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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 becomes the last, and vice versa. This is a technique used in music, specifically in twelve-tone technique, where the inversion and retrograde techniques are performed on the same tone row successively, " e inversion of the prime series in reverse order from last pitch to first." Conventionally, inversion is carried out first, and the inverted form is then taken backward to form the retrograde inversion, so that the untransposed retrograde inversion ends with the pitch that began the prime form of the series. In his late twelve-tone works, however, Igor Stravinsky preferred the opposite order, so that his row charts use inverse retrograde (IR) forms for his source sets, instead of retrograde inversions (RI), although he sometimes labele ...
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Stravinsky - Requiem Canticles Basic Row Forms
Igor Fyodorovich Stravinsky ( – 6 April 1971) was a Russian composer and conductor with French citizenship (from 1934) and American citizenship (from 1945). He is widely considered one of the most important and influential 20th-century classical music, composers of the 20th century and a pivotal figure in modernism (music), modernist music. Born to a musical family in Saint Petersburg, Russia, Stravinsky grew up taking piano and music theory lessons. While studying law at the Saint Petersburg State University, University of Saint Petersburg, he met Nikolai Rimsky-Korsakov and studied music under him until the latter's death in 1908. Stravinsky met the impresario Sergei Diaghilev soon after, who commissioned the composer to write three ballets for the Ballets Russes's Paris seasons: ''The Firebird'' (1910), ''Petrushka (ballet), Petrushka'' (1911), and ''The Rite of Spring'' (1913), the last of which caused a List of classical music concerts with an unruly audience respons ...
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Ludus Tonalis
''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 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'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 a different ton ...
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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 advocate of the ''Neue Sachlichkeit'' (New Objectivity) style of music in the 1920s, with compositions such as ''Kammermusik (Hindemith), Kammermusik'', including works with viola and viola d'amore as solo instruments in a neo-Bachian spirit. Other notable compositions include his song cycle ''Das Marienleben'' (1923), Das Unaufhörliche (1931), ''Der Schwanendreher'' for viola and orchestra (1935), the opera ''Mathis der Maler (opera), Mathis der Maler'' (1938), the ''Symphonic Metamorphosis of Themes by Carl Maria von Weber'' (1943), and the oratorio ''When Lilacs Last in the Dooryard Bloom'd (Hindemith), When Lilacs Last in the Dooryard Bloom'd'' (1946), a requiem based on When Lilacs Last in the Dooryard Bloom'd, Walt Whitman's poem. Hindem ...
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Nummer 2
''Nummer 2'' for thirteen instruments (also called ''Opus 2 for thirteen instruments'') is a composition written in 1951 by the Belgian composer Karel Goeyvaerts. ''Nummer 2'' has been claimed as the first "total serial" composition. though the same claim has been made for Milton Babbitt's ''Three Compositions for Piano'' (1947), which predates Goeyvaerts's work by four years. Form ''Nr 2'' is in a single movement, but falls into three large sections. Unlike its immediate predecessor in Goeyvaerts's catalog, ''Nr 1'' (1950–51) Sonata for Two Pianos, and two of its serial successors, the electronic ''Nr 4 met dode tonen'' (1952) and '' Nr 5 met zuivere tonen'' (1953), ''Nr 2'' uses a recurring twelve-tone row (B F F E G A E D A B D C). In the outer sections this row is played monodically by the piano, five times in succession in part one, and five more times in the third section, but in retrograde. Around this linear presentation, in a second layer, the other twelve instrume ...
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Karel Goeyvaerts
Karel August Goeyvaerts (8 June 1923 – 3 February 1993) was a Belgian composer. Life Goeyvaerts was born in Antwerp, where he studied at the Royal Flemish Music Conservatory; he later studied composition in Paris with Darius Milhaud and analysis with Olivier Messiaen. He also studied ondes Martenot with Maurice Martenot, who invented the instrument. In 1951, Goeyvaerts attended the famous Darmstadt New Music Summer School where he met Karlheinz Stockhausen, who was five years his junior. Both were devout Catholics and found ways of integrating religious numerology into their serial compositions. They found themselves deep in conversation, and performed a movement from Goeyvaerts's "Nummer 1", Sonata for Two Pianos, in the composition course by Theodor Adorno there. They were both astonished upon hearing for the first time Messiaen's " Mode de valeurs et d'intensités" (from '' Quatre études de rythme''), in a recording by the composer which Antoine Goléa played at a lectur ...
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Tadeusz Baird
Tadeusz Baird (26 July 19282 September 1981) was a Polish composer. Biography Baird was born in Grodzisk Mazowiecki, in Poland. His father Edward was Polish, while his mother Maria (née Popov) was Russian. In 1944 at the age of 16 he was deported to Germany as a forced labourer, and after a failed escape attempt was imprisoned in a concentration camp. After liberation by the Americans he spent six months recovering at the military hospital in Gladbeck, Zweckel before returning to Poland. Between 1947 and 1951 Baird studied composition and musicology in Warsaw under Piotr Rytek and Kazimierz Sikorski, and piano with Tadeusz Wituski. In 1949 he founded Group 49 along with Kazimierz Serocki and Jan Krenz. The aim of Group 49 was to write communicative and expressive music according to socialist realism, the dominant ideology in the Eastern Bloc at the time. After Stalin's death in 1953 he increasingly turned to serialism.Obituary, ''The Times'', 15 September 1981, p 14 In 1956, alo ...
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Igor Stravinsky
Igor Fyodorovich Stravinsky ( – 6 April 1971) was a Russian composer and conductor with French citizenship (from 1934) and American citizenship (from 1945). He is widely considered one of the most important and influential 20th-century classical music, composers of the 20th century and a pivotal figure in modernism (music), modernist music. Born to a musical family in Saint Petersburg, Russia, Stravinsky grew up taking piano and music theory lessons. While studying law at the Saint Petersburg State University, University of Saint Petersburg, he met Nikolai Rimsky-Korsakov and studied music under him until the latter's death in 1908. Stravinsky met the impresario Sergei Diaghilev soon after, who commissioned the composer to write three ballets for the Ballets Russes's Paris seasons: ''The Firebird'' (1910), ''Petrushka (ballet), Petrushka'' (1911), and ''The Rite of Spring'' (1913), the last of which caused a List of classical music concerts with an unruly audience respons ...
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Tone Row
In music, a tone row or note row ( or '), also series or set, is a non-repetitive ordering of a set of pitch-classes, typically of the twelve notes in musical set theory of the chromatic scale, though both larger and smaller sets are sometimes found. History and usage Tone rows are the basis of Arnold Schoenberg's twelve-tone technique and most types of serial music. Tone rows were widely used in 20th-century contemporary music, like Dmitri Shostakovich's use of twelve-tone rows, "without dodecaphonic transformations." A tone row has been identified in the A minor prelude, BWV 889, from book II of J.S. Bach's '' The Well-Tempered Clavier'' (1742) and by the late eighteenth century it is found in works such as Mozart's C major String Quartet, K. 157 (1772), String Quartet in E-flat major, K. 428, String Quintet in G minor, K. 516 (1790), and the Symphony in G minor, K. 550 (1788). Beethoven also used the technique but, on the whole, "Mozart seems to have employed seria ...
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Music Theory
Music theory is the study of theoretical frameworks for understanding the practices and possibilities of music. ''The Oxford Companion to Music'' describes three interrelated uses of the term "music theory": The first is the "Elements of music, rudiments", that are needed to understand Musical notation, music notation (key signatures, time signatures, and Chord chart, rhythmic notation); the second is learning scholars' views on music from Ancient history, antiquity to the present; the third is a sub-topic of musicology that "seeks to define processes and general principles in music". The musicological approach to theory differs from music analysis "in that it takes as its starting-point not the individual work or performance but the fundamental materials from which it is built." Music theory is frequently concerned with describing how musicians and composers make music, including Musical tuning, tuning systems and composition methods among other topics. Because of the ever-expan ...
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Twelve-tone Technique
The twelve-tone technique—also known as dodecaphony, twelve-tone serialism, and (in British usage) twelve-note composition—is a method of musical composition. The technique is a means of ensuring that all 12 notes of the chromatic scale are sounded equally often in a piece of music while preventing the emphasis of any one notePerle 1977, 2. through the use of tone rows, orderings of the 12 pitch classes. All 12 notes are thus given more or less equal importance, and the music avoids being in a Key (music), key. The technique was first devised by Austrian composer Josef Matthias Hauer, who published his "law of the twelve tones" in 1919. In 1923, Arnold Schoenberg (1874–1951) developed his own, better-known version of 12-tone technique, which became associated with the "Second Viennese School" composers, who were the primary users of the technique in the first decades of its existence. Over time, the technique increased greatly in popularity and eventually became widely ...
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Pitch (music)
Pitch is a perception, perceptual property that allows sounds to be ordered on a frequency-related scale (music), scale, or more commonly, pitch is the quality that makes it possible to judge sounds as "higher" and "lower" in the sense associated with musical melody, melodies. Pitch is a major auditory system, auditory attribute of musical tones, along with duration (music), duration, loudness, and timbre. Pitch may be quantified as a frequency, but pitch is not a purely objective physical property; it is a subjective Psychoacoustics, psychoacoustical attribute of sound. Historically, the study of pitch and pitch perception has been a central problem in psychoacoustics, and has been instrumental in forming and testing theories of sound representation, processing, and perception in the auditory system. Perception Pitch and frequency Pitch is an auditory sensation in which a listener assigns musical tones to relative positions on a musical scale based primarily on their percep ...
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