This paper details the empirical research that led to my eventual development of a quantitative model of musical harmony called tonalness theory. Tonalness theory postulates that the human auditory system perceives a tonalness curve of a given sound pressure signal rather than its frequency spectrum and that the tonalness curve should be regarded as the information content of human hearing. Models of consonance, dissonance, and harmonic gravity can be built directly from these curves. Tonalness curves can also model the perception of other psychoacoustic phenomena such as critical band, just noticeable difference, beats, combination tones, and missing fundamentals.
Built on ideas from the work of Ernst Terhardt and Paul Erlich, tonalness values are calculated using time-windowed Fourier transforms of sound pressure signals and weighting resultant virtual pitches using Farey sequence regions as a proxy for the perceptibility of the harmonic interval ratios contained within the signals. Tonalness curves effectively function as a psychoacoustic frequency spectrum for the signal from which they were calculated.
In a musical context, tonalness analysis concerns itself with the consonance, dissonance, and location of virtual pitches within individual chords as well as the progression of consonance, dissonance, and virtual pitches between consecutive chords. An investigation of these properties in a variety of common Western Common Practice harmonies and harmonic progressions revealed the extent to which various psychoacoustic phenomena underlie many of the foundational structures of tonality. These same principles were applied to post-tonal, non-Western, and spectral harmonies with similarly insightful results