Here is a dance with both a left and right chain....
The Balter Dance
Becket Left     Beg-Int    by Michael Fuerst  May 2021
Recent video 2025 Cabin Fever weekend in Knoxville TN
     
https://www.youtube.com/watch?v=wtTO2Jrsv4A
*A1*
 Robins chain to neighbor
 Left hand star once around
*A2*
Larks chain to partner.
Right hand star once around.
*B1*
With neighbor, right hand balance pull by across.
Partners swing on side they started the dance,  end facing across.
*B2*
Long lines forward and roll away with 1/2 sashay.
      (Larks slide right to robin's place while robins  roll in front of
lark to take larks place)
Partner balance towards each other and away (4)
With robins holding their place,  larks roll from right side
      to left side of partner, all finishing facing new neighbors (4).
(Partners' joined hands at end of roll can guide  robins  into A1's chain.)
Notes:
(1) Balter - to dance artlessly, without particular grace or skill, but
usually with enjoyment.
(2) Although neither expected nor intended, this dance is suitable for a
crowd with a high proportion of beginners, as one caller reported to me:"I
called a couple of your dances tonight. There were totally brand new
dancers in the mix--folks with not even other dance experience--so even
basic stuff required like 3 walk-thrus. We did Dave Found The Missing
Coffee Cup, and Balter Dance. Balter Dance was particularly well received
for its chains for both ladies and gents, which is rare, and works
beautifully with the alternating stars. One person commented that it was
great for helping new dancers, since you're in physical contact with either
a partner or neighbor almost all the time, so you don't get lost or wander
in the wrong direction."So by accident, this dance was aptly named.
On Mon, Mar 24, 2025 at 11:52 AM jim saxe via Contra Callers <
contracallers(a)lists.sharedweight.net> wrote:
  The second part of "Parson's Farewell",
published in Playford's _The
 English Dancing Master_ (1651), includes an action that (at least under
 some interpretations, such as the ones shown here
         
https://www.youtube.com/watch?v=3X4wpEIOZIM&t=40s
         https://www.youtube.com/watch?v=AQhvmA0UJYg&t=45s
 ) is recognizably ancestral to gents' and ladies' chains, a connection
 that, if I recall correctly, I first heard of from Colin Hume. First the
 men travel across and back, passing by left hands with each other (but with
 some sort of variously-interpreted feint with right hands); then the women
 do the same, but with contrary hands. The turns with opposite and partner
 are commonly interpreted as one-hand turns. (The so-called "courtesy turn"
 didn't become a standard styling until some time in the 20th century.)
 Several of the quadrilles in J. A. French's _The Prompter's Hand Book_
 (undated, but Library of Congress suggests circa 1893) include the figure
 "gents grand chain". French doesn't give definitions of the figures, but
my
 guess would be that gents begin by crossing the set by left hands with
 opposite gent, as in a left-hands-across star halfway around.
 --Jim
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