Tonal Frequencies, Consonance, Dissonance: A Math-Bio Intersection
This work addresses a foundational issue in music theory and neurobiology by providing a new mathematical approach to frequency calculation and explaining auditory perception, though it appears incremental in combining existing concepts.
The study tackled the problem of calculating musical note frequencies without a reference note by developing a mathematical model using first-order ordinary differential equations, and it theoretically and neurobiologically explained consonance and dissonance in music based on fundamental frequencies and human perception.
To date, calculating the frequencies of musical notes requires one to know the frequency of some reference note. In this study, first-order ordinary differential equations are used to arrive at a mathematical model to determine tonal frequencies using their respective note indices. In the next part of the study, an analysis that is based on the fundamental musical frequencies is conducted to theoretically and neurobiologically explain the consonance and dissonance caused by the different musical notes in the chromatic scale which is based on the fact that systematic patterns of sound invoke pleasure. The reason behind the richness of harmony and the sonic interference and degree of consonance in musical chords are discussed. Since a human mind analyses everything relatively, anything other than the most consonant notes sounds dissonant. In conclusion, the study explains clearly why musical notes and in toto, music sounds the way it does.