Leonardo Music Journal, Vol. 5, 1995, pp. 33-38.
Statistical methods for composition include serialism, randomness and statistical feedback. All three methods can fall short of what composers ask from them. This two-part article analyzes statistical methods under various scenarios with the intent of establishing thresholds of confidence. Part 1, published here, develops a music-theoretical basis that defines a threshold of confidence as a condition under which a composer can prescribe a distribution to a method and be reasonably sure that the resulting population will conform to this distribution. The music-theoretical basis for distributions is developed by examining reasons why a compositional state might be heavily or lightly weighted. From insights gained thereby comes a primary criterion of confidence: the number of samples necessary to make a distribution "speak." In addition, there are subsidiary issues such as how a distribution's states disperse over musical time and how readily different methods can be constrained.