Autosimilar melodies

Abstract

The present work originated from purely musical topics, namely the notion of ‘selfRep melody’ as defined by the composer Tom Johnson in his work Self-similar Melodies published in 1996, and reaped interesting mathematical as well as musical rewards. It is about melodies that contain themselves in augmentation, and some generalizations thereof. Some of the mathematical by-results are new to the best of the author's knowledge. Applications range from melodies to rhythms, and include some new results on mosaics. Finally, extensions to approximate and ‘non-invertible’ autosimilar melodies suggest that this notion is both widespread and universal.

Cite this work

No public copy is stored for this record, so only the metadata is cited.

Stored only when both papers are in the corpus — 10 citations exist upstream.

Papers that cite the same references — the relational fallback while embeddings are still backfilling.