  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.
