Main Page | See live article | Alphabetical index

Twelve-tone technique

Twelve-tone technique is a system of musical composition devised by Arnold Schoenberg. Music using the technique is called twelve-tone music. Josef Matthias Hauer also developed a similar system using unordered hexachords at the exact same time with no connection to Schoenberg.

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

Table of contents
1 The technique
2 History of the technique's use
3 Further reading
4 External Links:

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 intervalss 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 succesion or simultaneously, the latter of which may be ordered up or down, or not.

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

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(X) = 12 - PX. These two transformative techniques can be combined to give the retrograde inversion (RI). As with the prime series, R, I and RI can be transposed to any note of the chromatic scale.

{| border=1 |RI is: |RI of S, |R of I, |and I of R. |- |R is: |R of S, |RI of I, |and I of RI. |- |I is: |I of S, |RI of R, |and R of RI. |- |P is: |R of R, |I of I, |and RI of RI. |}


{| border=1 |P |RI |R |I |- |RI |S |I |R |- |R |I |S |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 which you can multiple a row by and still get all twelve tones. P0 = M1, I0 = M11, M7=I(M5). Even numbers remain unchanged under M7 and all odd numbers become transposed by a tritone.

{| border=1 |M1 |M5 |M7 |M11 |- |M5 |M1 |M11 |M7 |- |M7 |M11 |M1 |M5 |- |M11 |M7 |M5 |M1 |}

Suppose the prime series is as follows:

Then the retrograde is the prime series in reverse order:

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

And the retrograde inversion is the inverted series 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 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 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 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).

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 only by the Second Viennese School (Alban Berg, Anton Webern, and Arnold Schoenberg himself), though was later taken up by composers such as Luciano Berio, Pierre Boulez, Luigi Dallapiccola and 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.


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.


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. The term was first described by Milton Babbitt. Hexachordal inversional combinatoriality refers to any two rows, one of which is an inversion and one is not. The first row's first half, or six notes, are the second's last six notes, but not necessarily in the same order. Thus the first half of each row is the others complement, as with the second half, and, when combined, these rows still maintain a fully chromatic feeling and don't tend to reinforce certain pitches as tonal centers as would happen with freely combined rows. Babbitt also described the semi-combinatorial row and the all-combinatorial row, the latter being a row which is combinatorial with any of its derivations and their transpositions. Retrograde Hexachordal combinatoriality is considered trivial, since any set has retrograde hexachordal combinatoriality with itself. Combinatoriality may be use to create an aggregate, combinatorial rows stated together.

Semi-combinatorial sets are sets whose hexachords are capable of forming an aggregate with one of its basic transformations transposed.

All-combinatorial sets are sets whose hexachords are capable of forming an aggregate with any of its basic transformations transposed. There are six source sets, or basic hexachordally all-combinatorial sets, each hexachord of which may be reordered within itself:


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.


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.

Further reading

External Links: