On the Perception of Disharmony

Abstract

Our hearing system works roughly like a calculator for Fourier series, decomposing a sound waves in basic frequencies and then activating respective nerve channels. This relatively easy architecture of our sound perceiving system accounts for the fact that we can filter different sources and thus also that we can focus on a single sound of interest. Consequently, our brain is trained to assess an incoming stem of frequencies (1/n) to a single source, as if the input source is produced by a periodic sound wave. This understanding of our sound system is successfully applied in the development of what is one of the first and well known artificial cognition system: a cochlear implant, bypassing the system physical detection of sound. Two or more sound pitches that have relative fractional frequencies, are considered pleasing or “harmonic”. Although music is a cultural product, evoking individual emotions, perception of harmonics is largely a collective and individual phenomena. This also witnesses the peculiar and intriguing architecture of our sound system. So the question arises whether fractional frequencies is systematically necessary for perception of harmony; are two sound pitches played at substantially irrational (i.e. non fractional frequencies) perceived as non-harmonic? The golden ratio is the most irrational number in the sense that it has the most slowly converging continued fraction expansion. In this work, we present a hypothesis to generate non-harmonics. Insights can be used to enhance inputs in artificial hearing, by displaying different sound pitches at clearly distinguishable frequencies.