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Many standard accounts of musical metre (such as Lerdahl and Jackendoff 1983) assign equal value to each structural level, however empirically-tested cognitive preferences (see London 2012 for a summary) suggest a more nuanced quantification by weighting them on the basis of pulse salience (Parncutt 1994). These principles are modelled well by a Gaussian distribution relating the inter onset interval of a pulse to its salience. With this improved account of the relative importance of each pulse level, an additive system combining them can at last stand as a worthy model of metre. This paper sets out that model and advances applications.

First, the criteria for selecting tempo to optimise the net salience of a metre are identified. It is shown that maximal salience interacts in simple, categorical ways with the tempo, metrical structure, and the number of metrical levels represented. This model suggests a set of ‘default’ tempi specific to various categories of metres. The division of metres into these categories is intriguingly counter-intuitive. The model also provides a more rigorous basis for the definition of what it means for music to be ‘fast’ or ‘slow’ in those contexts.

Second is a model of categorical metrical listening after Large and Palmer's 2002 waves of expectation. This paper adapts Large and Palmer’s model to include the more subtle quantification of metrical weight described above. The implications include a categorical disparity between metrical positions formerly considered equal, and the prospective development of a quantification of metrical instability.