  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.
