I think that the most important innovations in musical form come about from building on the relationships of the three time regions: form, which is everything that happens between, say, eight seconds and half an hour; rhythm and metre, which is everything that happens between one-sixteenth of a second and eight seconds; and melody, which is everything that is organized between one-sixteenth and one-fourthousandth of a second, between 16 and 4000 cycles per second. It is almost technically possible to stretch a single sound lasting one second, to a length of half an hour, so that you have an overall form which has the characteristics structure of the original sound. On the other hand, if you are able to compress an entire Beethoven symphony into half a second, then you have a new sound, and its inner structures has been composed by Beethoven. Naturally it has a very particular quality compared to sound resulting from the compression of another Beethoven symphony. Not to mention a Schoenberg symphony, because there are many more aperiodicities in Schoenberg; that would be more of a noise, whereas the Beethoven would be a vowel, because it is more periodic in its structure.
Stockhausen was well aware of the rich relationships between sound and music and used them in many of his pieces. In ``.....how time passes....'', he discusses a system of composing ``phase-durations'' according to structures of pitch composition. He establishes the relations between beats in the same ways the overtones of harmonic sounds are related to each other. He also recognizes the fact that rhythms are perceived as textures, and from the idea of tone-colors devises a system for composing rhythm timbres which he calls ``formant-rhythms''. He used these ideas to compose Zeitmasse (1955-56), Gruppen für drei Orchester (1955-57), Klavierstück XI (1956), and Carreé (1959-60). In Gruppen, three orchestras surround the audience, with each orchestra having its own conductor, each playing in a different tempo. We can analyze this situation in the context of what has been mentioned in this chapter; it is as if every orchestra is a single instrument whose sound (timbre) is created by the musical structures played by the musicians of the orchestra using the sounds of their individual instruments.
Once we recognize the continuum of our perception in time, by controlling it we can use the continuum as a compositional tool. Stockhausen used this continuum as his basic medium of communication for the piece Kontakte (1959-60). About this composition he writes[47, page 95]:
There is a very crucial moment in my composition KONTAKTE for electronic sounds, beginning just before 17' 0,5" in the printed score. A translation of the title might be `Contacts', and the contacts are also between different forms and speeds in different layers. The moment begins with a tone of about 169 cycles per second, approximately F below middle C. Many of the various sounds in KONTAKTE have been composed by determining specific rhythms and speeding them up several hundred times or more, thereby obtaining distinctive timbres. What is interesting about this moment is that if I were to play little bits of the passage one after another, like notes on the piano, nobody would be able to hear the transition that takes place from one field of time perception to another. The fact that I make the transition continuously changes our whole attitude towards our acoustic environment. Every sound becomes a very mysterious thing, it has its own time.In this way, traditional meaning of parameters like rhythm and melodies become intertwined with the sound timbre qualities. In fact, we believe that the uniformity of the continuum of time connects the two concepts of the musical timbre and sound timbre. However, note that when this connection (the continuum itself) is used and made clearly apparent as a part of the composition, the traditional parameters (e.g., rhythm and melody) go through a circular transformation; meaning that for example, in listening to a process which is decelerating, rhythmic forms emerge out of timbral sounds while the contents of what creates the rhythmic from itself is a new, yet related timbre; therefore, timbral form also emerges out of rhythmic sounds. By slowing down or speeding up sounds, we are physically listening to the different scales of the signal, and for the signal to have a certain meaning by having a continuous uniform relationship among its different scales we are assuming a self-similar or self-affine structure in the sound and music. This view changes not only the way we compose music, but also how we listen to it analytically. Stockhausen says[47, page 95]:
The ranges of perception are ranges of time, and the time is subdivided by us, by the construction of our bodies and by our organs of perception. And since these modern means have become available, to change the time of perception continuously, from one range to another, from a rhythm into a pitch, or a tone or noise into a formal structure, the composer can now work within a unified time domain. And that completely changes the traditional concept of how to compose and think music, because previously they were all in separate boxes: harmony and melody in one box, rhythm and metre in another, then periods, phrasing, larger formal entities in another, while in the timbre field we had only names of instruments, no unity of reference at all. (I sometimes think we are fortunate in having such a poor language to describe sounds, much poorer than the visual field. That's why, in the visual field, almost all perception has been rationalized and no longer has any magic.)