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Music Has Its Own Geometry, Researchers Find:
Music Has Its Own Geometry, Researchers Find:
Now, three music professors — Clifton Callender at Florida State University, Ian Quinn at Yale University and Dmitri Tymoczko at Princeton University — have devised a new way of analyzing and categorizing music that takes advantage of the deep, complex mathematics they see enmeshed in its very fabric.

They take sequences of notes, like chords, rhythms and scales, and categorize them so they can be grouped into “families.” They have found a way to assign mathematical structure to these families, so they can then be represented by points in complex geometrical spaces, much the way “x” and “y” coordinates, in the simpler system of high school algebra, correspond to points on a two-dimensional plane.

Different types of categorization produce different geometrical spaces, and reflect the different ways in which musicians over the centuries have understood music. This achievement, they expect, will allow researchers to analyze and understand music in much deeper and more satisfying ways.