Musical tonality and synchronization

TL;DR

This paper explores how nonlinear dynamical effects, specifically self-excited oscillation and synchronization, can explain phenomena in musical tonality and influence musical composition through mathematical modeling.

Contribution

It introduces a hypothesis linking biological auditory nonlinearities to musical tonality, supported by models of SEO and synchronization, and demonstrates novel musical modulations based on these models.

Findings

Musical tonality phenomena can be explained by SEO and synchronization models.

Mathematical properties guide the creation of musical modulations.

Applied modulations produce new harmonic patterns in compositions.

Abstract

The current study is motivated by some observations of highly nonlinear dynamical effects in biological auditory systems. We examine the hypothesis that one of the underlying mechanisms responsible for the observed nonlinearity is self-excited oscillation (SEO). According to this hypothesis the detection and processing of input audio signals by biological auditory systems is performed by coupling the input signal with an internal element undergoing SEO. Under appropriate conditions such coupling may result in synchronization between the input signal and the SEO. In this paper we present some supporting evidence for this hypothesis by showing that some well-known phenomena in musical tonality can be explained by the Hopf model of SEO and the Arnold model of synchronization. Moreover, some mathematical properties of these models are employed as guidelines for the construction of some modulations that can be applied to a given musical composition. The construction of some intriguing patterns of musical harmony is demonstrated by applying these modulations to known musical pieces.