Expression and Random or Chaotic Behavior

Given that acoustic sounds have a tendency to behave as random or chaotic systems, it seems natural to manipulate parameters in this way in order to achieve variety in the synthesis of a musical gesture. When randomness and chaos are applied to spectral parameters they produce a characteristic aggregate noise found in woodwinds or bowed instruments [1, Chafe, 1995]. When applied to a sequence of pitches, they give elements of unpredictability and constant change [3, Sapp, 2000]. Randomness depends on probability distributions for obtaining a parameter or value. In musical applications we want discrete or integer values to map to a sequence of notes.

A chaotic signal is generated by a mathematical expression that contains some sort of randomness. The periodicity of the values given by the expression depends upon probability distributions and rules which also are dependent on past or present values. The behavior of these functions show symmetry or tendency causing attraction to the value with the highest periodicity. A chaotic behavior is considered as a quantified level of unpredictability [4, Schroeder, 1991] which needs to be normalized and mapped to values meaningful and within the bounds for synthesis of Physical Models.