On the Division of a String


Six-channel installation-performance

Photograph of loudspeaker

On the Division of a String is a six-channel installation-performance for monochord and electronics. It was first presented at the Orpheus Institute, Ghent, Belgium as part of the Open Circuit event, September, 2019.

Programme note

Historically, the monochord’s purpose was didactic. It was used mainly as a way of demonstrating intervallic relationships in musical sound, though there is some evidence that it was used as a performing instrument and, also, for pitch production in vocal pedagogy.1

In this installation-performance, the material properties of a string are taken as the basis for computer sound synthesis and the intervallic relationships or ‘divisions’ are used to create an algorithmic, electronic composition.

The performer establishes four, consecutive notes of a musical scale (tetrachord). This is done by replicating a method of determining superparticular proportions, as outlined in medieval treatises.

First, a given string length is divided into eight parts and a ninth is added (thus producing the ratio 9:8 or sesquioctava). Next, the same procedure is applied to this nine-part string length. Finally, the original string length is divided into three parts and a third is added.

This system produces two whole tones (9:8) and a Pythagorean semitone (256:243). Given that these divisions use superparticular proportions, each succeeding tone is lower in pitch than the previous tone.

Next, a sound is sculpted according to an analysis of the harmonic partials of the vibrating string. Finally, the two ratios are used to determine the computational operations performed upon the synthetic sound. The computer audio is therefore ‘tuned’ by an instrument designed for demonstrating the sonic properties of physical materials.

Photo of monochord installation at the Orpheus Institute

  1. see Adkins, Cecil. ‘The Technique of the Monochord’. Acta Musicologica 39, no. 1/2 (1967): 34–43.