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I just finished a new book, Countable Calculated Figures, which is just going into circulation.   Here are a couple dances (with music samples) from that book.   I do have several new dances that are not in the book.   As soon as I have a chance to test them with real people, I will put them up here.

Music Sample
The Happy Pilgrim
Music Sample


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 dance, I discovered that there are few if any dances in the English, Scottish, and Square dance repertoire with this characteristic.   In fact, I could not find a single one and I wondered why.   Working with Mathematics Professor Michael Bush, now at Washington and Lee University, I found the reason:

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 need to be the same, and the figures done the 2nd and 4th times through also must be the same, but the two sets must be different (in a narrowly prescribed way).

With this insight, I have now written six DP/DP dances.   The goal in each was to write a dance that felt more or less the same every time through, despite the DP/DP requirement, and avoid creating a sense that two entirely separate dances had simply been interwoven.   Actual dancers will have to decide whether or not I have met the 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" in A Sequence of Calculated Figures
      "Three's Company" in A Sequence of Calculated Figures
      "Quabbin Waltz"   in Countable Calculated Figures

"Three's Company" deserves special comment.   It is a DP/DP dance for four trios of dancers (rather than couples).  The mathematics behind solving this puzzle says that it is theoretically possible to devise such a dance.   I know that what is conceptually possible is not necessarily enjoyably danceable.   I think that "Three's Company" is enjoyable, but again dancers will have to tell me.

NOTE:   Kathryn Wright (of "The Wrights of Lichfield") has created a very useful, multi-colored diagram of the moves in "Three's Company".   It is especially helpful for keeping track of where everyone is as you teach the dance. Click Here to see it.

        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.

Ann Arbor Hornpipe
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


Trip to Stonington

Quabbin Waltz


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)
Lichfield's Ruby Surprise
A Quick Romp in the Hey
Ramblin' Rosie
Social Symmetry
(measure numbers)
Three's Company
(link to diagram)
The Woodcock
Woodlands Waltz
(measure numbers)