The weightiest assumption behind twelve-tone composition is this thesis:
Whatever sounds together (harmonies, chords, the result of part-writing) plays its part in expression and in presentation of the musical idea in just the same way as does all that sounds successively (motive, shape, phrase, sentence, melody, etc.) and it is equally subject to the law of comprehensibility.Let us, for the sake of comprehensibility, assume that an object is comprehensible2.8when a meaning is attached to it, and therefore, it is required to have a certain degree of self-sufficiency. This implies that now simultaneous notes (which are called chords in the tonal context) are used as content with musical meaning, and they do not imply any context resulting from the tonal relationship of the simultaneously sounding tones. Please note that here we are talking about musical content in what was previously considered as instantaneous sound. Therefore, the content of simultaneous sounds does not have to abide by any eternal prefixed rule; now the content of a simultaneous sound (which is the relationship of all the overtones to each other in conjunction with the development of those elements in the duration of the sound) can be anything that serves the underlying musical idea.
And it is following this idea that Schoenberg introduced the idea of Klangfarbenmelodien, which is progression of tone colors independent of pitch or harmony. On this idea Schoenberg writes[41, page 421]:
I think the tone becomes perceptible by virtue of tone color, of which one dimension is pitch. Tone color is, thus, the main topic, pitch a subdivision. Pitch is nothing else but tone color measured in one direction. Now, if it is possible to create patterns out of tone colors that are differentiated according to pitch, patterns we call ``melodies'', progressions whose coherence (Zusammenhang) evokes an effect analogous to thought process, then it must also be possible to make such progressions out of the tone colors of the other dimension, out of that which we call simply ``tone color'', progressions whose relations with one another work with a kind of logic entirely equivalent to that logic which satisfies us in the melody of pitches.And he ends his ``Theory of harmony'' by the following passage:
Tone-color Melodies! How acute the senses that would be able to perceive them! How high the development of spirit that could find pleasure in such subtle things!
In such domain, who dares ask for theory!2.9
Let us examine these two ideas, Klangfarbenmelodien and ``simultaneous sounds which are subject to the laws of comprehensibility.''2.10Please note how the role of pitch and tone color changes in the Klangfarbenmelodien concept. In traditional tonal music, the pitch structures are conceived and then the musical idea is orchestrated, which creates the sound of the music. However, as Schoenberg states, pitch is nothing but timbre reduced to a one dimensional instantaneous value. And therefore, the tonal system is dependent and capable of producing only a single type of (musical) timbre -- the natural harmonic timbre. Now pitch has become a secondary issue, and one is still capable of communicating a musical idea without any dependency on it. This is communication based upon a type of progression which we previously understood as sound.
The same analogy applies to the ``simultaneous sounds which are subject to the laws of comprehensibility.'' Here the simultaneous sounds create a single timbre which has to be understood. Again, please note, how the roles have reversed; in tonal context a unity was assumed, and pitches (melodies) or chords, and then timbres, were used to portray that unity. Any deviation from this unity was only to build a stronger context for affirmation of the assumed unity. However, in an atonal context the unity is created only when all the parts are combined together; it is a physical unity rather than a logical pre-assumed unity. As one of the steps which has to be taken for new music, Schoenberg says[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.
How far can we move away from this presumption? What Schoenberg attacked was tonality of pitch, and he created a method to substitute the function of form in his music. So, why not apply the same idea to all parameters of music? This principle was what many of the composers following Schoenberg's footstep used as agents of form for their music. They applied the serial idea to parameters such as duration (rhythm), loudness, and timbre (orchestration). Rhythm defines a constraint plane in the horizontal dimension. If we apply serialism to form and rhythm and finally to inner structures of the sounds, we create aperiodic waveforms. The most aperiodic sound is white noise. Thus, we can define a continuum between tones and noise. On periodicity and noise, Stockhausen says[47, page 93]:
So the continuum between sound of fixed pitch and noise is nothing more than that between a more and a less stable periodicity: the noisiest noise being the most aperiodic. This discovery of a continuum between sound and noise, the fourth criterion of electronic music, was extremely important, because once such a continuum becomes available, you can control it, you can compose it, you can organize it.
John Cage took a different route. He used organized chance to control the process of sound and not the sound itself, and in this way freed music from his own personal intentions. His approach is to move from thoughts about order to no thoughts about order. On choices of what to do with sounds he says[2, page 10]:
Or, as before, one may give up the desire to control sound, clear his mind of music, and set about discovering means to let sounds be themselves rather than vehicles for man-made theories or expressions of human sentiments.
How far can we push such ideas as serialism and organized chance? Understanding John Cage's philosophy about music requires a certain approach to life, and for now, we will refrain from any linear reasoning to interpret what he suggests. Serialism implies a complete breakdown of the channel of communication between the composer and the listener, since if we fully abide by the idea, we are left with nothing in common between the composer and the listener. Fifteen years after Schoenberg completed his ``Theory of Harmony'' he writes[40, page 259]:
Tonality's origin is found -- and rightly so -- in the laws of sound. But there are other laws that music obeys, apart from these and the laws that resulted from the combination of time and sound: namely, those governing the working of our minds.Why can we not apply the same argument against tonality to any other formal concept in music? If tonality is a uniform structure in music and sound, and if in fact, as Schoenberg seems to imply, the real content of music is our thought, why should we not find the same elements, which free pitch from tonality, in the ``rules governing the working of our minds''? In other words why can we not free ``rules governing the working of our minds'' from the rules governing the working of our mind? In fact we can, and in this way we will free music from communication and we will reach a subjective idea of music. Every person can have his own idea of music; however, the music cannot be communicated at all, perhaps not even to ourselves.