Codebook

Rudresh Mahanthappa

Wired Magazine

To the uninitiated, modern jazz can sound like a secret language, full of unpredictable melodies and unexpected rhythms. For alto saxophonist Rudresh Mahanthappa, however, the idea of jazz as code is more than just a metaphor.

Mahanthappa is best known for combining avant-garde jazz with Indian classical music. But for his latest release, Codebook, from Pi Recordings, the artist looked instead to cryptography and number theory for inspiration. (The album’s title pays homage to The Code Book, a history of cryptography by the British science writer Simon Singh.)

The very first track, "The Decider," is a groovy primer on how to turn math into music. Its bristling melody is derived from the Fibonacci sequence, an infinite series of integers that governs the structure of everything from pineapples to the Parthenon.

Fibonacci’s fingerprints can be found in the work of classical composers from Bach to Bartok, but intentionally basing a composition on the series is hardly standard practice in jazz. What’s most striking about "The Decider," however, is how closely its written melody resembles one of Mahanthappa’s improvised solos, a correspondence that reveals just how deeply the saxophonist has internalized what might have remained an abstruse, pencil-and-paper exercise.

Later on in the piece, drummer Dan Weiss spells his own name in Morse code, using short durations to represent dots and long ones to represent dashes. ("Play It Again Sam" begins in similar fashion, with every member of Mahanthappa’s quartet dotting and dashing his name.)

Returning to the realm of number theory, the tune "Further and In Between" is based on the cyclical number 142857. Like all cyclical numbers, this one has some very strange properties; for example, if you multiply it by 2, 3, 4, 5 or 6, you get the same digits in a different configuration (for example, 2 x 142857 = 285714).

By mapping particular musical pitches to each digit and running through his multiplication tables, Mahanthappa came up with a winding, circuitous melody that makes a surprising amount of sense. That’s partly because he wedded it to a strong, swinging rhythm, and partly because he gave himself permission to fudge things a bit in order to prevent the math from overwhelming the music.

"Frontburner," based on a heavily encrypted form of John Coltrane’s classic "Giant Steps," demonstrates a similar balance between musicality and mathematical rigor.

Cryptonerds will be pleased to know that Mahanthappa used a portion of the "Giant Steps" melody as a musical keyword in conjunction with several different scales to encipher the original tune. He used a similar method to generate the melody for "Play It Again Sam," further complicating matters by throwing in a biblical Hebrew cipher known as "atbash".

In cryptographic circles, this is known as a polyalphabetic substitution cipher, and it was the preferred form of military encryption right up through World War II.

In this particular case, it may have been too effective: The first, properly encrypted form of "Frontburner" didn’t quite work from a musical perspective, so Mahanthappa massaged the results until he got something that did. The end result is a tune that will keep both sides of your brain buzzing happily away.

Making avant-garde jazz accessible to the general public is no mean feat. Making math-based music easy on the ears is even harder. Yet somehow Mahanthappa has managed to do both. And that’s a code many musicians would doubtless like to crack.

– Alexander Gelfand

Seed Magazine

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."

– Alexander Gelfand

Science Magazine

COUNT THOSE BEATS. Modern jazz can be as complex as an exotic mathematical problem. But saxophonist Rudresh Mahanthappa’s music is inspired by math itself.

The New York-based jazz composer’s latest album, Codebook, conveys elements of number theory and cryptography in musical form. In some pieces, concepts such as the Fibonacci sequence--an infinite set of integers created by adding the last two numbers in the series--serve as the basis of the rhythm and melodies. In others, mathematical ideas dictate the evolution of the score. Encoded throughout the music are the names of the band members and famous jazz melodies.

"Math has always been at the core of what I do," says Mahanthappa, 35, who has been fascinated by math from an early age. He has made a name for himself by blending jazz with the complex rhythms of Indian classical music. Adding a mathematical component was an even bigger challenge. "Translating an idea from number theory or cryptography to music doesn’t automatically yield anything that’s playable or that sounds good," says Mahanthappa.

"He proves, by using musical notes, what mathematicians have always believed: that math is beautiful," says Princeton University mathematician Manjul Barghava, himself an acclaimed player of the tabla, an Indian percussion instrument. Codebook will be available from Pi Recordings on 26 September.

Jazz Times

Rudresh Mahanthappa composed the nine pieces on Codebook by taking inspiration from ideas and concepts found in cryptography; rhythms and melodies were encoded or convoluted in order to approach the music from newer, more challenging angles. Daunting as this may seem, the alto saxophonist wound up with results that justify the means without being overshadowed by them. Codebook might not win listeners immediately, but it keeps pulling you back to decipher its contours.

The rapid, complex alto melody of “The Decider” that launches the album presents a good jump-off point, with pianist Vijay Iyer, bassist Francois Moutin and drummer Dan Weiss keeping the music grounded, but lying in wait for a moment to push it in a different direction. This happens in “Enhanced Performance,” where an uneven time signature keeps increasing in tempo, stoking the saxophonist’s fire only to come to an abrupt end. “D (Dee-Dee)” begins with a more conventional theme, only to move in and out of tempo, landing in bass and piano solos marked by strange accents and torrents on clusters, respectively.

With a tone that could be described as pungent, Mahanthappa’s performance comes across much like a compelling narrator whose presence immediately puts you under his spell. But Iyer, Moutin and Weiss also perform at such a level that their accompaniment proves as intriguing as their solo sections.

– Mike Shanley

All About Jazz

Rudresh Mahanthappa’s previous quartet album, Mother Tongue (Pi,2004), explored the transposition of Indian dialects into the structural frameworks of acoustic jazz. Codebook builds on the alto saxophonist’s previous work by incorporating aspects of cryptography into his new compositions. He’s joined by his regular foil, pianist Vijay Iyer, as well as his usual quartet bassist, FranÁois Moutin. Mahanthappa also invites new drummer Dan Weiss into the fold.

Opening with the blistering assault of “The Decider,” Mahanthappa demonstrates potent virtuosity and a mischievous streak courtesy of his topical titling choices. But the thematic source behind the music is far more esoteric than armchair politics. The tune’s intricate structure is based on the Fibonacci sequence, an infinite series of integers used by classical composers ranging from Bach to Bartok. Such potentially restrictive compositional models are rarely used by jazz musicians. But Mahanthappa, like his innovative peer, Vijay Iyer, is no typical jazz musician.

Mahanthappa composed the entire album around such cyclic processes, using Simon Singh’s history of cryptography, The Code Book, for inspiration. “Play It Again Sam” features the entire quartet using Morse code to spell out their names with a sequence of musical dots and dashes. Even more intricate is Mahanthappa’s “Frontburner,” a visceral re-interpretation of John Coltrane’s “Giant Steps.” Using the tune’s title and scales drawn from the piece’s chord changes as ciphers to encrypt the song’s base melody, Mahanthappa arrived at a knotty, turbulent variation on the classic. “Enhanced Performance” is representative of the album’s versatility, modulating from one cell-like section to another. Varying tempos, rhythms and dynamic inflection, the quartet switches gears between spacious, casual swing, pneumatic M-Base funk and frenetic bop.

The majority of the tunes flirt with abruptly surging, propulsive energy. Even the album’s introspective moments periodically veer off into vociferous excursions. Navigating a labyrinthine maze of interlocking cyclic structures, Mahanthappa’s tart alto spews forth turgid coils of sound while the rhythm section alters tempos with metric modulation. A sincere collaborator, Mahanthappa provides ample solo room for his talented comrades, and Iyer matches the leader’s caustic wit in equal measure.

Despite the high-minded concept underscoring the album’s intricate compositions, Mahanthappa’s quartet fulfills its primary goal: to swing creatively, with passion and conviction. Codebook is a wonderful addition to its ever growing body of work.

– Troy Collins