Topological Considerations for Tuning and Fingering Stringed Instruments

摘要

We present a formal language for assigning pitches to strings for fingeredmulti-string instruments, particularly the six-string guitar. Given theinstrument's tuning (the strings' open pitches) and the compass of the fingersof the hand stopping the strings, the formalism yields a framework forsimultaneously optimizing three things: the mapping of pitches to strings, thechoice of instrument tuning, and the key of the composition. Final optimizationrelies on heuristics idiomatic to the tuning, the particular musical style, andthe performer's proficiency.