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m Difficulty is a bias and not relevant to the definition of siteswap. |
Clean up intro to make it concise. Moved more detailed explanation to Vanilla section. Moved Etymology to origin section. Created table of throw names with descriptions. |
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{{Redirect|Juggling beat|music|beat juggling}}
[[File:Siteswap relative visualized.png|thumb|Siteswap beats shown as relative height<ref>{{Cite news
'''Siteswap''' is a [[juggling notation]] used to describe or represent [[juggling pattern]]s. It is also referred to as '''Quantum Juggling''', or The '''Cambridge Notation.''' ''Siteswap'' may also be used to describe '''siteswap patterns''', possible patterns transcribed using siteswap. It encodes the number of '''beats''' of each throw, which is related to their relative height, and the hand to which the throw is to be made: "The idea behind siteswap is to keep track of the order that balls are thrown and caught, and only that."<ref name="FAQ">{{Cite web|url=http://www.juggling.org/help/siteswap/faq.html|title=Siteswap FAQ|last=Knutson|first=Allen|website=[[Juggling Information Service|Juggling.org]]|access-date=June 30, 2017}}</ref> It is an invaluable tool in determining which combinations of throws yield valid juggling patterns for a given number of objects, and has led to previously unknown patterns (such as 441). However, it does not describe body movements such as behind-the-back and under-the-leg. Siteswap assumes that, "throws happen on [[beat (music)|beats]] that are equally spaced in time."<ref name="B&L">{{Cite book|last=Beek|first=Peter J.|last2=Lewbel|first2=Arthur|chapter=The Mathematics of Juggling|title=The Science of Juggling|chapter-url=https://www2.bc.edu/~lewbel/jugweb/sciamjug.pdf|archive-url=https://web.archive.org/web/20160304104003/https://www2.bc.edu/~lewbel/jugweb/sciamjug.pdf|archive-date=March 4, 2016|url-status=dead|journal=[[Scientific American]]|issn=0036-8733|language=en|date=November 1995|volume=273|issue=5|pages=92–97|doi=10.1038/scientificamerican1195-92|bibcode=1995SciAm.273e..92B}} Also available at [http://www.juggling.org/papers/science-1/mathematics.html Juggling.org].</ref>▼
▲'''Siteswap''' is a numeric [[juggling notation]] used to describe or represent [[juggling pattern]]s. It is also referred to as '''Quantum Juggling''', or The '''Cambridge Notation.''' ''Siteswap'' may also be used to describe '''siteswap patterns''', possible patterns transcribed using siteswap.
For example, a three-ball cascade may be notated "3", while a [[shower (juggling)|shower]] may be notated "5 1".<ref name="B&L"/>
▲[[File:Siteswap relative visualized.png|thumb|Siteswap beats shown as relative height<ref>{{Cite news|url=http://discovermagazine.com/2004/dec/mathematics-of-juggling|title=The Mathematics of... Juggling|last=Donahue|first=Bill|date=December 3, 2004|work=[[Discover Magazine]]|access-date=June 30, 2017}}</ref><ref name="T&M">Tiemann, Bruce and Magnusson, Bengt (1991). "[https://web.archive.org/web/20120612161501/https://www.juggle.org/history/archives/jugmags/43-2/43-2,p31.htm A Notation for Juggling Tricks, A LOT of Juggling Tricks]", ''Juggle.org''. Accessed July 8, 2014. [https://www.juggle.org/history/archives/jugmags/43-2/43-2,p31.htm original url]</ref>]]
*3 = (3-ball) [[cascade (juggling)|cascade]] toss [between hands]▼
For example, a three-ball cascade may be notated "3", while a [[shower (juggling)|shower]] may be notated "5 1".<ref name="B&L"/> The name ''siteswap'' comes from the ability to generate patterns by "swapping" landing times of any 2 throws in a siteswap. For example, swapping the landing times of throws "5" and "1" in the siteswap "51" generates the siteswap "24" {{Citation needed|date=December 2017}}.▼
==Origin==
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*"...Bruce Tiemann (Boppo) and the late Bengt Magnusson....Other contributors to the development of site swap theory include Jack Boyce, Allen Knutson, Ed Carstens, and jugglers on the computer network."<ref name="Lewbel">Lewbel, Arthur (1996). "[http://www.juggle.org/history/archives/jugmags/49-2/v49no2-page%2057.htm The Academic Juggler: The Invention Of Juggling Notations] {{webarchive|url=https://web.archive.org/web/20140714182339/http://www.juggle.org/history/archives/jugmags/49-2/v49no2-page%2057.htm |date=July 14, 2014 }}", ''Juggle.org''.</ref>
*"Jack Boyce (also at Caltech) came up with the juggling state model to explain the phenomenon of excited-state tricks."<ref name="FAQ"/>
*"To give credit where it is due, the notation as presented here was independently (and previously) invented by Paul Klimek, with whom we have had helpful discussions."<ref name="T&M"/>}} The numbers derive from the number of balls used in the most common juggling patterns. Siteswap has been described as, "perhaps the most popular" name.<ref name="Sethares">{{Cite book|title=Rhythm and Transforms|last=Sethares|first=William Arthur|author-link=William Sethares|date=2007|publisher=[[Springer Publishing|Springer]]|isbn=9781846286407|oclc=261225487|page=40}}</ref>
▲
==Vanilla==
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Its simplest form, sometimes called vanilla siteswap, describes only patterns whose throws alternate hands and in which one ball is thrown from each hand at a time. If one were juggling while walking forward, something like the adjacent diagram would be seen from above, sometimes called a '''space-time diagram''' or '''ladder diagram'''. In this diagram, three balls are being juggled. Time progresses from the top to the bottom.
This pattern can be describe by stating how many throws later
{| class="wikitable"
|+Siteswap Throw Names
!Throw Name
!Beats object is in Air
!Switches hands
!Description
|-
|0
| -
| -
|Empty hand
|-
|1
|1
|Yes
|Throw from one hand to the other
|-
|2
|0
|No
|Momentary hold
|-
|3
|3
|Yes
|-
|4
|4
|No
|Throw from a 4 ball [[Fountain (juggling)|fountain]]
|-
|5
|5
|Yes
|Throw from a 5 ball [[Cascade (juggling)|cascade]]
|-
|6
|6
|No
|Throw from a 6 ball [[Fountain (juggling)|fountain]]
|-
|7
|7
|Yes
|Throw from a 7 ball [[Cascade (juggling)|cascade]]
|-
|8
|8
|No
|Throw from a 8 ball [[Fountain (juggling)|fountain]]
|-
|9
|9
|Yes
|Throw from a 9 ball [[Cascade (juggling)|cascade]]
|-
|a
|10
|No
|Throw from a 10 ball [[Fountain (juggling)|fountain]]
|-
|b
|11
|Yes
|Throw from a 11 ball [[Cascade (juggling)|cascade]]
|-
|...
|...
|...
|...
|}
There are three special throws: a ''0'' is a pause with an empty hand, a ''1'' is a quick pass straight across to the other hand, and a ''2'' is a momentary hold of an object. Throws longer than ''9'' beats are given letters starting with ''a''. The number of beats a ball is in the air usually corresponds to how high it was thrown, so many people refer to the numbers as heights, but this is not technically correct; all that matters is the number of beats in the air, not how high it is thrown. For example, bouncing a ball takes longer than a throw in the air to the same height, and so can be a higher siteswap value while being a lower throw.
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