A relaxation oscillator model of neural spiking dynamics is applied to the task of finding downbeats in rhythmical patterns. The importance of downbeat discovery or beat induction is discussed, and the relaxation oscillator model is compared to other oscillator models. In a set of computer simulations the model is tested on 35 rhythmical patterns from Povel and Essens (1985). The model performs well, making good predictions in 34 of 35 cases. In an analysis we identify some shortcomings of the model and relate model behavior to dynamical properties of relaxation oscillators.

Beat induction is best described by analogy to the activities of hand clapping or foot tapping, and involves finding important metrical components in an auditory signal, usually music. Though beat induction is intuitively easy to understand it is difficult to define and still more difficult to perform automatically. We will present a model of beat induction that uses a spiking neural network as the underlying synchronization mechanism. This approach has some advantages over existing methods; it runs online, responds at many levels in the metrical hierarchy, and produces good results on performed music (Beatles piano performances encoded as MIDI).In this paper the model is described in some detail and simulation results are discussed.

The investigation of metric structures in both music theory and the study of music perception requires the description of metric hierarchies generated by the notes of a piece. This paper applies a mathematical model that is based on pulses acting on the notes to infer the structural description of the metric organization of musical pieces. Furthermore, we use the model of Inner Metric Analysis to explain perceptual phenomena involved in the listening process. Inner Metric Analysis assigns metric weights to all note events. We show that these weights often reflect a metric hierarchy that is implied by the bar lines; hence the notes generate a hierarchy that corresponds to that of the abstract grid of the bar lines. We define such a correspondence as metric coherence. In addition, the model provides a precise means to describe metric conflicts intentionally introduced by the composer; these conflicts prevent metric coherence. We present results that show how our model characterizes different forms of interaction between different lines within the texture of a composition. Moreover, in our analysis we distinguish between different levels of metric organization based on local and global information. The application of these analytic perspectives to ragtimes provides differentiated explanations for the results of listening experiments. Hence, this article demonstrates how the structural description of the metric organization of musical pieces helps to answer questions arising from cognitive perspectives and thus links both music theory and perceptual studies. 1

This paper explores how data generated by meter induction models may be recycled to quantify metrical ambiguity, which is calculated by measuring the dispersion of metrical induction strengths across a population of possible meters. A measure of dispersion commonly used in economics to measure income inequality, the Gini coefficient, is introduced for this purpose. The value of this metric as a rhythmic descriptor is explored by quantifying the ambiguity of several common clave patterns and comparing the results to other metrics of rhythmic complexity and syncopation. 1