The Classical Music Book

324

See also: The Art of Fugue 10 8 –111 ■ Chopin’s Préludes 164 –165 ■ Prélude à

l’après-midi d’un faune 228–231 ■ Pithoprakta 308

T

he term “fractal” was first

used in 1975 by the

mathematician Benoit

Mandelbrot, though the concept is

much older. It describes images,

surfaces, sounds, or other patterns

made up of mini-versions of the

whole, which they continue to

resemble however tiny they are

and however often subdivided.

The composer György Ligeti

first came across fractals in 1984,

in images by the mathematician

Heinz-Otto Peitgen. Ligeti

recognized that the principle of

internal symmetry had been

present in his music for years. He

had used a technique he called

“micropolyphony,” overlaying

multiple closely related versions

of the same musical line to create

dense, shimmering textures.

Studies in fractal style

Ligeti began to employ ideas

derived from mathematics and the

broader theory of chaos. He had

also become interested in Central

African music, the pianola studies

of Conlon Nancarrow, and the jazz

piano music of Bill Evans and

Thelonius Monk. To synthesize

these influences, he turned to the

piano study, or étude, a form used

by Chopin, Liszt, and Debussy.

Ligeti’s 18 Études all employ

rhythmic and melodic processes

that interact, conflict, and even

cancel each other out. Their titles,

such as Disorder and Vertigo,

reflect the images their streams of

notes evoke. Works of fantasy, they

are a major contribution to the late

20th-century repertoire. ■

VOLCANIC, EXPANSIVE,

DAZZLING—AND

OBSESSIVE

ÉTUDES (1985–2001)

GYÖRGY LIGETI

IN CONTEXT

FOCUS

Fractal music

BEFORE

1915 Debussy’s 12 Études

introduce pictorial imagery

to the études genre.

1947 Conlon Nancarrow

writes rhythmically elaborate

studies for a pianola.

1959 Ligeti uses what he

later called “micropolyphony”

in his orchestral Apparitions.

1984 Charles Wuorinen’s

Bamboula Squared employs

a computer-generated tape

partly inspired by Benoit

Mandelbrot’s work on fractals.

AFTER

2003 Ligeti’s student Unsuk

Chin completes her own set

of 12 Études, continuing

her teacher’s interest in

complex rhythms.

In my music one finds ...

a unification of construction

with poetic, emotional

imagination.

György Ligeti

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