Square Dance Moves and Twelve-Tone Operators: Isomorphisms and New Transformational Models

Both twelve-tone composers and square dance callers use systematic permutations in order to balance variety with familiarity. This paper demonstrates connections between musical and square dance transformations, illustrating some ways in which the two disciplines might inform each other. With nearly seventy moves in the primary or "mainstream" program and a hundred in the more advanced "plus" program, square dance calls could not only augment music theorists' repertoire of transformational devices, but could help expand our fundamental notions of musical transformation. Indeed, non-canonical operations that are considered complex in atonal music theory (such as O'Donnell's split transformations, Mead's Oz, and even Klumpenhouwer's networks) can be modeled by moves that are customary even at the easiest levels of square dance. [PUBLICATION ABSTRACT]