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

Siteswap	Name	Props	Period	Symmetry (S/A)
0X	Empty hand	0	1	S
1X	Direct toss to other hand	1	1	S
2X	Holding a prop in each hand	2	1	S
3	Cascade,[4][6][7][8][9][10][11] reverse cascade,[12] etc.[13][14][15]	3	1	S
4	Fountain, etc.[4][10][11][16][17]	4	1	S
5	Cascade,[4][18][19] reverse cascade,[20] etc.[21]	5	1	S
6	Fountain[22][23]	6	1	S
7	Cascade	7	1	S
8	Fountain	8	1	S
9	Cascade	9	1	S
20X	Hold a prop in 1 hand, 0 in the other[6]	1	1	A
31X	Two prop shower[4][6][24]	2	2	A
40	2 in 1 (single handed column/fountain)[4][24][25] only valid two prop juggling pattern	2	2	A
42	2 in 1, hold 1 in the other[6][7][9][25]	3	2	A
51	Shower[4][6][9][24][26][27][28]	3	2	A
53	Half shower[4][6][7][29][30][31]	4	2	A
60	Three in one[24][32][33]	3	2	A
62	3 in 1, hold in the other	4	2	A
64	3 in 1, 2 in the other[4][7][34]	5	2	A
71	Shower[4][6][30][35]	4	2	A
73	Half shower (see synchronous)[7]	5	2	A
75	Half-shower[4][34]	6	2	A
80	Four in one[30]	4	2	A
82	Four in one, hold in the other	5	2	A
84	Four in one, two in the other[34]	6	2	A
86	Four in one, three in the other	7	2	A
91	Shower[4][34][36]	5	2	A
93	Half-shower[34]	6	2	A
95	Half-shower	7	2	A
97	Half-shower	8	2	A
312X	Shower alternating direction[4][24]	2	3	S
330X	Cascade with a "hole"[7][37]	2	3	S
423	Burke's barrage, etc.[4][6][7][10][24][38][39][40][41]	3	3	S
441	Half box[4][6][7][9][11][24][29][42][38][43][44] and reverse,[45] 441 Mills Mess[46]	3	3	S
453	453[6]	4	3
501	High shower variant[4][6][7][24]	2	3	S
504	504,[38][47] 450[6][11][48]	3	3	S
522	522[4][49]	3	3	S
531	531[4][6][7][9][10][24][50] and 531 Mills Mess[51][52]	3	3	S
534	534[4][7][10][38][53][54]	4	3	S
552	4 out of 5[4][7][55][56]	4	3	A
561	561[6][7][38]	4	3	S
612	See-saw[4][24][57]	3	3	S
615	615[4][58] 61616,[6]	4	3	S
633	633[4][6][7][10][38][59]	4	3	S
642	642[6][38]	4	3	S
645	645[4][6]	5	3	S
663	663[38]	5	3	S
714	714[4][6]	4	3	S
723	723[6]	4	3	S
726	726[4]	5	3	S
741	741[6]	4	3	S
744	744[4][38]	5	3	S
756	756[4]	6	3	S
771	771[4][6][38]	5	3	S
753	753[38]	5	3	S
801	801[4][24]	3	3	S
810	810[38]	3	3	S
831	831[38]	4	3	S
867	867[4]	7	3	S
915	915[4]	5	3	S
945	459[38]	6	3	S
978	978[4]	8	3	S
4413	4413[6][7]	3	4	A
4440	Gap/3 out of 4 (fountain)[6][60]	3	4	A
5223	Slow half-shower[61]	3	4	A
5241	5241[6]	3	4	A
5313	Asymmetric version of 531)[6][7]	3	4	A
5524	5524[7]	4	4	A
5551	5551[4][6][38][62][63]	4	4	A
6312	6312[64]	3	4	A
6424	6424[6]	4	4	A
7131	High-Low Shower[65]	3	4	A
7333	7333[4]	4	4	A
7531	7531[6][38]	4	4	A
7562	7562[6][38]	5	4	A
7571	7571[6]	5	4	A
8040	High-low three in one[4][57]	3	4	A
9955	9559[38]	7	4	A
40141X	40141[38]	2	5	S
42333	Marden's Marvel and Relf's Factory[66]	3	5	S
42423	Orinoco Flow[67] (423 with an extra 4)	3	5	S
44133	Frostbite and Mills Mess Shower[68]	3	5	S
45141	45141[48][38]	3	5	S
50505	Chase,[69] snake,[6][70][71] etc.[4][7]	3	5	S
51234	12345	3	5	S
51414	51414[72]	3	5	S
52233	Rubenstein's Revenge and Romeo's Revenge[73]	3	5	S
52512	Boston shuffle,[74] "baby",[6] etc.[7][75]	3	5	S
52512*	Burke's Slam,[76] (5251221525)	3	5	S
53133	Shuffler's mess[77]	3	5	S
53444	Tennis[70][78]	4	5	S
55014	55014[79]	3	5	S
55244	55244[7]	4	5	S
55500	"Flash" (3 out of 5)[6][7][9][70][4][57]	3	5	S
55514	55514[6][38][80]	4	5	S
55550	Gap/four out of five[6][7][81][82]	4	5	S
56414	56414[6]	4	5	S
66161	66161[4]	4	5	S
66661	66661[4][6]	5	5	S
67561	67561[6]	5	5	S
68141	68141[4]	4	5	S
75751	75751[6]	5	5	S
77731	77731[4]	5	5	S
81411	Super box[4]	3	5	S
88333	88333[4]	5	5	S
94444	94444[4]	5	5	S
95353	95353[4]	5	5	S
97333	97333[4]	5	5	S
97441	97441[4]	5	5	S
97522	97522[4]	5	5	S
517131	One up one down[4][83]	3	6	A
615150	Shower with a "leak"[7]	3	6	A
661515	661515[6]	4	6	A
719151	One high one low[4]	4	6	A
777171	777171[6]	5	6	A
5224233	Relf's Rubensteins[84]	3	7	S
7161616	7161616[6]	4	7	S
7272712	7272712[6]	4	7	S
33333342	Icelandic Shuffle[85]	3	8	A
123456789	123456789[4][86]	5	9	S
8483848034	8483848034[87]	5	10	A
53145305520	53145305520	3	11	S

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

Siteswap	Name	Props	Period	Symmetry (S/A)
(2x,4x)	Half-shower[88]	3	1	A
(4,2)	Fake Columns, yo-yo etc.[89] (identical to 42[7])	3	1	A
(4,2x)(2x,4)	Box[6][7][9][90][91]	3	2	S
(4,4)	Columns, etc.[92][93]	4	1	S
(4,4)(4,0)	Columns/One Up Two Up[7][9][94][95]	3	2	A
(4,4)(4x,0)*	Alternating columns[96]	3	4	S
(4,6x)(2x,4)	(4,6x)(2x,4)[97]	4	2	A
(4x,2x)	Shower[6][87][98]	3	1	A
(4x,2x)(4,2x)(2x,4x)(2x,4)	Double box[6]	3	4	S
(4x,4x)	Crossing columns[9][99]	4	1	S
(4x,6)(6,4x)	Box[4][97]	5	2	S
(6,2x)(6,2x)	Box[100]	4	2	S
(6,2x)(6,2x)(2x,6)(2x,6)	(6,2x)(6,2x)(2x,6)(2x,6)[6]	4	4	S
(6,4)	3 in 1, 2 in the other	5	1	A
(6,4x)(4x,2)	(6,4x)(4x,2)[97]	4	2	A
(6,6)(6,2)	3 in 1, 2 in the other[6]	5	2	A
(6,6)(6,6)(6,0)	3 in 1, 2 in the other[7]	5	3	A
(6x,2)(6,2x)(2,6x)(2x,6)	(6x,2)(6,2x)(2,6x)(2x,6)[6]	4	4	S
(6x,2x)	Shower[9][101]	4	1	A
(6x,2x)(2x,6x)	Box shower/shower box[6][102]	4	2	S
(6x,4)(4,2x)(4,4)(4,6x)(2x,4)(4,4)	Tennis[103]	4	6	S
(6x,4)(4,2x)(4,6x)(2x,4)	Synchronous 534[104]	4	4	S
(6x,4)(4,6x)	(6x,4)(4,6x)[15]	5	2	S
(6x,4x)	Half shower[7]	5	1	A
(6x,6x)(2x,2x)	(6x,6x)(2x,2x)[9]	4	2	S
(8,2x)(4,2x)(2x,8)(2x,4)	Dan Bennett's box[6]	4	4	S

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

Siteswap	Name	Props	Period	Symmetry (S/A)	Timing (S/A)
3p>	One-count[9]	6	1	S	A
3p3> or <33p|33p>	Two-count[9]	6	2	A	A
3p33>	Three-count	6	3	S	A
3p333>	Four-count	6	4	A	A
3p33333>	Six-count[105][106]	6	6	S	A
<5p333><335p3>	Simplest 4 count 7 prop[107]	7	4	A	A

Ladder diagrams

• 
  Half-box: 441
• 
  53145305520
• 
  Box: (4,2x)(2x,4)
• 
  Burke's barrage: 423
• 
  Cascade: 3
• 
  Columns: (4,4)(4,0)no i want 3 ball columns
• 
  Columns, alternating: (4,4)(4x,0)
• 
  Rubenstein's revenge: 52233
• 
  Shower (asynchronous): 51
• 
  Shower (synchronous): (4x,2x)
• 
  Fountain (asynchronous): 4
• 
  Fountain (synchronous): (4)(4)
• 
  Four-count pass juggling: <3p333|3p333>
• 
  4 count 7 prop 2 juggler pattern

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.

External links

• Siteswap.org