Notes and note pairs in Nørgård's infinity series

Abstract

The Danish composer Per Nørgård (born July 13, 1932) defined the “infinity series” by the rules , for , and for ; it figures prominently in many of his compositions. Here we give several new results about this sequence: first, the set of binary representations of the positions of each note forms a context-free language that is not regular; second, a complete characterization of exactly which note pairs appear; third, consecutive occurrences of identical phrases are widely separated. We also consider to what extent the infinity series is unique.