The systems of Ben Johnston and Ervin Willson: an intricate journey between Microtonality and Mathematics
The systems of Ben Johnston and Ervin Willson: an intricate journey between Microtonality and Mathematics

Summary/Abstract: The text reviews the basic principles of the systems of extended Just intonation by Ben Johnston and the Moments of Symmetry system of Ervin Wilson. Johnston bases his system on the vector 4:5:6 and applies it both by expanding its limit up to 31 and calculating the resultant tones from the 3rd, 5th, and 7th limits. Alongside the u-tonal and o-tonal reflections, this generates multidimensional lattices that are interconnected with common tones that Johnston uses to modulate from one tonal centre to another. Ervin Wilson’s Scale tree and Moments of Symmetry come from the idea of continued fraction and graph tree. Ervin Wilson’s approach is deeply connected with Joseph Yasser’s view on the evolution of the cardinalities of the known tonal systems.

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