WolframTones is based on a core discovery of
Stephen Wolfram [4]'s
A New Kind of Science [5]:
that in the computational universe even extremely simple rules or programs can give behavior of great complexity.
Each composition is produced by running a program found by searching the computational universe, taking the pattern the program produces, and converting it to a musical score. 
WolframTones uses a type of program known as a one-dimensional cellular automaton, or Wolfram automaton, studied by Stephen Wolfram since the early 1980s.
WolframTones [6]
What are Cellular Automata?
A cellular automaton (plural: cellular automata) is a discrete model studied in computability theory, mathematics, and theoretical biology.
-
Wikipedia
A cellular automaton is a collection of "colored" cells on a grid of specified shape that evolves through a number of discrete time steps according to a set of rules based on the states of neighboring cells. The rules are then applied iteratively for as many time steps as desired.
- Wolfram Mathworld [7]
The basic setup for Wolfram's cellular automata is very simple. There is a row of cells, each black or white. Then there is a rule that says what color each cell will be, based on the colors of a certain neighborhood of cells on the row above. What pattern one gets depends greatly on the rule one uses--which can be specified by saying what color a cell will be for every possible arrangement of neighboring cells.
Are cellular automata related to cellular phones?
No! It's just a coincidence of terminology. Cellular automata consist of discrete elements called "cells," while cellular phone networks consist of regions called "cells" served by single transmitters. Strangely, additive cellular automata are actually used in CDMA technology for phones. One day cellular automaton rules may well be used to control cellular phone networks--but we'll leave that confusion for later.
What is the "computational universe"?
It's the universe of possible computer programs. Programs have traditionally been complex artifacts created to for specific tasks. A key idea in Stephen Wolfram's A New Kind of Science is to think abstractly about all possible programs. What is then remarkable is that even among simple programs--that can for example be specified by short numbers--there is already rich and complex behavior. Exploring the abstract universe of these simple programs opens up many important new frontiers. There isn't anything that requires the programs to be computer programs: they're really just sets of abstract rules. But these days we're most familiar with such things in the context of computers.
Do WolframTones ideas apply to things other than music?
Absolutely! There are an amazing range of emerging applications of the ideas in A New Kind of Science to science, technology, medicine, the arts, etc. The visual arts and architecture are two areas closely related to WolframTones.