Autosimilar Melodies

submitted by: CLDouglas
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...
Authors: Emmanuel Amiot