Non-Octave Guitar and Keyboard Designs for Ervin M. Wilson

Reilly Smethurst
Proceedings of Bridges 2017: Mathematics, Art, Music, Architecture, Education, Culture
Pages 515–518 Short Papers


In 1966, Ervin M. Wilson invented his first combination product set – a rational, non-centric structure that musicians can use as a scale. In 2005, David C. Keenan invented a guitar fretboard that can play all twenty notes from a particular combination product set. I propose a Halberstadt keyboard design that makes use of a seventy-note combination product set. The combination product sets used by the two instruments are not reduced to the octave, and they do not repeat at the octave.