A Model for Musical Expression

• A reductuionist model for achiving musical expression can be thought of as an instatiation of two aspects of what can be termed as a ``generative'' approach to musical expression:
  1. A general characteristic of generative approaches to performance which is a system that maps structural features of the musical score onto expressive parameters in the performance.
  2. A particular kind of mapping (like Lerdahl and Jackendoff, 1983) on the one hand, and timing and dynamics on the other hand as suggested by empirical observations.
• In this respect there is a tendency for performers to increase tempo towards the middle of phrases and decrease tempo toward the endpoints. It has also been suggested that dynamic levels seem to be in proportion to tempo. Players tend to play the quietest at phrase boundaries and loudest between them.
• A good model for musical expression should propose a single hierarchical grouping structure should directly specify the moment-to-moment durations and dynamics of each event.
• Between maximum and minimum values, the model plots intermediate events along a curve. There is a direct link between tempo and dynamics by analogy with a physical system (such as hammer / string interaction), where tempo change becomes acceleration and dynamics become energy (intensity). This relationship reduces to the fact that intensity is proportional to the square of velocity (Todd, 1992). This direct link between tempo and dynamics may have aphysiological basis.
• Because of the model's insistence that timing and dynamics share a single mathematical function, the interonset intervals between events and their intensity will always be positively correlated.
• In addition to choosing an input structure which corresponds to hierarchical grouping structure, the expression algorithm also defines the maximum and minimum duration of the underlying pulse in the performance (upper and lower bounds of tempo) and the maximum and minimum dynamic levels and the user can choose to weight a proportion of expression that is assigned to each level of the phrase structure. Such weighting should not affect the overall changes in tempo and dynamics and should be a proportional decrease or increase ocurring at other levels.