''Quatre Études de rythme'' (Four Rhythm Studies) is a set of four piano compositions by

Olivier Messiaen Olivier Eugène Prosper Charles Messiaen (, ; ; 10 December 1908 – 27 April 1992) was a French composer, organist, and ornithology, ornithologist who was one of the major composers of the 20th-century classical music, 20th century. His m ...

, written in 1949 and 1950. A performance of them lasts between 15 and 20 minutes.

History

The four pieces which the composer collectively termed ''Études de rythme'' are not a "cycle" like Messiaen's earlier '' Vingt Regards sur l'enfant-Jésus'' (1944) or ''Visions de l’Amen'' (1943). Messiaen composed "Neumes rythmiques" and "Mode de valeurs et d’intensités" in 1949 (the latter at

Darmstadt Darmstadt () is a city in the state of Hesse in Germany, located in the southern part of the Rhine-Main-Area (Frankfurt Metropolitan Region). Darmstadt has around 160,000 inhabitants, making it the fourth largest city in the state of Hesse a ...

) and added the other two études in the following year, when he was at Tanglewood. The four

movement Movement may refer to: Common uses * Movement (clockwork), the internal mechanism of a timepiece * Motion, commonly referred to as movement Arts, entertainment, and media Literature * "Movement" (short story), a short story by Nancy Fu ...

s were premiered on 6 November 1950 in

Tunis ''Tounsi'' french: Tunisois , population_note = , population_urban = , population_metro = 2658816 , population_density_km2 = , timezone1 = CET , utc_offset1 ...

(at that time under the

French protectorate of Tunisia The French protectorate of Tunisia (french: Protectorat français de Tunisie; ar, الحماية الفرنسية في تونس '), commonly referred to as simply French Tunisia, was established in 1881, during the French colonial Empire era, ...

) by the composer himself, who shortly afterward made the first recording of the études. The French premiere was given in

Toulouse Toulouse ( , ; oc, Tolosa ) is the prefecture of the French department of Haute-Garonne and of the larger region of Occitania. The city is on the banks of the River Garonne, from the Mediterranean Sea, from the Atlantic Ocean and from Par ...

on 7 June 1951 by

Yvonne Loriod Yvonne Louise Georgette Loriod-Messiaen (; 20 January 1924 – 17 May 2010) was a French pianist, teacher, and composer, and the second wife of composer Olivier Messiaen. Her sister was the Ondes Martenot player Jeanne Loriod. Biography Loriod ...

Analysis

The work consists of four movements # "Ile de feu I" (Fire Island I) # "Mode de valeurs et d'intensités" (Mode of Durations and Intensities) # "Neumes rythmiques" (Rhythmic Neumes) # "Ile de feu II" (Fire Island II)

"Ile de feu I"

The title refers to

Papua New Guinea Papua New Guinea (abbreviated PNG; , ; tpi, Papua Niugini; ho, Papua Niu Gini), officially the Independent State of Papua New Guinea ( tpi, Independen Stet bilong Papua Niugini; ho, Independen Stet bilong Papua Niu Gini), is a country i ...

, and the thematic material of this movement has "all the violence of the magic rites of this country". The piece consists of five sections, in alternating pairs of musical ideas. The first part of each section is a melodic theme with accompaniment, the second is a departure which Messiaen calls a ''trait'' ("episode"). The first section consists of a thematic statement and ''trait''. The first half of the next three develop the initial theme. The fifth and final section introduces a new, longer theme in two periods which are immediately repeated before the etude is concluded by a final ''trait'' amounting to a short coda.

"Mode de valeurs et d'intensités"

This movement is the most-discussed of the four, as the first work by a European composer to apply numerical organisation to pitch, duration, dynamics, and mode of attack (timbre). Because the treatment of the parameters is modal and not serial (that is, the elements are treated simply as a scale, without any implications for how they are to be ordered), there is no question of the material determining the work's form. According to the composer's own description, there are separate modes composed of 36 pitches, 24 durations, 12 attacks, and 7 dynamics. The duration scale is separated into three overlapping scales, called "tempi" by the composer, which correspond to the high, middle, and low registers of the piano, and occur in simultaneous superimposition. The first tempo uses 12 chromatic durations applied to the demisemiquaver, the second does the same with the

semiquaver Figure 1. A 16th note with stem facing up, a 16th note with stem facing down, and a 16th rest. Figure 2. Four 16th notes beamed together. In music, a 1/16, sixteenth note ( American) or semiquaver (British) is a note played for half the dur ...

unit, and the third with the

quaver 180px, Figure 1. An eighth note with stem extending up, an eighth note with stem extending down, and an eighth rest. 180px, Figure 2. Four eighth notes beamed together. An eighth note ( American) or a quaver ( British) is a musical note pl ...

. According to Messiaen:

"Neumes rythmiques"

The first of the four to be composed, this étude alternates two separate sets of refrains with longer strophes given over to the rhythmic

neume A neume (; sometimes spelled neum) is the basic element of Western and Eastern systems of musical notation prior to the invention of five-line staff notation. The earliest neumes were inflective marks that indicated the general shape but not ne ...

s of the title. The first set of refrains is marked "rythme en ligne triple: 1 à 5, 6 à 10, 11 à 15", which means there are three durations, short, medium, and long, which are progressively expanded, upon each repetition, by the addition of a semiquaver unit. The second set of refrains is marked "Nombre premier en rythme non rétrogradable" (A

prime number A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...

in non- retrogradable rhythm) and, like the first set of refrains with which they alternate, are expanded upon repetition—in this case by a series of progressively larger prime numbers: 41, 43, 47, and 53 semiquavers. The strophes which occur between the refrains are marked "neumes rythmiques, avec résonances et intensités fixes" (rhythmic neumes, with fixed resonances and intensities). From his studies of the neumatic notation symbols of plainchant, Messiaen had formed the idea of exploring the rhythms corresponding to them. "In an interplay of transposition, the neumatic symbol as an indication of a sinuous melodic entity is now applied to a rhythmic motive. Each rhythmic neume is assigned a fixed dynamic and resonances of shimmering colours, more or less bright or somber, always contrasting." The

collage Collage (, from the french: coller, "to glue" or "to stick together";) is a technique of art creation, primarily used in the visual arts, but in music too, by which art results from an assemblage of different forms, thus creating a new whole. ...

-like rhythmic structure grows from the iambic rhythm found at the beginning of the first strophe. As in the refrains, there is a process of augmentation upon repetition, in which new duration units are added in order to form more complex rhythmic cells. The pitches grow out of the major seventh and the tritone found at the beginning of the first strophe and in its third bar, respectively. Five basic dynamic-envelope patterns are applied to different groups, while at the same time the melodic motives constantly re-emerge in different rhythms.

"Ile de feu II"

Although Messiaen's programme note for this étude says that it is, like the first étude, "also dedicated to Papua or New Guinea", his posthumously published analysis emphatically states that it refers only to the former, not the latter. " e principal theme, ferocious and violent, has the same character as the themes of the first étude; the variations on this theme alternate with permutations, successively permuted according to the same process and superimposed two by two; the piece closes with a cross-handed perpetual motion in the depths of the keyboard". The opening strophe from "Île de feu I" is modified to become the cyclic theme of this étude. As in the other pieces, this alternates with episodes, in this case based on a mode of twelve durations, twelve sounds, four attacks and five intensities. The rhythmic focus in this piece concerns a symmetrical permutation scheme for a duration scale initially given in descending order of durations. The elements are reordered according to a wedge-shaped process, which Messiaen elsewhere called "permutation in the form of an open fan". The first permutation produces a new ordering which Messiaen called "Interversion I". The same permutation scheme applied to this first interversion produces "Interversion II", and so on: : A peculiarity is that the successive applications of this permutation do not yield the twelve permutations which might be expected. This is because the values 10 and 5 map into each other under this operation—which can be seen by scanning down columns 3 and 8 in the table. Consequently, the original order returns once the remaining ten values have circulated. This unexpected restriction has been cited as an example of what Messiaen called the "charm of impossibilities". Messiaen later applied such permutation schemes in works of larger scale, such as the orchestral work '' Chronochromie'', completed in 1960.

Reception

The second of the études, "Mode de valeurs et d'intensités", overshadows all the others for having become the model for composers interested in the serialisation of musical parameters other than pitch. Initially, this influence occurred through works composed in 1950 and 1951 by two of Messiaen's pupils,

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 analysi ...

and Michel Fano. Messiaen's composition and one of the works inspired by it, Goeyvaerts's Sonata for Two Pianos, impressed

Karlheinz Stockhausen Karlheinz Stockhausen (; 22 August 1928 – 5 December 2007) was a German composer, widely acknowledged by critics as one of the most important but also controversial composers of the 20th and early 21st centuries. He is known for his groun ...

at the

Darmstädter Ferienkurse Darmstädter Ferienkurse ("Darmstadt Summer Course") is a regular summer event of contemporary classical music in Darmstadt, Hesse, Germany. It was founded in 1946, under the name "Ferienkurse für Internationale Neue Musik Darmstadt" (Vacation Cou ...

in 1951, prompting him to compose ''

Kreuzspiel (Crossplay) is a composition by Karlheinz Stockhausen written for oboe, bass clarinet, piano and four percussionists in 1951 (it was later revised for just three percussionists, along with other changes). It is assigned the number 1/7 in the comp ...

''—his first acknowledged work.

Pierre Boulez Pierre Louis Joseph Boulez (; 26 March 1925 – 5 January 2016) was a French composer, conductor and writer, and the founder of several musical institutions. He was one of the dominant figures of post-war Western classical music. Born in Mon ...

, after a period of estrangement from Messiaen caused by what Boulez viewed as the excessively sensual ''

Turangalîla-Symphonie The ''Turangalîla-Symphonie'' is the only symphony by Olivier Messiaen (1908–1992). It was written for an orchestra of large forces from 1946 to 1948 on a commission by Serge Koussevitzky in his wife's memory for the Boston Symphony Orchestr ...

'', belatedly discovered the "Mode de valeurs" in 1951 and composed his '' Structures, Book I'' as a gesture of conciliation to his former teacher, transforming the twelve "triplum" elements of the Mode's first division into ordered series and composed ''Structures 1a'' in a single night.

Discography

* Olivier Messiaen: ''Quatre Études de rythme''. Olivier Messiaen, piano. Sound Recording 2 discs, 78rpm, 30 cm. Columbia LFX 998/9 (CLX 2843; CLX 2844; CLX 2845; CLX 2846)

rance Rance may refer to: Places * Rance (river), northwestern France * Rancé, a commune in eastern France, near Lyon * Ranče, a small settlement in Slovenia * Rance, Wallonia, part of the municipality of Sivry-Rance ** Rouge de Rance, a Devonian ...

Columbia, 1951. Presumably the same recording reissued in: **''Les rarissimes de Olivier Messiaen''. CD 1: ''Trois petites liturgies de la présence divine''; ''Les offrandes oubliées''; ''Vingt regards sur l'enfant Jésus''; ''Trois préludes''; CD 2: ''Visions de l'amen pour deux pianos''; ''Quatre Études de rythme''. Olivier Messiaen and

, piano; Jeanne Loriod, ondes Martenot; Ensemble Vocal Marcel Couraud; Orchestre de Chambre André Girard; Orchestre de l'Association des Concerts Pierné; Marcel Couraud and

Roger Désormière Roger Désormière () (13 September 1898 – 25 October 1963) was a French conductor. He was an enthusiastic champion of contemporary composers, but also conducted performances of early eighteenth century French music. Life and career Désormièr ...

, conds. Recorded: Paris, Théâtre Apollo und Studio Albert, between 1942 and 1954. Audio restoration by EMI Music France. Compact disc, 2 sound discs: monaural, 12 cm. EMI Classics 0946 385275 2 7.

EMI Music France, 2007. * ''Premier festival de l'art d'avant-garde''. Anton Webern: Cinq Mélodies, op. 4; Variations pour piano, opus 27; Trois Chants, op. 23; Olivier Messiaen: ''Quatre Études de rythmes''; Pierre Boulez: Étude II ("Etude sur sept sons"); Jean Barraqué: Étude. Ethel Semser, soprano; Paul Jacobs, piano. Musique sur bande. LP recording, 1 disc, 33rpm, 30 cm. Barclay 89005. .p. Barclay Records, 1959. * Olivier Messiaen: ''Huit préludes''; ''Quatre Études de rythme''. Yvonne Loriod, piano. LP recording, 1 disc, 33rpm, stereo, 30 cm. Erato STU 70433. Paris: Éditions Costallat, 1968. Reissued as part of: **Messiaen: '' Petites esquisses d'oiseaux'', '' Huit Préludes''; ''Quatre Études de rythme''. Yvonne Loriod, piano. Erato 2292-45505-2/5 ECD 71589 (+). Previously released in 1968 (2nd–3rd works) and in 1988; Yvonne Loriod, piano./ Recorded at the Eglise Notre-Dame du Liban, Paris, October 1987 (1st work) and January 1968 (2nd and 3rd works). Compact disc, 1 sound disc: digital; 12 cm.

aris Aris or ARIS may refer to: People * Aris (surname) Given name * Aris Alexandrou, Greek writer * Aris Brimanis, ice hockey player * Aris Christofellis, Greek male soprano * Aris Gavelas, Greek sprinter * Aris Howard, Former President of the J ...

Erato, n.d. ** Olivier Messiaen: ''Vingt regards sur l'Enfant Jésus''; ''Petites esquisses d'oiseaux''; ''Huit préludes''; ''Quatre Études de rythme''. Yvonne Loriod, piano. Recorded at the Eglise Notre-Dame du Liban, Paris, October 1973 (CD 1 & CD 2); October 1987 & October 1968 (CD 3). Compact disc, 3 sound discs: analog/digital, stereo, 12 cm. Series: Piano français. Erato 4509-96222-2. France: Erato, 1987. * ''Piano Etudes by Bartók, Busoni, Messiaen, Stravinsky''. Olivier Messiaen: ''Quatre etudes de rythme''; Béla Bartók: Studies for Piano, op. 18; Ferruccio Benvenuto Busoni: Klavierübung (selections); Igor Fedorovich Stravinsky, Etudes for Piano, no. 7. Paul Jacobs, piano. LP recording, 1 disc: stereophonic. Nonesuch H-71334. Nonesuch Records, 1976. Reissued as part of ''The Legendary Busoni Recordings & Works by Bach, Bartók, Brahms, Messiaen, Stravinsky''. Paul Jacobs, piano. Compact disc, 2 sound discs: digital, stereo, 12 cm. Arbiter 124. New York: Arbiter, 2000. * Olivier Messiaen: ''Cantéyodjayâ''; "Neumes rythmiques"; "Île de feu" I and II. Robert Sherlaw Johnson: Piano Sonata No. 1; ''Seven Short Pieces''. Robert Sherlaw Johnson, piano. LP recording, sound disc: analog, 33⅓rpm, stereo. Argo ZRG 694. London: Argo, 1972. * Olivier Messiaen: Préludes & études. Michel Béroff, piano. LP recording, 1 disc, 33rpm, 30 cm. La voix de son maître 2 C 06916229. France: Pathé Marconi, 1978. * Iannis Xenakis: ''Evryali'' 1973; ''Herma'': 1962; Olivier Messiaen: ''Quatre etudes de rythme''. Yuji Takahashi, piano. Recorded at Arakawa Public Hall, Tokyo 21–22 May 1976. Compact disc, 1 sound disc: digital, stereo. ; 4 3/4 in. Denon 33CO-1052.

apan Apan is a city and one of the 84 municipalities of Hidalgo, in central-eastern Mexico. The municipality covers an area of 346.9 km². Overview As of 2005, the municipality had a total population of 39,247. It was an important site in the W ...

Denon, 1986. * César Franck: ''Prélude, choral et fugue''; Olivier Messiaen: ''Quatre études de rythme''; Edvard Grieg: Sonata in E Minor, op. 7; Sergei Rachmaninov: Variations on a Theme by Arcangelo Corelli, op. 42.

Shura Cherkassky Shura Cherkassky (russian: Александр (Шура) Исаакович Черкасский; 7 October 190927 December 1995) was a Ukrainian-American concert pianist known for his performances of the romantic repertoire. His playing was c ...

, piano. Compact disc, sound disc, digital, stereo, 12 cm. Nimbus Records NI5090. Monmouth: Nimbus records Ltd., 1988. * ''The Piano Music of Olivier Messiaen''. Préludes; ''Quatre Études de rythme''; ''Cantéyodjayâ'' . Peter Hill, piano. Previously released on analog discs in 1985 (1st work) and 1986 (remainder). Recorded in Rosslyn Hill Unitarian Chapel, 21–22 February 1984 and 25–26 September 1985. Compact disc, 1 sound disc: digital, stereo, 12 cm. London: Unicorn-Kanchana, 1989. Also packaged as part of ''Messiaen Edition vol. 1: Organ Works; Piano Works; Songs''. Willem Tanke; Peter Hill, piano; Ingrid Kappelle; Håkon Austbø, piano. Compact disc, 17 sound discs: digital, stereo, 12 cm. Brilliant Classics 8949/1–17. eeuwarden, The Netherlands Brilliant Classics, 2008. *Messiaen: ''Petites esquisses d’oiseaux''; ''Cantéyodjayâ''; ''Quatre eetudes de rhythme''; ''Pièce pour le tombeau de Paul Dukas''. Gloria Cheng, piano. Recorded 20–21 December 1993 at

SUNY Purchase The State University of New York at Purchase (commonly Purchase College or SUNY Purchase) is a public liberal arts college in Purchase, New York. It is one of 13 comprehensive colleges in the State University of New York (SUNY) system. It was fo ...

Recital Hall. Compact disc recording: digital, stereo, 12 cm. Koch International Classics 3-7267-2 H1. Port Washington, New York: Koch International L. P., 1994. * ''Études pour piano, vol. 1: Strawinsky, Bartók, Messiaen, Ligeti''. Igor Strawinsky: Quatre Études op. 7; Béla Bartók: Studies, op. 18; Olivier Messiaen: ''Quatre Études de rythme''. György Ligeti: Etudes pour piano, premier livre et deuxième livre. Erika Haase, piano. Recorded Frankfurt am Main, Festeburgkirche, 1997. Compact disc, sound disc: digital, stereo, 12 cm. Tacet 53. ermany Tacet, 1997. * Olivier Messiaen: Piano Music. Håkon Austbø, piano. Vol. 3; Préludes –8 Four rhythmic studies uatre Études de rythme Cantéyodjayâ.; Vol. 4; Les offrandes oubliées; Fantaisie burlesque; Pièce pour le tombeau de Paul Dukas; Rondeau; Prélude (1964); La fauvette des jardins. Compact disc, 4 sound discs Vol. 1– . .l. HNH International, 1999- * ''Angela Hewitt Plays Olivier Messiaen''. Préludes (selections): La colombe; Chant d'extase dans un paysage triste; Le nombre léger; Instants défunts; Les sons impalpables du rêve; Cloches d'angoisse et larmes d'adieu; Plainte calme; Un reflet dans le vent ...; Quatre études de rythme (selections): Île de feu 1; Île de feu 2; Vingt regards sur l'enfant Jésus (selections): Regard de la Vierge; Le baiser de l'Enfant-Jésus; Regard de l'esprit de joie. Angela Hewitt, piano. Recorded in the Reitstadel, Neumarkt in der Oberpfalz, Germany, 21–23 January 1998. Compact disc; 1 sound disc: digital, stereo, 12 cm. Hyperion CDA67054. London: Hyperion, 1998. * ''Composizioni per pianoforte''. Maurice Ravel: ''Le tombeau de Couperin''; Claude Debussy: ''Cinq preludes''; ''Jeux d'eau''; Olivier Messiaen: ''Quatre Études de rythme''. Luca Trabucco, pianist. Twentieth Century French Piano Music. Compact disc, 1 sound disc: stereo, digital, 12 cm. Sony PH 99504. ustria Sony, 1999. * Olivier Messiaen: ''Visions de l'amen''; ''Quatre Études de rythme''; ''Cantéyodjayâ''. Paul Kim, piano; Matthew Kim, 2nd piano (in 1st work). Compact disc. Recorded in Armonk, New York, August 2002 (1st work) and in New York City, September 2002 (remaining works). Compact disc 1 sound disc: digital; 12 cm. Centaur Records CRC 2668. aton Rouge, La. Centaur Records, 2003. * Olivier Messiaen: Préludes; Quatre Études de rythme ; Cantéyodjayâ. Martin Zehn, piano. Recorded in Cologne (Klaus-von-Bismarck-Saal). Compact disc 1 sound disc: digital, stereo, 12 cm. Arte Nova 82876 57833 2; urope BMG;

distrib. BMG, 2004 * ''Hommage à Messiaen''. Pierre-Laurent Aimard, piano. Compact disc, sound disc: digital, stereo, 12 cm. Deutsche Grammophon 477 7452 GH. Contents: ''Préludes pour piano'' (selection): "La bouscarle"; ''

Catalogue d'oiseaux ''Catalogue d'oiseaux'' ("Catalogue of birds") is a work for piano solo by Olivier Messiaen consisting of thirteen pieces, written between October 1956 and September 1958. It is devoted to birds and dedicated to his second wife Yvonne Loriod. Pre ...

'' (selection): "L'alouette Lulu"; ''Quatre Études de rythme'' (selections): "Ile de feu 1 et 2". Hamburg: Deutsche Grammophon, 2008. * ''Olivier Messiaen, 1908–1992. The Anniversary Edition'', vol. 7. ''Visions de l'amen''; ''Quatre Études de rythme''; ''Cantéyodjayâ''. In the 1st work: Alexandre Rabinovitch, Martha Argerich, pianos; 2nd work: Michel Béroff, piano; 3rd work: John Ogdon, piano. 1 sound disc: digital, 12 cm. EMI Classics 2174732. 2008 * Complete edition. Olivier Messiaen; Roger Muraro;

Olivier Latry Olivier Jean-Claude Latry (born 22 February 1962) is a French organist, improviser, and composer. He is professor of organ in the Conservatoire de Paris. He became interested in the organ after listening to recordings by Pierre Cochereau. His ...

. Compact disc 32 sound discs: digital; 12 cm. Deutsche Grammophon (set) 480 1333; Deutsche Grammophon 480 1365-480 1334. CD 2: ''Petites esquisses d'oiseaux''; ''Quatre Études de rythme''; ''Cantéyodjayâ''; ''Rondeau''; ''Fantasie burlesque''; ''Prélude pour piano''; ''Piéce pour le tombeau de Paul Dukas''. Roger Muraro, piano. Germany: Deutsche Grammophon, 2008.

References

Sources * * * * * * * *

'' 3, no. 2:4–11. * D'âčkova, Lûdmila Sergeevna (Дьячкова, Людмила Сергеевна). 2002. "Парадигма как научный метод познания" aradigm as a scholarly method of cognition In Музыковедение к началу века: Прошлое и настоящее usicology at the Turn of the Century: Past and Present edited by Tat'âna Ivanovna Naumenko (Татьяна Ивановна Науменко), 24–41. Moscow: Rossijskaâ Akademiâ Muzyki imeni Gnesinyh. . * Firnkees, Gertrud. 1980. "Improvisation als Einführung in die zeitgenössische Musik". ''Zeitschrift für Musikpädagogik'' 5, no. 12:192–195. * . 1981. "Musik aus Zahlen. Prinzipien der musikalischen Formgestaltung in der seriellen Kompositionspraxis". In ''Reflexionen über Musik heute: Texte und Analysen'', edited by

Wilfried Gruhn Wilfried Gruhn (born 15 October 1939) is a German violinist, musicologist, music educator, and professor emeritus at universities in Germany and abroad. His focus is the music education of small children. He founded and directed the Gordon Instit ...

, 24–57. Mainz: Schott Musik International. * Kämper, Dietrich. 2004. "Olivier Messiaen und die musikalische Avantgarde der fünfziger Jahre: Zur Rezeption der Etüde 'Mode de valeurs et d'intensités'". In ''Kompositorische Stationen des 20. Jahrhunderts: Debussy, Webern, Messiaen, Boulez, Cage, Ligeti, Stockhausen, Höller, Bayle'', edited by

Christoph von Blumröder Christoph von Blumröder (born 18 July 1951) is a German musicologist. Career Born in Northeim, Blumröder studied musicology at the Albert-Ludwigs-Universität Freiburg in Breisgau with Hans Heinrich Eggebrecht, philosophy and history of the ...

and Tobias Hünermann, 24–34. Signale aus Köln 7. Münster: Lit Verlag. . * Kämper, Dietrich. 2006. "Messiaen und die Darmstädter Ferienkurse: eine Begegnung". In ''La cité céleste: Olivier Messiaen zum Gedächtnis—Dokumentation einer Symposienreihe'', edited by Christine Wassermann Beirão, 181–190. Berlin: Weidler. . * Kinzler, Hartmuth. 1997. "Viereinhalb Marginalien zum ersten Stadium von Stockhausens ''Kreuzspiel''". ''Musiktheorie'' 12, no. 1 (Analysieren und Hören neuer Musik): 71–86. * Krumhansl, Carol L. 1991. "Internal Representations for Music Perception and Performance". In ''Cognitive Bases of Musical Communication'', edited by Mari Riess Jones and Susan Holleran, 197–211. Washington, D.C.:

American Psychological Association The American Psychological Association (APA) is the largest scientific and professional organization of psychologists in the United States, with over 133,000 members, including scientists, educators, clinicians, consultants, and students. It has ...

. . * Lee, John Madison. 1972. ''Harmonic Structures in the 'Quatre Études rythmiques' of Olivier Messiaen''. Ph.D. diss. Tallahassee: Florida State University. * Nichols, Roger. 1975. ''Messiaen''. Oxford Studies of Composers 13. Oxford and New York: Oxford University Press. * Puspita, Amelia. 2008. ''The Influence of Balinese Gamelan on the Music of Olivier Messiaen''. DMA diss. Cincinnati: University of Cincinnati. * Schweizer, Klaus. 1973. "Olivier Messiaens Klavieretude Mode de valeurs et d'intensités". ''

Archiv für Musikwissenschaft The ''Archiv für Musikwissenschaft'' is a quarterly German-English-speaking trade magazine devoted to music history and historical musicology, which publishes articles by well-known academics and young scholars. It was founded in 1918 as the su ...

'' 30, No. 2:128–146. * Song, Sun-ju. 2008. ''Music Analysis and the Avant-Garde Compositions of Post–World War II: Four Case Studies''. PhD diss. Nathan:

Queensland Conservatorium Griffith University Queensland Conservatorium Griffith University (formerly the Queensland Conservatorium of Music) is a selective, audition based music school located in Brisbane, Queensland, Australia, and is part of Griffith University. History The Conservatori ...

. * . 1986. "O. Messiaen: Mode de valeurs et d'intensités". In ''Werkanalyse in Beispielen'', edited by Siegmund Helms and Helmuth Hopf, 360–369. Regensburg: . . *

Toop, Richard Richard Toop (1945 – 19 June 2017) was a British-Australian musicologist. Toop was born in Chichester, England, in 1945. He studied at Hull University, where his teachers included Denis Arnold. In 1973 he became Karlheinz Stockhausen's teach ...

. 2000. "Von der 'Sternenmusik' zur Musik des Weltraums: Karlheinz Stockhausens musikalischer Kosmos". ''

Neue Zeitschrift für Musik 'Die'' (; en, " heNew Journal of Music") is a music magazine, co-founded in Leipzig by Robert Schumann, his teacher and future father-in law Friedrich Wieck, and his close friend Ludwig Schuncke. Its first issue appeared on 3 April 1834. His ...

'' 161, no. 6 (November–December): 38–43. * Trawick, Eleanor F. 1999. "Order, Progression, and Time in the Music of Messiaen". ''Ex Tempore'' 9, no. 2 (Spring–Summer): 64–77. * Zheng, Zhong (郑中). 2005. 梅西安的多维准序列创作观——以钢琴作品《调式化的音值与音强》为例 essiaen's Multi-level Serial Composition Technique: On the Example of the Piano Piece 'Mode de valeurs et d'intensités' ''Huangzhong: Zhongguo Wuhan Yinyue Xueyuan xuebao''/''Huangzhong: Journal of Wuhan Conservatory of Music, China'' 1, no. 73:57–63.

External links

* ,

{{DEFAULTSORT:Quatre etudes de rythme Piano études Compositions by Olivier Messiaen Music with dedications 1950 compositions