Rudresh Mahanthappa brings mathematics to the music room.

Rudresh Mahanthappa   Courtesy of Pi Recordings

Eventually, nearly every man comes to believe that he’s turning into his father. For alto saxophonist and composer Rudresh Mahanthappa, a pioneering figure on the avant-garde jazz scene, the sneaking suspicion arrived early.

In 1980, when Rudresh was a fifth grader, a schoolmate brought an article into current affairs class announcing the discovery of plasma in Saturn’s rings by the Voyager I space probe. The teacher was agog: Who knew there was blood in outer space?

“I was the kid who stood up and said, ‘No, plasma is when electrons and protons are disjointed, and orbiting each other,’” Rudresh recalled. “That was my dad speaking.”

Rudresh’s father is K.T. Mahanthappa, a theoretical particle physicist at the University of Colorado, Boulder whose interests include neutrinos, superstrings, and grand unification theories that seek to unify the fundamental physical forces in the universe.

Around the house, K.T. enjoyed discussing lighter topics with his three boys, such as why the Earth goes around the sun. He was the kind of father who thought nothing of driving 70 miles to find a knot theorist who could help young Rudresh complete a 9th-grade science fair project on Mobius strip variants. The Mahanthappa boys—Rudresh, his older brother Nagesh and younger brother Mahesh—dominated the local science fair circuit: Both Nagesh—who is currently a neuroscientist at a biotech firm in Cambridge, Mass.—and Mahesh qualified for the Westinghouse International Science and Engineering Fair, now sponsored by Intel. Mahesh, now a professor of chemistry at the University of Wisconsin, Madison, won it.

Long fascinated by mathematics and cryptography, Rudresh was addicted to Martin Gardner’s “Mathematical Games” column in Scientific American, and was forever devising codes to use with his neighborhood friends. For many years, he saw himself becoming a mathematician or a computer programmer or a businessman—someone who made his living with numbers rather than words.

Even today, mathematics is constantly on his mind: “It’s funny how much I think about math on a daily basis,” he said.

Nonetheless, by the end of high school, Rudresh had concluded that he lacked the patience to pursue the kinds of increasingly sophisticated problems that interested him. Rudresh was stuck on a difficult tiling problem involving the most efficient arrangement of pentominoes (shapes composed of five contiguous squares, similar to the four-square tetrominoes of Tetris) for yet another science fair, and faced with the prospect of having to learn the computer programming language Pascal in order to write an algorithm to solve it, when he began to consider other career options.

“That’s when I started to become much more interested in saxophone,” he said. “Do I want to try to learn this Charlie Parker solo, or do I want to learn Pascal? For me, it was a no-brainer.”

For K.T. Mahanthappa, the choice was less obvious.

“I was concerned about him making a living,” K.T. said. “I even told him, ‘Rudresh, you can be a third-rate physicist and still make a living, but if you’re a third-rate musician, you won’t be able to.’”

In a last-ditch effort to highlight the risks of a career in the arts, K.T. sent Rudresh to a summer program at Boston’s Berklee College of Music, hoping that his son would be discouraged by the strength of the competition.

“It completely backfired,” said K.T. “He was one of the best students there.”

Rudresh had been playing recorder and clarinet since grade school, but it wasn’t until he encountered works by mathematically oriented composers like Bela Bartok and Arnold Schoenberg in college that he realized he wouldn’t have to leave numbers behind.

“I felt like I could bridge whatever abilities I had as a musician with whatever I was doing all the time in my mind with numbers,” he said.

Around the same period, as an undergraduate at Berklee, Rudresh developed a parallel interest in the music of India—both his parents hail from Bangalore. In his music, the culture’s signature tones and rhythms mingle with complex melodies based on patterns dreamed up in his mathematical mind.

His recent quartet recording, Codebook, represents a significant return to his roots—not Indian, but mathematical—nearly every tune on the album was inspired by cryptography or number theory. That reliance on both logic and creativity is central to math and music alike, and Rudresh hopes that his experimentations on Codebook, will help people understand just how intimately the two fields are related.

Rudresh had been playing recorder and clarinet since grade school, but it wasn’t until he encountered works by mathematically oriented composers like Bela Bartok and Arnold Schoenberg in college that he realized he wouldn’t have to leave numbers behind.

“The Decider,” for example, harkens back to Rudresh’s science fair days as well as his fascination with Bartok’s use of the Fibonacci sequence in pieces like “Music for String Instruments, Percussion and Celeste”: The melodic intervals in the composition are all derived from the same series of integers—0,1,1,2,3,5,8…—that underlies the structures of nautilus shells and flower petals, Sanskrit poetry and Virgil’s Aeneid. Mahanthappa uses similar relationships to structure his improvisations, generating melodic patterns based on underlying harmonic progressions derived from Fibonacci numbers and the ratios between them.
The tune “Further and In Between” takes its basis from the cyclical number 142,857. Cyclical numbers are actually the inverse of certain prime numbers. For example, the number 142,857 represents the first six repeating digits of 1/7 in decimal form (0. 142857142857142857…). Also, a cyclical number with n digits, when multiplied by any whole number from 1 through n, will generate a product consisting of the same digits, which in every case except for when the multiple is 1, will be in a different sequence. Mahanthappa took various forms of his chosen number (142,857; 428,571; etc.), strung them end-to-end, and assigned a musical pitch to each digit. Allowing some leeway in melodic direction—tweaking pitch as needed—and working in some funk-based, start-and-stop rhythms, he constructs a jagged, leaping melody as visceral as it is intellectual.

“Frontburner” is a musico-cryptographic tour de force. Inspired by Simon Singh’s The Code Book, an exhaustive history of codes from ancient times to the present, Rudresh used the musical equivalent of a poly-alphabetic substitution cipher—the kind encrypted and decrypted by the German Enigma machine during WWII—to encode John Coltrane’s classic tune, “Giant Steps.” To create the “Frontburner” melody, first, Rudresh assembled a set of three scales, roughly analogous to the alternate “cipher alphabets” that cryptologists use as substitutes for the standard alphabet. Then, using a portion of the original “Giant Steps” melody, he devised a musical “keyword,” or short sequence of pitches, to determine the order in which he would move between his three scales while encrypting Coltrane’s melody. Finally, he encrypted the entire tune, replacing its original pitches with notes from his cipher scales.

The initial results were unplayable. Unlike more conventional cryptographers, Rudresh’s goal was not, in fact, to create the appearance of random noise. As with many of his other compositions structured around sophisticated elements of number theory, he had to tweak his coded message until it could be classified as music.

It’s in this careful calibration between the complex calculations in his head and the music in his heart through which Rudresh communicates and flourishes.

“I think that Fermat and Coltrane were equally brilliant in similar ways,” Rudresh said. “It just happened to be that one played the saxophone.”

It’s a balance he’s struck so well, even his practical father can rest easy.

“In any artist’s world, there are just two categories of people: the highest and the lowest,” K.T. Mahanthappa said. “I’m glad he’s reached the upper echelon.”

Originally published November 1, 2006

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