List of siteswaps

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

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>

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)
0XEmpty hand01S
1XDirect toss to other hand11S
2XHolding a prop in each hand21S
3Cascade,[4][6][7][8][9][10][11]
reverse cascade,[12] etc.[13][14][15]
31S
4Fountain, etc.[4][10][11][16][17]41S
5Cascade,[4][18][19]
reverse cascade,[20] etc.[21]
51S
6Fountain[22][23]61S
7Cascade71S
8Fountain81S
9Cascade91S
20XHold a prop in 1 hand,
0 in the other[6]
11A
31XTwo prop shower[4][6][24]22A
402 in 1 (single handed column/fountain)[4][24][25]
only valid two prop juggling pattern
22A
422 in 1, hold 1 in the other[6][7][9][25]32A
51Shower[4][6][9][24][26][27][28]32A
53Half shower[4][6][7][29][30][31]42A
60Three in one[24][32][33]32A
623 in 1, hold in the other42A
643 in 1, 2 in the other[4][7][34]52A
71Shower[4][6][30][35]42A
73Half shower (see synchronous)[7]52A
75Half-shower[4][34]62A
80Four in one[30]42A
82Four in one, hold in the other52A
84Four in one, two in the other[34]62A
86Four in one, three in the other72A
91Shower[4][34][36]52A
93Half-shower[34]62A
95Half-shower72A
97Half-shower82A
312XShower alternating direction[4][24]23S
330XCascade with a "hole"[7][37]23S
423Burke's barrage,
etc.[4][6][7][10][24][38][39][40][41]
33S
441Half box[4][6][7][9][11][24][29][42][38][43][44]
and reverse,[45] 441 Mills Mess[46]
33S
453453[6]43
501High shower variant[4][6][7][24]23S
504504,[38][47] 450[6][11][48]33S
522522[4][49]33S
531531[4][6][7][9][10][24][50] and
531 Mills Mess[51][52]
33S
534534[4][7][10][38][53][54]43S
5524 out of 5[4][7][55][56]43A
561561[6][7][38]43S
612See-saw[4][24][57]33S
615615[4][58] 61616,[6] 43S
633633[4][6][7][10][38][59]43S
642642[6][38]43S
645645[4][6]53S
663663[38]53S
714714[4][6]43S
723723[6]43S
726726[4]53S
741741[6]43S
744744[4][38]53S
756756[4]63S
771771[4][6][38]53S
753753[38]53S
801801[4][24]33S
810810[38]33S
831831[38]43S
867867[4]73S
915915[4]53S
945459[38]63S
978978[4]83S
44134413[6][7]34A
4440Gap/3 out of 4 (fountain)[6][60]34A
5223Slow half-shower[61]34A
52415241[6]34A
5313Asymmetric version of 531)[6][7]34A
55245524[7]44A
55515551[4][6][38][62][63]44A
63126312[64]34A
64246424[6]44A
7131High-Low Shower[65]34A
73337333[4]44A
75317531[6][38]44A
75627562[6][38]54A
75717571[6]54A
8040High-low three in one[4][57]34A
99559559[38]74A
40141X40141[38]25S
42333Marden's Marvel and Relf's Factory[66]35S
42423Orinoco Flow[67] (423 with an extra 4)35S
44133Frostbite and Mills Mess Shower[68]35S
4514145141[48][38]35S
50505Chase,[69] snake,[6][70][71] etc.[4][7]35S
51234 12345 3 5 S
5141451414[72]35S
52233Rubenstein's Revenge
and Romeo's Revenge[73]
35S
52512Boston shuffle,[74] "baby",[6] etc.[7][75]35S
52512*Burke's Slam,[76] (5251221525)35S
53133Shuffler's mess[77]35S
53444Tennis[70][78]45S
5501455014[79]35S
5524455244[7]45S
55500"Flash" (3 out of 5)[6][7][9][70][4][57]35S
5551455514[6][38][80]45S
55550Gap/four out of five[6][7][81][82]45S
5641456414[6]45S
6616166161[4]45S
6666166661[4][6]55S
6756167561[6]55S
6814168141[4]45S
7575175751[6]55S
7773177731[4]55S
81411Super box[4]35S
8833388333[4]55S
9444494444[4]55S
9535395353[4]55S
9733397333[4]55S
9744197441[4]55S
9752297522[4]55S
517131One up one down[4][83]36A
615150Shower with a "leak"[7]36A
661515661515[6]46A
719151One high one low[4]46A
777171777171[6]56A
5224233Relf's Rubensteins[84]37S
71616167161616[6]47S
72727127272712[6]47S
33333342Icelandic Shuffle[85]38A
123456789123456789[4][86]59S
84838480348483848034[87]510A
5314530552053145305520311S

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]42S
(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>One-count[9]61SA
3p3>
or <33p|33p>
Two-count[9]62AA
3p33>Three-count63SA
3p333>Four-count64AA
3p33333>Six-count[105][106]66SA
<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.CS1 maint: bot: original URL status unknown (link). Cited in Rosenberger, Phillip (2011). Juggling Basics, Why and How To. ISBN 9780983339700.
  4. 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. Knutson, Allen (1993). "Siteswap FAQ", Juggling.org, one page. Accessed: October 30, 2016.
  7. Phillips, Greg (2001). "Understanding Siteswap". Accessed 11 3 2016.
  8. "Cascade". LibraryofJuggling.com. Retrieved October 24, 2016.
  9. "Siteswap notation", JugglingLab. Accessed: October 24, 2016.
  10. Burns, Aiden. "Notations: Ladder Diagrams", p.11. Aidan's Juggling Page. Accessed: 11 10 2016.
  11. 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. Beever (2001), p.6.
  16. "Fountain", "Four Ball Mills Mess", and "Four Ball Half-Mess". LibraryofJuggling.com. Retrieved October 24, 2016.
  17. "Four Ball Fountain", Aidan's Juggling Page. Accessed: November 3, 2016.
  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. 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. "Two In One Hand", Adian's Juggling Page. Accessed November 3, 2016.
  26. "Shower". LibraryofJuggling.com. Retrieved October 24, 2016.
  27. Beever (2001), p.8.
  28. "The Three Ball Shower", Aidan's Juggling Page. Accessed: 11 10 2016.
  29. Beever (2001), p.13.
  30. 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. 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. 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. 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.
  57. Morgan, Alan (1996). "Siteswaps for the Masses", Juggling.org. Accessed: October 24, 2016.
  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. 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. 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. 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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