In order to resolve the square - in other words, get every dancer back to their original partner to Promenade Home in the correct order - there are several important details about the dancers' positions that a square dance caller must recognize and manipulate. For each of these details, there is a standardized term, approved by Callerlab, which allows callers to communicate this information with other callers.
The most essential terms are: Formation, Arrangement, Sequence, and Relationship. These four are often referred to collectively as 'FASR'. For "at-home" choreography, two additional terms are required to fully specify the setup or "Total FASR". A few additional terms are important and are explained later below. Be aware that some older publications refer to some of these same terms in a different order or with slightly different names.
For additional reference see Diagrams of common FASRs (or with plain text diagrams)
Quick Overview of FASR ( click links for more detailed explanations )
How mixed up could dancers be in an unresolved square? Two parts to this question:
How many formations?...
See Square Dance Combinations for a look at the math behind the theoretical number of combinations
How many partner scrambling possibilities?...
|6 arrangements X 4 sequences X 4 relationships = 96 dancer position states|
See Square Dance Combinations for a different explanation of why there are 96
|4 sequences X 4 relationships = 16 dancer position states|
See 16 Combinations with Standard Arrangement - learn to recognize the patterns
|2 pairing states X 2 sequence states = 4 dancer position states|
See The Easiest Resolve - resolving the square from DPT Formation
See How to Resolve the Square for an example resolve process
Refer also to Diagrams of common FASRs (plain text diagrams)
I use a standardized shorthand notation throughout this web site to identify the formation, and optionally arrangement, sequence, and relationship. This shorthand notation is based as much as possible on that published by Callerlab. Be aware that I have made some common-sense extensions to Callerlab's notation. I try to point this out where the notation is explained.
FASR notation is easy to spot on this web site - a few letters and numbers enclosed in square brackets [ ]. This notation has 4 parts that always appear in this specific order: Arrangement Formation Sequence Relationship....
Example: [L] --- Facing Lines, any arrangement. Sequence and relationship not relevant
Example: [L1p] - Facing Lines, standard arrangement, in sequence, all with partner
( [L1p] implies [0L1p] )
|Sequence||1||Boys IN sequence, Girls IN sequence|
|Relationship||p||Reference boy with his partner|
See also Diagrams of common FASRs (plain text diagrams)
|Detailed Explanations of Important Terms|
The formation specifies two things....
Formation Letter Designations
* indicates my extensions - notation not recognized by Callerlab [B] "Box" 8 Chain Thru [C] Column [D] Diamonds [F] 2 Face Lines [I] * "I" Formation [L] Facing Lines [LO] * Lines Facing Out [I.L] * Inverted Lines ([O.L] Out-verted lines) [M] Completed Double Pass Thru [F.C] * Magic Column ([X.C] left handed) [P] (Beginning) Double Pass Thru [Q] (One) Quarter Tag formation [QB] * (One) Quarter Box formation [QF] * (One) Quarter 2 Face Line formation [R] Three Quarter Tag formation [RB] * Three Quarter Box formation [RF] * Three Quarter 2 Face Line formation [S] Squared Set (Static Square) [T] Trade By [TD] * Point To Point Diamonds [TF] * Tidal 2-Face Line (as couples wave) [TL] * Tidal Line (4 facing one way, 4 the other) [TW] * Tidal Wave [W] Parallel Waves
Left-hand and Mixed-hand Formation Notation
The prefixes L. F. and X. may be added before the formation letter of formations that have "handedness" to modify the presumed right-hand variant of these formations. If you can describe a formation as a right-hand or left-hand formation, then this formation has "handedness" and may be modified by one of these prefixes.
Some formations, namely columns and diamonds, could have a part of the formation that can be described as being right handed and another part that can be described as being left-handed. The most common case is a formation with centers and ends having opposite handedness. In these situations, the formation could be called a "mixed-handed" formation.
_ = formation designator (one or two letters as described above)... [_] Right-hand or non-handed formation [L._] * Left-hand formation [F._] * Ends Right-hand / Centers Left-hand (think "R-H Facing") [X._] * Ends Left-hand / Centers Right-hand (think "Cross handed")
Note -- "L.", "F.", and "X." is website extended notation, not recognized by Callerlab.
Note -- "L.", "F.", and "X." is website extended notation, not recognized by Callerlab.
|The absence of "L.", "F.", or "X." explicitly denotes a right-hand (abbreviated R-H) formation if any part of the formation has handedness, and all of those parts are right handed. Examples include R-H Waves, R-H Quarter Tag, and R-H Tidal Line.|
|"L." is used when any part of the formation has handedness, and all of those parts are left-handed. Examples include L-H Columns, L-H Two Face Line, and L-H Diamonds.|
|"F." or "X." is only used when a formation is mixed-handed, specifically when center's handedness is different from the end's handedness. Examples include Facing Diamonds and Magic Columns.|
|Formations with mixed handedness may still be referred
to as Right-handed or Left-handed formations if the word "facing" or "magic" is used.
In these cases, the handedness of the whole formation is determined by the ends or outsides.
Examples... [F.D] - R-H Facing Diamonds - R-H points, L-H wave [F.C] - R-H Magic Column - Ends have R-H, Centers have L-H [X.D] - L-H Facing Diamonds - L-H points, R-H wave [X.C] - L-H Magic Column - Ends have L-H, Centers have R-H
|Formations possessing 3 (or more) parts that have
handedness are possible, but this system does not attempt to describe them.
Example: From [SS]: Side Boys Run; Heads Pass The Ocean; Very Centers Hinge (This gives a facing diamond between column ends)
For more information on formations see....
Arrangement is where the boys and girls are within the formation. When the arrangement is symmetric (which is usually the case), there can only be 2 boys and 2 girls at one time in any half of the square. Symmetry says the other half will be a mirror image copy of the first half.
In half of a square, there are only 6 possible ways to arrange 2 boys and 2 girls into 4 positions. As an example we use one wave - half of parallel waves or a tidal wave....
These 6 ways to arrange the boys and girls translate to the 6 Callerlab arrangement states: 0, 1/2, 1, 2, 3, and 4. I use 5 for 1/2 arrangement (think 0.5) so on this website the six arrangement states are: 0, 5, 1, 2, 3, and 4. Callerlab assigns these numbers to the 6 arrangements for the most common formations. While there are general trends for assigning numbers to arrangement (see below), the assignment depends on the specific formation. See Arrangement Diagrams for the specific assignments.
Throughout this website, I have assigned numbers to the 6 arrangements of a number of additional formations beyond the ones assigned by Callerlab. I tried to make the most rational choice for assignments based on general trends. I detail the method I used for each of these formations in Arrangement Diagrams.
Key to Arrangement Notation / General Trends for gender arrangement
The arrangement number immediately precedes the formation letter(s).
_ = formation (one or two letters as described above)... [0_] (zero) everyone in Normal/Standard Arrangement (Boy on the left, Girl on the right) [5_] (0.5 = 1/2 = half) everyone in Sashayed Arrangement (Girl on the left, Boy on the right) [1_] (one) typically boys on or toward the outside [2_] (two) typically girls on or toward the outside [3_] (three) typically Normal/Standard on or toward the outside [4_] (four) typically Sashayed on or toward the outside [1/2_] Older notation for "half" (sashayed) arrangement. See [5_]
Example: [5B] = Sashayed 8 Chain Thru formation
Example: [L.0D] - Left-hand Diamonds, boys in center wave
Sequence is the order of the dancers going around the formation in promenade direction (C.C.W.). Callers commonly use the word "sequence" when all dancers are near their partners to describe weather or not everyone is in the proper order (in sequence) or not in the proper order (out of sequence) to call Promenade Home or Allemande Left, etc. "Sequence" as defined by Callerlab refers to the boys' and girls' sequence collectively. The girls can be in or out of sequence and the boys can be in or out of sequence and the single FASR term "sequence" describes both at once with a number 1...4.
Sequence is denoted by a number 1...4:
How to determine sequence
|In sequence||In sequence||1|
|Out sequence||Out sequence||2|
|In sequence||Out sequence||3|
|Out sequence||In sequence||4|
Symmetry describes a specific kind of balance. It indicates that when some condition exists on one side of the formation, it exists on the other side as well. There are different kinds of symmetry. Three important kinds are: Formation Symmetry, Arrangement Symmetry, and Sequence Symmetry. If the dancers don't make any mistakes and dance what is typically called at most open dances, all of these symmetries exist at the same time. In fact, these symmetries exist at all times. It is possible, and in fact interesting at times, to have 'Asymmetric Choreography' that deliberately upsets one or more of these symmetries causing certain kinds of imbalance in the square.
Symmetry is very powerful for the sight caller because it substantially reduces the number of combinations possible with 8 dancers.
Sequence and Sequence Symmetry
Here is an illustration. Let's arbitrarily choose a formation and an arrangement and then let same gender dancers mill around and randomly exchange places with other same-gender dancers. The boys must end up in one of the 4 boy "spots" and the girls must end up in one of the 4 girl "spots" in our formation. This sort of swapping does not affect formation nor arrangement, but it does affect sequence and sequence symmetry.
When the sequence is symmetric, knowing were one boy is automatically establishes where his mirror opposite is - diagonally across the square from him, equidistant from the flagpole center of the square. With 2 boys positions' established, that leaves only 2 other boys and 2 other boy spots. These other 2 boys are each other's mirror opposites and the only possible way to scramble them is to have them exchange places with each other. That means there are only 2 ways to sequence the boys. One way is (using the boys' couple number) 1-2-3-4 Clockwise, the other is 1-2-3-4 Counter Clockwise.
The same is true of the girls.
There are only these 2 possible sequence states for each of the genders when the sequence is symmetric:
Note that all of the following have the same sequence (in sequence)...
Here are just a few examples of asymmetric sequence...
Even with all of these ways the square can be asymmetric, almost all choreography is symmetric meaning that all of these symmetries exist at all times. Without mistakes, each dancer dancing symmetric choreography dances the exact same parts of every call, enjoys the same flow, and solves the same part of the "puzzle" as their mirror opposite. The caller is creating 4 unique experiences as there are only 4 distinct dance threads in symmetric choreography.
Relationship is how the boy sequence is related to the girl sequence -or- how a reference dancer is positioned relative to his or her partner.
Once the formation, arrangement, and sequence are specified, there is yet another piece of information we will need before we can call an Allemande Left or Right and Left Grand, etc. That is Relationship. The simplest way to illustrate relationship is to start with a squared set and have everyone Join Hands and Circle To The Left. Each boy has his partner girl to his right. Now call Put The Ladies In And The Men Sashay. Notice that the formation is still a circle, the arrangement is still alternating B, G, B, G, etc., and both the boys and girls are "in sequence" (1, 2, 3, 4 going around the ring in promenade direction). But each boy no longer has his partner girl to his right. What changed was the relationship the dancers have with their partners.
There are 4 relationships denoted by the letters p, c, o, r...
What is a reference boy?
The reference boy is the boy dancer of the reference pair. The reference pair is comprised of 2 opposite gender dancers in the formation that we will use to determine how the boy sequence is related to the girl sequence. This will determine which of the 4 relationships we have. It is somewhat arbitrary which dancers we choose for the reference pair and it unfortunately makes a definite difference, affecting which letter (p, c, o, r) gets assigned, especially in sequence states 3 and 4 where one of the boys may have his partner while the other has opposite girl. It is important that reference dancers be chosen based on positions within a formation, rather than by any one specific dancer throughout the tip, otherwise Relationship will depend on the Sequence, and that would be undesirable. (this is explained further below)
Which is the reference pair?
This could still be a topic of debate. There are convenient choices one can make, but ultimately the choice is somewhat arbitrary. What has been agreed upon is which dancers make up the reference pair (the reference boy and the one girl he is adjacent to for purposes of establishing the relationship) in 4 formations with standard gender arrangement only: [L], [B], [F], and [W].
Reference Pair shown in RED
|Lines||Box / 8-Chain||2-Face Lines||R-H Waves|
|Because of the limited scope and "messiness" of the definition of Relationship using a reference pair, I've started working on another FASR notation called 'bang' setup notation.|
If we were to take the entire formation and all dancers in it, and rotate everything 90 degrees clockwise or counter clockwise about an imaginary flag pole rising up out of the floor from the very center of the formation, we would be changing only the Orientation of the formation. There are 4 Orientation states corresponding to 0 deg, 90 deg, 180 deg, and 270 deg and they are expressed in terms of a how a reference boy is positioned relative to his home.
Reference Boy shown in RED
Callers typically end dance sequences with Promenade Home which instructs the dancers to Promenade as far as necessary to reach home, thus eliminating the need to worry about Orientation. However, if the caller wanted to resolve the square "at home" (everyone landing exactly on their home spot on the last call), s/he would need to manage the Orientation of the square in addition to FASR.
At first glance, you might say the following two diagrams differ in Orientation, but in fact they have the same Orientation and differ only in Occupation. The difference is that in one case the Reference Boy was a Head, and the other, a Side.
If the call was Centers Star Thru and Back Away, there would be no difference - all end at home. However if the call was Heads Trade, the result would be quite different in the two cases. Occupation only comes into play if the caller uses Heads or Sides or couple numbers for a designator.
There are only two Occupation states: "Head" and "Side" and they are specified by a trailing ' (prime character) or a + (plus sign) in the FASROO notation.
See FASROO for a focused look at Orientation and Occupation notation.