twelve-tone technique

The twelve-tone technique—also known as dodecaphony, twelve-tone serialism, and (in British usage) 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 (1874–1951) 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".¶

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 (On the Essence of Music, 1923), 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 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".¶

Tone row

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:¶

The row is a specific ordering of all twelve notes of the chromatic scale (without regard to octave placement). No note is repeated within the row. 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). 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). (In Hauer's system postulate 3 does not apply.) 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; see the sections on derived rows and invariance below.)¶

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 (so that a rising minor third becomes a falling minor third, or equivalently, a rising major sixth):¶

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 (thus, only 24 forms of this tone row are available).¶

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. (Thus, for example, postulate 2 does not mean, contrary to common belief, that no note in a twelve-tone work can be repeated until all twelve have been sounded.) 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 (beyond their all being derived from the prime series, as already explained). However, individual composers have constructed more detailed systems in which matters such as these are also governed by systematic rules (see serialism).¶

Topography

Analyst Kathryn Bailey has used the term 'topography' to describe the particular way in …¶

The text above is adapted from the Wikipedia article “Twelve-tone technique”, available under the Creative Commons Attribution-ShareAlike 4.0 licence.¶

twelve-tone technique is musical composition method using all 12 chromatic scale notes equally often & not in a key, according to the structured record cited below. This entry was generated automatically from that record and has not yet been reviewed by a person familiar with the tradition.¹¶

The source record links this tradition to 28 external registers, which can be verified through the citation.¹¶