The Play of Music

Numbers, ars combinatoria

The Music of Play

Mediterranean, light

Albrecht Dürer, Melencolia I

Copperplate engraving, 1514, 24.5 x 19.2 cm.

Along the left edge of Albrecht Dürer’s Melencolia I is a magic square. These mysterious numerical relationships fit into the artist’s cryptic symbol-laden imagery. As a composer, Cerha also worked with magic squares: The one from Dürer’s copperplate engraving became the basis for several works.

Image source: MET Museum

Friedrich Cerha, Drei Orchesterstücke, III. Tombeau,
sketch of a magic square, 2011


I have always seen technical means, whether serial or 12-tone or magic squares, as an aid to realising my musical ideas – and indeed realising them as precisely as possible. And when the circumstances were so complex that they became difficult to comprehend in terms of solidification and execution, then I reached for such technical aids, but always precisely those ones that were useful for addressing the task at hand.

Friedrich Cerha

Deutschlandfunk interview at the premiere of Drei Orchesterstücke

If you look beneath the surface of music, hidden worlds open up which reach towards the realm of mathematics. Within tone intervals and frequencies, rhythms and shapes, numerical proportions are found that have been explored as far back as Antiquity. It is no coincidence that, in the educational canon of the “seven liberal arts”, music was found in the scientific branch of the Quadrivium, along with arithmetic, geometry, and astronomy.

The creative implementation of musical mathematical relationships fascinated composers as early as the Middle Ages. In several important compositions of the twentieth century, numbers also dominate the deeper compositional layers of the music: Here, (manipulated) series of numbers are used to generate sounds.

Cerha stays away from the pure numbers fetish decried by Adorno in the 1950s when looking at the avant-garde. But “juggling” with numbers is nonetheless an essential aspect of his work. His often playful approach is not left untouched by Josef Matthias Hauer’s 12-tone games, in which both components—rational numbers and the relaxed handling of them—are already apparent in the title. Cerha implements numbers in diverse ways, ranging from ordering cycles to cycles such as in the early Buch von der Minne (4 times 11 songs), to the numeric symbolism of Monumentum, to the organisation of sound using magic squares, as in the Konzert für Schlagzeug und Orchester.

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Dû bist mîn, ich bin dîn…


Ein Buch von der Minne, 1946—64

Im Zeichen des Jupiters


Konzert für Schlagzeug und Orchester, 2007



Monumentum, 1988