Dodecaphony Józef Koffler

Dodecaphony, also known as dodecaphonic technique, twelve-tone technique, or twelve-note composition, represents one of the most significant compositional innovations of the twentieth century.

Arnold Schönberg (1874–1951) is considered the father of dodecaphony. This Viennese composer and innovator challenged centuries-old principles of pitch organization in musical works, which had been based on the existence of a central reference point determining the relationships between individual notes.

Previously, composers had worked within a system where each pitch occupied a specific position in a hierarchy, and musical tensions were resolved according to established rules. The new approach broke with this tradition, treating all pitches as equal elements within the composition.

Arnold Schönberg (1927), photo by Man Ray (Wikimedia Commons)

This represents the culmination of these experiments - an innovative compositional method utilizing all twelve pitches of the chromatic scale with equal status. Schönberg termed it "the method of composing with twelve tones which are related only to one another" ('Methode des Komponierens mit zwölf nur aufeinander bezogenen Tönen'). The fundamental structural unit in this method is the series (twelve-tone row) – an ordered succession of all twelve pitches, where each degree of the chromatic scale appears exactly once. This original series serves as the primary material for the entire composition.

As can be calculated, there exists an enormous number of possible orderings of twelve tones in a series—precisely 479,001,600 (factorial 12).

Naturally, composers do not select random tone sequences. Series are typically well-conceived structures containing potential for further musical development. Thus, a series might offer possibilities for subdivision into smaller pitch groups that can function as motifs or characteristic melodic gestures. The harmonic possibilities of the series are equally significant—that is, the manner in which its individual elements or fragments can create sonorities when performed simultaneously.

Some composers employ series with symmetrical intervallic construction, which provides specific transformation possibilities. An excellent example of such an approach is the series from Anton Webern's Symphony Op. 21—Schönberg's pupil—which comprises two hexachordal fragments with identical intervallic content that mirror each other. Conversely, another of his pupils, Alban Berg, created series containing subtle references to the tonal system, exemplified by his Violin Concerto with its series constructed from triads and a fragment of the whole-tone scale.

The composer can operate with the series in its basic form, but also in three transformations. Each transformation preserves the essential properties of the original series, thus ensuring coherence of pitch material throughout the composition. The initial ordering of pitches and intervals may be read backwards (i.e., beginning with the final pitch and proceeding to the first), in which case we encounter the retrograde form of the series. Let us examine this phenomenon in the following examples.

Here is the prime form of the series from the String Trio Op. 10:

Here is the retrograde form of this series:

And here is the theme from the first movement of Koffler's String Trio Op. 10, based (in the first violin melody) on the prime and retrograde forms of the series:

The series may also be inverted (i.e., in terms of reversing the melodic intervals between one pitch and the next). Such a transformation is called inversion. Thus, if in the original series there was, for example, an ascending minor third between pitches, in the inversion this would become a descending minor third. This form can also be read from end to beginning, in which case we encounter the retrograde inversion. Let us listen to the following examples:

Here is the inversion of the prime form from the String Trio Op. 10:

Here is the retrograde inversion of this series:

And here is the theme of the second couplet from the rondo forming the third movement of Koffler's String Trio Op. 10, which is based on the retrograde inversion:

It must also be remembered that each of the four forms of the series can be transposed, meaning that a specific intervallic arrangement can create sequences beginning on each of the twelve pitches of the chromatic scale (i.e., from C, C-sharp/D-flat, D, D-sharp/E-flat, E, F, F-sharp/G-flat, G, G-sharp/A-flat, A, A-sharp/B-flat, and B).

In total, therefore, we can work with 12 transpositions of the prime form, 12 transpositions of its retrograde, 12 transpositions of the inversion of the prime form, and 12 transpositions of the retrograde inversion. This yields a total of 48 forms of a single twelve-tone series.

Despite its systematic structure, the twelve-tone method of composition affords manifold possibilities for musical development.

Koffler was keenly aware of this potential. As he argued, "the twelve-tone technique serves primarily as a means of formal construction, enabling, through the maintenance of the basic row, an unprecedented unity of both individual works and cycles" (J. Koffler, '12 tonów' [12 Tones], Wiadomości Literackie 1936, no. 10, p. 6).

To help his readers and listeners understand the nature of dodecaphony and its departure from traditional compositional methods, Koffler employed the following comparison:

Consider how we have played chess for centuries—on a board of eight by eight squares, with eight pieces and eight pawns. Let us suppose that all possible groupings and combinations on this board become exhausted, rendering further play essentially futile, as the consequences of each sequence become predictable and the game grows tedious. Then appears an ingenious chess player who creates a new board of twelve by twelve squares, with twelve pieces and twelve pawns. In essence, the fundamental nature of the game remains unchanged; only the number of possible combinations and groupings increases immensely, making the game once again fascinating and exciting

(ibid.).

Dodecaphony, also known as dodecaphonic technique, twelve-tone technique, or twelve-note composition, represents one of the most significant compositional innovations of the twentieth century.

As can be calculated, there exists an enormous number of possible orderings of twelve tones in a series—precisely 479,001,600 (factorial 12).

In total, therefore, we can work with 12 transpositions of the prime form, 12 transpositions of its retrograde, 12 transpositions of the inversion of the prime form, and 12 transpositions of the retrograde inversion. This yields a total of 48 forms of a single twelve-tone series.

Despite its systematic structure, the twelve-tone method of composition affords manifold possibilities for musical development.

Iwona Lindstedt English translation by Iwona Lindstedt

^{Iwona Lindstedt
English translation by Iwona Lindstedt}