Nested Spheres

6 Integers

by Carl

“Nothing can be reasonable or beautiful unless it’s made by one central idea, and the idea sets every detail.”

—Architect Howard Roark from Ayn Rand’s novel The Fountainhead.


6 Integers is music striving towards Roark’s modern ideal. In the course of 4:56 a single, coherent process explores the integers 1 through 6 by means of 5292 notes and four independent channels of audio. It is the first full piece generated by the Xi Operator. Its “every detail” (but the timber of the piano and marimba!) are determined by a simple, “central” algorithm; neither chance nor human intervention play any role in the work. The entire piece, including its double binary structure, arises, essentially, from modulo division and the integers 1 through 6.

6 Integers was premiered January 25th 2000 at the CCM Studio Theater.

Two recordings of 6 Integers are available as variable bitrate mp3 files:

Creative Commons License

NOTA BENE: This work is licensed under a Creative Commons License, and is Copyright © 2000 by Carl . Please contact me if you would like either to create a derived work, or to use this piece for commercial purposes.


Copyright © 1999–2014 by Carl (surname at jhu dot edu)