Ludus Tonalis ("Play of Tones"), subtitled Kontrapunktische, tonale, und Klaviertechnische Übungen (Counterpoint, tonal and technical studies for the piano), is a 1942 piano work by Paul Hindemith. It was composed during his stay in the United States and was his last piano piece. The suite of 25 pieces demonstrates Hindemith's ideas about tonality and his mastery of counterpoint.

Background While Paul Hindemith was teaching at the Yale School of Music, he began writing small three-voice fugues for keyboard.Desbruslais, Simon. The Music and Music Theory of Paul Hindemith. Boydell & Brewer, 2018. When he decided to base their key sequence on his theoretical writing, the collection expanded. He settled on the title Ludus Tonalis with medieval liturgical dramas as a model. "Play of Tones" most directly reflects Hindemith's meaning, rather than translations of "ludus" as a game.Neumeyer, David. The Music of Paul Hindemith. Yale University Press, 1986. 225–238.

Ludus Tonalis is the most direct application of Hindemith's theory that the twelve tones of the equally tempered scale all relate to a keynote or tonic. In this system, the major-minor duality is meaningless. The affinity of each note with the keynote is directly related to its position on the harmonic scale.Carner, Mosco. A Study of Twentieth-Century Harmony; a Treatise and Guide for the Student-Composer of to-Day. London: J. Williams, 1942. 72–77.

It was first performed on February 15, 1943 in Chicago by Willard MacGregor.Luttmann, Stephen. Paul Hindemith: a guide to research. Routledge, 2005. 357. The program included Hindemith's sonatas for flute and two pianos.Smith, Cecil. "Composers to Chicago", Modern Music, Volume XXI, Number 4. May-June 1944. 245. Hindemith had low commercial expectations for the piece, even though he saw its completion as a moral victory. He harangued Associated Music Publishers to quickly bring out an engraved edition as part of their "responsibility to history". The first printing sold out in three months.Noss, Luther. Paul Hindemith in the United States. University of Illinois Press, 1989. 117f.Skelton, Geoffrey. Selected Letters of Paul Hindemith. Yale University Press, 1995. 187–90.

Ludus Tonalis is often compared to Johann Sebastian Bach's The Well-Tempered Clavier.Vignal, Marc (1990). Liner notes to Hindemith: Sonata no. 2 and Ludus Tonalis, performed by Sviatoslav Richter. Pyramid Records, no. 13497. In its abstraction, it might be more akin to The Art of the Fugue.Del Mar, Norman. "Paul Hindemith" in European Music in the Twentieth Century. Edited by Howard Hartog. Taylor & Francis, 2025. 70f. It functions as a kind of catalogue for Hindemith's mature style.Satola, Mark. "Ludus Tonalis", All Music Guide to Classical Music. Hal Leonard, 2005. 612.

Hindemith created a special edition of the score for his wife's birthday. He called it Ludi leonum, and it features his own drawings on the AMP score. The primary characters are lions, and they often parody the musical architecture.Hindemith, Paul. Paul Hindemith: der Komponist als Zeichner = The composer as graphic artist. Edited by Susanne Schaal-Gotthardt and Angelika Storm-Rusche, Atlantis Musikbuch-Verlag, 1995. Hindemith accompanies each entrance of the fugue subject with a lion.Roberts, Gareth E. From Music to Mathematics: Exploring the Connections. Johns Hopkins University Press, 2016. 179.

Structure In The Craft of Musical Composition, Paul Hindemith devised the tonal relationships that create the structure for Ludus Tonalis. Instead of proceeding chromatically through all twelve pitches, the suite's tonal centers proceed in what Hindemith called "Serie 1": C–G–F–A–E–E–A–D–B–D–B–F.Tippett, Michael (1995). Tippett on Music, p.77. Oxford University. . Between each three-part fugue, Hindemith composes an interlude that links the preceding and ensuing key.Tischler, Hans. "Hindemith's Ludus tonalis and Bach's Well-Tempered Clavier—A Comparison", The Music Review, vol. 20, nos. 3–4. August–November, 1959. 217–27. The suite opens with a "Praeludium" which is repeated in retrograde inversion in the "Postludium". The fugues catalog nearly every variety of the form, including double, triple, retrograde, and canonic fugues.Schubert, Giselher. "Hindemith, Paul." Grove Music Online. Oxford University Press, 2001. The interrelations between the components of each movement consistently reflect their relation to the cycle as a whole.Forte, Allen. Contemporary Tone-Structures. Teachers College, Columbia University, 1955. 109.

Content Praeludium. Partly in C (mm. 1–32) and partly in F (mm. 34–47) Fuga prima in C: Triple fugue Interludium: Romantic improvisation Fuga secunda in G: Dance in time Interludium: Pastorale Fuga tertia in F: Mirror fugue, where the second half is an exact retrograde of the first, except with voice paddings at their end exits. Interludium: Folk dance (Gavotte) Fuga quarta in A: Double fugue Interludium: Baroque prelude Fuga quinta in E: Gigue Interludium: Romantic miniature (Chopin style) Fuga sexta in E: Rococo style Interludium: March - The mirrors of the fugues and interludes pause at the mid-point of the cycle with a straightforward parody of a march.Bruhn, Siglind. "Symmetry and dissymmetry in Paul Hindemith's Ludus Tonalis", Symmetry: Culture and Science, vol. 7, no. 2. 1996. 116–132. Adapted in Bruhn, Siglind. Hindemiths große Instrumentalwerke, Hindemith-Trilogie, volume 3. Germany: Edition Gorz, 2009. 46–56. Fuga septima in A: Romantic style Interludium: Romantic miniature (Brahms style) Fuga octava in D: Dance in time (though notated in ) Interludium: Baroque toccata Fuga nona in B: Subject transformation fugue Interludium: Pastorale Fuga decima in D: Inversion fugue Interludium: Folk dance (Courante) Fuga undecima in B (canon): Accompanied canon Interludium: Romantic waltz Fuga duodecima in F: Stretto fugue Postludium: Retrograde inversion of the Praeludium.

References

Further reading Delaere, Mark. "Analysing contrapuntal music: some remarks on the fugues in C and F from Hindemith’s Ludus Tonalis". In Hindemith-Jahrbuch, vol. 24. 1996. 66–86. Saguer, Louis. "Ludus Tonalis de Paul Hindemith", Contreponts 4. Mai-Juin, 1946. 20–40.

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