Plactic Classification of Modes

Abstract

Classification of scales began to take shape in the nineteenth century through the works of Camille Durutte, Hoëne Wronski, Anatole Loquin and some others, but it really took a new start in the twentieth century. The aim of this paper is to study a new classification of modes based on the plactic congruences. These congruences mimic a small perturbation from one mode to the other by the move of only one note. Two modes are in the same plactic class if they are related by a path of modes which are pairwise linked by plactic congruences. In this paper, a mode is an ordered series of musical intervals (or steps). A scale is an ascending or descending series of notes, representing a class of modes under circular permutations. In traditional Western music, the C major scale represents the circular permutations of the seven usual modern modes (Ionian, Dorian, Phrygian, etc.)