Summary and Conclusion

Let us briefly review the content of this chapter. We first established an awareness of physical and psychological effects and connected those effects to the concepts of like sound and music. We established a dichotomy between the two, thus separating them from each other as poles, and suggested that for music to be coherent and meaningful it has to bring these two poles together in a natural way. We also tried to establish an awareness of a finely detailed plexus of communication whose axes could be transformed one to the other. In section 2.3, we discussed Schoenberg's theory of harmony and the function of form in general, which according to Schoenberg is comprehensibility. We explained that Schoenberg established a physical continuum between consonances and dissonances by recognizing that tonality's origin can be found in the physics of its material, which is harmonic sound. This is a theory of the relationship between form and content in tonal form. We briefly explained serialism and explained that it is in accord with electronic music, where it can be used as a technique for creating high-level sounds. In section 2.3.3, we discussed the tonality of atonality, which in our opinion concerns the inner musical necessities and aesthetics of music. In the sense of defining atonality as an act which is musical and exists outside the system of form, it becomes a social and political issue of questioning authority in our societies. Tonality of atonality has to be worked on in every moment of the aesthetical process and deserves far more attention than can be provided in the context of this thesis. Finally we explained the idea of uniformity in musical time, and unity in our perception. We showed, however, that this unity implies a sense of self-similarity, while self-similarity provides us with a convenient and consistent tool to model the relationships of sound and music.

The serialist composers extended the physical continuum between consonances and dissonances to a continuum between tone and noises. We suggest in this thesis that this is actually a continuum between sound and music, or in other words a continuum between out physical and logical beings.

Schoenberg reduced his concept of music to the relationship between two tones and stopped himself from the manipulation of the structure of harmonic sound, even though as we have suggested, he freed its structures. Perhaps, he found such thought silly and strictly theoretical without any musical foundation; in that respect he remained ``tonal''. Stockhausen took a step further by reducing his musical entity to a single sinusoidal function. He writes[47, page 88]:

Until around 1950 the idea of music as sound was largely ignored. That composing with sounds could also involve the composition of sounds themselves, was no longer self-evident. It was revived as a result, we might say, of a historical development. The Viennese School of Schoenberg, Berg, and Webern had reduced their musical themes and motifs to entities of only two sounds, to intervals. Webern in particular, Anton von Webern. And when I started to compose music, I was certainly a child of the first half of the century, continuing and expanding what the composers of the first half had prepared. It took a little leap forward to reach the idea of composing, or synthesizing, the individual sound.

Electronic music was one story; computer music is a different one. We not only have the capability to generate any relationship in the structure of sound, and not only can we control them with practically unlimited precision, but we can also define logical processes which take over such controls as well. We have total control and no material; therefore the sound or the music using computers is all form in every scale, and it is the relationship among these forms in different scales which constitutes the composition. The material is nothing, and therefore the form has to be infinitely detailed. Self-similarity is the form for nothing.