Fractals, fuzzy logic and expert systems to assist in the construction of musical pieces

摘要

The authors present a suite to assist in the creation of musical pieces, whose foundation lies on fractals, fuzzy logic and expert systems. Even though algorithmic music has been explored, some gaps still exist. The favored approach has consisted in mapping numbers to notes to create appealing pieces. This, we contend, is a necessary but not a sufficient condition. Our suite, besides the necessary mapping, possesses the following advantages. First, it is possible to define notes, tempos, and notes durations. Notes evolve according to the selected fractal. Tempos and durations can remain fixed or they also can follow a fractal. Second, it is possible to translate the resultant fractal notes into notes belonging to a musical scale. This is done by firing appropriate rules in a rule base. Third, interpretation templates are provided. Also, melodies or harmonies are available. The suite currently contains several known fractal systems, and we also proposed one dynamical, recursive computation based on Mamdani fuzzy rule bases. The suite we present helps promoting and monitoring the creative process of composing musical scores. The actual implementation of the suite was done on the Java language.