What is ludus tonalis?

Ludus Tonalis is a piano cycle composed by the German composer Paul Hindemith between 1942 and 1943. The piece consists of 25 interconnected movements, or "thoughts," which are organized in a three-part structure resembling the three movements of a sonata.

Ludus Tonalis is characterized by its use of strict counterpoint and tonality, which reflects Hindemith's interest in the Baroque era. The piece is also notable for its use of a "theme and variation" structure, in which a main theme is introduced at the beginning and is transformed throughout the subsequent movements.

Hindemith described Ludus Tonalis as a "musical arithmetic game," and the piece is often studied by music students as an example of mathematical relationships in music. Despite its complex structure, Ludus Tonalis is also considered to be highly expressive and emotionally engaging.