A Model of Metric Coherence

This paper discusses a notion of metric coherence, based upon a mathematical model of the inner metric structure of a piece of music as implemented in the ’RUBATO Worksta-tion for Musical Analysis and Performance’. The inner metric analysis studies the metric structure expressed by the notes of a given piece without considering the time signature and barlines and results in a metric weight for each note of the score. The given time signature defines a certain regular accent structure upon the possible notes or onsets of a bar which we call outer metric structure. The notion of metric coherence describes the correspondences of varying degrees between the outer and inner metric structure. As a result of the explorative work with the model, a higher degree of coherence was detected within those works, which are typical representations of the accent scheme given by the time signature. Furthermore, metric ambiguities within pieces of different composers, such as the works of Johannes Brahms, can be described as divergence between inner and outer metric structure. Since RUBATO enables the transformation of analytical results into var-ious performance parameters, the definition of metric coherence was tested furthermore by using metric weights to shape a performance of the analyzed piece and to evaluate these performances within an empirical experiment. As the outcome a relationship was detected between metric coherence and the understanding of the corresponding interpretation by the listeners.