Topological Considerations for Tuning and Fingering Stringed Instruments

We present a formal language for assigning pitches to strings for fingered multi-string instruments, particularly the six-string guitar. Given the instrument's tuning (the strings' open pitches) and the compass of the fingers of the hand stopping the strings, the formalism yields a framework for simultaneously optimizing three things: the mapping of pitches to strings, the choice of instrument tuning, and the key of the composition. Final optimization relies on heuristics idiomatic to the tuning, the particular musical style, and the performer's proficiency.