What is the Slonimsky-Schillinger Symmetric System? What's the theory behind it? How is it used in composition?
In short, it's a way of approaching scales based on regular divisions of one or more octaves.
Schillinger used the term symmetric scale to describe a set of notes increasing by the same interval. These include:
You can, of course, create music based around these. Debussy famously used whole-tone quite a bit. Whether you apply rigors of symmetry to your chords and melodies or just use these notes as the 'space' within which your composition can operate is a matter of whim.
Slonimsky extended this to more octaves (for example, you can play perfect fourths until you reach the same note as your starting note, several octaves up) and experimented with combinations of such patterns. His book Thesaurus of Scales and Melodic Patterns gives many patterns which can be useful for practicing technique as well as for finding inspiration for composition and improvisation.
The Octatonic Scale is a nice scale which we can think of as two diminished seven chords a half-step apart. Here's a fairly contemporary example which draws from that heavily, and, to my ears, very effectively:
Here's a quick intro of the SSSS concept as well.