The main idea of serial music is that elements of the row are all equal in rights and governed by the order in which they appear. To abolish the notion of hierarchy between sounds, Schoenberg used serialism, but applied it to only one of the four fundamental parameters (pitch, duration, timbre, dynamics): the pitch. Using the twelve tones of the chromatic scale, Schoenbergian serialism reveals itself to be also dodecaphonic, which is why we often associate the twelve tone technique with serialism.

Technically, the tone-row is composed of twelve tones of the tempered chromatic scale, set in an order defined by the composer but each tone can appear once and only once in the row. The number of possible rows is very high, in mathematical terms, it is a permutation of 12 elements, 12! (1x2x3x4. … x12) So 479,001,600 possibilities. The composer, once the row has been defined, can use it in various forms:

• - prime form (Grundgestalt) , so without change
• - retrograde , the prime form is taken backwards (from the last note to the first)
• - inversion : prime form turned upside-down.
• - Retrograde inversion combination of the two previous changes

Each of these forms can also be transposed to the other eleven degrees of the chromatic scale, bringing the number of possible forms of the same row to 4+4×11=48. The composer may play several tones of the row simultaneously (in vertical form, so “chords”) or horizontally, but change registry, or overlay different speeds. We can clearly see that the possibilities are almost endless, but more important, the row can not be regarded as a theme in a classical meaning, as it is not easily recognizable melodically, but is more like a succession of intervals.

One can deduce important conclusions from the foregoing :

• 1. Serial does not mean dodecaphonic: the tone-row may be composed of less than twelve sounds (in Stravinsky for instance), more than twelve sounds (in microtonal music) or affect other parameters than the pitch (the rhythm for example).
• 2. Serial does not mean atonal: Some series can be chosen to evoke a tonal character
• 3. If works written by Schoenberg with his “method of composition with twelve tones which are not related” are basically atonal, dodecaphonic and serial, this is only a special case of atonality and serialism.

We have only spoken of Schoenbergian dodecaphonic serialism but we could also speak of dodecaphonic serialism in Western tonal music, also based on the twelve tones of the chromatic scale. Here are some examples you might find surprising : we can find a twelve-tone row in the recitatives of Mozart’s Don Giovanni , or at the beginning of Liszt’s Faust Symphony or in the fugue of Strauss’ Also sprach Zarathustra … Amazing, isn’t it?

Related posts:

1. The twelve-tone technique
2. Atonal Music
3. The little story of musical notation 1/4

Back to the twelve-tone technique. One can easily understand the word dodecaphonic, invented by Rene Leibowitz in France (later, I will speak longer of him as very close to Pierre Boulez). Dodeca, twelve and phonic, sound: Twelve sounds. Why twelve? Twelve is the number of pitches that consitute the chromatic scale. Roughly, the twelve-tone technique is a compositional technique that uses a row of the twelve distinct sounds of the chromatic scale which can’t be repeated until they have all been played. I will not dwell on the technique itself, we will have later the opportunity to speak about prime, inversion, retrograde, and retrograde-inversion.

The twelve-tone system gives equal weight to each note of the semitonal scale, avoiding any hierarchy of sounds, then avoiding a priori any form of tonality.

The number twelve is fascinating : besides the fact that its mathematical properties are interesting to group notes equally, and thus enable games of symmetries, imitations, etc. within the same tone row. The division by twelve is one of the most common in our mind: 12 months, 2 × 12 hours, the alexandrine comprising 12 syllables, twelve zodiacal signs, dodecastyle temples … My idea is not to show a mystical of the number twelve, but to show that its properties have certainly had a strong influence on the elaboration of the tempered system, and thus the twelve-tone technique, using this temperament as it is.

The set of all twelve pitch classes form what is called the total chromatic. Surprising because it is only a total according to the conventions of the temperament, so conventions of the tonal system … The ear is capable of perceiving more than twelve pitches in an octave. Huge paradox for composers to use a material inherited by a system that they wished by every means to avoid. This may explain Schoenberg’s development towards a twelve-tone music rehabilitating tonal functions, and the race to complexity initiated by certain composers.

Related posts:

1. Serialism (1/3)
2. Atonal Music
3. The little story of musical notation 3/4

Atonal: having no established key (Collins). Atonality is a state in which all the rules and tonal functions are suspended. No more tonic, dominant, disappearance of consonance-dissonance axis, etc, in fact it represents the simple end of the laws on which has been based all Western music since the Baroque period (even middle ages, since modal system is not atonal). In an atonal system, the twelve tones of the chromatic scale are considered as equal, and the dissonance is not an episodic thing anymore.

It is difficult to date precisely the emergence of atonality because the atonal system did not appear suddenly but is a result of a slow evolution of the tonal system. We could see its roots in the Wagnerian chromaticism and since the mid-nineteenth century, and atonality gradually invaded the harmonic and contrapuntal writing. One of the most striking examples of the late nineteenth century is perhaps the prescient Bagatelle without tonality of Franz Liszt, composed in 1885.

But soon a character quickly became a key figure in the atonal world: Arnold Schoenberg. Upon his sextet Transfigured Night written in 1899, his path was defined. But we have to wait until 1908 and his second quartet to speak of conscious and systematic atonality which culminates in 1912 with Pierrot Lunaire. As for Schoenberg, the abolition of rules, the total freedom of the latter work has raised the question of the coherence of this new atonal world. He quickly felt the need to organize this chaotic world with new rules. The dodecaphonic system was born.

If Arnold Schoenberg and the Viennese School characterize the early atonal music, they are not the only ones to seriously blow the tonal system. Indeed, the French Impressionists were already deviating from this system and other composers have used atonal elements in their writing: for example Arthur Honneger, Bela Bartok or Stravinsky who, even after refusing almost all his life this system, introduced serialism into his works after Schoenberg’s death.

I would like to recall a word of Pierre Boulez, which is a good definition of this period: “The atonality is essentially a transitional period, being strong enough to break the tonal universe, not being coherent enough to generate a non-tonal one.” (« L’atonalité est essentiellement une période de transition, étant assez forte pour briser l’univers tonal, n’étant pas assez cohérente pour engendrer un système non tonal. »). In the next post, we will focus on the construction of a coherence in the atonal universe through dodecaphonism.

Related posts:

1. Serialism (1/3)
2. The twelve-tone technique
3. The little story of musical notation 4/4