Derived Row Geometries


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Spring 2018


This project was designed in collaboration with Matthew McDonald, Associate Professor (Music) at Northeastern University.

How many different ways are there to derive a tone row? In 12-tone music, a particular ordering of the twelve chromatic pitch classes — the row — is used as the basis to compose a piece. Some composers were interested in ways of generating a 12-tone row from a single set class: a collection of unordered pitch-class sets where all sets are the same size and relate to one another by transposition or inversion. In a derived row, a single set class partitions the chromatic scale into discrete, non-overlapping segments. This chart uses visualization to show all possible partition geometries of tone rows for valid set classes, revealing the symmetries and asymmetries of derivation.