Monstrous Musical Moonshine:
Explorations of Harmonic Spaces

Abstract

This commentary provides context for a collection of compositions whose underlying structures are derived from and extend the harmonic theory based on rational intervals between pitches introduced by composer and music theorist James Tenney. The core component taken from Tenney is the measure of harmonic distance (distinct from pitch distance) between two notes. I have extended this to a measure of harmonic dispersion within any number of notes and applied this to developing chord sequences that are either gradually increasing or decreasing in harmonic dispersion. Furthermore, within such sequences the gradation in dispersion is as smooth as possible, both in terms of voicing (usually only one voice in the chord changes at a time) and dispersion level changing by a minimal amount at each stage. A further structural change, developed in later works, is what I term ‘unfolding’, by which a controlled level of repetition is introduced into the sequence, determined by both parametrised and aleatoric elements. The musical results are often microtonal but take into account the pragmatics of performance, and so are often quarter-tonal or based on the usual twelve-tone equal-tempered system. The resulting compositions are scored for live performers (soloists and ensembles), electronic synthesis, and hybrid scoring. The
culminating work is a setting of texts from Zen Buddhist sources for vocal soloists, choir, chanters, an instrumental ensemble and electronic synthesisers. Aside from the structural technicalities, my music focuses on non-narrative, often long-duration expressions, influenced by composers such as Morton Feldman and Eliane Radigue. While technicalities are interesting, the key objective is always to produce music, not mathematics, with the hope that the work will be of interest to listeners, not mathematicians. Ultimately, this project has been experimental, researching how complex structures could be manifest in music.

Data Access Statement:

The accompanying data can be accessed at: https://collections.durham.ac.uk/collections/r20k225b12z