Erv Wilson is a contemporary American music theorist who is best known for his innovative approaches to tuning. While his ideas on Moments of Symmetry (MOS) are gaining currency, his exploration of a subset of scales called Secondary MOS sometimes also referred to as “sub-moments”, “nested MOS” or “bi-level MOS” is perhaps less recognised. This presentation introduces the concept of Secondary MOS as a set of interrelated scales derived from a parent MOS to form a family of variations. It also considers the significance of traditional Japanese scales in Wilson’s understanding and development of his ideas by analysing one of his documents entitled “The Tanabe Cycle and Parallelogram from the Tanabe Cycle” (1998). This article is named after the Japanese musicologist Hisao Tanabe who showed how various five-tone scales found in traditional Japanese music are derived from a seven-tone cyclical scale (c. 1947).
My presentation focuses on ways in which Wilson transforms and extends Secondary MOS through methods of transposition and rotation of pitches to create a varied but unified scheme of scales. It also identifies the “disjunction” (or leftover interval that closes the cycle) as an important signpost for determining one’s place in a scale. The discussion includes audio examples and illustrations in which Secondary MOS are mapped onto various lattice diagrams as well as Wilson’s generalized keyboard to reveal the structural properties of these scales as well as suggest numerous ways for how they might be applied to music. The paper concludes with the suggestion that Secondary MOS exemplify Wilson’s approach to tuning by which he extrapolates the inherent features of systems and transforms their patterns into general principles to provide new tools and creative resources for musicians to explore.