A Compact Enharmonically Viable Subset of Harmonic Space, 2020 with Marc Sabat
While temperament may present some apparent advantages, it necessarily sacrifices the distinct “JI fusion sonority” of intervals that are precisely tuneable by ear. These manifest a vast gradation of consonance and dissonance, as yet largely unexplored and with fascinating potential for new compositions. This article proposes a novel approach, based on a mathematical structure called the Stern-Brocot Tree, allowing a finite set of pitches to be generated in just intonation within which music may modulate freely without relying on temperament.
(Published in Živá hudba 2020/11)


The Helmholtz-Ellis JI Pitch Notation, 2020 with Marc Sabat
Revised symbols for primes up to 47, legend and harmonic/subharmonic series


Farey sequences map playable nodes on a string, 2019 with Marc Sabat
Natural harmonics, i.e. partials and their harmonic series, may be isolated on a vibrating string by lightly touching specific points along its length. In addition to the two endpoints, stationary nodes for a given partial n present themselves at n − 1 locations along the string, dividing it into n parts of equal length. It is not the case, however, that touching any one of these nodes will necessarily isolate the nth partial and its integer multiples. The subset of nodes that will activate the nth partial (termed playable nodes by the authors) may be derived by following a mathematically predictable pattern described by so-called Farey sequences. The authors derive properties of these sequences and connect them to physical phenomena. This article describes various musical applications: locating single natural harmonics, forming melodies of neighbouring harmonics, sounding multiphonic aggregates, as well as predicting the relative tuneability of just intervals.
(Published in TEMPO 74, issue 291 January 2020)


Microtonal playback in Dorico, 2018
Software review with technical examples of Dorico 2’s microtonal just intonation playback capabilities


Fundamental Principles of Just Intonation and Microtonal Composition, 2018 with Marc Sabat

Surprising Connections in Extended Just Intonation, 2021
This essay documents some initial speculations regarding how harmonies (might) evolve in extended just intonation, connecting back to various practices from two perspectives that have been influential to my work. The first perspective, which is the primary investigation, concerns itself with an intervallic conception of just intonation, centring around Harry Partch’s technique of Otonalities and Utonalities interacting through Tonality Flux: close contrapuntal proximities bridging microtonal chordal structures. An analysis of Partch’s 1943 composition Dark Brother, one of his earliest compositions to use this technique extensively, is proposed, contextualised within his 43-tone “Monophonic” system and greater aesthetic interests. This is followed by further approaches to just intonation composition from the perspective of the extended harmonic series and spectral interaction in acoustic sounds. Recent works and practices from composers La Monte Young, Éliane Radigue, Ellen Fullman, and Catherine Lamb are considered, with a focus on the shifting modalities and neighbouring partials in Lamb’s string quartet divisio spiralis (2019). Finally, I connect this discussion to my current compositional interests, which have been exploring a method of microtonal modulation through arbitrarily near enharmonic connections in Harmonic Space called “enharmonic proximities”. (Masters Thesis, Universität der Künste Berlin)


Harmonic Series Spiral Synth
In-broswer synthesiser and interactive visualisation of the harmonic series in the form of a logarithmic spiral, based on Erv Wilson’s 1965 publication and Catherine Lamb’s related creative/pedagogical practice


String instrument physical model
SuperCollider synth – useful for generating a more realistic string timbre (slight inharmonicitiy, bow attack, bow position, etc.) and example mockup with James Tenney’s KOAN for string quartet
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The 'helmholtz-ellis-ji-notation' package, 2020
This package is a simple LaTeX implementation of the Helmholtz-Ellis JI Pitch Notation that allows for in-line typesetting of microtonal accidentals for use within theoretical texts, program notes, symbol legends, etc.


Plainsound Harmonic Space Calculator, 2020
In-browser tool for analysis, composition, and performance preparation of music composed in microtonal just intonation, Version 2.5