2.3 Composition Techniques: Counterpoint and Permutation

The definition of visual proportionality based on the musical model was accompanied at the beginning of the twentieth century by a transfer of the principles and structures of composition, whereby — thanks to great enthusiasm for Bach at that time — a polyphonic composition, the fugue, was predominant.

Generally, neither a specific fugue nor even the form of the fugue was taken as a model or starting point, rather the counterpoint as a musical principle, which may equally be described as countervoices or countermotifs.^[5] A horizontal arrangement of interreferential motifs is recognizable, and attention is drawn, therefore, not only to the temporal sequence of the piece but also to the motif’s ramifications within the fugue as a whole.

Eggeling thus began work in 1915 on a basso continuo of painting and, inspired by Futurist musician Ferruccio Busoni, became interested in musical counterpoint. From this ensued his concept of optical counterpoint, a theory of visual composition based on the polarity of pairs of opposites of abstract elements, such as he attempted to realize in his film Symphonie Diagonale (1924).

Itten also oriented himself to the contrapuntal method as a combinatorial principle. In Der Bachsänger (The Bach Singer; 1916), the figure of the Bach singer is employed symbolically in order to develop a pictorial structure whose complexity, transparency, and, above all, crystalline rigor were meant to reflect the polyphony of a Bach fugue. The musical correlative contrapuntality of colors rests on an elaborate pictorial construction proportioned so as to approximate the golden ratio.

Paul Klee’s concept of polyphonic painting made the most direct reference to Bach and the fugue. Klee borrowed the musical term polyphonic to describe a visual structure composed of several pictorial elements that permeate and overlay one another in constant flux, from which ensues simultaneous visual polyphony, a consonance of all the pictorial means employed. In Polyphon gefaßtes Weiß (White Framed Polyphonically; 1930), for example, he used circular layers of color that extend in all directions while the colored forms in Fuge in Rot (Fugue in Red; 1921) progress horizontally from dark towards light, overlaying one another like the voices in a fugue.

In 1917, Klee noted in his diary what it was about this method of musical composition that interested him: Polyphonic painting is superior to music insofar as the temporal is more spatial in this genre. The concept of simultaneity is even richer here.^[6]

Similar transfers of the fugue-style method of interweaving and developing different voices can be found in the work of Mikalojus Konstantinas Čiurlionis — Fuga (Fugue) from the diptych Preliudai ir fugos (Prelude and Fugue; 1907), Josef Albers — Fuge (Fugue; 1925), and others. Musical methodology based on permutations or mathematics was explored as a means of pictorial composition, in addition to the contrapuntal development of visual structures.

John and James Whitney, for example, thus drew on the compositional principles of twelve-tone music to create serial permutations of a set of geometric forms for their Five Film Exercises (1943–1944), a practice that John Whitney would later develop further using an analog computer. Mary Ellen Bute availed of Joseph Schillinger’s mathematically generated compositional system, while Peter Kubelka used arithmetical processes in musical scores to develop the structure of his metric films.