
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…
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