  The Danish composer Per Noergaard defined the "infinity series" s =
(s(n))_n>=0 by the rules s(0) = 0, s(2n) = -s(n) for n >= 1, and s(2n + 1) =
s(n) + 1 for n >= 0; 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, that consecutive occurrences of identical phrases are
widely separated. We also consider to what extent the infinity series is
unique.
