These concepts can often be analyzed in terms of some pairs of people
in the original ("2x2") call being expanded to three people while
others are reduced to one. However, it is probably best to think in
terms of 3x3, with some of the groups of three reduced to a single
person. 3x1 Checkmate provides an example:
\sxhBBBstwelve{b4w,g3e,b5w,g2e,b6w,g1e}
\sxhBBBstwelve{b3s,g6s,b2s,g5s,b1s,g4s}
before 3x3 Checkmate
after
We reduce some of the groups to 1:
\sxhBBBstwelve{.+.,g3e,b5w,g2e,.+.,g1e}
\sxhBBBstwelve{.+.,g6s,b2s,g5s,.+.,g4s}
before 3x3 Checkmate
after
The 3x1 version is formed by compressing both the "before" and "after"
pictures:
\syhlines{b2e,g1e,g2e,b1e}
\syhlines{b4n,g3s,g4s,b3s}
before 3x1 Checkmate
after
Of course the dancers don't actually have the luxury of making
pictures and compressing them. So the principal problem in doing
3x1-types of calls is identifying what 3 real people remain the
"real" 3x3 people and what individual person is associated with two
phantoms to become the other 3x3 group. After making that
determination, do the 3x3 call, and then compress out the extra
phantoms to make the final setup.
First, there is a convention about how to choose the "3" people and the "1"
person. For many calls it is easy to make the determination based on facing
direction. 3x1 Cross Roll is an example:
\phfour{bAn,bBn,bCn,gDs}
\phsix{bAn,bBn,bCn,.+.,gDs,.+.}
before 3x1 Cross Roll
mentally expand to 3x3
\phsix{.+.,bAs,gDn,bBs,.+.,bCs}
\phfour{bAs,gDn,bBs,bCs}
do the 3x3 call
recompress
This is a good point to notice something tricky about calls like
this — person "D" had to go into the center spot, that is, take
hands with the centermost of the other 3 people. This is sometimes
hard to see. This will show up in things like 1x3 Transfer.
In cases like Cross Roll, in which the facing direction determined how
people were grouped, it doesn't matter whether the caller says "3x1"
or "1x3".
The other situation is the one in which the 3 people who are grouped
and the one who is single are facing the same direction. In that case
the convention is that, if they are in tandem, they count from the
front to the back, and if they are side-by-side they count from right
(belle side) to left (beau side.) That is, 3x1 in columns means that
the front 3 people are grouped and the last person is single, whereas
1x3 means that the front person is single and the remaining 3 are
grouped. From back-to-back lines, 3x1 means that the 3 rightmost
people are grouped and the leftmost one is single.
\syhlines{b2e,g1e,g2e,b1e}
\syhlines{g3s,b2n,g4s,b3s}
before 3x1 Transfer
after
Notice that the side boys had to be very careful here. After the Cast Off 3/4,
they are facing 3 people. They come out to the center of those people, and
take right hands. Compare this with the 3x1 Checkmate shown previously.
\syhlines{b2e,g1e,g2e,b1e}
\syhlines{b2n,g1n,b3s,g2n}
before 1x3 Transfer
after
In this 1x3 Transfer, the head boys have to deal with the center of the 3
people extending to them.
Recompression is sometimes necessary and sometimes not:
\syhlines{b4n,g4n,b1n,g1n}
\syhDBDs{g4s,b4s,b1s,g1s}
before 3x1 Turn and Deal
after
\sxhlines{b2s,g2s,b3s,g3s}
\syhlines{b4s,g3n,b3n,g2n}
before 3x1 Turn and Deal
after
This last example shows that the recompression can be quite nonintuitive.
Even though 3x1 Turn and Deal is a 4-person call, and there are conventions
about gluing subformations together within non-overlapping rectangles,
that rule is not followed when the 3x1 concept is in use. The side boys are
not lined up with the 3 people with whom they were working.
Here are some examples showing the need to be careful about identifying the group
of people with whom you are working.
\sxvlines{b3s,g3s,b4s,g4s}
\syvBBBs{.+.,g2n,b3s,b2n,.+.,g1n}
before 3x1 Split Recycle
mentally spread out groups
\sxhBBBs{.+.,g2s,g3n,.+.,b1s,b2s}
\syhlines{g1s,b3n,b2s,g2s}
\cbox{do the 3x3 call
mdash; this is very hard!}
recompress
\sxvlines{b3s,g3s,b4s,g4s}
\syvBBBs{b3s,.+.,g3s,g2n,b4s,.+.}
\syhDBDs{b4s,g2n,g3s,b3s}
before 1x3 Walk and Dodge
mentally spread out groups
do the call
This is not the "obvious" thing people might be tempted to do when they
hear 1x3 Walk and Dodge.
When doing a 3x1 or 1x3 version of a call that normally starts in a wave,
the center 2 people of the actual line determine the handedness of the 6-person
wave that people need to think about. Those people will often say "right" or
"left" to indicate the handedness that the end people should infer. Those
end people then spread out appropriately to make a wave of 6 with the correct
handedness, and do the 3x3 version of the call.
\syhlines{b1n,b2s,g4n,g3n}
\sxhBBBs{.+.,g3n,b3s,.+.,b4n,g4n}
before 3x1 Ah So
mentally spread out groups to match handedness of center 2
\syvBBBs{.+.,g3s,b2n,g4s,.+.,b1s}
\sxvlines{b2n,b3n,g2n,g1n}
do the 3x3 call
recompress
\syhlines{b1n,b2s,g4n,g3n}
\syhlines{b2w,b3w,g2w,g1w}
before 3x1 Follow Your Leader
finished
Here is an example that is just hard:
\syhlines{b1s,g4n,g3n,b4n}
\sxhBBBs{.+.,b4n,b3n,g3n,.+.,g4n}
before 3x1 Scatter Circulate
mentally spread out groups
\sxhBBBs{g2n,.+.,.+.,b4s,g1n,b3n}
\syhlines{g4s,g3s,b3n,b4s}
\cbox{do the 3x3 call
mdash; head boy goes to center miniwave}
recompress
And another one. Only the wave version of Cross and Divide can be done with these
concepts, so the people spread out into 3 miniwaves. As usual for calls that start in
waves, the handedness of the center 2 determine the handedness of these miniwaves.
\syhlines{b1n,b2s,g4n,g3n}
\sxhBBBs{.+.,g3n,b3s,.+.,b4n,g4n}
before 3x1 Cross and Divide
mentally spread out groups to match handedness of center 2
\syvBBBs{b1e,.+.,g4e,b2w,g3e,.+.}
\sxvlines{b1e,g4e,g3e,b4e}
do the 3x3 call (3x3 Slither and 3x3 Retreat the Line)
invasively recompress
How Hard Can it Be?
And of course no challenge dance is complete without this:
\syhlines{g3s,b3s,g2s,b2s}
\sxhBBBs{.+.,b2s,g1n,g2s,.+.,b3s}
before 1x3 Load the Boat
mentally spread out groups
\sxhBBBs{b4w,.+.,g4e,g3e,b1w,.+.}
\syhlines{b2e,g2w,b3e,g3e}
do the 3x3 call (huge Wheel Around and each couple 1/4 In)
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