Calculated Figures--New Dances and Old

DIFFERENT PARTNERS & DIFFERENT PLACES

Over the last several years, I have written some 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.

"Quabbin Waltz": Here is a slightly modified version of the original dance that might be a little easier to teach and remember. It simply rearranges the figures in A1 and A2. Either version is fine with me.

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 has 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.

OLD DANCES REVISITED

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	Dovetail
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
Quabbin Waltz	Terpsicourante	Trip to Stonington

CORRECTIONS

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 (music)	Far Away (instruction)	Helene('s Gavotte) (name change)
Lichfield's Ruby Surprise (typo)	A Quick Romp in the Hey (typo)	Ramblin' Rosie (music)	Social Symmetry (measure numbers)
Three's Company (link to diagram)	The Woodcock (instruction)	Woodlands Waltz (measure numbers)

Go HOME