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“I would say the year 1980 was a major turning-point for mu- sic and art, including my music.”216

“For now, the Great Composing Machine is still utopian, but today, in the second half of the ‘eighties, we stand at the threshold of fundamentally new regions of art. At the mo- ment, that applies above all to the visual arts, but the reper- cussions for music will not be long in coming. This threshold, I think, was first reached by experimental mathematics, when Benôit Mandelbrot for the first time pulled the ‘apple mani- kins’ from his high-speed printer in 1980.”217

After the completion of Le Grand Macabre, Ligeti’s compositional productivity stalled. During the period until 1982, he did not succeed in completing any new work. The starts he made into composing a piano concerto did not lead to any satisfactory results. People who were close to him and knew his usually admirable productivity began to speak of a creative crisis. There were several reasons for this situation. For one thing, Ligeti twice needed prolonged hospi- tal treatments. For another, the believed he might experience a decisive turn- ing-point in contemporary art and music – one that gave him a great deal of trouble. He would not, and could not, take the road to the then rapidly spreading post-modernism. But neither did he feel that he belonged any long- er to the avant-garde.

While searching for a new direction, he received impulses from the American composer Conlon Nancarrow, from the study of Central-African music, and from fractal geometry, especially the viewing of fractal images. In addition, there were stimuli he had gained from the area of computer music that had now become virulent.

From January to July of 1974, Ligeti resided at Stanford University. Here he was introduced to the realm of computer music by John M. Chowning,218 _who

worked at the Laboratory for Artificial Intelligence. What interested Ligeti in this area was the projection of sound into space, the transformations of sound color (timbre), the control of pitch and time and, not least, the precise construction of tonal systems. Upon his return to Europe, he ceaselessly propagated the new medium.

In 1980/81, he then became familiar with Conlon Nancarrow’s music for mechanical pianos. Here what fascinated him, besides the technical perfec- tion, was especially the concurrence of several tempo levels – a compositional possibility that had occupied him already earlier.219

In the fall of 1982, the Puerto Rican composer Roberto Sierra drew Ligeti’s attention to recordings of instrumental and vocal music of the Banda Linda, a tribe active in the Central African Republic.220 _{After repeatedly listening to the}

recordings, Ligeti was stunned by the complexity of this both polyphonic and polyrhythmic music (see the graphic representations, p. 64). Later he also had opportunities to hear other recordings of sub-Saharan music, especially music of the Pygmies and the Gbaya.221

In the spring of 1984, he met the ethnomusicologist Simha Arom in Jerusa- lem, who had made the recordings of the Banda linda music. Arom showed him his transcriptions of Central-African music and explained its melodic and rhythmic structures to him. Ligeti quickly noticed a remarkable discrepancy between the formal structure of this music and its internal nature: the un- changing repetition of periods of equal length contrasted sharply, he thought, with the highly complex inner structure of these periods, which were notable for their superimposition of diverse rhythmic patterns.222 _{Arom’s essays, his}

further recordings, and above all his voluminous book Polyphonies et polyrhyth-

mies instrumentales d’Afrique centrale acquired a fundamental importance for Li-

geti.

Once Ligeti’s interest for sub-Saharan music had been aroused, he sought to expand his knowledge of the subject. In 1986, he read the book Musik in Af-

rika, edited by Arthur Simon and published in 1983 and was particularly taken

with the contributions by Gerhard Kubik, especially his disquisitions about xylophone music (amadinda) in the ancient kingdom of Buganda and about “inherent patterns.” By “inherent patterns” Kubik meant “audible, structured tone patterns that stand out from the total picture of a musical process as if from a picture-puzzle.” Emerging only in the act of perception they are “not played as such by the musicians but nevertheless are compositionally provid- ed for in most cases.”223 _{Considering Ligeti’s lively interest in the illusionary,}

Kubik’s theory was bound to fascinate him.

Ligeti was strongly fascinated also by pictures of fractal shapes, which he saw for the first time in 1983. The following year, the biochemist Manfred Eigen presented him with a catalogue of the exhibition Morphologie komplexer Grenzen (complex liomits) of the Bremen research group headed by Heinz-Otto Peit- gen and Peter H. Richter – a volume containing highly impressive illustra-

tions. In 1986, he became acquainted with Peitgen and Richter’s book The

Beauty of Fractals,224 _{which increased his already potent enthusiasm for the sub-}

ject (see the fig. below).

Computer fractal image of increasing resolution (see Ligeti, “Computer and Composition”, below)

Fractal geometry is a branch of mathematics established in the 1960’s by Be- noît Mandelbrot.225 _{In contrast to Euclidian geometry, which analyzes rela-}

tively simple figures such as circle, triangle, square, etc., fractal geometry con- cerns itself with the morphology of the “amorphous.” It endeavors to de- scribe the irregular and splintered forms of nature, starting from the realiza- tion that clouds are not spherical, mountains not conical, coastal lines not cir- cular. “Bark is not smooth”, Mandelbrot says, “and lightning does not force its way in a straight line.” To describe these irregular forms adequately, Man- delbrot coined the term fractal, derived from the Latin adjective fractus = bro- ken. The most useful fractals, he thought, encompassed the fortuitous in its regularities as well as its irregularities.

With the aid of a computer experiment, Mandelbrot, in 1980, obtained the famous Mandelbrot set, sometimes called “apple manikin”, whose chief as- pect is its self-similarity: up to infinite magnification, parts of a figure display always the same structure as the parent figure. Now Ligeti, as we know, al- ways took a lively interest in the results of the latest branches of mathematics, as well as in computer composition. Yet he saw little sense in a direct transfer of mathematical principles to the realm of composition. As much attention as he paid to the ideas, methods and results of Gottfried Michael Koenig,226 _Ian-

nis Xenakis227 _{and Klarenz Barlow, he confessed to have reservations about}

algorithmic composition. What seemed particularly problematic to him was the tendency to put the main emphasis in composition on the method and to regard the result as secondary. In his view, what matters is less the production of the artifact than the work of art “as value in itself.”228

He expressed similar misgivings about the naïve transfer of computer- generated images to music – an experiment made by several composers in Western Europe and the United States. He argued that such computer pic- tures were spatial structures that could not simply be converted to temporal analogues. His object was to find musical analogies to fractal images without a computer and without mathematics. In the fourth movement of his Piano

Concerto, for example, there were melodic sources, he explained, that are built

into an iterated, that is to say, feed-back system. “The music starts very thinly, with isolated figures; it gradually thickens in that the figures are multiplied with themselves.”229

“Only the imagination has to be kindled”: with this turn of phrase Ligeti ex- pressed his conviction that impulses alone do not suffice for the creative act, but that they have to be fertilized. His Piano Etudes, his Piano Concerto and his

Violin Concerto demonstrate impressively that he was able to convert the im-

pulses he had received from various directions creatively.

In his essay, “Computer and Composition”, he spoke graphically of an “igni- tion effect”, which the interaction of the rhythmic worlds of Nancarrow and the music of sub-Saharan Africa, the computer impulse from Stanford and the fractal images had had on his latest creations.230

Undoubtedly, the occupation with Central-African music was one of the artis- tically most fecund experiences in Ligeti’s life – an experience that left deep traces in his oeuvre. He owed to this music an inspiration as rich as the one Pablo Picasso had derived for his art from African masks (see fig., p. 192). It enabled Ligeti to supply his music with new, unworn rhythmic energies and to develop highly ingenious polyrhythmic techniques.

On October 23, 1986, I attended the world premiere of the three-movement version of the Piano Concerto in Graz. Profoundly impressed by the novelty of the work, I gained the conviction that with it Ligeti had entered a new phase of his creative career. “You will understand the work better”, Ligeti told me when I spoke with him about it, “once you have examined the Piano Etudes more closely.” He was right, as it turned out.