''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 and American 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 advo ...

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

Johann Sebastian Bach Johann Sebastian Bach (German: Help:IPA/Standard German, �joːhan zeˈbasti̯an baχ ( – 28 July 1750) was a German composer and musician of the late Baroque music, Baroque period. He is known for his prolific output across a variety ...

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 virt ...

s, and ends with a Postludium which is an exact

retrograde inversion In music theory, 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 ...

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

fugue In classical music, a fugue (, from Latin ''fuga'', meaning "flight" or "escape""Fugue, ''n''." ''The Concise Oxford English Dictionary'', eleventh edition, revised, ed. Catherine Soanes and Angus Stevenson (Oxford and New York: Oxford Universit ...

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'' referred to a variety of keyboard instruments, ...

''. Vignal, Marc (1990). Liner notes to ''Hindemith: Sonata no. 2 and Ludus Tonalis'', performed by

Sviatoslav Richter Sviatoslav Teofilovich Richter ( – August 1, 1997) was a Soviet and Russian classical pianist. He is regarded as one of the greatest pianists of all time,Great Pianists of the 20th Century and has been praised for the "depth of his interpreta ...

. Pyramid Records, 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 Musical tuning#Tuning systems, tuning system that approximates Just intonation, just intervals by dividing an octave (or other interval) into steps such that the ratio of the frequency, frequencie ...

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 Signal modulation is the process of varying one or more properties of a periodic waveform in electronics and telecommunication for the purpose of transmitting information. The process encodes information in form of the modulation or message ...

is dropped, although subject modulation occurs in the second fugue, to create growing tension. The first performance of ''Ludus Tonalis'' in Italy was played by Eunice Katunda in 1948 at the Teatro Piccolo in Milan.

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, 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 Gap, Hautes-Alpes, Pays de Gap region of Dauphiné in the southeast of France, where the dance originated, accordin ...

) # 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 ...

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

March March is the third month of the year in both the Julian and Gregorian calendars. Its length is 31 days. In the Northern Hemisphere, the meteorological beginning of spring occurs on the first day of March. The March equinox on the 20 or 2 ...

# Fuga septima in A: Romantic style # Interludium: Romantic miniature ( Brahms 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 pair ...

) # Fuga undecima in B (

canon Canon or Canons may refer to: Arts and entertainment * Canon (fiction), the material accepted as officially written by an author or an ascribed author * Literary canon, an accepted body of works considered as high culture ** Western canon, th ...

): Accompanied canon # Interludium: Romantic

waltz The waltz ( , meaning "to roll or revolve") is a ballroom dance, ballroom and folk dance, in triple (3/4 time, time), performed primarily in closed position. Along with the ländler and allemande, the waltz was sometimes referred to by the ...

# Fuga duodecima in F: Stretto 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