Self-similar Synthesis:
On the Border Between Sound and Music

Shahrokh D. Yadegari

Master Thesis submitted to
Media Arts and Sciences Section, (Media Lab)
School of Architecture and Planning
at
Massachusetts Institute of Technology
on
August 25, 1992

Thesis Supervisor: Tod Machover, Associate Professor of Music and Media, Media Arts and Sciences
Reader: Rosalid Picard, Associate Professor of Music and Media, Media Arts and Sciences
Reader: Xavier Rodet, Professor of Computer Science, Universite Paris VI; Maitre de Recherches at IRCAM

Abstract:

A study of the application of self-similarity to music synthesis was conducted with special emphasis on the relationship of form and matrial in art. Tonal and serial form in music was put in perspective in relation to self-similarity. The relationship between form and content was presented both in ambiguous communication systems such as music, and in mathematical systems in relationship with Gödel's incompleteness theorem[30]. These communication systems were related to the main topic of Schoenberg's ideas of form[40], which is ``comprehensibility'', and to the uncommunicatability of Kierkegaard's ``faith''[21].

Auditory qualities were defined as ``sound'' and ``music'' using a definition for musical communication over a self-similar channel whose plexus is the relationship between form and content. The term ``musical timbre'' was introduced in contrast to the timbre of sound, and a uniformity among the different time scales of musical perception (i.e., form, rhythm, and pitch) was established. Schoenberg's theory of harmony was studied and the physical continuum of consonances and dissonances was extended to the relationship between sound and music (i.e. physical and psychological effects of music).

Self-similarity, self-referentiality, and chaos were briefly explained. A simple but intuitive, explanation of a class of self-similar signals were represented. The results of an analysis of some pieces in this context was presented.

It was established that serialism is a powerful basis for computer music, and the use of self-similarity is a logical step toward the evolution of music. A synthesis method based on self-similarity was devised and implemented. No distinction is made between sound and music, or form and content in this paradigm. A few techniques for using this system were described and the results were presented as audio examples on an accompanying digital audio cassette.