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Just a note on the passing of the Mexican/American (dual national) tuning theorist, Ervin M. Wilson on December 8th. Wilson, born in Colonia Pacheco, Chihuahua, Mexico was a non-academic theorist specializing in alternative tuning systems, their notation, and designs for keyboard instruments to accommodate them. Principle points of departure for his work were the generalized keyboards of Bosanquet, the theory of "evolving tonality" of the Polish-American musicologist and theorist Joseph Yasser, from which Wilson extrapolated wider varieties of new scalar types (his "scale tree"), typically identified by a total number of tones and a generating interval, and the arithmetic insights of the Mexican theorist Agusto Novaro. He collaborated with Harry Partch, Adrian Fokker, John H. Chalmers, Jr., and Lou Harrison. Wilson explored scales and tuning systems in just intonation, equal temperaments, and systems that do not easily fall into either category. He designed a large number of instruments, principally keyboards (the 19-tone generalized Hackleman-Wilson clavichord was a notable example) and mallet percussion and experimented with novel guitar frettings and collected a large number of indigenous flutes with equally-spaced fingers holes, thus approximating subharmonic series, along the lines described by Kathleen Schlesinger.
Above and beyond the large number of practical solutions for instruments and notations typically presented in his virtuoso draughtsman's manuscript (he was employed, for many years, in the aerospace industry, as a draughtsman while also managing his ranch in Chihuahua where he carried out experiments in corn and chenepod hybrids) and the huge variety of techniques he developed for generating new scales and systems with musically useful potential (see especially the articles on the "Marwa Pemutations" and the "Purvi Modulations" as well as his later work with sequences of intervals associated with patterns in Pascal's Triangle, the "meta-meantone", "meta-slendro", "meta-pelog" and "metal-mavila", in particular,) I believe one of his most valuable contributions was the "combination-product set" which built upon his insight that the "tonality diamond" of Partch (with a precedent in Novaro, a diamond was basically a harmonic series multiplied by its subharmonic mirror) was, at base, a selection of tones based on globally organizing the factors of the (just) intervals between them. While the diamonds tended, inevitably, to reinforce a single tonal center, the Combination-Product Sets tended instead to be locally tonal while globally centerless, rich in symmetrical intervallic structures, but also rich in the total varieties of relationships found relative to each tone, and all in a compact system of just intonation of, typically, 6, 20 or 70 tones in total. To some degree, one could find in such a rich system a compelling alternative to many contemporary atonal practices in 12-equal.