This is a brief introduction to the premises that underlie Wigout and TrikTraks.
The reader need not be a mathematician to understand this paper. If you know arithmetic, and basic high-school algebra, you will be able to follow the discussion.
Both Wigout and TrikTraks are time-domain synthesis programs. That means they manipulate and synthesize sounds by way of the duration and amplitude of the waveforms.
These programs take up on the ideas first explored by Herbert Brün, with his sound synthesis program SAWDUST, designed and implemented by Gary Grossman, and enhanced by Jody Kravitz and Keith Johnson. In particular, the idea of treating the square wave as the fundamental building block for sound synthesis comes from SAWDUST.
I'll start with an explanation of how a computer makes sound, and then how one can, with the help of a program, compose the waveforms the computer creates.
Above all, the reader is invited to enter into this program in a spirit of play, despite all the ``imposing mathematics'' and whatnot. The pleasure of the program, for me and for a few other people at least, is the pleasure in the unpredictability of its output, despite a totally determined input. (If you can enjoy that last thought, then you'll have a good time with this program.)
As Glouster says of his bastard son Edmund at the beginning of King Lear ``Though the knave came something saucily into the world before he was sent for, yet was his mother fair, there was good sport at his making, and the whoreson must be acknowledged.'' Something of that applies to my relationship to these programs as well ...