Words.

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, text

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 Zivá hudba, issue 11, 2020, article

The Helmholtz-Ellis JI Pitch Notation (2020) with Marc Sabat: Revised symbols for primes up to 47 including a detailed legend explaining each symbol and a notation example of the harmonic and subharmonic series. Published by Plainsound Music Edition in 2020. Legend & example

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, article

Microtonal playback in Dorico (2018): A software review of Dorico 2’s microtonal just intonation playback capabilities, with technical examples. Published on the Scoring Notes website in 2018, review

Fundamental Principles of Just Intonation and Microtonal Composition (2018) with Marc Sabat. Published by Plainsound Music Edition in 2018, article