Playing Music in Just Intonation: A Dynamically Adaptive Tuning Scheme

Abstract

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.

On Representing Consonance Structures

“…More specifically, in case there is no pitch drift throughout the piece, we have 1 [8]. Restricting ourselves to tunings such that two notes occupying the same point on the stave are represented by the same frequency, a number of forms of just intonation are described in Benson's book [1].…”