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To see the principles from technique class in action on the stage, watch closely this video of Sara Mearns, principal dancer at New York City Ballet, performing Balanchine's Walpurgisnacht.
(If you open in a browser you can watch in full-screen HD).
First, in 0:34-0:49 there are nine examples of Ms. Mearns reaching out of the supporting side wrist/arm to create counterbalance—either to sustain the equilibrium over the pointe shoe or locomote more efficiently in coordination with pressing the ground away with her toes.
Then, at 0:50 Ms. Mearns begins a series of piqué turns. The first four alternate between en dedans turns attitude derrière and en dehors turns attitude devant, followed by two standard piqué turns, two "lame ducks" (sometimes called step-over turns), and one more piqué turn. In all nine turns, the principle of the leading arm and shoulder going back to turn the body is evident.
This exquisite video demonstrates the fundamentals we work on in elementary classes applied to dancing at the highest level. When turning (whether in pirouette or a simple facing change like battement tendu en tournant), let the leading arm start taking the spine around and don't lose the integrity of the supporting side.
For beginners applying this to your work: instead of pushing the shoulder of the second side into the turn (which often spoils the balance by sending too much weight in one direction) reach out of the arm on the supporting side to make and maintain a muscular connection between the upper and lower body, as well as keep your weight off the heel. Once you've learned to pirouette with the arms in second position—like a birds wings energetically soaring—you can start moving the arms to other positions.
Eventually, to increase speed for multiple turns one can practice pulling the arms in, which decreases the moment of inertia and increases velocity (as one goes down the other goes up to conserve angular momentum). This action, however, is a trick for increasing speed after you've already set a turn in motion, not the the technique for starting the turn.
Thanks to Finis Jhung for steering me to this video.
Sara Mearns performing Walpurgisnacht. Movement with opposition creates equilibrium.
In his 2018 book, Finis Jhung describes the conflict between his love of Madame Perey, his 'Imperial Russia personified' and 'magnificent' teacher, and his realization that his dancing ability was declining as he tried to contort his body to meet her demands. This period of his career seemed to be the start of his vehement adherence to the principle that dancing from the feet—and feeling the interaction with the floor—is far more important to technical achievement and well-being than creating textbook positions.
Keep in mind this was 1960 and these were not new ideas. Years before, William Christensen had taught Finis an intelligent way of moving that worked within the natural limitations of his body without ever demanding perfect fifth positions or using the easy-to-misinterpret cue pull up.
The idea of dancing from the feet is often absent in the teaching I observe. I hear from my students it is missing from the classes they have taken as well.
Perhaps there is something about naming bodily shapes that allows them to persist with less effort than muscular engagements identified by proprioception. I hope to hear your thoughts.
The account of dancing for Madame Perey begins on page 68. Although the book is out of print, it is available as an eBook through Amazon.