Siteswap beats shown as relative height[1][2]
<3p3|3p4|3p5|3p1|3p2><3|3|3|3|3><3|3|3|3|3><3|3|3|3|3>

Below is a list of siteswaps or juggling patterns by siteswap.

Toss juggling requires more balls than hands.[3] Thus tricks such as the one ball cascade toss back and forth, 300,[4] for example, may not be considered valid patterns. Throws back and forth shower style, odd numbers, are the most common one prop practice. Invalid or practice patterns and tricks are marked with an X.

The numbers are as follows:[5]

  • 0 = "missing"/rest [empty hand]
  • 1 = pass [between hands]
  • 2 = hold [one hand/no toss]
  • 3 = (3-ball) cascade toss [between hands]
  • 4 = (4-ball) fountain or columns toss [up and into same hand]
  • 5 = high toss [between hands]
  • ...
  • a = 10 = high columns/fountain toss
  • ...

Symbols:

  • Number: Relative height of a toss. 1, 2, 3...
  • Brackets []: Multiplex. [333]33.
  • Chevrons and vertical bar <|>: Simultaneous and passing patterns.
    • P: Pass. <333P|333P>
    • Fraction: Pass 1/y beats later. <4.5 3 3 | 3 4 3.5>
  • Parentheses (): Synchronous pattern.
    • *: Synchronous pattern that switches sides. (4,2x)(2x,4) = (4,2x)*
    • x: Toss to the other hand during a synchronous pattern.

Asynchronous

Animations
531
Cascade: 5
Cascade: 7

A pattern is symmetrical (S) if both hands play the same role and asymmetrical (A) if not. All asynchronous patterns whose periods are odd are symmetrical, and all asynchronous patterns whose periods are even are asymmetrical.

Juggling patterns by siteswap
SiteswapNamePropsPeriodSymmetry
(S/A)
0
X
Empty hand01S
1
X
Direct toss to other hand11S
2
X
Holding a prop in each hand21S
3
Cascade,[4][6][7][8][9][10][11]
reverse cascade,[12] etc.[13][14][15]
31S
4
Fountain, etc.[4][10][11][16][17]41S
5
Cascade,[4][18][19]
reverse cascade,[20] etc.[21]
51S
6
Fountain[22][23]61S
7
Cascade71S
8
Fountain81S
9
Cascade91S
20
X
Hold a prop in 1 hand,
0 in the other[6]
11A
31
X
Two prop shower[4][6][24]22A
40
2 in 1 (single handed column/fountain)[4][24][25]
only valid two prop juggling pattern
22A
42
2 in 1, hold 1 in the other[6][7][9][25]32A
51
Shower[4][6][9][24][26][27][28]32A
53
Half shower[4][6][7][29][30][31]42A
60
Three in one[24][32][33]32A
62
3 in 1, hold in the other42A
64
3 in 1, 2 in the other[4][7][34]52A
71
Shower[4][6][30][35]42A
73
Half shower (see synchronous)[7]52A
75
Half-shower[4][34]62A
80
Four in one[30]42A
82
Four in one, hold in the other52A
84
Four in one, two in the other[34]62A
86
Four in one, three in the other72A
91
Shower[4][34][36]52A
93
Half-shower[34]62A
95
Half-shower72A
97
Half-shower82A
312
X
Shower alternating direction[4][24]23S
330
X
Cascade with a "hole"[7][37]23S
423
Burke's barrage,
etc.[4][6][7][10][24][38][39][40][41]
33S
441
Half box[4][6][7][9][11][24][29][42][38][43][44]
and reverse,[45] 441 Mills Mess[46]
33S
453
453[6]43
501
Snowball[4][6][7][24]23S
504
504,[38][47] 450[6][11][48]33S
522
522[4][49]33S
531
531[4][6][7][9][10][24][50] and
531 Mills Mess[51][52]
33S
534
534[4][7][10][38][53][54]43S
552
4 out of 5[4][7][55][56]43S
561
561[6][7][38]43S
612
See-saw[4][24][57]33S
615
615[4][58] 61616,[6] 43S
633
633[4][6][7][10][38][59]43S
642
642[6][38]43S
645
645[4][6]53S
663
663[38]53S
714
714[4][6]43S
723
723[6]43S
726
726[4]53S
741
741[6]43S
744
744[4][38]53S
756
756[4]63S
771
771[4][6][38]53S
753
753[38]53S
801
801[4][24]33S
831
831[38]43S
867
867[4]73S
915
915[4]53S
945
459[38]63S
978
978[4]83S
4413
4413[6][7]34A
4440
Gap/3 out of 4 (fountain)[6][60]34A
5223
Slow half-shower[61]34A
5241
5241[6]34A
5313
Asymmetric version of 531)[6][7]34A
5524
5524[7]44A
5551
5551[4][6][38][62][63]44A
6312
6312[64]34A
6424
6424[6]44A
7131
High-Low Shower[65]34A
7333
7333[4]44A
7531
7531[6][38]44A
7562
7562[6][38]54A
7571
7571[6]54A
8040
High-low three in one[4][57]34A
9955
9559[38]74A
40141
X
40141[38]25S
42333
Marden's Marvel and Relf's Factory[66]35S
42423
Orinoco Flow[67] (423 with an extra 4)35S
44133
Frostbite and Mills Mess Shower[68]35S
45141
45141[48][38]35S
50505
Chase,[69] snake,[6][70][71] etc.[4][7]35S
51234
1234535S
51414
51414[72]35S
52233
Rubenstein's Revenge
and Romeo's Revenge[73]
35S
52512
Boston shuffle,[74] "baby",[6] etc.[7][75]35S
52512*
Burke's Slam,[76] (5251221525)35S
53133
Shuffler's mess[77]35S
53444
Tennis[70][78]45S
55014
55014[79]35S
55244
55244[7]45S
55500
"Flash" (3 out of 5)[6][7][9][70][4][57]35S
55514
55514[6][38][80]45S
55550
Gap/four out of five[6][7][81][82]45S
56414
56414[6]45S
66161
66161[4]45S
66661
66661[4][6]55S
67561
67561[6]55S
68141
68141[4]45S
75751
75751[6]55S
77731
77731[4]55S
81411
Super box[4]35S
88333
88333[4]55S
94444
94444[4]55S
95353
95353[4]55S
97333
97333[4]55S
97441
97441[4]55S
97522
97522[4]55S
517131
One up one down[4][83]36A
615150
Shower with a "leak"[7]36A
661515
661515[6]46A
719151
One high one low[4]46A
777171
777171[6]56A
5224233
Relf's Rubensteins[84]37S
7161616
7161616[6]47S
7272712
7272712[6]47S
33333342
Icelandic Shuffle[85]38A
123456789
123456789[4][86]59S
8483848034
8483848034[87]510A
53145305520
53145305520311S

Synchronous

(6x,4)(4,2x)(4,6x)(2x,4)

A pattern is symmetric if all throws made by the right hand are made by the left hand in the same order. It follows that a synchronous pattern is symmetric if the sequence of throws made by one hand in the siteswap notation is a rotation of the other.

Juggling patterns by siteswap
SiteswapNamePropsPeriodSymmetry
(S/A)
(2x,4x)
Half-shower[88]31A
(4,2)
Fake Columns, yo-yo etc.[89]
(identical to 42[7])
31A
(4,2x)(2x,4)
Box[6][7][9][90][91]32S
(4,4)
Columns, etc.[92][93]41S
(4,4)(4,0)
Columns/One Up Two Up[7][9][94][95]32A
(4,4)(4x,0)*
Alternating columns[96]34S
(4,6x)(2x,4)
(4,6x)(2x,4)[97]42A
(4x,2x)
Shower[6][87][98]31A
(4x,2x)(4,2x)(2x,4x)(2x,4)
Double box[6]34S
(4x,4x)
Crossing columns[9][99]41S
(4x,6)(6,4x)
Box[4][97]52S
(6,2x)(6,2x)*
Box[100]44S
(6,2x)(6,2x)(2x,6)(2x,6)
(6,2x)(6,2x)(2x,6)(2x,6)[6]44S
(6,4)
3 in 1, 2 in the other51A
(6,4x)(4x,2)
(6,4x)(4x,2)[97]42A
(6,6)(6,2)
3 in 1, 2 in the other[6]52A
(6,6)(6,6)(6,0)
3 in 1, 2 in the other[7]53A
(6x,2)(6,2x)(2,6x)(2x,6)
(6x,2)(6,2x)(2,6x)(2x,6)[6]44S
(6x,2x)
Shower[9][101]41A
(6x,2x)(2x,6x)
Box shower/shower box[6][102]42S
(6x,4)(4,2x)(4,4)(4,6x)(2x,4)(4,4)
Tennis[103]46S
(6x,4)(4,2x)(4,6x)(2x,4)
Synchronous 534[104]44S
(6x,4)(4,6x)
(6x,4)(4,6x)[15]52S
(6x,4x)
Half shower[7]51A
(6x,6x)(2x,2x)
(6x,6x)(2x,2x)[9]42S
(8,2x)(4,2x)(2x,8)(2x,4)
Dan Bennett's box[6]44S

Passing

Animations
<3p2|3p1|3><3|3|3><3p3|3|3p1><3|3|3>
<3|3p3|3p2|3><3|3|3|3><3p2|3p1|3p4|3p3><3|3|3|3>
Four-count
Juggling patterns by siteswap
SiteswapNamePropsPeriodSymmetry
(S/A)
Timing
(S/A)
<3p|3p>
One-count[9]61SA
<3p3|3p3>
or <33p|33p>
Two-count[9]62AA
<3p33|3p33>
Three-count63SA
<3p333|3p333>
Four-count64AA
<3p33333|3p33333>
Six-count[105][106]66AA
<5p333><335p3>
Simplest 4 count 7 prop[107]74AA

Ladder diagrams

References

  1. After Donahue, Bill (2004). "The Mathematics of...Juggling", DiscoverMagazine.com.
  2. Tiemann, Bruce and Magnusson, Bengt (1991). "A Notation for Juggling Tricks, A LOT of Juggling Tricks Archived 2012-06-12 at the Wayback Machine", Juggle.org. Accessed July 8, 2014.
  3. For example, ""1. What is juggling?", IJDb". Archived from the original on December 1, 2008. Retrieved 2016-11-06.{{cite web}}: CS1 maint: bot: original URL status unknown (link). Cited in Rosenberger, Phillip (2011). Juggling Basics, Why and How To. ISBN 9780983339700.
  4. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 Darley, Vincent (1996). "Site Swaps: Examples", Juggling.org. Accessed: October 24, 2016.
  5. "Juggling by numbers: How notation revealed new tricks", BBC.com (BBC article with explanatory video)
  6. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 Knutson, Allen (1993). "Siteswap FAQ", Juggling.org, one page. Accessed: October 30, 2016.
  7. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 Phillips, Greg (2001). "Understanding Siteswap". Accessed 11 3 2016.
  8. "Cascade". LibraryofJuggling.com. Retrieved October 24, 2016.
  9. 1 2 3 4 5 6 7 8 9 10 11 12 13 "Siteswap notation", JugglingLab. Accessed: October 24, 2016.
  10. 1 2 3 4 5 6 Burns, Aiden. "Notations: Ladder Diagrams", p.11. Aidan's Juggling Page. Accessed: 11 10 2016.
  11. 1 2 3 4 Buhler, Joe; Graham, Ron (2004). "Juggling Patterns, Passing, and Posets". In Hayes, David F.; Shubin, Tatiana (eds.). Mathematical Adventures for Students and Amateurs. The Mathematical Association of America. pp. 100–1. ISBN 0-88385-548-8. Retrieved February 17, 2011.
  12. "Reverse Cascade". LibraryofJuggling.com. Retrieved October 24, 2016.
  13. "Statue of Liberty", Tunbridge Wells Juggling Club.
  14. "Mills Mess", "Reverse Mills Mess", "Flipped Mess", "Boston Mess", "Half-Shower", "Cherry Picker", "Chops", "Reverse Chops", "Statue of Liberty", "Half-Mess", "Mike's Mess", "Crossed Arm Cascade", "Crossed-Arm Reverse Cascade", "Inverted Shower", "Backcrosses", "Flo's Mess", "Windmill", "Chop Shower", "Frantic Cascade", "Kraken", "Relf's Revenge 6", and "Juggler's Tennis". LibraryofJuggling.com. Retrieved October 24, 2016.
  15. 1 2 Beever (2001), p.6.
  16. "Fountain", "Four Ball Mills Mess", and "Four Ball Half-Mess". LibraryofJuggling.com. Retrieved October 24, 2016.
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  18. "Five Ball Cascade". LibraryofJuggling.com. Retrieved October 24, 2016.
  19. "The Five Ball Cascade", Aidan's Juggling Page. Accessed: November 3, 2016.
  20. "Five Ball Reverse Cascade". LibraryofJuggling.com. Retrieved October 24, 2016.
  21. "Shuffle" and "Low Shuffle". LibraryofJuggling.com. Retrieved October 24, 2016.
  22. "Six Ball Fountain". LibraryofJuggling.com. Retrieved October 24, 2016.
  23. "The Six Ball Fountain", Aidan's Juggling Page. Accessed: November 3, 2016.
  24. 1 2 3 4 5 6 7 8 9 10 11 Beever, Ben (2001). "Siteswap Ben's Guide to Juggling Patterns", p.60, JugglingEdge.com. BenBeever.com at the Wayback Machine (archived August 10, 2015).
  25. 1 2 "Two In One Hand", Adian's Juggling Page. Accessed November 3, 2016.
  26. "Shower". LibraryofJuggling.com. Retrieved October 24, 2016.
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  28. "The Three Ball Shower", Aidan's Juggling Page. Accessed: 11 10 2016.
  29. 1 2 Beever (2001), p.13.
  30. 1 2 3 Beever (2001), p.61.
  31. "Four Ball Half-Shower", Aidan's Juggling Page. Accessed: November 3, 2016.
  32. "Three in One". LibraryofJuggling.com. Retrieved October 24, 2016.
  33. Burns, Aidan. "Three In One Hand", Aidan's Juggling Page. Accessed: November 3, 2016.
  34. 1 2 3 4 5 Beever (2001), p.62.
  35. "Four Ball Shower". LibraryofJuggling.com. Retrieved October 24, 2016.
  36. "Five Ball Shower". LibraryofJuggling.com. Retrieved October 24, 2016.
  37. "Three Ball Gap", Adian's Juggling Page. Accessed November 3, 2016.
  38. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Borwein, Jonathan M.; ed. (1997). Buhler, Eisenbud, Graham, Wright. "Juggling Drops and Descents", Organic Mathematics: Proceedings of the Organic Mathematics Workshop, December 12–14, 1995, Simon Fraser University, Burnaby, British Columbia, p.141-2. American Mathematical Soc. ISBN 9780821806685.
  39. "423", "Follow", "Burke's Barrage", "Relf's Revenge", "Fake Mess", "Takeouts", and "The W". LibraryofJuggling.com. Retrieved October 24, 2016.
  40. "Four Two Three", Aidan's Juggling Page. Accessed: 11 10 2016.
  41. "Weave". LibraryofJuggling.com. Retrieved October 24, 2016.
  42. "Half-Box". LibraryofJuggling.com. Retrieved October 24, 2016.
  43. Burns, Aidan. "The Three Ball Cascade", Aidan's Juggling Page. Accessed: November 3, 2016.
  44. "Four Four One", Aidan's Juggling Page. Accessed: 11 10 2016.
  45. "Reverse Half-Box". LibraryofJuggling.com. Retrieved October 24, 2016.
  46. "441 Mills Mess". LibraryofJuggling.com. Retrieved October 24, 2016.
  47. "Five O Four", Aidan's Juggling Page. Accessed: 11 10 2016.
  48. 1 2 Wright, Colin and Lipson, Andrew (1996). "SiteSwaps, How To Write Down A Juggling Pattern: A Guide For The Perplexed", Juggling.org. Accessed: October 24, 2016.
  49. Beever (2001), p.15.
  50. "531". LibraryofJuggling.com. Retrieved October 24, 2016.
  51. "531 Mills Mess". LibraryofJuggling.com. Retrieved October 24, 2016.
  52. "Five Three One", Aidan's Juggling Page. Accessed: 11 10 2016.
  53. "534" and "534 Mills Mess". LibraryofJuggling.com. Retrieved October 24, 2016.
  54. "Five Three Four", Aidan's Juggling Page. Accessed: November 3, 2016.
  55. "552". LibraryofJuggling.com. Retrieved October 24, 2016.
  56. "Five Five Two", Aidan's Juggling Page. Accessed: November 3, 2016.
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  58. "Six One Five", Aidan's Juggling Page. Accessed: November 3, 2016.
  59. "Six Three Three", Aidan's Juggling Page. Accessed: November 3, 2016.
  60. "Four Ball Gap", Aidan's Juggling Page. Accessed: November 3, 2016.
  61. "The Slow Half-Shower", Aidan's Juggling Page. Accessed: 11 10 2016.
  62. "5551". LibraryofJuggling.com. Retrieved October 24, 2016.
  63. "Five Five Five One", Aidan's Juggling Page. Accessed: November 3, 2016.
  64. Beever (2001), p.37.
  65. "High-Low Shower". LibraryofJuggling.com. Retrieved October 24, 2016.
  66. "Marden's Marvel", LibraryofJuggling.com and "Relf's Factory". LibraryofJuggling.com. Retrieved October 24, 2016.
  67. "Orinoco Flow". LibraryofJuggling.com. Retrieved October 24, 2016.
  68. "Frostbite" and "Mills Mess Shower". LibraryofJuggling.com. Retrieved October 24, 2016.
  69. Burns, Aidan. "The Chase", Aidan's Juggling Page. Siteswap: 55050. Accessed: November 3, 2016.
  70. 1 2 3 Lee, Xah (2005). "Siteswap", XahArts.org. Accessed: November 8, 2016.
  71. "Snake". LibraryofJuggling.com. Retrieved October 24, 2016.
  72. "Five One Four One Four", Aidan's Juggling Page. Accessed: 11 10 2016.
  73. "Romeo's Revenge". LibraryofJuggling.com. Retrieved October 24, 2016.
  74. "Boston Shuffle". LibraryofJuggling.com. Retrieved October 24, 2016.
  75. "Peter's Shuffle". LibraryofJuggling.com. Retrieved October 24, 2016.
  76. "Burke's Slam". LibraryofJuggling.com. Retrieved October 24, 2016.
  77. "Shuffler's Mess". LibraryofJuggling.com. Retrieved October 24, 2016.
  78. "Four Ball Tennis", Aidan's Juggling Page. Accessed: November 3, 2016.
  79. "Five Five 0 One Four", Aidan's Juggling Page. Accessed: November 3, 2016.
  80. "Five Five Five One Four", Aidan's Juggling Page. Accessed: November 3, 2016.
  81. "55550". LibraryofJuggling.com. Retrieved October 24, 2016.
  82. "Five ball Gap ", Aidan's Juggling Page. Accessed: November 3, 2016.
  83. "Shower-Cascade". LibraryofJuggling.com. Retrieved October 24, 2016.
  84. "Relf's Rubensteins". LibraryofJuggling.com. Retrieved October 24, 2016.
  85. "Icelandic Shuffle". LibraryofJuggling.com. Retrieved October 24, 2016.
  86. Diaconis, Persi and Graham, Ron (2011). Magical Mathematics: The Mathematical Ideas That Animate Great Magic Tricks, p.144. Princeton University. ISBN 9781400839384. "Mathematically interesting siteswap patterns, such as 123456789."
  87. 1 2 Beever (2001), p.9.
  88. "The Three Ball Half-Shower (4x,2x)", Aidan's Juggling Page. Accessed: November 3, 2016.
  89. "Fake Columns", "Yo-Yo", and "Oy-Oy". LibraryofJuggling.com. Retrieved October 24, 2016.
  90. "Box". LibraryofJuggling.com. Retrieved October 24, 2016.
  91. "The Box (4,2x)(2x,4)", Aidan's Juggling Page. Accessed: November 3, 2016.
  92. "Four Ball Columns", "Pistons", "Synchronous Pistons", and "Synchronous Fountain"; LibraryofJuggling.com. Accessed October 24, 2016.
  93. "Synchronous Four Ball Fountain", Aidan's Juggling Page. Accessed: 11 10 2016.
  94. "Columns". LibraryofJuggling.com. Retrieved October 24, 2016.
  95. "One Up Two Up", Aidan's Juggling Page. Accessed: November 3, 2016.
  96. "Infinity" and "Reverse Infinity". LibraryofJuggling.com. Retrieved October 24, 2016.
  97. 1 2 3 Burns, p.19.
  98. Burns, p.18.
  99. "Synchronous Four Ball Crossing Pattern", Aidan's Juggling Page. Accessed: 11 10 2016.
  100. "Four Ball Box". LibraryofJuggling.com. Retrieved October 24, 2016.
  101. "Synchronous Half Shower (6x,2x)", Aidan's Juggling Page. Accessed: November 3, 2016.
  102. "Six Two (6x,2x)(2x,6x)", Aidan's Juggling Page. Accessed: November 3, 2016.
  103. "Synchronous Four Ball Tennis", Aidan's Juggling Page. Accessed: November 3, 2016.
  104. "'Synchronous 534' (6x,4)(4,2x)(4,6x)(2x,4)", Aidan's Juggling Page. Accessed: November 3, 2016.
  105. Besmehn, Bobby (1994). Juggling Step-by-Step, p.65. "Use four balls of one color and two of another color...every time an odd-colored ball reaches your right hand, pass it." Sterling. ISBN 0-8069-0815-7
  106. Cassidy, John and Rimbeaux, B.C. (1988). Juggling for the Complete Klutz, p.38. "It helps...if one of you counts out loud every time a toss leaves your right hand[s]...On a pre-arranged number, say three [six beats], instead of tossing across to your own left hand, throw your bag...over to your friend's left hand." Klutz Press. Third edition. ISBN 0-932592-00-7
  107. Beever (2001), p.43.
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