Perfect balance: Difference between revisions
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These scales along with the evenly spaced scales of [[2edo]], [[3edo]], and [[5edo]] are the full set of "minimal" perfectly balanced scales in 30edo, which cannot be expressed as the union of two disjoint perfectly balanced scales. | These scales along with the evenly spaced scales of [[2edo]], [[3edo]], and [[5edo]] are the full set of "minimal" perfectly balanced scales in 30edo, which cannot be expressed as the union of two disjoint perfectly balanced scales. | ||
Searching for minimal perfectly balanced scales is nontrivial. Milne et al. | Searching for minimal perfectly balanced scales is nontrivial. Milne et al.<ref>Milne, A. J., Bulger, D., & Herff, S. A. (2017). Exploring the space of perfectly balanced rhythms and scales. Journal of Mathematics and Music, 11(2–3), 101–133. https://doi.org/10.1080/17459737.2017.1395915</ref> computed all such patterns for products of three distinct primes up to ''N'' = 102. | ||
== Outside EDOs == | == Outside EDOs == | ||
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Search procedures for perfectly balanced scales under other optimization criteria are conceivable. Minimizing [[harmonic entropy]] is one such approach. | Search procedures for perfectly balanced scales under other optimization criteria are conceivable. Minimizing [[harmonic entropy]] is one such approach. | ||
== References == | |||
[[Category:Scale]] | [[Category:Scale]] | ||