WF scales, ME sets, and Christoffel words

Abstract

With a few exceptions (Chemillier and Truchet 2003), (Chemillier 2004), musical scale theory and combinatorial word theory have remained unaware of each other, despite having an intersection in methods and results that by now is considerable. The theory of words has a long history, with many developments coming in the last few decades; see Lothaire 2002 for an account. The authors thank Franck Jedrzejewski for an initial reference in word theory. The purpose of this paper is to translate between the language of two closely related scale theories and that of the theory of words. © 2009 Springer-Verlag.