Music professors Clifton Callender at Florida State University, Ian Quinn at Yale University, and Dmitri Tymoczko at Princeton University have developed a new way of analyzing and categorizing music using the complex mathematics found in music. The new method, called "geometrical music theory," looks at sequences of notes, chords, rhythms, and scales, and categorizes them so they can be grouped into "families." The families can be given a mathematical structure that can be represented by points in complex geometrical spaces, similar to x-y graphing used in algebra. Different categorizations produce unique geometrical spaces, reflecting the various ways musicians in different times understood music. The researchers say that having tools for conceptualizing music could lead to a variety of applications, such as creating new instruments, new musical toys, and new visualization tools. Tymoczko says the most satisfying part for him is being able to see the logical structure that links many different musical concepts. "To some extent, we can represent the history of music as a long process of exploring different symmetries and different geometries," he says.