Ludus Tonalis ("Play of Tones" or "Tonal Game"), subtitled Kontrapunktische, tonal, und Klaviertechnische Übungen (counterpoint, tonal and technical studies for the piano), is a piano work by Paul Hindemith that was composed in 1942 during his stay in the United States.
The piece starts with a three-part Praeludium in C resembling Bach's toccatas, and ends with a Postludium which is an exact retrograde inversion of the Praeludium. In between, there are twelve three-part fugues separated by eleven interludes, beginning in the tonality of the previous fugue and ending in the tonality of the next fugue (or in different tonality which is very close to that). The tonalities of the fugues follow the order of his Serie 1 and use the keynote C (see The Craft of Musical Composition). Ludus Tonalis was intended to be the twentieth-century equivalent to Bach's Well-Tempered Clavier. Unlike Bach's piece, though, the non-fugal pieces in Ludus Tonalis frequently repeat the work's main theme, which makes listening to the work as a whole slightly less daunting to the novice.
Ludus Tonalis can be thought of as the most direct application of Hindemith's theory that the twelve tones of the equally tempered scale all relate to a single one of them (called a tonic or keynote). The affinity of each note with the keynote is directly related to its position on the harmonic scale. In this system, the major–minor duality is meaningless and the practice of modulation is dropped.