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From Crypto to Jazz

From Crypto to Jazz
From Crypto to Jazz,71658-0.html 

By Alexander Gelfand
Aug, 31, 2006

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 [1], 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 (.mp3) [2] 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 (.mp3) [3] his 

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 (.mp3) [4] 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 (.mp3) [5]. 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 (.mp3) [6] 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.


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