The Ludus Tonalis (‘Play of Tones’), written in 1942 and premiered by Willard MacGregor in 1943, is the quintessential model of Hindemith's music theory in practice. It was written five years after the first published edition of the Unterweisung, and shared proximity with Unterweisung II (1939), the second edition of Unterweisung I (1940), Craft I (1942) and the preparatory work towards Unterweisung III. Though Hindemith wrote many other compositions during this time, such as three organ sonatas (1937–1940), eleven instrumental sonatas and the ballet The Four Temperaments (1938), none have the explicit reference to music theory found in the Ludus: where all twelve of the starting pitches for the fugues correspond to the ordering of Series 1. If Hindemith's early works show the composer at his most pluralistic, the Ludus presents the composer at his most cerebral. It provides the strongest indication of how Hindemith's music theory might be transferred into free composition, and lends itself more suitably to a theoretical analysis than any of his other compositions. Hindemith invites us to analyse his piano cycle with his theory in mind.

The Ludus was completed two years after Hindemith's appointment at the Yale School of Music, and four years before he received American citizenship. It marked a watershed moment in Hindemith's life – the closing of his troubled chapter in Germany in the mid- to late 1930s, and the widespread acceptance of the refined compositional style in the Ludus, brought about by his intensive theoretical activity. The work is a unique example in the history of Western Music of the relationship between music theory and compositional practice. While for previous works, it is questionable whether Hindemith's theorising, or his composing, came first; with the Ludus it is absolutely clear. The theory came first.