''Ludus Tonalis'' ("Play of Tones", "Tonal Game", or "Tonal Primary School" after the Latin ''Ludus Litterarius''), subtitled ''Kontrapunktische, tonale, und Klaviertechnische Übungen'' (''Counterpoint, tonal and technical studies for the piano''), is a piano work by

Paul Hindemith Paul Hindemith (; 16 November 189528 December 1963) was a German composer, music theorist, teacher, violist and conductor. He founded the Amar Quartet in 1921, touring extensively in Europe. As a composer, he became a major advocate of the ''Ne ...

that was composed in 1942 during his stay in the United States. It was first performed in 1943 in Chicago by

Willard MacGregor Willard MacGregor (October 15, 1901, in Boston – July 30, 1993, in New York City) was an American classical pianist. He studied piano in St. Louis with Rudolph Ganz and Leo C. Miller, then in Paris with Isidor Philipp and Nadia Boulanger and ...

. The piece explores "matters of technique, theory, inspiration, and communication. It is in effect, a veritable catalogue of the composer's mature style." The piece, which comprises all 12 major and/or minor keys, starts with a three-part

Praeludium A prelude (german: Präludium or '; la, praeludium; french: prélude; it, preludio) is a short piece of music, the form of which may vary from piece to piece. While, during the Baroque era, for example, it may have served as an introduction t ...

in C resembling

Johann Sebastian Bach Johann Sebastian Bach (28 July 1750) was a German composer and musician of the late Baroque period. He is known for his orchestral music such as the '' Brandenburg Concertos''; instrumental compositions such as the Cello Suites; keyboard w ...

toccata Toccata (from Italian ''toccare'', literally, "to touch", with "toccata" being the action of touching) is a virtuoso piece of music typically for a keyboard or plucked string instrument featuring fast-moving, lightly fingered or otherwise virtuo ...

s, and ends with a Postludium which is an exact

retrograde inversion Retrograde inversion is a musical term that literally means "backwards and upside down": "The inverse of the series is sounded in reverse order." Retrograde reverses the order of the motif's pitches: what was the first pitch becomes the last, and ...

of the Praeludium. In between, there are twelve three-part

fugue In music, a fugue () is a contrapuntal compositional technique in two or more voices, built on a subject (a musical theme) that is introduced at the beginning in imitation (repetition at different pitches) and which recurs frequently in the c ...

s separated by eleven interludes, beginning in the tonality of the previous fugue and ending in the tonality of the next fugue (or in a different tonality 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'').Tippett, Michael (1995). ''Tippett on Music'', p.77. Oxford University. . ''Ludus Tonalis'' was intended to be the twentieth-century equivalent to J.S. Bach's ''

The Well-Tempered Clavier ''The Well-Tempered Clavier'', BWV 846–893, consists of two sets of preludes and fugues in all 24 major and minor keys for keyboard by Johann Sebastian Bach. In the composer's time, ''clavier'', meaning keyboard, referred to a variety of in ...

''.Liner Notes by

Marc Vignal Marc Vignal (born 21 December 1933 in Nogent-sur-Marne) is a noted French musicologist, writer and radio producer for France Musique and program manager at Radio France (1975–99), a journalist for ''Harmony'' (1964–84), ''Le Monde de la musique' ...

to "Hindemith, 2nd Sonata & Ludus Tonalis"; played by Sviatoslav Richter – Pyramid Records, Inc. NY catalogue no. 13497" Unlike Bach's work, though, the non-fugal pieces in ''Ludus Tonalis'' frequently repeat the work's main theme. ''Ludus Tonalis'' can be thought of as the most direct application of Hindemith's theory that the twelve tones of the

equally tempered An equal temperament is a musical temperament or tuning system, which approximates just intervals by dividing an octave (or other interval) into equal steps. This means the ratio of the frequencies of any adjacent pair of notes is the same, w ...

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 In electronics and telecommunications, modulation is the process of varying one or more properties of a periodic waveform, called the ''carrier signal'', with a separate signal called the ''modulation signal'' that typically contains informatio ...

is dropped, although subject modulation occurs in the second fugue, to create growing tension.

Structure

''Ludus Tonalis'' consists of 25 movements:Bruhn, Siglind (1996). ''Symmetry and dissymmetry in Paul Hindemith's Ludus Tonalis'', Symmetry: Culture and Science, vol. 7, no. 2, 116–132. # 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 A mirror fugue is a fugue, or rather two fugues, one of which is the mirror image of the other. It is as though a mirror were placed above or below an existing fugue, producing inversions of each interval in each part, as well as inverting the posi ...

, where the second half is an exact retrograde of the first, except with voice paddings at their end exits. # Interludium: Folk dance (

Gavotte The gavotte (also gavot, gavote, or gavotta) is a French dance, taking its name from a folk dance of the Gavot, the people of the Pays de Gap region of Dauphiné in the southeast of France, where the dance originated, according to one source. Ac ...

) # Fuga quarta in A: Double fugue # Interludium: Baroque prelude # Fuga quinta in E:

Gigue The gigue (; ) or giga () is a lively baroque dance originating from the English jig. It was imported into France in the mid-17th centuryBellingham, Jane"gigue."''The Oxford Companion to Music''. Ed. Alison Latham. Oxford Music Online. 6 July 200 ...

# Interludium: Romantic miniature ( Chopin style) # Fuga sexta in E:

Rococo style Rococo (, also ), less commonly Roccoco or Late Baroque, is an exceptionally ornamental and theatrical style of architecture, art and decoration which combines asymmetry, scrolling curves, gilding, white and pastel colours, sculpted moulding, ...

# Interludium:

March March is the third month of the year in both the Julian and Gregorian calendars. It is the second of seven months to have a length of 31 days. In the Northern Hemisphere, the meteorological beginning of spring occurs on the first day of Marc ...

# Fuga septima in A: Romantic style # Interludium: Romantic miniature (

Brahms Johannes Brahms (; 7 May 1833 – 3 April 1897) was a German composer, pianist, and conductor of the mid-Romantic period. Born in Hamburg into a Lutheran family, he spent much of his professional life in Vienna. He is sometimes grouped with ...

style) # Fuga octava in D: Dance in time (though notated in ) # Interludium: Baroque

# Fuga nona in B: Subject transformation fugue # Interludium: Pastorale # Fuga decima in D: Inversion fugue # Interludium: Folk dance (

Courante The ''courante'', ''corrente'', ''coranto'' and ''corant'' are some of the names given to a family of triple metre dances from the late Renaissance and the Baroque era. In a Baroque dance suite an Italian or French courante is typically paired ...

) # Fuga undecima in B (

canon Canon or Canons may refer to: Arts and entertainment * Canon (fiction), the conceptual material accepted as official in a fictional universe by its fan base * Literary canon, an accepted body of works considered as high culture ** Western can ...

): Accompanied canon # Interludium: Romantic

waltz The waltz ( ), meaning "to roll or revolve") is a ballroom and folk dance, normally in triple ( time), performed primarily in closed position. History There are many references to a sliding or gliding dance that would evolve into the wa ...

# Fuga duodecima in F:

Stretto In music, the Italian term ''stretto'' (plural: ''stretti'') has two distinct meanings: # In a fugue, ''stretto'' (german: Engführung) is the imitation of the subject in close succession, so that the answer enters before the subject is complete ...

fugue # Postludium: Retrograde inversion of the Praeludium. There is a striking symmetry around the center of the cycle (the march).

References

External links

* {{Authority control Compositions for solo piano Compositions by Paul Hindemith Preludes (music) Fugues 1942 compositions

Hindemith Paul Hindemith (; 16 November 189528 December 1963) was a German composer, music theorist, teacher, violist and conductor. He founded the Amar Quartet in 1921, touring extensively in Europe. As a composer, he became a major advocate of the ' ...