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
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. 
Consonance Pattern

Toso Pankovski
Fast calculation algorithm for discrete resonance-based band-pass filter
Elsevier - Alexandria Engineering Journal
July 2016
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.
Audio Spectral Analisys with DRBF

Educational videos - The Monkey and the Hunter - Best Intuitive Explanation

February 2018
Summary: The Monkey and the Hunter is a famous problem from the physics of projectile motion (mechanics). There are plenty of YouTUbe videos and other Internet pages that explains the math behind - which is not difficult. Still, it is difficult to accept what the math is telling us - that if we shot directlyat the monkey along a straight line while it is hanging on the tree and it drops at the exact same moment, we are going to hit it - no miss! This will happen regardless the speed of the projectile...
We made a video that shows simply and clearly why will that happen, so your mind will accept the facts easily.

Our video is featured on Wikipedia's Monkey and the Hunter page.
Monkey and Hunter video link

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