In June, I performed Tom Johnson’s Nine Bells, a nine movement piece which uses various patterns for the performer to walk through a 3×3 grid. The tuning system I employed placed the bells on a plane of harmonic space with one axis in fifths (3/2) and the other in pure major thirds (5/4). The image below shows my tuning scheme overlaid with Johnson’s hand drawing (first movement). This video shows the ninth movement, which has a triangular pattern that approximates a 45-45-90 triangle, which when reduced has sides of 1, 1, and √2. Using steps as the unit of measurement, Johnson represents this with a triangle of 5, 5, 7 (just short of 5√2). This movement uses only the 4 outer bells forming a square. As the triangle’s orientation changes, the exact dimensions remain intact while the resultant chord changes each time (a total of 4 possibilities).
Thanks to Janie Geiser and Automata for filming and hosting.