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Toso Pankovski & Eva Pankovska

**Emergence of the consonance pattern within synaptic weights of a neural network featuring Hebbian neuroplasticity**

Elsevier - Biologically Inspired Cognitive Architectures

October 2017

**doi:10.1016/j.bica.2017.09.001**

Summary: Consonance is a perception phenomenon that evokes pleasant feelings when listening to complex sounds. Since Pythagoras, people have attempted to explain consonance and dissonance, using diverse methodological means, with limited success and without providing convincing underlying causes. We demonstrate that a specific auditory spectral distribution caused by non-linearities, as a first phenomenon, and the Hebbian neuroplasticity as a second, are sufficient set of phenomena a system should possess in order to generate the consonance pattern — the actual two-tone interval list ordered by consonance. The emergence of this pattern is explained in a step-by-step manner, utilizing an artificial neural network model. In an reverse engineering manner, our simulations are testing all the possible spectral distributions of auditory stimuli (within particular precision scales and applying certain abstractions) and reveal those that produce a result with a pattern perfectly
matching the consonance ordered two-tone interval list, the one that is widely accepted in the Western musical culture. The results of this study suggest that the consonance pattern should be an expected outcome in any system containing the asserted set of phenomena. The intent of this study is not to realistically model the human auditory system, but to demonstrate a set of features an abstract and generic system should poses in order to produce the consonance pattern.

Toso Pankovski

**Fast calculation algorithm for discrete resonance-based band-pass filter**

Elsevier - Alexandria Engineering Journal

July 2016

**doi:10.1016/j.aej.2016.06.017**

Summary: Inner ear (cochlear) simulation research triggered the creation of this fast-calculation algorithm
for a novel discrete resonance-based time-to-frequency transformation method.
The presented stand-alone calculation algorithm related to this filter produces its output with a delay of
just one sampling period. The algorithm’s calculation cost is only 3 multiplications and 3 additions per sample,
and does not require long memory buffers. The presented transformation does not surpass the precision of the
Discrete Fourier and Discrete Wavelet Transformations. However, it may prove essential when the noise-artifacts of
the near-real-world simulation are necessary in order to produce some specific auditory-perception phenomena.

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