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Notes and Note-Pairs in Noergaard's Infinity Series
- Publication Year :
- 2014
- Publisher :
- arXiv, 2014.
-
Abstract
- 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.
Details
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....01a6755c4cd30fababd0040429d5f896
- Full Text :
- https://doi.org/10.48550/arxiv.1402.3091