Undetermined rests in dance performance

A polyrhyth­mic piece “765432” com­posed by Andréine Bel for her CRONOS dance pro­duc­tion (1994) illus­trates the use of unde­ter­mined rests. Six dancers were on stage: Suresh Shetty, Smriti Mishra, Olivier Rivoirard, Vijayshree Chaudhary, Arindam Dasgupta and Andréine Bel.

In this gram­mar, “SUB1” indi­cates a sub­sti­tu­tion that needs to be per­formed only once. Using it in replace­ment of “SUB” saves com­pu­ta­tion time.

Glyphs “” are unde­ter­mined rests, mean­ing silences whose dura­tion is a pri­ori unknown and will be pre­cise­ly cal­cu­lat­ed by the poly­met­ric expan­sion algorithm.

The whole struc­ture is con­struct­ed on reg­u­lar arith­metic divi­sions. For instance, Suresh moves at “speed 7”, Smriti at “speed 6” and Olivier at “speed 5”.

“CR47” and “C46” are patch­es of the Roland D-50 synthesizer.

ORD
GRAM#1[1] S --> Internal C47 Part1 Canon C46 _vel(90) Part2
GRAM#1[2] Part1 --> {Suresh1, Smriti1, Olivier1, Vijayshree1, Arindam1, Andreine1}
GRAM#1[3] Part2 --> {Suresh2, Smriti2 , Olivier2 , Vijayshree2 , Arindam2 , Andreine2 }
GRAM#1[4] Internal --> _script(MIDI con­troller #98 = 0 chan­nel 1) [D50 stuff]

ORD
GRAM#2[1] Suresh1 --> SuMov7x7 SuSil7x7 SuMov6x7 SuSil6x7 SuMov5x7 SuSil5x7 SuMov4x7 SuSil4x7 SuMov3x7 SuSil3x7 SuMov2x7 SuSil2x7 SuMov1x7 SuSil1x7
GRAM#2[2] Smriti1 --> SmMov6x6 SmSil6x6 SmMov5x6 SmSil5x6 SmMov4x6 SmSil4x6 SmMov3x6 SmSil3x6 SmMov2x6 SmSil2x6 SmMov1x6 SmSil1x6
GRAM#2[3] Olivier1 --> OlMov5x5 OlSil5x5 OlMov4x5 OlSil4x5 OlMov3x5 OlSil3x5 OlMov2x5 OlSil2x5 OlMov1x5 OlSil1x5
GRAM#2[4] Vijayshree1 --> ViMov4x4 ViSil4x4 ViMov3x4 ViSil3x4 ViMov2x4 ViSil2x4 ViMov1x4 ViSil1x4
GRAM#2[5] Arindam1 --> ArMov3x3 ArSil3x3 ArMov2x3 ArSil2x3 ArMov1x3 ArSil1x3
GRAM#2[6] Andreine1 --> AnMov2x2 AnSil2x2 AnMov1x2 AnSil1x2

ORD
GRAM#3[1] Suresh2 --> SuMov7x7 SuMov6x6 SuMov5x5 SuMov4x4 SuMov3x3 SuMov2x2 SuMov1x1
GRAM#3[2] Smriti2 --> SmMov6x6 SmMov5x5 SmMov4x4 SmMov3x3 SmMov2x2 SmMov1x1
GRAM#3[3] Olivier2 --> OlMov5x5 OlMov4x4 OlMov3x3 OlMov2x2 OlMov1x1
GRAM#3[4] Vijayshree2 --> ViMov4x4 ViMov3x3 ViMov2x2 ViMov1x1
GRAM#3[5] Arindam2 --> ArMov3x3 ArMov2x2 ArMov1x1
GRAM#3[6] Andreine2 --> AnMov2x2 AnMov1x1

ORD
GRAM#4[1] SuMov1x7 --> SuCycle7
GRAM#4[2] SuSil1x7 --> SuMov1x7
GRAM#4[3] SuMov2x7 --> SuCycle7 SuCycle7
GRAM#4[4] SuSil2x7 --> SuMov2x7
GRAM#4[5] SuMov3x7 --> SuCycle7 SuCycle7 SuCycle7
GRAM#4[6] SuSil3x7 --> SuMov3x7
GRAM#4[7] SuMov4x7 --> SuCycle7 SuCycle7 SuCycle7 SuCycle7
GRAM#4[8] SuSil4x7 --> SuMov4x7
GRAM#4[9] SuMov5x7 --> SuCycle7 SuCycle7 SuCycle7 SuCycle7 SuCycle7
GRAM#4[10] SuSil5x7 --> SuMov5x7
GRAM#4[11] SuMov6x7 --> SuCycle7 SuCycle7 SuCycle7 SuCycle7 SuCycle7 SuCycle7
GRAM#4[12] SuSil6x7 --> SuMov6x7
GRAM#4[13] SuMov7x7 --> SuCycle7 SuCycle7 SuCycle7 SuCycle7 SuCycle7 SuCycle7 SuCycle7
GRAM#4[14] SuSil7x7 --> SuMov7x7
GRAM#4[15] SuMov1x1 --> SuCycle1
GRAM#4[16] SuSil1x1 --> SuMov1x1
GRAM#4[17] SuMov2x2 --> SuCycle2 SuCycle2
GRAM#4[18] SuSil2x2 --> SuMov2x2
GRAM#4[19] SuMov3x3 --> SuCycle3 SuCycle3 SuCycle3
GRAM#4[20] SuSil3x3 --> SuMov3x3
GRAM#4[21] SuMov4x4 --> SuCycle4 SuCycle4 SuCycle4 SuCycle4
GRAM#4[22] SuSil4x4 --> SuMov4x4
GRAM#4[23] SuMov5x5 --> SuCycle5 SuCycle5 SuCycle5 SuCycle5 SuCycle5
GRAM#4[24] SuSil5x5 --> SuMov5x5
GRAM#4[25] SuMov6x6 --> SuCycle6 SuCycle6 SuCycle6 SuCycle6 SuCycle6 SuCycle6
GRAM#4[26] SuSil6x6 --> SuMov6x6

ORD
GRAM#5[1] SmMov1x6 --> SmCycle6
GRAM#5[2] SmSil1x6 --> SmMov1x6
GRAM#5[3] SmMov2x6 --> SmCycle6 SmCycle6
GRAM#5[4] SmSil2x6 --> SmMov2x6
GRAM#5[5] SmMov3x6 --> SmCycle6 SmCycle6 SmCycle6
GRAM#5[6] SmSil3x6 --> SmMov3x6
GRAM#5[7] SmMov4x6 --> SmCycle6 SmCycle6 SmCycle6 SmCycle6
GRAM#5[8] SmSil4x6 --> SmMov4x6
GRAM#5[9] SmMov5x6 --> SmCycle6 SmCycle6 SmCycle6 SmCycle6 SmCycle6
GRAM#5[10] SmSil5x6 --> SmMov5x6
GRAM#5[11] SmMov6x6 --> SmCycle6 SmCycle6 SmCycle6 SmCycle6 SmCycle6 SmCycle6
GRAM#5[12] SmSil6x6 --> SmMov6x6
GRAM#5[13] SmMov1x1 --> SmCycle1
GRAM#5[14] SmSil1x1 --> SmMov1x1
GRAM#5[15] SmMov2x2 --> SmCycle2 SmCycle2
GRAM#5[16] SmSil2x2 --> SmMov2x2
GRAM#5[17] SmMov3x3 --> SmCycle3 SmCycle3 SmCycle3
GRAM#5[18] SmSil3x3 --> SmMov3x3
GRAM#5[19] SmMov4x4 --> SmCycle4 SmCycle4 SmCycle4 SmCycle4
GRAM#5[20] SmSil4x4 --> SmMov4x4
GRAM#5[21] SmMov5x5 --> SmCycle5 SmCycle5 SmCycle5 SmCycle5 SmCycle5
GRAM#5[22] SmSil5x5 --> SmMov5x5

ORD
GRAM#6[1] OlMov1x5 --> OlCycle5
GRAM#6[2] OlSil1x5 --> OlMov1x5
GRAM#6[3] OlMov2x5 --> OlCycle5 OlCycle5
GRAM#6[4] OlSil2x5 --> OlMov2x5
GRAM#6[5] OlMov3x5 --> OlCycle5 OlCycle5 OlCycle5
GRAM#6[6] OlSil3x5 --> OlMov3x5
GRAM#6[7] OlMov4x5 --> OlCycle5 OlCycle5 OlCycle5 OlCycle5
GRAM#6[8] OlSil4x5 --> OlMov4x5
GRAM#6[9] OlMov5x5 --> OlCycle5 OlCycle5 OlCycle5 OlCycle5 OlCycle5
GRAM#6[10] OlSil5x5 --> OlMov5x5
GRAM#6[11] OlMov1x1 --> OlCycle1
GRAM#6[12] OlSil1x1 --> OlMov1x1
GRAM#6[13] OlMov2x2 --> OlCycle2 OlCycle2
GRAM#6[14] OlSil2x2 --> OlMov2x2
GRAM#6[15] OlMov3x3 --> OlCycle3 OlCycle3 OlCycle3
GRAM#6[16] OlSil3x3 --> OlMov3x3
GRAM#6[17] OlMov4x4 --> OlCycle4 OlCycle4 OlCycle4 OlCycle4
GRAM#6[18] OlSil4x4 --> OlMov4x4

ORD
GRAM#7[1] ViMov1x4 --> ViCycle4
GRAM#7[2] ViSil1x4 --> ViMov1x4
GRAM#7[3] ViMov2x4 --> ViCycle4 ViCycle4
GRAM#7[4] ViSil2x4 --> ViMov2x4
GRAM#7[5] ViMov3x4 --> ViCycle4 ViCycle4 ViCycle4
GRAM#7[6] ViSil3x4 --> ViMov3x4
GRAM#7[7] ViMov4x4 --> ViCycle4 ViCycle4 ViCycle4 ViCycle4
GRAM#7[8] ViSil4x4 --> ViMov4x4
GRAM#7[9] ViMov1x1 --> ViCycle1
GRAM#7[10] ViSil1x1 --> ViMov1x1
GRAM#7[11] ViMov2x2 --> ViCycle2 ViCycle2
GRAM#7[12] ViSil2x2 --> ViMov2x2
GRAM#7[13] ViMov3x3 --> ViCycle3 ViCycle3 ViCycle3
GRAM#7[14] ViSil3x3 --> ViMov3x3

ORD
GRAM#8[1] ArMov1x3 --> ArCycle3
GRAM#8[2] ArSil1x3 --> ArMov1x3
GRAM#8[3] ArMov2x3 --> ArCycle3 ArCycle3
GRAM#8[4] ArSil2x3 --> ArMov2x3
GRAM#8[5] ArMov3x3 --> ArCycle3 ArCycle3 ArCycle3
GRAM#8[6] ArSil3x3 --> ArMov3x3
GRAM#8[7] ArMov1x1 --> ArCycle1
GRAM#8[8] ArSil1x1 --> ArMov1x1
GRAM#8[9] ArMov2x2 --> ArCycle2 ArCycle2
GRAM#8[10] ArSil2x2 --> ArMov2x2

ORD
GRAM#9[1] AnMov1x2 --> AnCycle2
GRAM#9[2] AnSil1x2 --> AnMov1x2
GRAM#9[3] AnMov2x2 --> AnCycle2 AnCycle2
GRAM#9[4] AnSil2x2 --> AnMov2x2
GRAM#9[5] AnMov1x1 --> AnCycle1
GRAM#9[6] AnSil1x1 --> AnMov1x1

ORD
GRAM#10[1] Canon --> Twist Walk Stretch Bend Jump Turn
GRAM#10[2] Twist --> Sm Tik Tik Tik Tik Tik Su Tik Tik Tik Tik Ol Tik Tik Tik Ar Tik Tik Vi Tik An
GRAM#10[3] Walk --> Sm Su Tik Ol Tik Tik Ar Tik Tik Tik Vi Tik Tik Tik Tik An Tik Tik Tik Tik Tik
GRAM#10[4] Stretch --> Twist
GRAM#10[5] Bend --> Walk
GRAM#10[6] Jump --> Twist
GRAM#10[7] Turn --> Walk

SUB1
GRAM#11[1] SuCycle7 --> Su Tik Tik Tik Tik Tik Tik
GRAM#11[2] SuCycle6 --> Su Tik Tik Tik Tik Tik
GRAM#11[3] SuCycle5 --> Su Tik Tik Tik Tik
GRAM#11[4] SuCycle4 --> Su Tik Tik Tik
GRAM#11[5] SuCycle3 --> Su Tik Tik
GRAM#11[6] SuCycle2 --> Su Tik
GRAM#11[7] SuCycle1 --> Su
GRAM#11[8] SmCycle6 --> Sm - - - - -
GRAM#11[9] SmCycle5 --> Sm - - - -
GRAM#11[10] SmCycle4 --> Sm - - -
GRAM#11[11] SmCycle3 --> Sm - -
GRAM#11[12] SmCycle2 --> Sm -
GRAM#11[13] SmCycle1 --> Sm
GRAM#11[14] OlCycle5 --> Ol - - - -
GRAM#11[15] OlCycle4 --> Ol - - -
GRAM#11[16] OlCycle3 --> Ol - -
GRAM#11[17] OlCycle2 --> Ol -
GRAM#11[18] OlCycle1 --> Ol
GRAM#11[19] ViCycle4 --> Vi - - -
GRAM#11[20] ViCycle3 --> Vi - -
GRAM#11[21] ViCycle2 --> Vi -
GRAM#11[22] ViCycle1 --> Vi
GRAM#11[23] ArCycle3 --> Ar - -
GRAM#11[24] ArCycle2 --> Ar -
GRAM#11[25] ArCycle1 --> Ar
GRAM#11[26] AnCycle2 --> An -
GRAM#11[27] AnCycle1 --> An

SUB1
GRAM#12[1] Su --> {1,do4-}
GRAM#12[2] Sm --> {1,mi4-}
GRAM#12[3] Ol --> {1,sol4-}
GRAM#12[4] Vi --> {1,do5-}
GRAM#12[5] Ar --> {1,mi5-}
GRAM#12[6] An --> {1,sol5-}
GRAM#12[7] Tik --> {1,do7-}

The fol­low­ing out­put was record­ed on a Roland D-50 synthesizer.

This per­for­mance was part of chore­o­graph­ic work CRONOS per­formed at the National Centre for the Performing Arts (Mumbai, India) and Shri Ram Center (Delhi) in October 1994. An excerpt is dis­played from 4mn 50s to 5mn 10s:

References

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