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.
DOI
10.5642/jhummath.YQDS5836
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. DOI: 10.5642/jhummath.YQDS5836. Available at: https://scholarship.claremont.edu/jhm/vol13/iss1/8
Terms of Use & License Information
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