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Tonalness Theory

Greg’s research since his 2014 dissertation has been primarily into something he calls Tonalness Theory. Tonalness Theory defines a mathematical quantity called tonalness that can be calculated directly from any sound wave. Tonalness can be used to model the information content of human hearing and give us new insights into our perceptions of harmony, intonation, and timbre in both musical and non-musical settings.

The following video provides a mostly math-free introduction to the basic ideas behind Tonalness Theory.

The following paper provides a more mathematically rigorous introduction to Tonalness Theory.

The following document conveniently lists all the Tonalness equations cited in the Introducing Tonalness Theory paper.

The following two scripts are written in Python. The script named “single_chord” is able to calculate SST and TV curves and consonance and dissonance values for individual chords. The one named “progression” calculates progression values and consonance and dissonance gains for chord progressions. All of these calculations are based on the equations cited in the documents posted above. In order to run these scripts, open the entirety of the code with any Python 3 interpreter (see python.org for details). Special thanks to Leslie Cochran for writing these.