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adam ricci

abstract

"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, [3]). 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.

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