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World Premiere in Kitchener

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Dr. Coxeter Dr. Coxeter

As Canada's famous author Yann Martel recently said at a talk in Guelph, “art is a selective view of reality.” When that view is constructed mathematically, and then expressed in music, the result is both startling and impressive.


That was the treat delivered to an audience in downtown Kitchener when Princeton University professor Dimitri Tymoczko premiered an orchestral piece The Thousand Faces of Form. This world premiere was preceded by the annual Bridge's Lecture at St. Jerome's and the University of Waterloo, where Tymoczko and his collaborator Nathan Selikoff delved into the mathematics behind the music that was later performed to great effect by the K-W Symphony Orchestra.


Selikoff occupies the “intersection between visual art and computation.” He provided the entrancing visuals that accompanied the concert. He likened it to a “50-dimensional mirrored donut. It sounds like the most delicious thing I've ever heard of!”


In explaining how he invests the math with visual form, he said “I think of the mathematical spaces as a landscape I can explore. I liken it to wandering through a forest with a camera.”


Dr. TymoczkoDr. TymoczkoBut it is a finely balanced act. Tymoczko bemoaned the fact that “20th century music went wrong when it emphasized math over intrinsic beauty. I wish I had blind faith that mathematical beauty translated into intrinsic beauty, but I don't.”


He described the task of a musical geometer this way. “There are a variety of patterns that are analogous. All versions of a chord are strung together like beads on a necklace. The challenge for us is that since these things don't sound alike, how do we take these relationships that are real and manifest them in a way even a casual listener can recognise.”


The issue was resolved in his own composition, which began in a twinkling chaos of static that proved quite entrancing. The concert, which included many other works, was introduced by curator Krista Blake, who said the music on offer explored the intersection of geometry, symmetry and music based on Donald Coxeter's work. He was a famous professor of mathematics at the University of Toronto, and is pictured at the beginning of this article.


Blake said “Coxeter considered himself an artist and a mathematician, obsessed with thinking about the 4th dimension. He believed geometry is everywhere, and most definitely it is in music.” Several pre-recorded videos of his own compositions were offered to the audience on a big screen above the orchestra.


This so-called “Intersection” concert was the the brainchild of KWS Music Director Edwin Outwater. Over the past few years he has created several in collaboration with various experts in a wide range of fields. For example, in the concert he created with Raymond Laflamme, Director of the Institute for Quantum Computing at the Unversity of Waterloo, the music score was circular and the music was something almost unimaginable - raggedly beautiful and jarring to the senses. The orchestra likewise did justice to The Thousand Faces of Form, which was rendered in a tumultuous fashion full of beauty and intrigue.


In an interview for Sun News Miami, Tymoczko told me in rehearsal he “made dozens of very small adjustments” to the way it was performed. “You learn a lot of very delicate things with the orchestra,” he said. For him the composition is an “emotional expression, it's very meaningful to me. Almost all of nature is related through a series of similarities, and the math that explores that is beautiful. The goal here was to sculpt it into something that has the force of narrative or drama.”


Listening to The Thousand Faces of Form was a ride on a geometric spaceship. Tymoczko certainly expressed what was felt by the Kitchener audience when he termed it “the joy of geometry!”

 The new season of the KWSO begins Sept. 23, 2016 with famed figure skater Kurt Browning. Next after that is an evening of Rachmaninoff and Tchaikovsky on Sept. 30 and Oct. 1. Visit their website for details:

Photo of Dr. Tymoczko with this article is from the Univ. of Princeton website.

Clifford Cunningham

Dr. Clifford Cunningham is a planetary scientist. He earned his PhD in the history of astronomy at the University of Southern Queensland, and has undergraduate degrees in science and ancient history from the University of Waterloo. In 2014 he was named a contributor to Encyclopedia Britannica. He is the author of 14 books on asteroids and the history of science. In 1999 he appeared on the TV show Star Trek: Deep Space Nine. Asteroid 4276 was named in his honor in 1990 by the International Astronomical Union based on the recommendation of its bureau located at Harvard-Smithsonian Center for Astrophysics.

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