Twelve-tone technique

Arnold Schoenberg, the inventor of Twelve-tone technique

Twelve-tone technique (also dodecaphony, especially in British usage, twelve-note composition) is a method of musical composition devised by Arnold Schoenberg. 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.[1] All 12 notes are thus given more or less equal importance, and the music avoids being in a key. The technique was tremendously influential on composers in the mid-twentieth century.

Schoenberg himself described the system as a "Method of Composing with Twelve Tones Which are Related Only with One Another".[2] However, the common usage (in English) at the present time is to describe this method as a form of serialism.

Josef Matthias Hauer also developed a similar system using unordered hexachords, or tropes, at the exact same time and country but with no connection to Schoenberg. Other composers have created systematic use of the chromatic scale, but Schoenberg's method is historically most significant.

Contents

History of the technique's use

Founded by Austrian composer Arnold Schoenberg in 1921 and first described privately to his associates in 1923,[3] the method was used during the next twenty years almost exclusively by the Second Viennese School (Alban Berg, Anton Webern, Hanns Eisler and Arnold Schoenberg himself).

The twelve tone technique was preceded by "freely" atonal pieces of 1908–23 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".[4] 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.[5] Oliver Nieghbour 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.[6] "Essentially, Schoenberg and Hauer systematized and defined for their own dodecaphonic purposes a pervasive technical feature of 'modern' musical practice, the ostinato".[7]

Rudolph Reti, an early proponent, says: "To replace one structural force (tonality) by another (increased thematic oneness) is indeed the fundamental idea behind the twelve-tone technique," arguing it arose out of Schoenberg's frustrations with free atonality,[8] providing a "positive premise" for atonality.[9]

Schoenberg's idea in developing the technique was for it to "replace those structural differentiations provided formerly by tonal harmonies".[10] 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 (particularly the tonic and the dominant note).

The technique became widely used by the fifties, taken up by composers such as Milton Babbitt, Luciano Berio, Pierre Boulez, Luigi Dallapiccola, Ernst Krenek and, after Schoenberg's death, Igor Stravinsky. Some of these composers extended the technique to control aspects other than the pitches of notes (such as duration, method of attack and so on), thus producing serial music. Some even subjected all elements of music to the serial process.

Charles Wuorinen claimed 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."[11]

Tone row

Main article: Tone row

The basis of 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 set on which a work or section is based:[12]

  1. The set is a specific ordering of all twelve notes of the semitonal scale.
  2. No note is repeated within the set
  3. The set may be stated in any of its "linear aspects": prime, inversion, retrograde, and retrograde-inversion.
  4. The set in any of its four transformations may be started upon any degree of the semitonal scale.

When twelve-tone technique is strictly applied, a piece consists of statements of certain permitted transformations of the prime series. Note that these statements may appear consecutively, simultaneously, or may overlap, giving rise to harmony.

Transformations

The tone row chosen as the basis of the piece is called the prime series (P). Untransposed, it is notated as P0. Given the twelve pitch classes of the chromatic scale, there are (12!) (factorial, i.e. 479,001,600) unique tone rows.

Appearances of P can be transformed from the original in three basic ways:

The various transformations can be combined. These give rise to a set-complex of forty-eight forms of the set, 12 transpositions of the four basic forms: P, R, I, RI. The combination of the retrograde and inversion transformations is known as the retrograde inversion (RI).

RI is: RI of P, R of I, and I of R.
R is: R of P, RI of I, and I of RI.
I is: I of P, RI of R, and R of RI.
P is: R of R, I of I, and RI of RI.

thus, each cell in the following table lists the result of the transformations in its row and column headers:

RI: R: I:
RI: P I R
R: I P RI
I: R RI P

More recently, composers such as Charles Wuorinen have also used multiplication of the row. However, there are only a few numbers by which one may multiply a row and still end up with twelve tones. Larry Solomon has applied reflection across the axis of pitch and time, creating "quadrates".[13]

Example

Suppose the prime series is as follows:

B, Bb, G, C#, Eb, C, D, A, F#, E, Ab, F

Then the retrograde is the prime series in reverse order:

F, Ab, E, F#, A, D, C, Eb, C#, G, Bb, B

The inversion is the prime series with the intervals inverted (so that a rising minor third becomes a falling minor third):

B, C, Eb, A, G, Bb, Ab, C#, E, F#, D, F

And the retrograde inversion is the inverted series in retrograde:

F, D, F#, E, C#, Ab, Bb, G, A, Eb, C, B

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).

Note that 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 this internal consistency both positively and negatively.

When rigorously applied, the technique demands that one statement of the tone row must be heard in full (otherwise known as aggregate completion) before another can begin. Adjacent notes in the row can be sounded at the same time, and the notes can appear in any octave, but the order of the notes in the tone row must be maintained. Durations, dynamics and other aspects of music other than the pitch can be freely chosen by the composer, and there are also no rules about which tone rows should be used at which time (beyond their all being derived from the prime series, as already explained).

Derivation

Derivation is transforming segments of the full chromatic, less than 12 pitch classes, to yield a complete set, most commonly using trichords, tetrachords, and hexachords. A derived set can be generated by choosing appropriate transformations of any trichord except 0,3,6, the diminished triad. A derived set can also be generated from any tetrachord that excludes the interval class 4, a major third, between any two elements. The opposite, partitioning, uses methods to create segments from sets, most often through registral difference.

Combinatoriality

Main article: Combinatoriality

Combinatoriality is a side-effect of derived rows where combining different segments or sets such that the pitch class content of the result fulfills certain criteria, usually the combination of hexachords which complete the full chromatic.

Invariance

Invariant formations are also the side effect of derived rows where a segment of a set remains similar or the same under transformation. These may be used as "pivots" between set forms, sometimes used by Anton Webern and Arnold Schoenberg.[14]

Invariance describes the portions of rows which have been so designed that they remain invariant under the allowable transformations (inversion, retrograde, retrograde-inversion, multiplication). George Perle describes their use as "pivots" or non-tonal ways of emphasizing certain pitches. Invariant rows are also combinatorial and derived.

Other

In practice, the "rules" of twelve-tone technique have been bent and broken many times, not least by Schoenberg himself. For instance, in some pieces two or more tone rows may be heard progressing at once, or there may be parts of a composition which are written freely, without recourse to the twelve-tone technique at all. Offshoots or variations may produce music in which:

Also, some composers have used cyclic permutation, or rotation, where the row is taken in order but using a different starting note.

Although usually atonal, twelve tone music need not be—several pieces by Berg, for instance, have tonal elements.

One of the best known twelve-note compositions is Variations for Orchestra by Arnold Schoenberg. "Quiet", in Leonard Bernstein's Candide, satirizes the method by using it for a song about boredom, and Benjamin Britten used a twelve-tone row—a "tema seriale con fuga"—in his Cantata Academica: Carmen Basiliense (1959) as an emblem of academicism.[15]

Schoenberg's mature practice

Ten features of Schoenberg's mature twelve-tone practice are characteristic, interdependent, and interactive:[16]

  1. Hexachordal inversional combinatoriality
  2. Aggregates
  3. Linear set presentation
  4. Partitioning
  5. Isomorphic partitioning
  6. Invariants
  7. Hexachordal levels
  8. Harmony, "consistent with and derived from the properties of the referential set"
  9. Metre, established through "pitch-relational characteristics"
  10. Multidimensional set presentations

See also

Further reading

Notes

  1. ↑ Perle 1977, 2.
  2. ↑ Schoenberg 1975, 218.
  3. ↑ Schoenberg 1975, 213.
  4. ↑ Perle 1977, 9-10.
  5. ↑ Perle 1977, 37.
  6. ↑ Neighbour 1955, 53.
  7. ↑ Perle 1977, 37.
  8. ↑ Reti, 1958
  9. ↑ Perle 1977, 2.
  10. ↑ Schoenberg 1975, 218.
  11. ↑ Chase 1992, 587.
  12. ↑ Perle 1977, 3
  13. ↑ Solomon 1973,.
  14. ↑ Perle 1977, 91–93.
  15. ↑ Brett 2007.
  16. ↑ Haimo (1990), p.41.

Sources

External links