Dodecaphony

Twelve-tone technique (also known as dodecaphony, twelve-tone serialism, and (in British usage) twelve-note composition) is a method of musical composition devised by Austrian composer Arnold Schönberg (1874–1951). The technique is a means of ensuring that all 12 notes of the chromatic scale are sounded as often as one another 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 influential on composers in the mid-20th century.

Schönberg 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.

Schönberg’s countryman and contemporary Josef Matthias Hauer also developed a similar system using unordered hexachords or tropes – but with no connection to Schönberg’s twelve-tone technique. Other composers have created systematic use of the chromatic scale, but Schönberg’s method is considered to be historically and aesthetically most significant.

The basis of the twelve-tone technique is the tone row, an ordered arrangement of the twelve notes of the chromatic scale (the twelve equal tempered pitch classes). There are four postulates or preconditions to the technique which apply to the row (also called a set or series), on which a work or section is based:

1 – The row is a specific ordering of all twelve notes of the chromatic scale (without regard to octave placement).
2 – No note is repeated within the row.
3 – The row may be subjected to interval-preserving transformations – that is, it may appear in inversion (denoted I), retrograde (R), or retrograde-inversion (RI), in addition to its »original« or prime form (P).
4 – 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. (Transposition being an interval-preserving transformation, this is technically covered already by 3.) 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 (similarly I₁ is an upward transposition of the inverted form, R₁ of the retrograde form, and RI₁ of the retrograde-inverted form).

A particular transformation (prime, inversion, retrograde, retrograde-inversion) 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. (Some rows have fewer due to symmetry.)