Towards a Cognitively Based Quantification of Metrical Dissonance

Metrical dissonance is a powerful tool for creating and manipulating musical tension. The relative extent of tension can be more or less acute depending (in part) on the type of dissonance used and moving among those dissonance types can contribute to the shape of a musical work. This chapter sets out a model for quantifying relative dissonance that incorporates experimentally substantiated principles of cognitive science. A supplementary webpage [**html page] provides an interactive guide for testing out these ideas, and a further online supplement [**URL—included in the main text as Section \ref{sec:online}] provides mathematical formalizations for the principles discussed. We begin with a basic model of metre where a metrical position’s weight is given simply by the number of pulse levels coinciding there. This alone enables a telling categorization of displacement dissonances for simple metres and a first sense of the relative differences between them. These arbitrary weighting ‘values’ are then refined on the basis of tempo and pulse salience. This provides a more subtle set of gradations that reflect the cognitive experience of metre somewhat better while still retaining a clear sense of the simple principles that govern relative dissonance. Additionally, this chapter sees the model applied in a brief, illustrative analysis and in a preliminary extension to ‘mixed’ metres (5s, 7s,…). This sheds light on known problems such as the relative stability of mixed metres in different rotations, and suggests a new way of thinking about mixed metres’ relative susceptibility to metrical dissonance.