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Here are five new dances I have written since A Group of Calculated Figures appeared:   "Autumn Moon" (tune by Rebecca King), "Silver Lining" and "Forget Me Not" (tunes by Debbie Jackson), "It's a Draw" (tune by Greg Allen), and "Three's Company" (tune by Susan Conger).   There are recordings for the first three dances on our new CD, Good Friends, and there will probably be recordings for the last two on our next CD.   Great music for all five, as you will see.
Autumn Moon Silver Lining Forget Me Not It's a Draw Three's Company


Over the last few years, I have written several four-couple dances in which every dancer is in a different place with a different partner every time through the dance.   When I started trying to write this kind of a dance, I thought I would find many like it in the existing repertoire.   But as I searched on my own and informally surveyed knowledgeable English, Scottish, and Square dance leaders, I found not a single one.   I soon realized that it is more difficult to concoct a DP/DP dance that it appears at first.

I remained stumped about how to do it until I showed the problem to Michael Bush, who is now an Assistant Professor of Mathematics at Washington and Lee University.   Michael helped me analyze this puzzle using Group Theory, a branch of mathematics that analyzes symmetries.   The most important thing we discovered is this:

The DP/DP effect can not be achieved by doing exactly the same figures four times in a row.   Rather, the figures done the 1st and 3rd times through the dance must be different (in a narrowly prescribed way) from the figures done the 2nd and 4th times through.

This insight helped get me moving.   As in all dance writing, the challenge is to create something that is fun to do, makes sense, and is not obviously contrived.   I hoped to avoid writing two entirely separate dances and simply interweaving them.  Rather, I wanted the dance to feel more or less the same throughout, with just small differences each time (e.g., “In B1, men circle left the 1st and 3rd times, women circle right 2nd and 4th times”).

I have now written four DP/DP dances (plus one more that I will comment on below).   Actual dancers will have to decide whether or not I have met my goal.
      “The Invitation” in A Group of Calculated Figures
      “Mevagissey Car Park” in A Group of Calculated Figures
      “Social Symmetry” in A Group of Calculated Figures
      “Silver Lining” forthcoming in A Sequence of Calculated Figures (and see above)

ONE MORE DP/DP DANCE:   The mathematics behind this puzzle shows that it is possible to devise a DP/DP dance for four trios of dancers (not just pairs).   Again the challenge for the choreographer is to come up with something that is both fun and rememberable.   I know from experience that what is conceptually possible is not necessarily enjoyably danceable.   My one attempt at this is called “Three’s Company”.   It’s a square with three dancers on each side.   (It will be included in A Sequence of Calculated Figures, but also see above.)

FYI, Michael Bush and I have written two versions of a paper on this topic.   The first one is a careful mathematical statement of how we figured things out.   It recently appeared in Journal of Mathematics and the Arts.   The second paper tries to motivate the key ideas from the first paper without being too rigorous about it.   It is addressed to people with some mathematical knowledge (but not too much) and an interest in dancing.   The arguments in the second paper are relatively easy to follow, but it may not always be obvious why they are always true.   To get that part, you probably need the first paper.*
First Paper Second Paper

* In addition to Michael Bush's help in solving this puzzle, I want to acknowledge the members of the informal ECD Society of Dancing Mathematicians, who saw my query on the ECD List about the existence of such dances and sent me valuable comments and ideas.   Al Blank and Robert Messer were particularly enthusiastic about helping me figure things out.

Occasionally, there is a dance of mine that I wish I could tinker with and re-release.  Also, I sometimes think of a way I could have made the instructions for a dance clearer.   The changes I have wanted to make are all pretty small, but I offer them here anyway for your consideration.

Cadgers' Caper
Charlene's Celebration
Coming and Going

Designing Woman

Far Away

Henry's Hornpipe

Honeysuckle Cottage

Laisteridge Lane

The Matching Pair

Mevagissey Car Park

Mr. Chopin's Waltz

Mr. Roodman's Fancy

Promise of Spring



Here are some minor typographical and musical-notation errors that have snuck into my books.  There are probably others I have not found yet, but here are the ones I know about.
Alexander's Birth Day
(tempo marking)
Designing Woman
Far Away
Helene('s Gavotte)
(name change)
A Quick Romp in the Hey
Ramblin' Rosie
Social Symmetry
(measure numbers)
Woodlands Waltz
(measure numbers)