Fingering systems for electronic musical instruments

Abstract

Consider an electronic musical instrument that plays sequences of notes, one at a time, from the Western chromatic scale. The instrument has a set of keys and pressing each combination of keys with the fingers corresponds to a note. In this paper (which includes an online supplement) we consider the question: What mapping from combinations of keys to notes results in an instrument that is optimally easy to play? We operationalize the notion ‘easy to play’ by looking for mappings that (1) require a small number of simple finger movements when playing various common structured sequences of notes (such as scales and arpeggios) as well as samples of melodies from Western music; and (2) are conceptually simple, where the keys are partitioned into two groups so that one group selects the octave and the other group selects the pitch class.

Keywords:

• musical instrument design
• Gray codes
• combinatorial optimization

AMS Codes:

• 90C27
• 05A99

Acknowledgements

The author would like to thank Gerald Beauregard (2010 e-mail exchange; unreferenced) for sharing his insights.