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Exploring harmonies of math and music

SANTA FE, N.M. — The theater is cloaked in darkness. Slowly, you notice a low, rumbling C note.

Then the full symphonic glory of the beginning of “Also Sprach Zarathustra” by Richard Strauss – known more popularly as a theme from the movie “2001: A Space Odyssey” – builds a crescendo that rebounds within the walls.

A fitting, goose-bump-inducing introduction for a presentation entitled “The Majesty of Music and Mathematics.”

Perhaps the juxtaposition of those two subjects jolts you.

But Greg Heltman and Cris Moore hope that the presentation they piloted will reveal the harmony between the two.

Cris Moore is a mathematician and professor at the Santa Fe Institute.

Cris Moore is a mathematician and professor at the Santa Fe Institute.

“I wanted to take the opportunity to try to get across to people what math means to someone like me, what it’s like under the surface, under the crust of just doing arithmetic,” said Moore, a mathematician at the Santa Fe Institute.

“It’s about beauty, patterns and wonder. I think it’s really true that the part of the brain that is excited by music is the same part excited by mathematics.”

Heltman, founder and general director of the Santa Fe Symphony, equates music with drama, so he’s going for the “wow factor,” he said. He’s looking for discovery, whether it’s people leaving saying, “I never knew pi went on forever,” or “I didn’t know Ravel’s ‘Bolero’ could be played like that.”

Santa Fe Symphony Orchestra and Chorus Founder and General Director Greg Heltman.

Santa Fe Symphony Orchestra and Chorus Founder and General Director Greg Heltman.

He’s hoping to reveal the different colors of music that go beyond notes on a page.

All this will be done, they hope, with live music by the symphony orchestra, a narration by Moore, visuals on a screen and active demonstrations. You can see how the rich tonal variations of an instrument are reflected in sand vibrating across the surface of a vibrating plate, or how PVC pipes of different lengths produce different notes.

You’ll be shown how different mathematical relationships among notes can evoke different emotions.

Oh, yes, and there will be a 40,000-year-old flute, a ceramic trumpet from Peru that was played long before Europeans came to the continent, and an 84-year-old theremin – you know, that instrument that produces sounds suited for a haunted house or, oddly enough, the sunnier music of the Beach Boys.

“We had far more possibilities for the repertoire than we had time,” Heltman said in explaining the choice of musical bits. “We could have used music just from the last 50 years, but I think we would have had lots of resistance as far as attracting an audience, simply because people are not familiar with it.”

As it is, the selections chosen to illustrate mathematical concepts in music range across 3,000 years, from “an ancient hymn found on a cuneiform tablet” to Bach and Tchaikovsky to John Williams and the soundtracks from “Harry Potter” and “Mission Impossible,” Heltman said.

Moore will use these bits to demonstrate how certain ratios of musical notes are used to tune instruments and sound more pleasing to us than others; how composers use symmetry, repeating themes, but sometimes echoing them on different scales. That repeating pattern in different scales, Moore added, “is what a fractal is,” physically reflected in the shape of a fern or pattern of a coastline.

The best music – and this can be said about a number of things – offers a pattern, but also some unanticipated breaks in that pattern. “It’s the tension between order and chaos, predictability and surprise,” Moore said. “It’s how every scientist and mathematician is trying to understand the natural world … . We’re surprised all the time.”

And while Western musicians use a 12-tone scale and a lot of Eastern music relies on a five-tone scale, sounding very different to our ears, they are still based on some very simple fractions, Moore said.

He will talk about resonance in music, both in a way that a singer can break a glass and in the intervals of moons orbiting Jupiter. Prime numbers, sine waves and more will enter the conversation.

Thanks to a donation from the Andrew and Sydney Davis Foundation, a truncated version of this presentation will be performed at no cost for middle-school students, both from public (“all of Capshaw Middle School”) and private schools, from Santa Fe and even a few from Albuquerque, Heltman said. The two student performances are “packed,” he added.

“It’s a great age for them to start seeing the deeper beauty of math,” Moore said, adding that he is unhappy with the way math is taught, geared toward testing and right-wrong answers, rather than the ideas that underlie the numbers.

This presentation is the fourth in a series of “Voyages of Discovery” programs put together by the symphony and the Santa Fe Institute. Others have compared the explorations of Charles Darwin and Felix Mendelssohn, astronomy and Gustav Holst’s “The Planets,” and the relationship between neuroscience and the music of Johann Sebastian Bach.