Chapter 2, Sound or Music, is a study of Schoenberg's theory of tonality. The main purpose of this chapter is to establish a physical continuum between the physical and psychological effects of music, which we call sound and music. In the context of the problems presented in this chapter, the object is to establish a relationship between sensations and meanings in music. We shall also establish the fact that this continuum is non-linear, and can be modeled by a self-similar structure. The most important idea to understand from this chapter is that all forms come from the inner necessity of the material, or as Kandinsky says[3, page 152]: ``The form is the outer expression of the inner content.'' We will also show the unity of form and material in the context of some of the works of Stockhausen. We have tried to show that self-similarity is the natural necessity and outcome of the unity of form and material. We make no assumption about the knowledge of the reader concerning self-similarity in this chapter, and hope that the concept will intuitively emerge from the arguments. However, one can read chapter 3 before reading this chapter, if one is interested to read this chapter with some knowledge of self-similarity.
Chapter 3, What is Self-similarity?, is a portrait of self-similarity and its underlying concept, self-referentiality.
Chapter 4, Self-similarity in Sound
and Music, is a technical presentation of a few cases of self-similarity
in music. Specifically, we have tried to make the problem of
noise more intuitive. Even though in this chapter very little technical
knowledge is assumed, and no formulas have to be understood, this chapter
may be skipped by those who do not like to look at formulas. This
chapter very lightly suggests that it is possible to study music (i.e. meaning)
without making any judgment on the ``intelligence'' (e.g. memory or musical
training) of the listener.
Chapter 5, Self-similar Synthesis, is the most original part of this thesis. In this chapter, we shall put the problem of composition with computers in context, explaining that the process of composition has to define not only the organization of the piece but also of the material. We shall define a synthesis technique based on the principles of self-similarity and present some of the results we have obtained. Many audio examples accompany this chapter.
Chapter 6 is the conclusion.
Appendix A has the results of a
simple analysis we did on 57 different pieces. The analysis is related to
chapter 4 and noise.
Appendix B provides simple descriptions of the examples on the accompanying audio tape. Much care has been taken for the sound quality of the audio examples, and we suggests that the examples be listened to on an audio system with good low and high frequency response.
Appendix C is an explanation of the principles used in composing Morphosis (1992), which is a piece composed by the author using the synthesis technique described in this thesis.