Twelve-tone technique

The twelve-tone technique—also known as dodecaphony, twelve-tone serialism, and twelve-note composition—is a method of musical composition. The technique is a means of ensuring that all 12 notes of the chromatic scale are sounded equally often in a piece of music while preventing the emphasis of any one note through the use of tone rows, orderings of the 12 pitch classes. All 12 notes are thus given more or less equal importance, and the music avoids being in a key.
The technique was first devised by Austrian composer Josef Matthias Hauer, who published his "law of the twelve tones" in 1919. In 1923, Arnold Schoenberg developed his own, better-known version of 12-tone technique, which became associated with the "Second Viennese School" composers, who were the primary users of the technique in the first decades of its existence. Over time, the technique increased greatly in popularity and eventually became widely influential on mid-20th-century composers. Many important composers who had originally not subscribed to or actively opposed the technique, such as Aaron Copland and Igor Stravinsky, eventually adopted it in their music.
Schoenberg himself described the system as a "Method of composing with twelve tones which are related only with one another". It is commonly considered a form of serialism.
Schoenberg's fellow countryman and contemporary Hauer also developed a similar system using unordered hexachords or tropes—independent of Schoenberg's development of the twelve-tone technique. Other composers have created systematic use of the chromatic scale, but Schoenberg's method is considered to be most historically and aesthetically significant.

History of use

The twelve-tone technique is most often attributed to Austrian composer Arnold Schoenberg. He recalls using it in 1921 and describing it to pupils two years later. Simultaneously, Josef Matthias Hauer was formulating a similar theory in his writings. In the second edition of his book Vom Wesen Des Musikalischen, Hauer wrote that the law of the atonal melody requires all twelve tones to be played repeatedly.
The method was used during the next twenty years almost exclusively by the composers of the Second Viennese School—Alban Berg, Anton Webern, and Schoenberg himself. However, another important composer in this period, Elisabeth Lutyens, wrote over than 50 pieces using the serial method.
The twelve tone technique was preceded by "freely" atonal pieces of 1908–1923 which, though "free", often have as an "integrative element ... a minute intervallic cell" which in addition to expansion may be transformed as with a tone row, and in which individual notes may "function as pivotal elements, to permit overlapping statements of a basic cell or the linking of two or more basic cells". The twelve-tone technique was also preceded by "nondodecaphonic serial composition" used independently in the works of Alexander Scriabin, Igor Stravinsky, Béla Bartók, Carl Ruggles, and others. Oliver Neighbour argues that Bartók was "the first composer to use a group of twelve notes consciously for a structural purpose", in 1908 with the third of his fourteen bagatelles. "Essentially, Schoenberg and Hauer systematized and defined for their own dodecaphonic purposes a pervasive technical feature of 'modern' musical practice, the ostinato". Additionally, John Covach argues that the strict distinction between the two, emphasized by authors including Perle, is overemphasized:

The distinction often made between Hauer and the Schoenberg school—that the former's music is based on unordered hexachords while the latter's is based on an ordered series—is false: while he did write pieces that could be thought of as "trope pieces", much of Hauer's twelve-tone music employs an ordered series.

The "strict ordering" of the Second Viennese school, on the other hand, "was inevitably tempered by practical considerations: they worked on the basis of an interaction between ordered and unordered pitch collections."
Rudolph Reti, an early proponent, says: "To replace one structural force by another is indeed the fundamental idea behind the twelve-tone technique", arguing it arose out of Schoenberg's frustrations with free atonality, providing a "positive premise" for atonality. In Hauer's breakthrough piece Nomos, Op. 19 he used twelve-tone sections to mark out large formal divisions, such as with the opening five statements of the same twelve-tone series, stated in groups of five notes making twelve five-note phrases.
Felix Khuner contrasted Hauer's more mathematical concept with Schoenberg's more musical approach. Schoenberg's idea in developing the technique was for it to "replace those structural differentiations provided formerly by tonal harmonies". As such, twelve-tone music is usually atonal, and treats each of the 12 semitones of the chromatic scale with equal importance, as opposed to earlier classical music which had treated some notes as more important than others.
The technique became widely used by the fifties, taken up by composers such as Milton Babbitt, Luciano Berio, Pierre Boulez, Luigi Dallapiccola, Ernst Krenek, Riccardo Malipiero, and, after Schoenberg's death, Igor Stravinsky. Some of these composers extended the technique to control aspects other than the pitches of notes, thus producing serial music. Some even subjected all elements of music to the serial process.
Charles Wuorinen said in a 1962 interview that while "most of the Europeans say that they have 'gone beyond' and 'exhausted' the twelve-tone system", in America, "the twelve-tone system has been carefully studied and generalized into an edifice more impressive than any hitherto known."
American composer Scott Bradley, best known for his musical scores for works like Tom & Jerry and Droopy Dog, utilized the 12-tone technique in his work. Bradley described his use thus:
An example of Bradley's use of the technique to convey building tension occurs in the Tom & Jerry short "Puttin' on the Dog", from 1944. In a scene where the mouse, wearing a dog mask, runs across a yard of dogs "in disguise", a chromatic scale represents both the mouse's movements, and the approach of a suspicious dog, mirrored octaves lower. Apart from his work in cartoon scores, Bradley also composed tone poems that were performed in concert in California.
Rock guitarist Ron Jarzombek used a twelve-tone system for composing Blotted Science's extended play The Animation of Entomology. He put the notes into a clock and rearranged them to be used that are side by side or consecutive. He called his method "Twelve-Tone in Fragmented Rows."

Tone row

The basis of the twelve-tone technique is the tone row, an ordered arrangement of the twelve notes of the chromatic scale. There are four postulates or preconditions to the technique which apply to the row, on which a work or section is based:

The row is a specific ordering of all twelve notes of the chromatic scale.
No note is repeated within the row.
The row may be subjected to interval-preserving transformations—that is, it may appear in inversion, retrograde, or retrograde-inversion, in addition to its "original" or prime form.
The row in any of its four transformations may begin on any degree of the chromatic scale; in other words it may be freely transposed. Transpositions are indicated by an integer between 0 and 11 denoting the number of semitones: thus, if the original form of the row is denoted P₀, then P₁ denotes its transposition upward by one semitone.

A particular transformation together with a choice of transpositional level is referred to as a set form or row form. Every row thus has up to 48 different row forms.

Example

Suppose the prime form of the row is as follows:
Then the retrograde is the prime form in reverse order:
The inversion is the prime form with the intervals inverted :
And the retrograde inversion is the inverted row in retrograde:
P, R, I and RI can each be started on any of the twelve notes of the chromatic scale, meaning that 47 permutations of the initial tone row can be used, giving a maximum of 48 possible tone rows. However, not all prime series will yield so many variations because transposed transformations may be identical to each other. This is known as invariance. A simple case is the ascending chromatic scale, the retrograde inversion of which is identical to the prime form, and the retrograde of which is identical to the inversion.
Image:P-R-I-RI.png|thumb|350px|Prime, retrograde, inverted, and retrograde-inverted forms of the ascending chromatic scale. P and RI are the same, as are R and I.
In the above example, as is typical, the retrograde inversion contains three points where the sequence of two pitches are identical to the prime row. Thus the generative power of even the most basic transformations is both unpredictable and inevitable. Motivic development can be driven by such internal consistency.

Application in composition

Note that rules 1–4 above apply to the construction of the row itself, and not to the interpretation of the row in the composition. While a row may be expressed literally on the surface as thematic material, it need not be, and may instead govern the pitch structure of the work in more abstract ways. Even when the technique is applied in the most literal manner, with a piece consisting of a sequence of statements of row forms, these statements may appear consecutively, simultaneously, or may overlap, giving rise to harmony.
Durations, dynamics and other aspects of music other than the pitch can be freely chosen by the composer, and there are also no general rules about which tone rows should be used at which time. However, individual composers have constructed more detailed systems in which matters such as these are also governed by systematic rules.