Investigating the energy of musical chords

Abstract

In western music, each octave is divided into 12 semitones. The number of semitones between notes played at the same time largely determines whether a chord sounds pleasing or not. In a mathematical sense, a relative energy can be defined for chords. In this sense, consonant (pleasant) chords should be of lower energy than dissonant ones. A function of frequency ratios has been developed to calculate relative energies of chords. This project aims to modify this function to improve its accuracy with respect to expectations from music theory.