A Classification of Heptatonic Scales Using Binary Sequences

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  • We identify seven-tone (heptatonic) scales as a sequence of minor and major thirds, where we use a zero to indicate a minor third and a one for a major third. Each proper seven-tone scale is then represented by a {0,1}-sequence of length seven. On these {0,1}-sequences we define group operations such as a left-shift, a right-shift and a mirror symmetry. This allows a full classification of all proper heptatonic scales into four scale families: the major scale family, the harmonic minor scale family, the melodic minor scale family, and the harmonic major scale family. Each scale family contains exactly seven scales, which cover a wide range of well known and lesser known scales. For example, the modes (dorian, phrygian,...) are well known in Jazz music, while Romanian, Gypsi or Hindu-scales have clear cultural roots. 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.

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    Attribution-NonCommercial 4.0 International