By breaking the logical barrier between consonances and dissonances in a physical way, Schoenberg freed the structures of sound. However, perhaps he himself was not aware of the full implications of his ideas. We repeat one of Schoenberg's quotes for its importance[40, page 137]:
The path to be trodden here seems to me the following: not to look for harmonies, since there are no rules for those, no values, no laws of construction, no assessment. Rather, to write parts. From the way these sound, harmonies will later be abstracted.Aesthetically, the idea is simple. Art is not up for judgment unless it is done for its own sake. However, when we think about that idea and take it to its formal end, we reach some very complex issues. Where does harmony of communication come from if it is not worked on? Will god write the harmonies for us? If so, that is faith, and, as we have very briefly mentioned, faith is a paradox that cannot be communicated; concerning these issues we showed that there is a certain compromise between originality and comprehensibility. From this quote, we conclude, that art, which is really a way of life, is not a job and the artist cannot be concerned with the assessment of his or her work; not because it is not important, but because it does not help in any way and perhaps can never be ``known''.
Technically, Schoenberg's ideas opened so many doors in music that the problem was not how to find an original idea but rather how to make such originality aesthetically accessible. Schoenberg stopped himself from manipulating the structures of sound since he thought there were no instruments that could play what his imagination would have created[41, page 424]. He broke the preestablished forms up to the boundaries of note intervals in the well-tempered scale. Many composers who followed his path (such as Cage, Boulez, and Stockhausen) devised their own language of form. Stockhausen went a step further in understanding the relationships between material and organization, and introduced the idea of synthesis or the composition of sound.
There is perhaps very little argument about the fact that a real work of art has a certain homogeneity. The idea of a musical theme defining the music as well as the sound, or in other words unity of form and content, made Stockhausen aware of the unity in different levels of our perception. As we have shown, the requirements of homogeneity in a balanced (random vs. correlated) piece of music and the unity of form and content are the requirements of unity in our different perceptual levels. Every one of these factors points to the concept of self-similarity. The homogeneity of music implies that every part of the piece sends the same information; that should be true not only for the smaller sections which follow one another but also for the larger sections as well which are composed of those smaller sections. The relationship of the macro-structures and micro-structures are in fact the relationships between the material and organization of the piece. The different levels of our perception, which in music are represented by the feeling of form, rhythm, and pitch, are connected to each other with self-similar structures. The sensation of pitch comes from a rhythmical organization of vibrations; rhythms are created from the repetition of simple forms of pitches with related variations. The feeling of form comes from a certain coherency in the rhythmical structures of pitch. And finally for the form to have any meaning, for example in the tonal form, the feeling of form connects itself to a large-scale feeling of pitch. This is one possible view of how form works in tonality.
Pitch is timbre reduced to a single dimension according to harmonic relationships. Serialism simply implies that the unifying concept relating our different levels of perception does not have to be the harmonic relationship. By this fact, serialism implies that not only the composition has to define how this relationship is used, but also that it has to define the relationship in the first place. Before electronic music existed, it was difficult to conceive of such an idea since we had very few instruments that could create inharmonic sounds that could be precisely controlled. Every piece of music has to be adapted for its instruments, while at the same time, it is the sound of the instrument which defines what kind of music should be played on it. Having a computer in our hands which could create any sound with any type of relationship, and being able to control them with any precision we pleased, implied a reconsideration of the relationship of the content as form, and the form as the relationships in the content.