URL:

files/proceedings/2007/57.pdf

Abstract:

Autosimilar melodies put together the interplay of several melodies within a monody, the augmentations of a given melody, and the notion of autosimilarity which is well known in fractal objects. From a mathematical study of their properties, arising from experimentations by their inventor, composer Tom Johnson, we have generalized the notion towards the dual aspects of the group of symmetries of a periodic melody, and the creation of a melody featuring a set of given symmetries. This is now a straightforward tool, both for composers and analysts, in OpenMusic visual programming language.