  We investigate a dynamically adapting tuning scheme for microtonal tuning of
musical instruments, allowing the performer to play music in just intonation in
any key. Unlike other methods, which are based on a procedural analysis of the
chordal structure, the tuning scheme continually solves a system of linear
equations without making explicit decisions. In complex situations, where not
all intervals of a chord can be tuned according to just frequency ratios, the
method automatically yields a tempered compromise. We outline the
implementation of the algorithm in an open-source software project that we have
provided in order to demonstrate the feasibility of the tuning method.
