Chords, melodies: a look at harmony by numbers; Tuning Bach
lecture-concert (Organo, Musikkitalo, Helsinki, 2024) • videoChords, melodies: a look at harmony by numbers; Part I: Using harmonic radius to compare rational pitch collections
journal article • Ziva Hudba 2023/13A Compact Enharmonically Viable Subset of Harmonic Space: The Stern-Brocot Tree and Some Thoughts About Lattices and Spirals
by Marc Sabat and Thomas Nicholsonjournal article • Ziva Hudba 2020/11
Farey Sequences Map Playable Nodes on a String
by Marc Sabat and Thomas Nicholsonjournal article • Tempo Vol. 74, No. 291, Jan 2020
Relative Dissonance
on my music for string quartetjournal article (2019) • MusikTexte 163
Well temperament revisited
journal article (2019) • Xenharmonikon • pdfFundamental Principles of Just Intonation and Microtonal Composition
monograph by Marc Sabat and Thomas Nicholson (2018) • pdfIntroducing my work in microtonally extended just intonation
lecture at Ostrava Days (2017) • pdfThree Tables for Bob
journal article • Tempo Vol. 70, No. 278, Oct 2016Pantonality Generalised:
Ben Johnston’s artistic researches in extended just intonation
journal article (2014 corr. 2018) • MusikTexte 144 & Tempo Vol. 69, No. 272, Apr 2015
Shadings in the Chromatic Field: Intonations after Morton Feldman
journal article (2012) • MusikTexte 133Stay Still / Still Stehn
journal article (2011) • Positionen 89Some Reflections About Sound, Music and Art
journal article (2010) • Positionen 84On Ben Johnston’s Notation and
the Performance Practice of Extended Just Intonation
monograph for Ben Johnston and Sylvia Smith (2009 corr. 2018) • pdf
An algorithm for real-time harmonic microtuning
conference paper (2008) • congress on Sound and Music ComputingThree Crystal Growth Algorithms in 23-limit constrained Harmonic Space
based on an article by James Tenneyjournal article (2007) • MusikTexte 112 & Contemporary Music Review Vol. 27 Part I, 2008
Towards an Expanded Definition of Consonance:
Tuneable Intervals on Horn, Tuba and Trombone
by Marc Sabat and Robin Hayward (2006) • monograph
Double Horn in B*f and F: tuning in Just Intonation
microtonal chart (2005) • pdfNatural Harmonics on Cello and Violin
microtonal chart (2005) • pdf23-Limit Tuneable Intervals above and below A
microtonal chart (2005) • partially deprecated original version
The Harmonic Series 1-64
microtonal chart (2005) • partially deprecated original version
The Extended Helmholtz Ellis JI Pitch Notation
monograph (2005) • partially deprecated original version
Helmholtz Ellis JI Pitch Notation: Introduction and Simple Legend
microtonal chart (2005) • partially deprecated original version
Helmholtz Ellis JI Pitch Notation: Full Legend
microtonal chart (2005) • partially deprecated original version
Note: in 2020 the HEJI notation was updated so that all modifications would be based on tertial (3-limit, Pythagorean) pitches. Alteration ratios and symbols for 17° and 29° were redefined; additional symbols were added up to prime limit 47. The partially deprecated charts above are included as they relate to my pre-2020 scores and articles.
Johann Sebastian Bach RICERCAR Musikalisches Opfer 1 INTONATION :
an experimental application of Extended Rational Tuning
monograph (2003) • pdf