Twelve-tone Technique The Technique History Of The Technique's

Schoenberg himself described the system as a "method of composing with 12 notes which are related only to one another".

1 The technique

The basis of twelve-tone technique is the tone row or set, an ordered arrangement of the twelve notes of the chromatic scale (the twelve equal tempered pitch classes), or, rather, an ordered arrangement of intervals which produce those notes. When the technique is applied most rigorously, an entire piece must be built up from statements of any transposition of this tone row in strict order or transformations of this row. Both melody and harmony may be created in this way. The set may be used in succession or simultaneously, the latter of which may be ordered up or down, or not. Given twelve pitch classes, there are 12! (12 factorial) possible tone rows, though invariance often reduces the number of distinct rows.

The initial tone row, or set form, used is called the prime series (P), untransposed it is P₀. P can be used starting on any one of the twelve notes of the chromatic scale (P_χ) - so long as the intervals are the same, the rows are equivalent. P_χ = P₀ + χ.

Additionally, P can be transformed in two basic ways: it can be turned backwards to get the retrograde (R) or turned upsidedown to give the inversion (I) or the reverse contour direction. I(χ) = 12 - P_χ. These two transformative techniques can be combined to give the retrograde inversionCounterpoint is a musical device where two or more melodic phrases occur simultaneously. The term comes from the Latin punctus contra punctum (note against note). A note moves against another note when the interval between those two notes either grows or (RI). As with the prime series, R, I and RI can be transposed to any note of the chromatic scale.

More recently composers such as Charles WuorinenCharles Wuorinen (born June 9, 1938 in New York City) is an American composer. Co-founder of the Group for Contemporary Music, Wuorinen writes serial instrumental music. Some of his pieces are influenced by fractal geometry and Benoit Mandelbrot, while hi have also used multiplicationArithmetic In its simplest form, multiplication is a quick way of adding identical numbers. The result of multiplying numbers is called a product''. The numbers being multiplied are called coefficients or factors and individually as the multiplicand and m of the row. However, there are only a few numbers which one may multiply a row by and still end up with twelve tones. Multiplication is indicated by MX, X being the multiplier. As with the other compound operations multiplication is carried out and then transposition. P₀ = M1₀, I₀ = M11₀, M7₀=I(M5₀). Thus, for the untransposed form of all:

Even numbers remain unchanged under M7 and all odd numbers become transposed by a tritone. The chromatic scale may be mapped onto the circle of fourths with M5, and the circle of fifths with M7.

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

P, R, I and RI can each be started on any of the twelve notes of the chromatic scale, meaning that 47 permutationIn music and the terminology of the twelve tone technique a permutation is one of the many forms a tone row or twelve tone series. That is, prime form and any transposition, inversion, retrograde or retrograde-inversion, a total of 48 permutations. Howeves 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 tranposed 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).

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 octaveIntervals : For the numerical computation software, see GNU Octave. In music, an octave (sometimes abbreviated 8ve or 8va is the interval between one musical note and another with half or double the frequency. For example, if one note is pitched at 400 Hz, but the order of the notes in the tone row must be maintained. Durations, dynamicsIn music, dynamics refers to the volume or loudness of the sound, in particular to the range from soft to loud. The term is also applied to the written or printed musical notation used to indicate dynamics. The renaissance composer Giovanni Gabrieli was o 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 them all being derived from the prime series, as already explained).

Schoenberg's idea in developing the technique was for it to act as a replacement for tonal harmony as a basic grounding force for music. 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).

2 History of the technique's use

Founded by Austrian composer Arnold Schoenberg around the late 1910s, the method was used during the next 20 years almost exclusively by the Second Viennese School ( Alban Berg, Anton Webern, Hanns Eisler and Arnold Schoenberg himself). 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 (Reti, 1958). The technique became widely used by the fifties, taken up by composers such as Luciano Berio, Pierre Boulez, Luigi Dallapiccola 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.

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:

the full chromatic is used and constantly circulates, but permutational devices are ignored
permutational devices are used but not on the full chromatic

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." (Chase 1992, p.587)

2.1 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 is partitioning, the use of methods to create segments from sets, most often through registral difference.

2.1.1 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.

2.1.2 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, see George Perle.

2.2 Other

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.

3 Further reading

Serial Composition and Atonality: An Introduction to the Music of Schoenberg, Berg, and Webern by George Perle, BooksEnthsiast.com
Simple Composition by Charles Wuorinen, BooksEnthsiast.com.

4 Source

Chase, Gilbert (1992). America's Music: From the Pilgrims to the Present. University of Illinois Press, BooksEnthsiast.com.

5 External links

Wikiquote has a collection of quotations by or about .

6 Source

Reti, Rudolph (1958). Tonality, Atonality, Pantonality: A study of some trends in twentieth century music. Westport, Connecticut: Greenwood Press. BooksEnthsiast.com.

Twelve-tone technique

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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.

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

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