Maximal Evenness as Conceptual Apparatus for a Course on Post-Tonal Theory and Analysis
"Music Theory's New Pedagogability," Richard Cohn observes that as recently as 25 years ago "the boundary between research and teaching at the introductory levels seemed inevitable and unbreachable...[and that]...we are at a somewhat different juncture now. A number of central concepts have emerged...that can be taught at the introductory level" (Cohn 1998, ). Among the central concepts that he mentions is Clough and Douthett's concept of maximal evenness. A maximally even set "is a set whose elements are distributed as evenly as possible around the chromatic circle" (Clough and Douthett 1991, 96). Each maximally even set is labeled ME(c,d), where c is the cardinality of the universe - in the case of the chromatic scale, 12 - nd d is the cardinality of the set contained within it. Timothy Johnson's textbook Foundations of Diatonic Theory, as if in answer to Cohn's call, puts maximal evenness front and center; indeed, Johnson himself acknowledges the connection in his Preface. As to the intended audience, the "material in this text was originally designed for use as a supplement in traditional Theory I courses, but...is equally appropriate for courses in the fundamentals of music...and for stand-alone courses [in]...mathematics and music" (Johnson 2003, vii). Maximal evenness can also profitably be used as a central concept for a course on twentieth-century music theory and analysis. In such a course, typically the final one in the undergraduate curriculum, students possess substantial music theory knowledge, and therefore maximal evenness can serve synthetic ends, as a means of consolidating (and expanding) what students already know. Such synthetic ends are appropriate in a course that often constitutes the conclusion of a student's formal training in music theory.This paper will outline such a course, based on one that I teach at my own institution. In this course, instead of introducing theoretical concepts using musical examples, a typical strategy in required music theory courses, the focus is more on music theory - on exploring the underlying structure of the objects students have been studying and tasks students have been carrying out for the previous two years. What I offer here is a new way to organize the final course in the undergraduate theory curriculum, a way that suggests a different ordering and combination of topics - and manner of talking about topics - than that offered by current approaches. Central to the course is the concept of maximal evenness, but woven in are closely related ideas from neo-Riemannian theory and elementary combinatorial theory.
"Maximal Evenness as Conceptual Apparatus for a Course on Post-Tonal Theory and Analysis,"
Journal of Music Theory Pedagogy: Vol. 22, Article 2.
Available at: https://digitalcollections.lipscomb.edu/jmtp/vol22/iss1/2