  Music composition using digital audio sequence editors is increasingly
performed in a visual workspace where sound complexes are built from discrete
sound objects, called gestures that are arranged in time and space to generate
a continuous composition. The visual workspace, common to most industry
standard audio loop sequencing software, is premised on the arrangement of
gestures defined with geometric shape properties. Here, one aspect of fractal
set theory was validated using audio-frequency sets to evaluate self-affine
scaling behavior when new sound complexes are built through union and
intersection operations on discrete musical gestures. Results showed that
intersection of two sets revealed lower complexity compared with the union
operator, meaning that the intersection of two sound gestures is an almost
disjoint set, and in accord with formal logic. These results are also discussed
with reference to fuzzy sets, cellular automata, nanotechnology and
self-organization to further explore the link between sequenced notation and
complexity.
