An algorithm for real-time harmonic microtuning

Publication Type:

Conference Paper


Marc Sabat


SMC Conference 2008 (2008)




Subtle inflections of pitch, often performed intuitively by musicians, create a harmonically sensitive expressive intonation. As each new pitch is added to a simultaneously sounding structure, very small variations in its tuning have a substantial impact on overall harmonic comprehensibility. In this project, James Tenney’s multidimensional lattice model of intervals (‘harmonic space’) and a related measure of relative consonance (‘harmonic distance’) are used to evaluate and optimize the clarity of sound combinations. A set of tuneable intervals, expressed as whole-number frequency ratios, forms the basis for real-time harmonic microtuning. An algorithm, which references this set, allows a computer music instrument to adjust the intonation of input frequencies based on previously sounded frequencies and several user-specified parameters (initial reference pitch, tolerance range, pitch-class scaling, prime limit). Various applications of the algorithm are envisioned: to find relationships within components of a spectral analysis, to dynamically adjust a computer instrument to other musicians in real time, to research the tuneability of complex microtonal pitch structures. More generally, it furthers research into the processes underlying harmonic perception, and how these may lead to musical applications.