Kimo Johnson, Larry Polansky, Douglas Repetto, Daniel Rockmore
Paper #: 08-05-023
In this paper we propose a mathematical framework for the optimization of tuning systems. We begin with an informal definition of "tuning system." We then propose five general constraints that seem common to their evolution. The central idea is a formulation of those constraints as a set of numerical preferences and weights. From these parameter values we use appropriate optimization methods to produce an optimal tuning for a specific set of values. Finally, we consider some historical tunings from this perspective, and use the framework to generate a few examples of novel tuning systems.