    16    , 2
    16    , 3
    16    , 3
    32    , 5
    8    , 5
    16    , 5
    32    , 7
    8    , 7
    16    , 8
    8    , 11
    16    , 13
    16    , 15
    16    , and 43
    16    .[331]
  • The Long and the Short by Charles Wuorinen has 1
    4    , 1
    8    , 1
    16     (in additive time signatures such as 5
    4    +1
    16    ), 3
    16    , 4
    4     (subdivided as 3
    32    +7
    16    +3
    8    +3
    32    ), 4+1⁄4
    4    , 5
    4    , 5
    8    , 5
    16    , 7
    4    , 7
    8    , 7
    16    , 7+1⁄4
    4    , 8
    4    , 9
    32    , 11+1⁄2
    4    , 12
    4    , 13
    32    , 24
    4    , 25
    4    , and 40
    4    .[332]
  • Love Duet by Andrew Violette has 1
    4    , 5
    4    , 9
    4     (grouped 2+2+2+3), 15
    8    , 18
    8    , and 21
    8    .[333]
  • Organ Sonata by Andrew Violette has 5
    4    , 5
    8    , 18
    8    , and 24
    16    .[334]
  • Pastorale by Andrew Violette has 20
    16     and 24
    16    .[335]
  • Piano Concerto No. 5 by Kaikhosru Shapurji Sorabji has 5
    4    , 5
    8    , 6
    4+1⁄2     (six dotted quarter notes), 7
    4    , 7
    8    , 8
    4    , 8
    8    , 10
    8    , 11
    4    , 11
    8    , 13
    8    , 14
    8    , and 15
    8    . [336]
  • Piano Sonata No. 1 by Kaikhosru Shapurji Sorabji has 5
    4    , 5
    8    , 7
    4    , 7
    8    , 7
    16    , 8
    8    , 10
    8    , 11
    8    , 13
    8    , 14
    8    , 15
    8    , and 30
    16    .[337]
  • Piano Sonata No. 1 by Andrew Violette has 5
    2    , 5
    4    , 5
    8    , and 7
    8    .[338]
  • Piano Sonata No. 2 by Charles Wuorinen has 1
    4    , 1
    8    , 3
    16    , 5
    8    , 5
    16    , 7
    4    , 7
    8    , 7
    16    , 7
    32    , 8
    4    , 9
    8     (grouped 4+2+3), 9
    32    , 10
    4    , 10
    16    , 10
    32    , 11
    8    , 11
    16    , 11
    32    , 12
    4    , 15
    16    , 15
    32    , 18
    32    , and 20
    32     (written as 4
     +     ).[339]
  • Piano Sonata No. 3 by Andrew Violette has 1
    4     (in additive time signatures such as 3
    4    +1
    4    ), 1
    8    , 1
    16     (in additive time signatures such as 4
    4    +1
    16    ), 5
    4    , 5
    8    , 7
    4    , 7
    8    , 7
    16    , 8
    8    , 8
    16    , 9
    16     (grouped 4+5), 10
    4    , 10
    8    , 10
    16    , 11
    8    , 11
    16    , 13
    4    , 13
    16    , 14
    8    , 14
    16    , 15
    4    , 15
    8    , 15
    16    , 16
    16    , 17
    8    , 17
    16    , 18
    8    , 19
    8    , 19
    16    , 20
    16    , 21
    8    , 21
    16    , 24
    16    , 27
    16     (written as 3
     +     ), 28
    16    , 31
    8    , 34
    8    , 36
    8    , 40
    8    , 56
    8    , 60
    4    , 60
    8    , 74
    8    , 90
    16    , and 93
    16    .[304]
  • Piano Sonata No. 3 by Charles Wuorinen has 6
    8    +1
    32    , 3
    16    , 3
    32    , 4+1⁄2
    4    , 5
    4    , 5
    8    , 5+1⁄2
    4    , 6+1⁄3
    4    , 7
    8    , 7
    16    , 7+1⁄3
    8    , 9
    16     (grouped 4+5), 9
    32    , 10
    16    , 11
    8    , 11
    16    , 13
    16    , 15
    16    , and 17
    16    .[340]
  • Piano Sonata No. 4 by Charles Wuorinen has 5
    4    , 5
    8    , 7
    8    , 7
    16    , 8
    8    , 9
    8     (both 4+5 and 6+3), 4+5
    16    , 10
    16    , 11
    8    , 11
    16    , 15
    16    , and 21
    16    .[341]
  • Quirl by Brian Ferneyhough has 1
    8    , 3
    16    , 3
    32    , 5
    8    , 5
    16    , 5
    32    , 5
    64    , 7
    8    , 7
    16    , 7
    32    , 7
    64    , 8
    8    , 9
    32    , 10
    8    , 11
    16    , 11
    32    , 13
    16    , and 15
    64    .[342]
  • Quintet No. 1 by Kaikhosru Shapurji Sorabji has 2
    1    , 2+1⁄2
    4    , 5
    4    , 5
    4+1⁄2     (five dotted quarter notes), 7
    4    , 7
    8    , 8
    4    , 8
    8    , 10
    4    , 10
    8    , 11
    8    , 13
    4    , 14
    8    , 15
    8    , and 20
    8    .[343]
  • Salve Regina, the second of 4 Madrigals by Andrew Violette, has 5
    4    , 5
    8    , 7
    4    , 7
    8    , 9
    8     (4
    4    +1
    8    ), 13
    8    , and 18
    8     (3+4+5+6
    8    ).[344]
  • Sonata for Cello and Piano by Elliott Carter has 5
    4    , 5
    8    , 5
    16    , 7
    16    , 14
    32    , and 21
    32    .[345]
  • Storm Suite from The Tempest (also known as The Tempest Symphony) has 1
    8    , 5
    4    , 5
    8    , 7
    4    , and 7
    8    .[346]
  • String Quartet No. 1 by Elliott Carter has 2
    16     (as part of an additive time signature), 4
    16    , 5
    4    , 5
    8    , 5
    16    , 7
    8    , 7
    16    , 8
    16    , 9
    32     (written as 3
     .    ), 10
    8    , 10
    16    , 12
    32     (written as 4
     .    ), 14
    16    , 15
    8    , 15
    16    , 18
    8    , 18
    16    , 20
    16    , and 21
    8    .[347]
  • String Quartet No. 2 by Elliott Carter has 4
    16    , 5
    4    , 5
    8    , 15
    8    , 7
    16    , 10
    8    , 10
    16    , 14
    16    , 15
    8    , 15
    16    , and 21
    16    .[348]
  • String Quartet No. 3 by Elliott Carter has 3
    16    , 3
    32     (in an additive time signature), 5
    4    , 5
    8    , 5
    16    , 7
    8    , 7
    16    , 9
    32    , 11
    16    , 12
    32     (in an additive time signature), 24
    16    , 24
    32    , and 27
    32    .[349]
  • Structures by Pierre Boulez.[350][351]
    • Ia: 3
      16      , 4
      16      , 5
      16
    • Ib: 1
      8      , 1
      32      , 2
      16      , 2
      32      , 3
      16      , 3
      32      , 4
      16      , 4
      32      , 5
      4      , 5
      8      , 5
      16      , 5
      32      , 6
      32      , 7
      8      , 7
      16      , 7
      32      , 8
      32      , 9
      32
    • Ic: 3
      16      , 5
      16      , 5
      32
    • II, Chapter 1: 1
      4      , 1
      8      , 1
      16      , 3
      16      , 5
      8      , 5
      16      , 7
      8      , 7
      16      , 3+5
      16
    • II, Chapter 2: 5
      4      , 7
      4      , 11
      4
  • Superscriptio by Brian Ferneyhough has 1
    8    , 1
    16    , 1
    32    , 3
    16    , 3
    32    , 3
    64    , 5
    16    , 5
    32    , 5
    64    , 7
    16    , 7
    32    , and 7
    64    .[321]
  • Suite from The Tempest for violin and piano has 3
    16    , 5
    4    , 5
    8    , 5
    16    , 7
    8    , and 7
    16    .[352]
  • Thrak by King Crimson switches between 5
    8    , and 7
    8     throughout the head section.[353]
  • Traced Overhead by Thomas Adès has 1
    2    , 1
    4    , 1
    8    , 2
    1    , 3
    16    , 5
    4    , 5
    8    , and 7
    4    .[322]
  • Tract, the eighth part of Fictions by Richard Barrett, has 1
    8    , 2
    16    , 4
    32    , 5
    8    , 5
    16    , 5
    [32]    , 6
    [32]    , 7
    8    , 7
    16    , 7
    32    , 8
    8    , 8
    [32]    , 9
    32    , 10
    32    , 11
    8    , 11
    16    , 11
    32    , 12
    [32]    , 13
    16    , 13
    32    , 14
    32    , 15
    8    , 15
    16    , 15
    32    , 18
    8    , 19
    32    , 20
    8    , and 21
    8    .[354]
  • Zeitmaße by Karlheinz Stockhausen uses 1
    2    , 1
    8    , 1
    16    , 2
    16    , 2
    32    , 3
    16    , 3
    32    , 4
    16    , 8
    8    , 8
    32    , 11
    16    , 12
    32    , 17
    32    , 23
    32    , and 30
    32    .[155][355]

See also

edit

Notes and references

edit
  1. ^ Ian Waugh first lists 2
    2    , 2
    4    , 2
    8    , 3
    2    , 3
    4    , 3
    8    , 4
    2    , 4
    4    , 4
    8    , 6
    4    , 6
    8    , 6
    16    , 9
    4    , 9
    8    , 9
    16    , 12
    4    , 12
    8    , and 12
    16     (Waugh 2003, 76), then says "we've listed all the popular time signatures" (Waugh 2003, 77).
  2. ^ Britten 1945b.
  3. ^ "Variations on an Original Theme "Enigma", Op. 36 (Elgar, Edward) – IMSLP: Free Sheet Music PDF Download". imslp.org. Retrieved 24 August 2021.
  4. ^ Birtwistle, Harrison (1965). Entr'actes and Sappho Fragments. London: Universal Edition, plate U. E. 12948L.
  5. ^ a b c d e Read, Gardner (1978). Modern rhythmic notation. Bloomington: Indiana University Press. ISBN 0-253-33867-0. OCLC 3447628.
  6. ^ Stockhausen, Karlheinz (1966). Mixtur. Universal Edition, plate UE 14261.
  7. ^ a b c d e Boulez, Pierre (1958). Pli selon pli - No. 3 Improvisation II. London: Universal Edition 32836.
  8. ^ "Rhythmicana, HC 557 (Cowell, Henry) - IMSLP: Free Sheet Music PDF Download". imslp.org. Retrieved 21 January 2022.
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  54. ^ Chávez 1972, 3–4.
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    4    , but this is completely split up into more unusual sub-groupings: It's 5+5+3+5+5+4+5. [...] The thirty-five beat cycle [of Nairian Odyssey] is generally divided up into a 6
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  292. ^ "Split Open and Melt". Phish.net. 10 April 2013. Archived from the original on 15 August 2013. Retrieved 20 July 2013. "SOAM's" complex improv segment is notorious for its time signature, which involves three sections of eight eighth-notes and then a fourth section with nine eighth-notes in a steady pulse (listen to Fishman's hi-hat)
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  294. ^ Davis, Chip (1987). Fresh Aire II. Omaha, Nebraska, United States: Dots and Lines Ink. p. 55.
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  329. ^ Sheet music, published by New Hidden Valley Music and Casa David, copyright 1966
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  • Ginastera, Alberto. 1969. Don Rodrigo: Opera in Three Acts and Nine Scenes, Op. 31. Vocal Score. London: Boosey& Hawkes Music Publishers Limited.
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