The twelve-tone technique, also called dodecaphony, twelve-tone serialism, or twelve-note composition (in British usage), is a way of writing music. This method ensures that all 12 notes of the chromatic scale are used equally often in a piece of music. It avoids giving special importance to any single note by using tone rows, which are specific orders of the 12 different pitches. This system makes all 12 notes equally important and prevents the music from being in a key.

The technique was first created by Austrian composer Josef Matthias Hauer, who introduced his "law of the twelve tones" in 1919. In 1923, Arnold Schoenberg (1874–1951) developed a more widely known version of the twelve-tone technique. Schoenberg’s version became linked with the "Second Viennese School" composers, who were the main users of the technique in its early years. Over time, the method became very popular and greatly influenced many composers in the mid-20th century. Some composers, like Aaron Copland and Igor Stravinsky, who initially did not support the technique, later used it in their music.

Schoenberg described the system as "a method of composing with twelve tones which are related only with one another." It is often seen as a type of serialism. Schoenberg’s contemporary, Hauer, also created a similar system using unordered groups of six notes, called hexachords or tropes, which were separate from Schoenberg’s development. While other composers used the chromatic scale in organized ways, Schoenberg’s method is considered the most important historically and artistically.

History of use

The twelve-tone technique is most often credited to Austrian composer Arnold Schoenberg. He used it in 1921 and explained it to students two years later. Around the same time, Josef Matthias Hauer was developing a similar theory in his writings. In the second edition of his book Vom Wesen Des Musikalischen (On the Essence of Music, 1923), Hauer wrote that an atonal melody must include all twelve tones repeated.

The method was used almost exclusively by composers of the Second Viennese School—Alban Berg, Anton Webern, and Schoenberg himself—for the next twenty years. However, another important composer, Elisabeth Lutyens, wrote more than 50 pieces using the serial method during this time.

The twelve-tone technique followed "freely" atonal compositions from 1908–1923. Though these pieces were called "free," they often included a small group of notes, called an "intervallic cell," which could be expanded or changed like a tone row. Individual notes might also act as links between different sections of music. The twelve-tone technique was also preceded by "nondodecaphonic serial composition," used by composers such as Alexander Scriabin, Igor Stravinsky, Béla Bartók, Carl Ruggles, and others. Oliver Neighbour argued that Bartók was the first composer to use a group of twelve notes intentionally for a structural purpose in 1908. He used this in the third of his fourteen bagatelles. Schoenberg and Hauer later organized and defined a common musical feature of modern practice—the ostinato—for their own purposes. John Covach noted that the strict differences between these systems, as emphasized by some authors, are overstated.

The Second Viennese School’s strict ordering of tones was sometimes adjusted based on practical needs, as composers balanced ordered and unordered groups of notes. Rudolph Reti, an early supporter of the technique, stated that the twelve-tone method replaced traditional tonality with a stronger sense of unity in themes. He believed the method developed from Schoenberg’s dissatisfaction with free atonality, offering a clear structure for atonal music. In Hauer’s piece Nomos, Op. 19 (1919), he used twelve-tone sections to divide the music into large parts, such as the opening five statements of the same twelve-tone series, grouped into five-note phrases.

Felix Khuner compared Hauer’s mathematical approach to Schoenberg’s more musical one. Schoenberg’s goal was to replace the structural roles once provided by tonal harmonies. As a result, twelve-tone music is usually atonal, treating each of the 12 semitones of the chromatic scale equally, unlike earlier classical music, which gave more importance to certain notes like the tonic and dominant.

The technique became widely used by the 1950s, adopted by composers such as Milton Babbitt, Luciano Berio, Pierre Boulez, Luigi Dallapiccola, Ernst Krenek, Riccardo Malipiero, and Igor Stravinsky after Schoenberg’s death. Some composers expanded the technique to control aspects like note duration and attack methods, creating serial music. Others applied the serial process to all elements of music.

Charles Wuorinen said in a 1962 interview that while many European composers claimed they had moved beyond the twelve-tone system, American composers had studied it thoroughly and developed it into a more complex structure than any before.

Scott Bradley, an American composer known for scores in cartoons like Tom & Jerry and Droopy Dog, used the twelve-tone technique in his work. He described using it to build tension in the Tom & Jerry short Puttin' on the Dog (1944). In a scene where a mouse wearing a dog mask runs past dogs in disguise, a chromatic scale represents both the mouse’s movement and the approaching dog, played in mirrored octaves lower. Bradley also composed tone poems performed in concerts in California.

Rock guitarist Ron Jarzombek used a twelve-tone system to compose Blotted Science’s extended play The Animation of Entomology. He placed the notes on a clock and rearranged them to create consecutive or side-by-side sequences. He called his method "Twelve-Tone in Fragmented Rows."

Tone row

The twelve-tone technique uses a tone row, which is a specific order of all twelve notes in the chromatic scale (the twelve equal-tempered pitch classes). There are four rules that apply to the tone row, which serves as the foundation for a musical piece or section:

• The tone row includes all twelve notes of the chromatic scale, but the octave placement of each note does not matter.
• No note is repeated within the tone row.
• The tone row can be changed using transformations that preserve the intervals between notes. These transformations include inversion (reversing the direction of intervals), retrograde (reversing the order of notes), and retrograde-inversion (reversing both the order and direction of intervals). The original form of the row is called the prime form (P).
• The tone row can begin on any note of the chromatic scale, meaning it can be transposed (shifted up or down in pitch). Transpositions are marked by numbers from 0 to 11, representing semitone intervals. For example, P0 is the original form, and P1 is the same row shifted up by one semitone.

In some systems, like Hauer’s, the third rule does not apply.

A specific transformation (prime, inversion, retrograde, or retrograde-inversion) combined with a transposition level is called a set form or row form. Each tone row can have up to 48 different forms (some may have fewer due to symmetry).

For example, if the prime form of a row is:
C D E F G A B C# D# E# F# G#
Then:
– The retrograde is the reverse of this order: G# F# E# D# C# B A G F E D C
– The inversion flips the direction of intervals (e.g., a rising minor third becomes a falling minor third).
– The retrograde-inversion is the inversion reversed in order.

The prime form, inversion, retrograde, and retrograde-inversion can each start on any of the twelve chromatic scale notes. This creates 48 possible variations of the row, though some rows may have fewer due to repeated patterns (called invariance). For example, the ascending chromatic scale has only 24 unique forms because some transformations produce identical results.

The term "topography" describes how notes in a row are arranged. In Webern’s music, two types are identified:
– Block topography: Rows are played one after another in the order they appear, regardless of musical texture.
– Linear topography: Multiple rows are played simultaneously across different voices (not limited to instruments), creating a layered structure.

Rows can be connected through elision, where two rows overlap by sharing one or more notes. If multiple rows share the same overlapping notes, it forms a row chain or row chain cycle, organizing groups of rows systematically.

The tone row used as the basis of a piece is called the prime series (P0). There are 12 factorial (479,001,600) possible tone rows, but many are equivalent after considering transformations. There are 9,985,920 unique classes of tone rows and 836,017 distinct 12-tone cycles without fixed starting or ending pitches.

Transformations of the prime form include:
– Transposition (Pχ): Shifting the row up or down by a specific number of semitones.
– Retrograde (R): Reversing the order of notes.
– Inversion (I): Flipping the direction of intervals.

Combining these transformations creates 48 variations of the row: 12 transpositions of the four basic forms (P, R, I, RI). The combination of retrograde and inversion is called retrograde-inversion (RI).

Derived sets are created by using smaller segments of the chromatic scale (like trichords, tetrachords, or hexachords) and applying transformations to complete the set. For example, trichords other than 0,3,6 (the diminished triad) can generate derived sets. Combinatoriality occurs when segments of a row combine to form complete chromatic scales. Invariant formations are parts of a row that remain unchanged under certain transformations, often used as "pivots" between set forms.

Invariance refers to properties of a set that remain unchanged after a transformation, similar to mathematical invariance. This concept is used by composers like Anton Webern and Arnold Schoenberg.

Schoenberg's mature practice

Ten key aspects of Schoenberg's mature twelve-tone method are connected, work together, and influence each other:

• The way six-note segments can be flipped and combined to create new musical patterns.
• The complete group of twelve unique pitches used in the system.
• Showing the set in a single, continuous sequence.
• Splitting the set into smaller groups for different musical sections.
• Creating similar groupings with different arrangements.
• Elements that remain unchanged even when the music changes.
• Different layers of six-note segments that interact with each other.
• Harmony that comes from the main set of pitches.
• Rhythm determined by how pitches relate to each other.
• Using the set in various forms and dimensions.