A Classification of Musical Scales Using Binary Sequences

Abstract

Every beginning music student has gone through the four main musical scales: major, natural minor, harmonic minor, and melodic minor. And some might wonder, why those four and not five, or six, or just three? Here we show that a mathematical classification can be used to identify these scales as representatives of certain scale families. Moreover, the classification reveals another scale family, which is much less known: the harmonic major scale. We find that each scale family contains exactly seven scales, which include the modes (dorian, phrygian,...) and other scales such as the Romanian, Gypsi or Hindu-scales. Besides of giving a complete classification of proper heptatonic scales, we also emphasize the pedagogical potential of these {0,1}-representations of scales, as these can help students to navigate and remember complicated scales.