Friday, March 6, 2015

Variations on Odette: A Biomechanical Review of Swan Lake

After experiencing an amazing bout of ballet in 2014, I was inspired to put together the random skills I have, and offer a fresh perspective on the art form I love most. Friends also started asking about how one might begin to appreciate it, thus here is my best effort to do a very different kind of review -- a biomechanical review -- to lend both new insight and introduction to ballet!

What Makes a Swan Queen?
I have always loved classical ballet because of its fascinating duality. It is a highly structured art form, with a fixed vocabulary of steps that is centuries-old -- yet within this rigidity is in fact room for incredible flexibility, interpretation and artisty. Shades of variation exist in every performance that can make the audience's heart leap or gut clench, even in works like Swan Lake that has enthralled ballet-goers for 138 years.

What is it that makes every performance of Swan Lake unique? What makes one Swan Queen garner reviews such as "intensely dramatic", and another "touchingly vulnerable"? How can one dance "with bravura", versus "poise and subtlety"? How is it that audiences talk of discernible 'American' or 'Russian' or 'English' styles? My engineering insides hoped that Biomechanics would lend an answer (...perhaps because to a hammer, every problem is a nail!).

What is Biomechanics?
Biomechanics can be defined as an engineering study of the human body, where movements are described in great numerical detail. By obtaining data on where each part of your body is at all time, you can determine metrics such as the angle of your knee joint as you walk, or the speed of your arm as you throw a ball.

Biomechanics has been used in ballet to do everything from research how weight is distributed inside a pointe shoe, to how hip anatomy can affect the maximum height of a développé. Here, I hoped it would lend a new lens through which to appreciate ballet, eyeing out nuances in style that I wouldn't normally be able to perceive as an audience member. Thus, I set out to analyse the biomechanics of 4 magnificent Swan Queens, in an attempt to see what made each one so unique.

The Chosen Ones
The first Odette I chose was Zenaida Yanowsky, in the Royal Ballet's 2012 production of Swan Lake. (As this blog would perhaps betray,) her dancing captivates and moves me in ways that I feel compelled to better understand. Next I chose another much-loved, technically-astounding, Royal Ballet principal, Marianela Núñez, in the RB's 2009 production. These two dancers would provide an interesting contrast for how styles vary even within the same company.

The Swan Queens chosen for analysis: Svetlana Zakharova, Zenaida Yanowsky, Margot Fonteyn, Marianela Nunez

The next Odette was Svetlana Zakharova, a Russian dancer at the Bolshoi Ballet and La Scala Theatre Ballet, renowned worldwide for her prodigious extensions. Here, her 2005 performance at La Scala would give insight into the difference in styles internationally. Finally, the last choice was none other than Margot Fonteyn of the Royal Ballet, perhaps the queen of 20th century ballet, and one of the foremost ballerinas of all time. The performance I chose dates back to 1960 at the Royal Ballet, allowing yet another comparison, for dancers in the same company separated temporally.

Doing the Math
With my Odettes chosen, I dove straight into the analysis. Since this is written more for a ballet audience (or ballet audience-to-be!) I skip through the computational details -- but would love to hear more from you if you have thoughts or questions about it!

In (very) brief summary, what I did was convert 2D videos of the performances into 3D models of each dancer. I extracted the performances I wanted off YouTube, which was part of the White Swan Pas De Deux in Act 2 -- the first time Odette and Prince Siegfried dance together. I then wrote a programme to break each 20 second video clip down into a series of 100 pictures, in which I could identify a set of key points on each dancer's body. Armed with an arsenal of trigonometry, I used these key points to 'back-calculate' where the dancer would have been in real life, and therefore got data on their joint angles and velocities.

Locating each dancer's joints manually using a custom-made interface in Matlab

Suffice to say, it was a Huge Effort. When this kind of analysis is done in sports or movies, the athlete or actor is usually wearing reflective markers that help a camera to automatically locate where all their joints are. But with no likely way of convincing the Royal Opera House to add these shiny silver balls to all their costumes, I had to manually 'find' Odette in each video frame, marking what I thought was a knee, elbow, chin, etc.

Even Siegfried has trouble locating her

Mountains of white feathers later, I hope you enjoy the results below as much as I enjoyed making them!

The Biomechanics of a Swan Queen

The Choreography
Before even taking a deeper look into the movements, the choreography itself was unexpectedly different between the four Pas De Deuxs. The graphic below helps to show the different steps chosen by each dancer and their approximate timing within the score, in the specific excerpt that I analyzed.

The steps performed within the chosen extract of the White Swan Pas de Deux, and their corresponding timings in the score.

In general, all start with an allongé as Odette pulls away from Prince Siegfried. Each turns to varying degrees, with Zakharova also adding a small arabesque. As they move to the next step, the développé devant, Fonteyn goes straght into the développé, while Núñez and Zakharova insert a retiré passe en route, and Yanowsky does a small but distinct fourth. The subsequent cambré into Siegfried's arms is kept largely the same, but with slight deviations in the angle of the body. Fonteyn in particular, does more of a side than back bend, and notably, falls into someone else's arms altogether.

The final step is again performed quite differently, with Yanowsky and Núñez doing a penché, Zakharova adding a fondu; and the step is absent altogether in Fonteyn's version, replaced instead by a 'loving embrace' with Siegfried. Overall, Fonteyn's excerpt is also markedly different in terms of speed. Back in 1960, the same segment concluded within a speedy 11 seconds -- practically double-time of the other 3 performances!

These variations in the steps can come about as producers in different companies and eras stage their own versions of Swan Lake -- sometimes editing the choreography to add whole new steps, such as the penché in the modern stagings. Each dancer however, makes their own subtle choreographic choices as well, such as whether to do a retiré passe or a fourth -- so as to adapt the steps to their body type, strengths, or to say different things with their movement.

Though small, these choices can produce such varied interpretations of the same role, and the resulting story that is told. Yanowsky, with her deeper allongé than the rest, and the effect of cutting her flow of movement as she stops in fourth, comes across as a far more hesitant and skittish Odette than Fonteyn, whose body remains much closer to Siegfried in the allongé, and leans into Siegfried at the end. The resulting impact is a Fonteyn-Odette who is vulnerable, seeking protection; and a Yanowsky-Odette who is far flightier, "yearning for freedom [in] every step".

Joint Range of Motion
One of the most common things people identify when watching a ballet is just how high the dancers' legs go. In biomechanical terms, this is known as their joint range of motion (or ROM), describing how many degrees the joint can rotate through. When Sylvie Guillem does her famous 6 o'clock developpé for example, she's exhibiting a huge hip ROM.

The following graph shows a sample of the dancers' joint ROMs over the course of this extract of choreography. Note that this is far from comprehensive though -- not only are there hundreds of joints in the human body, each joint has different component angles. Hip flexion, for example, refers to joint movement only in the devant and derrière directions, while hip abduction refers to movement in the plane of an a la sèconde. Neck rotation is the head shaking 'no', while head flexion is it nodding 'yes'.

Though there's quite a bit of information in the graph, one observable distinction is that Fonteyn has a much lower ROM in her legs than the other dancers. This is in fact the result of a trend which Daprati et al. at UCL did such an incredible job analysing a few years ago -- where modern dancers' limbs have taken on greater and greater heights, in response to audience's preferences for certain geometric shapes.

But while the trend has been towards greater leg ROM, it is fascinating to note that Fonteyn had a far more generous use of her torso and neck than today's dancers. She exhibits a greater overall trunk rotation (the twisting angle of the torso between shoulders and hips), trunk flexion (which increases with hunching), as well as increased neck flexion and rotation.

Looking at the ROM for individual steps also teases out additional insights -- in executing the developpé devant, for example, Zakharova does her reputation for "achingly long lines" justice, raising her leg the highest at 148 degrees (a good 32 degrees higher than Fonteyn's). Núñez, however, exhibits the greatest split ROM (measuring the angle between left and right thighs) at a full 180 dergrees in the penché, as shown below. What's also clear from the graph is her incredibly expansive use of arms -- a perfect example of the "sensuous breadth of her upper body".

Joint Velocity
In some ways, joint ROM is something that can be discerned fairly directly by the audience. More imperceptible, however, is the metric of joint velocity, measuring how fast the dancer's limbs are moving with respect to one another. It's a messy lump of information, but the graphs below give a quick visual summary of each dancer's joint velocities as they come out of the cambré to execute the developpé -- highlighting some unique traits such as how Fonteyn and Zakharova complete most of the motions earlier on in the step.

Joint "Arrival" and Musicality
In looking at joint velocity, I became particularly keen to explore the specific question of joint arrival. How does each dancer decide when to "arrive" at each step, i.e. reduce their joint velocities so as to place themselves in each pose? Do they tend to arrive on the note itself, or after? Does the whole body move as one piece, with all joint velocities going to 0 at once? In a sense it corresponds with the oft-critiqued quality of a dancer's musicality -- which, though no one really has a definition for, could potentially be seen in a new light with these numbers.

As it turns out, each dancer rarely came to a complete stop in executing each step -- meaning that while some joint velocities would go to 0, most would only slow down, before picking up speed again to go into the next step. As such I found the 'local minimum' for each value of joint velocity -- referring to the minimum speed that the joint reached when it was near the completion of the step. Again, it's a mass of points, but I've highlighted some joints in colour, and plot them relative to the dotted lines, which indicate when the music is played for each step.

I was fascinated to see how unique each dancer was in their timing and velocities at the point of arrival. Núñez's arrival velocities come closest to zero, meaning that every joint will essentially stop as she moves through the step, even if at different times. She can choose, however, to do more 'transitory' steps, as evinced by her penché where less of her joints come to a stop. As for Zakharova, her joint arrivals tend to be clustered together in time, arriving very close to the note itself, going cleanly from pose to pose -- perfectly mirroring the review that she "[hits] isolated climactic effects without notable through-lines". Fonteyn, with her joints that tend to keep moving through the note, is perhaps demonstrating here what contributed to her reputation as an "intensely musical dancer".

And I was most intrigued to discover in this graph much of what has been reviewed of Yanowsky's dancing -- as seen above, her moves ride the tail of each note, where "the score's impulses [become] her impulses". Her joint arrivals are also spread out longer in time, perhaps driving other reviews that she "draws the choreography in beautifully sustained lines". What is interesting to note as well is that her neck joint consistently retains the highest velocity and never stops, passing through each step independent of the rest of her body -- a feature I began to suddenly see in many of her other performances, now that I knew to look for it.

More Than Just The Biomechanics
After all the numbers and graphs I've just thrown at ballet, it is perhaps ironic to say that the very last thing I want to do is bring objectivity to such a beautiful art form. But the fact is that no numbers will ever describe how Fonteyn would somehow command attention in her absolute stillness; how Roberto Bolle, Nehemiah Kish, Thiago Soares and Michael Soames fall deeply in love with Odette; how Marius Petipa formed patterns with the corps de ballet that make the music swell with their energy. This is, at the end of a day, a mere 20 second extract of stick figures, tugging on the coat tails of a 2.5 hour stunning work of moving art.

My hope is that this biomechanical review gave you some new things to appreciate about ballet! If you're new to ballet, I hope you watch lots of YouTube and eye out which aspect of different dancers' styles jump out at you, and use that as a starting point to find out much more about the art. You can discover a lot about its history and the thought behind each production on the Royal Opera House's fantastically prolific channel. I also love reading others' opinions on forums, blogs or twitter (where you can actually follow the Royal Ballet's run of Swan Lake right now with #ROHSwanLake)!

"Art is a lie that makes us realize truth" -- and perhaps by seeing it mathematically, emotionally, through others' eyes, one might realize more and more of it.


  1. Hey carolyn, i was wondering why fonteyn doesn't do a penche? And what is a 'split' under the joint range of motion?

    this is really cool, i'm going to share it with my ballet class :) :)

    1. Helluuu! haha yah no penche, really curious when then got added! and yup 'split' is kind of an invented not-real-biomechanics metric.. but which corresponds better to how we 'see' penches/developpes :p heh glad you enjoyed!! :)

  2. Oh about fonteyn... it's because she doesn't do a penche heh

  3. I really like your analysis on joint arrival and musicality! I've long been wanting to see something like that for some of my favourite moments in figure skating, in which a jump is perfectly timed and there is great flow out of the jump.

    Todd Eldredge

    Michelle Kwan, 1998 World Pro

    Michelle Kwan, 2001, US Nationals short program

    1. Glad you enjoyed it Andrew! Thanks for those Amazing clips.. especially Michelle Kwan's '98 one. That definitely would be a cool analysis.. let me see how I can get round to it ;)

  4. Is ZenMech available for download? I want to give it a try!

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