Abstract / Synopsis
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.
Recommended Citation
Thomas Hillen, "A Classification of Musical Scales Using Binary Sequences," Journal of Humanistic Mathematics, Volume 13 Issue 1 (January 2023), pages 118-130. . Available at: https://scholarship.claremont.edu/jhm/vol13/iss1/8
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