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.
Introduction
The following video provides a mostly qualitative introduction to Tonalness Theory.
Tonalness Paper and Calculators
The following paper provides a mathematically rigorous introduction to Tonalness Theory.
The following document conveniently lists all the Tonalness equations cited in the Tonalness paper.
Any of the tonalness, dissonance, and progression quantities referenced in the paper can be calculated easily using the following Python 3 scripts. For any of the scripts to work, they need to all be located in the same folder. Special thanks to Leslie Cochran for helping to write these scripts.
Compositions based on Tonalness Theory
In the summer of 2023, Greg composed a set of pieces in the French art song tradition. Each melody depicts a scene using harmonies and harmonic progressions based in his theories of tonalness. Each of these demonstrates how the tonalness theories of harmony can be blended seamlessly with more traditional harmonic structures in a variety of musical contexts to create a rich and vibrant harmonic language. Below is a link to download the score to these pieces for study purposes. A recording can be found here.
Conference Presentation
In November of 2022, Greg was invited to present his Tonalness Theory research for a music theory conference entitled 1722–2022: trois siècles du Traité de Jean-Philippe Rameau in Paris, France. Below is a video recording of Greg’s presentation.