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Pina Bausch Le Sacre du Printemps/The Rite of Spring /Tavaszi áldozat 1978

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Harvard Natural Sciences Lecture Demonstrations

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Érik Baqueiro (2013, rev. 2017) Due(t)empi

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Érik Baqueiro (2013, rev. 2017) Due(t)empi

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Flauta: Joaquín Melo
Clarinete: Paolo Dorio
Composición y electroacústica: Érik Baqueiro(2013, rev. 2017)

Obra comisionada por el programa Suigéneris Lab 2013, en Mérida, Yucatán, México. Presentada en el Museo Universitario de Arte Contemporáneo (MUAC), UNAM, 2013.

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Ligeti - Symphonic Poem for 100 Metronomes - Casey Cangelosi

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Michel van der Aa (2015) The book of sand

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Michel van der Aa (2015) The book of sand

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With The Book of Sand composer Michel van der Aa has invented a completely new genre: the digital, interactive song cycle. Created in partnership with the Holland Festival, Sydney Festival, Google Cultural Institute, BBC The Space and other partners, and created exclusively in digital format, The Book of Sand was launched as a website and smartphone app.

Inspired by the allusions to infinity and the use of mazes and mirrors in the fantastical stories of Jorge Luis Borges, Van der Aa puts you in a space where all places in the world exist simultaneously. A young woman (played by the Australian singer-songwriter Kate Miller-Heidke) collects up sand which is being moved between the film layers by a mysterious machine. Three parallel film layers reveal alternative points of view and introduce new elements to the story, which allows you to choose a new route through the narrative at any point.

The Book of Sand takes its title from a short story by Jorge Luis Borges, and is based on this and four other Borges stories, The Zahir, The Aleph, The Library of Babel, and The House of Asterion. In Borges' story, the Book of Sand is a book with infinite pages, with no beginning and no end, that becomes an obsession and gradually consumes its owner. The other stories all deal in similar Borgesian visions of the infinite - a point that contains all other points in the universe, an object that holds the attention so much that it becomes all of reality itself, a library of all possible books, the Minotaur in an infinite labyrinth.

Mirrors and self-replication are common themes in Van der Aa's work, from his first opera One to the cello concerto Up-Close, so the stories of Borges are an ideal match. Borges is often described as having foretold the Internet, and Van der Aa uses online technology to explore his ideas in ways the writer could not have foreseen,

Incorporating three audiovisual layers of film and music, which the user can jump between as they wish. Each layer is based around the same vocal line, but the accompaniment and the film are different for each, meaning that users can create their own paths. The first layer is intimate and abstract; the second builds on Van der Aa's previous forays into pop-electronica in Sunken Garden and Hysteresis; and the third features 12-voice a-cappella choir. Each layer of film shows a different perspective on the story, introducing different alter egos of the central female protagonist.

Listen, watch and interact at thebookofsand.net

Reviews

Intricate design of the interrelations and cross-pollinations

"Van der Aa has surpassed himself in his intricate design of the interrelations and cross-pollinations between music, video and digital technology. [...] The music contains beautiful vocals by the Netherlands Chamber Choir, very recognisable Van der Aa-esque melodies (Miller-Heidke) and a rock music type middle layer. [...] Van der Aa has once again proved himself to be the consummate composer to see and explore new possibilities without compromising his own distinct themes."
- NRC, Mischa Spel, 1/6/2015

Beautiful, sweeping melody lines

"Based on the work of Jorge Luis Borges, Van der Aa wrote his piece for the fantastic Australian mezzo-soprano Kate Miller-Heidke, the Netherlands Chamber Choir and electronics. With a length of 12 minutes, the piece is a cross between an arty music video, a musical and a chamber opera video. Stylistically it's closely related to the mesmerisingly beautiful aria 'I have these dreams', the high point in Van der Aa's much-discussed opera 'Sunken Garden', combined with influences from pop music as heard through the ears of a modern composer.
With 'The Book of Sand', Van der Aa has invented a new form, which only exists in digital media. A live performance of the piece is impossible, or at least would compromise the essence of the piece, because the user (listener / viewer) is the director of the performance.
The music is dream-like with ethereal choral parts, beautiful, sweeping melody lines for Miller-Heidke and subdued beats and synth sounds. According to Borges' widow María Kodama (78), who was present at the launch, if he were still alive the late author would have been appreciative of the work, as it has been written 'in the spirit of my husband'. A beautiful and deserved compliment."
- Parool, Erik Voermans, 1-6-2015

The Book of Sand's dream logic is impressive (*****)

"The Book of Sand is not an ordinary song cycle. Rather than performed at a concert hall, it can only be watched, for free, via the website or mobile app. The viewer can switch between the layers, which contain different pieces of music. Only Ms Miller-Heidke's vocal line is the same in each layer. The background varies from a modern choral piece, sung by the Netherlands Chamber Choir, to a catchy, but not everyday pop tune and a surreal, alienating electronic patchwork of sound. The elements are all interrelated and it's all gripping, beautiful and mesmerising stuff. Together, the three layers have a duration of 12 minutes, but they form a labyrinth where one could roam endlessly.
With this ultimate video, set in a variety of visual and musical dimensions, Van der Aa is making confident strides into unexplored terrain. What's most impressive over and beyond his control of multimedia technologies, is the dream logic of the world he has created, sustained by strange, yet captivating sounds.
- De Volkskrant, Frits van der Waa, 5-6-2015

A completely new genre [...] a giant leap forward

Exactly nine words were added by composer Michel van der Aa to the enigmatic texts he distilled from Jorge Luis Borges' stories. Borges' texts form the basis for his latest project, the digital, interactive song cycle 'The Book of Sand' - a work which introduces a completely new genre. The nine words Van der Aa has added are: three, five, six, twelve, fourteen, seventeen, eighteen, nineteen and - of course - the number nine itself. Intriguing, because you start wondering almost immediately - and to no avail - why he's chosen just these words. Is there any logic to this series of numbers? It's vintage Van der Aa, as is the technical wizardry of the piece.
From his earlier work, we had already gathered that Van der Aa loves to apply different layers, but with 'The Book of Sand', the courageous Dutch director does more than take a bold step forward - it's a giant leap. Combining three layers of sound with three layers of film, he allows his audience to switch between these three layers at any point during the twelve minute piece, offering them different points of view as well as different music. The only constant factor is the melody, which is performed with poise and conviction by the Australian pop singer Kate Miller-Heidke, who also starred in Van der Aa's film opera 'Sunken Garden'. In The Book of Sand's three film layers she appears in a desert landscape, a kind of factory works and a mysterious vaulted cellar. Depending on which layer we see her in, she's accompanied by an a capella choir (the Netherlands Chamber Choir), electronic sounds or the kind of delightful classic techno which also featured in Sunken Garden. Rougly eight minutes in, just before the third song starts, the three Kates come together. From that point onwards, the music is the same in all three layers, the sand streaming upwards from the singer's mouth in Bill Viola-esque images. Simply beautiful.
All the technical wizardry might make you forget that Van der Aa's music, with its instantly recognisable chord progressions and distinct orchestration, is just superb. What's more, he's avoided a scenario of sensationalist expectations for a long awaited premiere, and the piece subsequently sinking into oblivion, never to be performed again. In contrast, The Book of Sand will always be available, everywhere. That's quite an achievement, and very clever."
- Trouw, Peter van der Lint, 13-06-2015

A revolutionary app

"A revolutionary app from the Holland Festival [...] In many ways a wonder of cultural-technological significance. Experiencing 'The Book of Sand' you flow from one level to the next, buoyed by the continuous, completely synchronic music.
The music reviewers who praised Van der Aa for his use of modern techniques, didn't actually realise quite how revolutionary the result was. Championed by the Holland Festival, which under Ruth Mackenzie is spearheading the development of new digital art, the work does more than just that: in his piece, Van der Aa, who also directed the project's three films, delves deeper, reflecting on different forms of representation of music and image.
For a few decades now, interactive art has been a kind of holy grail [...] Van der Aa has managed to actually give it substance, by creating an artistic metaphor of our current, virtual existence; a work which invites you to zapp and surf without necessarily staying on the surface. It's almost as if he's managed to square the circle."
- NRC, Hans Beerekamp, 22-6-2015

Een wonderbaarlijke poëtische eenheid

"Kate Miller-Heidke zingt en speelt prachtig. De muziek is fascinerend, op de grens van nieuwe muziek en pop. De tekst is helder en de beelden zijn strak en overtuigend [...]
Het levert een wonderbaarlijke poëtische eenheid op, die juist de zapper uitnodigt om goed te luisteren en te kijken. 'The Book of Sand' van Michel van der Aa is een klein muzikaal en visueel doolhof, waarin het goed toeven is. Ook omdat het geen moment prijs geeft hoeveel programmeerwerk er in is gestoken. Chapeau!"
- Cultuurpers, Fransien van der Putt, 4-6-2015

Michel van der Aa is een dapper mens. Hij schreef zijn liederencyclus naar verhalen van Jorge Luis Borges. Eén verhaal van Borges is al moeilijk in 12 minuten te vatten, laat staan meerdere verhalen, zonder dat je de draad volkomen kwijt raakt in zijn magisch realistische wereld. Toch weet van der Aa een mooi werk te maken waarin je zelf de koers bepaalt, maar waarin de verschillende lagen steeds naar elkaar verwijzen.
Kate Miller-Heidke zingt de sterren van de hemel [...] De 3 lagen zijn onafhankelijk van elkaar prachtig gemaakt, zoewel muzikaal als filmisch. [...] The Book of Sand is een klein en gesloten universum (misschien is multiversum hier een betere term) waarin het goed toeven is. Het nodigt uit tot spelen en ontdekken, op rondjes klikken en aan het klokje draaien. Gaande weg ontdek je meer hoe de lagen ten opzichte van elkaar zijn gestructureerd en hoe ze elkaar beinvloeden. Het resultaat is, hoe je er ook doorheen navigeert, prachtig.
- Cultuurpers, Helen Westerik, 1-6-2015

De muziek is, zoals altijd bij Van der Aa, adembenemend mooi en de beelden zijn prachtig

Michel van der Aa lijkt een voorliefde te hebben voor ronddolende vrouwen, die spiegels, kelders, dromen en vooral zichzelf tegenkomen. Dat gebeurt hier in drie fictieve ruimtes, waar je als kijker tussen heen en weer kunt bewegen. Boven dwaalt zij in een uitgestrekte zandwoestijn. In het midden manoeuvreert zij in een lege ruimte met een raadselachtige machine. En beneden dwaalt zij rond in geheimzinnige stenen gangen. Zand stroomt op geheimzinnige wijze van de ene naar de andere verdieping. Je zou er haar - herinneringen in kunnen zien, die worden opgeroepen,- doorgedacht en weer verstuiven.
De muziek is, zoals altijd bij Van der Aa, adembenemend mooi en de beelden zijn prachtig. De zang is in de drie lagen gelijk, maar de achtergrond kan variëren van rock of elektronische muziek tot a capella koorzang. Het duurt maar twaalf minuten, maar je kunt het zo lang maken als je wilt door telkens op een andere manier te schakelen naar de verschillende niveaus, al dan niet met ondertitels, want de betekenis ontging me nog wel eens in de schoonheid."
- De Groene, Max Arian, 3-6-2015

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With The Book of Sand composer Michel van der Aa has invented a completely new genre: the digital, interactive song cycle. Created in partnership with the Holland Festival, Sydney Festival, Google Cultural Institute, BBC The Space and other partners, and created exclusively in digital format, The Book of Sand was launched as a website and smartphone app.

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1. Satz: Allegro molto; energico
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2. Satz: Comodo
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3. Satz: Largo
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4. Satz: Allegro
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DURATION: ca. 32 Min.

PUBLISHER: G. Schirmer ( Music Sales Classical)

Arnold Schönberg composed his Fourth String Quartet op. 37 within six weeks in 1936. If one includes the quartet written in 1897 without an opus number, this was Schönberg's fifth string quartet. He never realised plans for a sixth, for which he had made sketches. The work on his Fourth String Quartet came at a difficult time for Schönberg: having emigrated from Germany in 1933, he moved to the East Coast of the United States following a short stay in Paris. At first he taught at two conservatories - in Boston and New York - but his travel between the two cities as well as the climate were seriously injurious to his health, forcing him to cancel concerts and lectures. This, in turn, had a negative effect on the family's financial situation, which was already strained. Largely because of the more pleasant climate, the family decided to move to California, where Schönberg accepted a professorship at the University of California at Los Angeles in the autumn of 1936, following a year's study at the University of Southern California. At the time of the move, Schönberg had just started writing the Quartet op. 37. On 3 August 1936, he wrote to the music patron Elizabeth Sprague Coolidge, who had commissioned both the Third and Fourth String Quartets, that he had completed the quartet on 26 July: "[...] I would have sent it to you long ago, had I known where you are now [...]. You are probably surprised not to have heard anything from us. But you cannot imagine how much work we had because of the arrival of our furniture. I lost four weeks and have still not put my library and manuscripts in order. [...] But I used every free quarter of an hour to continue work on the string quartet. [...] I am very pleased with the work and believe that it is more pleasing than the Third. But I think that every time!" In its revue, the Los Angeles Times confirmed Schönberg's feeling about the work, describing the quartet as: "[...] less revolutionary than expected [...] and it awakens feelings that are not far from those caused by euphony." The first movement begins with a catchy theme. It opens with a descending minor second, followed by a descending third. The third tone of the row is repeated three times in quavers, followed by an ascending second, also a quaver and the fourth tone of the basic row. The seventh and eleventh tones of the row also have this characteristic repetition, which is emphasised by accents. The basic row is presented in the first five bars; starting in bar six it is contrasted with a lyrical secondary theme. Over the course of the movement, lyrical episodes develop from this theme, which is repeatedly contrasted with the striking main theme. In addition to the basic row, which is notable for its tone repetition, thirds and sixths are heard not only as horizontal intervals but also as chordal elements of the accompaniment. The second movement - Comodo - shows a proximity to the classic quartet model. While there are only vague references to the classical sonata form in the first movement, here the relationship is more clearly recognisable, for example, in the A B A form, making it comparable to a minuet or scherzo movement. The trio, however, is closely tied to a development section that introduces new material as well as developing what has been previously heard. The third movement - Largo - is set off from the preceding movements by the presentation of the main theme. Schönberg dispenses with a contrapuntal accompaniment, letting the theme sound in unison. At the beginning of the A B A B form, he first quotes the motif of the main theme of the first movement in fortissimo, but exactly one tone lower than the original. The emphasised intervals of a third as well as the cadence of the melodic-thematic phrase, ending in a fifth, create a harmonious feeling. The B sections are dominated by the rhythmic character of the second movement, again combined with motivic elements from the first movement. The reintroduction of the A section is clearly heard in the fortissimo, unison entrance, but the direction of the intervals is inverted. The transition to the B section is now more blurred. Elements of the first transition are combined with motifs of the B section, and the boundaries are not clearly recognisable. Arnold Schönberg gives a reason for this change in his "Bemerkungen zu den vier Streichquartetten"( "Introduction to My Four Quartets"): "The departure from the first formulation of this section is quite extensive because of the different purpose. The first time, the B section serves as a lyrical contrast to the dramatic outbreak of the recitative, which it must overcome by the power of its inner warmth. The second time, when the inserted section has already lessened the tension of the beginning, its purpose is to prepare for the conclusion." The final movement is in rondo form. The theme appears five times in variation, contrasted with three episodes, each of them a kind of development after the third and fourth appearance of the varied rondo theme, and a coda. About this movement Schönberg writes: "This Allegro movement contains a great wealth of thematic material, because each repetition is extensively altered, introducing new formulations." The harmonic relationships in this movement are particularly audible. One reason for this is that the notes B-flat and E-flat are heard twice in the basic form of the row. The latent feeling of tonality that this produces is confirmed in the tonal reference of the final cadence (E-flat major fourth and A minor fifth).

Mirjam Schlemmer
© Arnold Schönberg Center

This string quartet also has been commissioned by the great patron of chamber music Mrs. Elizabeth Sprague Coolidge. It was first performed on the occasion of a festival given by Mrs. Coolidge to the students of the University of California at Los Angeles. As there were no speeches made by the officials at this occasion, the public perhaps did not realize that Mrs. Coolidge wanted to honor me in choosing the programs of the four concerts performed by the world-renowned Kolisch Quartet. In each of this programs was played one of my four string quartets and one of the last four Beethoven string quartets. Even if I had not known the intention of Mrs. Coolidge, I would certainly have considered it an honor to appear in such a program, in such a neighborhood. But I had meanwhile become a California composer and professor of composition at this University. And, while every one of my premieres had caused a great sensation and excitement, so that whole cities were agitated, and visitors and critics came from neighboring towns to attend these events, and while, besides the riots with the first two quartets, there were long articles in the papers - this time it was a perfectly commonplace affair. There was no special excitement and, at least, the anticipation was in no way exaggerated. Nevertheless, I was very content with the attitude of the public. The whole audience listened with respect and sincerity to the strange sounds with which they were faced and it seems a number of them were really impressed. Of course, the appreciation for the first and second quartets was much more intense and it could not be expected that a work of my present period would provoke such enthusiasm as does my "Verklärte Nacht," this work of my first period. But, I will never forget how long it took until there was an understanding for the work of my first period and I will also not forget that even "Verklärte Nacht" caused riots and real fighting, and that the first critics in Vienna wrote "This sextett seems like a calf with six feet, such as is often shown at fairs." This string quartet, if also a calf, has at least only four feet.

(Arnold Schönberg, introductory note for the private recording with the Kolisch Quartet, Los Angeles 1936/37; vgl. Fred Steiner "A History of the First Complete Recording of the Schönberg String Quartets," in Journal of the Arnold Schönberg Institute 2 (February 1978), no.2, 122-137)

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1. Satz: Allegro molto; energico Your browser does not support the audio element. 2. Satz: Comodo Your browser does not support the audio element. 3. Satz: Largo Your browser does not support the audio element. 4. Satz: Allegro Your browser does not support the audio element. DURATION: ca. 32 Min.

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This work is likely not in the public domain in the US (due to first publication with the required notice after 1925, plus renewal or "restoration" under the GATT/TRIPS amendments), nor in the EU and those countries where the copyright term is life+70 years. However, it in Canada (where IMSLP is hosted) and in other countries (China, Hong Kong, New Zealand) where the copyright term is life+50 years.

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General Information

Work Title

String Quartet No.4

Name Translations

Strijkkwartet nr. 4; 4. Streichquartett; quatuor à cordes n° 4

Name Aliases

Strijkkwartet nr. 4 (Schonberg)

Authorities

BNF: 13969656t

Composer

Schoenberg, Arnold

Movements/Sections Mov'ts/Sec's

4 movements

1. Allegro molto, energico ( = 152)

2. Comodo ( = 54)

3. Largo ( = 78)

4. Allegro ( = 128) - Agitato ( = = 128)

First Performance .

1937 January 8, Los Angeles, University of California at Los Angeles, Josiah Royce Hall

Kolisch Quartet

Dedication

To the ideal patron of chamber music Elizabeth Sprague Coolidge and to the ideal interpreters of it The Kolisch Quartet

Composer Time Period Comp. Period

Early 20th century

Piece Style

Early 20th century

Instrumentation

2 violins, viola, cello

External Links

Schoenberg Center
Wikipedia article (Dutch)

Re "21" in the above study score :"21" is from my own very-late-1940s-or-even-later reprint copy, front cover and from back cover, list of study scores with edition numbers (which contains works not composed, let alone published, in 1939, e.g. Roger Sessions' symphony no.2 of 1944-6 published in 1949.--E.S.)

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String Quartet No.4, Op.37 (Schoenberg, Arnold)

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This work is likely not in the public domain in the US (due to first publication with the required notice after 1925, plus renewal or "restoration" under the GATT/TRIPS amendments), nor in the EU and those countries where the copyright term is life+70 years.

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Arnold Schoenberg (1936) Fourt string quartet, op. 37

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Arnold Schoenberg (1936) Fourt string quartet, op. 37

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Schoenberg String Quartet No.4 - I. Allegro molto, energico

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Milton Babbitt (1947-48) Composition for four instruments

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Milton Babbitt (1947-48) Composition for four instruments

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Milton Babbitt - Composition for Four Instruments (1947-48) [Score-Video]

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Érik Baqueiro (2016, rev. 2018) Devenir en aire, hilo y papel

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Érik Baqueiro (2016, rev. 2018) Devenir en aire, hilo y papel

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Elliott Carter, Shard | Zsombor Sidoo, guitar

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Elliott Carter: Two Diversions (w/ score) (1999)

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Two Diversions 1st Mov - Elliott Carter - Marc Hannaford

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Conlon Nancarrow (1961) Study for Player Piano No. 21 (Canon X)

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Conlon Nancarrow (1961) Study for Player Piano No. 21 (Canon X)

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Conlon Nancarrow, Study for Player Piano No. 21 (Canon X)

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Igor Stravinsky (1913) Le Sacre du printemps

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Igor Stravinsky (1913) Le Sacre du printemps

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Stravinsky The Rite of Spring // London Symphony Orchestra/Sir Simon Rattle

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Stravinsky - The Rite of Spring (Official Score Video)

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Composition for Four Instruments (1948) is an early serial music composition written by American composer Milton Babbitt. It is Babbitt's first published ensemble work, following shortly after his Three Compositions for Piano (1947). In both these pieces, Babbitt expands upon the methods of twelve-tone composition developed by Arnold Schoenberg. He is notably innovative for his application of serial techniques to rhythm. Composition for Four Instruments is considered one of the early examples of "totally serialized" music. It is remarkable for a strong sense of integration and concentration on its particular premises-qualities that caused Elliott Carter, upon first hearing it in 1951, to persuade New Music Edition to publish it.

Composition for Four Instruments is scored for flute, clarinet, violin, and cello. An immediate division is apparent between the two wind instruments and the two strings. In addition to this, Babbitt makes use of every possible subset of the ensemble group within the different sections of the piece. He uses every combination of instruments only once, saving the full ensemble for the conclusion. The piece can be broken up into fifteen sections according to the subset of instruments playing: four solos, four trios, six duos, one tutti. The instrumental subsets are arranged in complementary pairs, so that each instrument plays only once in every pair of sections. The four solos occur with increasing frequency (at intervals of five, four, and three sections), "converging", so to speak, on the final quartet, which is just two sections after the violin [ sic, recte: flute] solo.

The twelve-tone row upon which the entire composition is based is given by the composer as 0 4 1 11 3 2 : 8 6 5 10 7 9, and generates the four main trichords of the piece. It never once appears complete as a melodic succession, however, though several authors Cone 1967 have given different conflicting versions of a row claimed to be "made explicit only in the final section". While the set given by Babbitt concatenates the first trichords of all four instruments in the order of their entrances at the very beginning of the work, Perle's "basic set" from the end of the composition can be transformed into the composer's version "by wholesale inversion plus individual retrogression of the trichords". The pitch array used in the first 35 bars of the piece is as follows:

The first section of the piece begins with a solo in the clarinet, using the (014) trichord or its retrograde. The notes of this solo are separated by register into four distinct voices, though the notes of any one trichord are usually interrupted by notes from other trichords in other registers, making it hard to hear these structures individually. Babbitt presents several instances of tone rows in the opening bars of the piece. A note-by-note analysis of the first nine measures reveals two such tone rows, the first beginning at measure one and the second at measure seven. A closer look at the separation of the opening into the four registers reveals two additional tone rows. The set of notes contained in the two high registers form a tone row, as do the notes in the lower two registers.[citation needed ]

The piece begins with a three-note motive, or trichord (a collection of three distinct pitch classes), in the next-to-lowest register: B-E-C, with a succession of +4 then −3 semitone intervals. The following measures present three transformations of this opening trichord, in retrograde-inversion, retrograde, and inverse forms (D-B-D, G-A-F, and A-E-G, respectively) separated into the mid-high, high, and lowest registers, respectively (therefore with interval patterns of −3 +4, −4 + 3, and −4 +3). However, these three trichords overlap in time, so that the temporal order of the nine notes is D-G-A-E-B-A-G-D-F. In this way, the twelve-tone aggregate is compositionally ordered into a chromatic, thematic surface, with the properties of another ordered set underneath it. The clarinet solo continues by adding more forms of the basic trichord until a complete twelve-tone aggregate is unfolded in each register.

As a result, seeking for "the row" caused "even the friendliest people" to become baffled and resentful, because of a fundamental misunderstanding about Babbitt's approach to his material:

That's not the way I conceive of a set. This is not a matter of finding the lost set. This is not a matter of cryptoanalysis (where's the hidden set?). What I'm interested in is the effect it might have, the way it might assert itself not necessarily explicitly.

The entire opening clarinet solo can be analyzed as an array of these trichords-an "array"" being two or more simultaneous sets presented in such a way that the sums of their horizontal segments form columnar twelve-tone aggregates-and their various inversions and retrogrades. The trichordal relationships between the notes in the four registers of the clarinet foreshadow the interaction between the four instrument voices in the conclusion of the piece. Also, the way in which the instruments unfold throughout the piece directly corresponds to the progression of the trichords in the clarinet solo. The organization of the pitch classes throughout the piece is consistently and undeniably self-referential.

In addition to his use of multi-dimensional tone rows,[clarification needed ][clarification needed ][clarification needed ] Babbitt also serialized rhythmic patterns. He uses the duration row as his primary rhythmic structure in Composition for Four Instruments, each of which consist of four different durations. The durations can be represented by the sequence of numbers 1 4 3 2: the second note is four times the duration of the first, etc. The duration of the initial note changes every phrase, varying the durations throughout the piece. For example, the first four notes of the opening clarinet solo follow the 1 4 3 2 duration pattern. This rhythmic pattern is then manipulated under the same transformations as the pitches in a tone row. These transformations include the retrograde (2 3 4 1), the inversion (4 1 2 3) and the retrograde inversion (3 2 1 4). Babbitt expands this idea in later pieces, for example working instead with a set of twelve unique durational units in Composition for Twelve Instruments.

As he does in the pitch domain, Babbitt achieves additional variety in the rhythmic patterns of Composition for Four Instruments by manipulating the duration row and its three variations in different ways. At times, he expands the row by multiplying each duration in the pattern by the four other members. Applying this transformation to the original row 1 4 3 2 results in the duration rows 1 4 3 2, 4 16 12 8, 3 12 9 6, and 2 8 6 4. Following the same procedure with the multipliers for the retrograde, 2 3 4 1, yields 4 6 8 2, 6 9 12 3, 8 12 16 4, 2 3 4 1. The inversion of the multipliers is 4 1 2 3, and the retrograde inversion is 3 2 1 4, producing 16 4 8 12, 4 1 2 3, 8 2 4 6, 12 3 6 9, and 9 6 3 12, 6 4 2 8, 3 2 1 4, 12 8 4 16, respectively. In the final three bars of the piece, the clarinet plays the retrograde of the opening duration row with each element multiplied by 4, giving the pattern 8 12 16 4.[citation needed ]

Composition for Four Instruments holds a significant position as one of the early serial compositions, which draws from and reinvents techniques introduced in the work of Arnold Schoenberg and Anton Webern. Babbitt continued to explore serialism throughout his career.

Milton Babbitt: Composition for Four Instruments (1948), Composition for Viola and Piano (1950); John Bavicchi: Trio No. 4, op. 33, Short Sonata for Violin and Harpsichord, op. 39. John Wummer (flute), Stanley Drucker (clarinet), Peter Marsh (violin), Donald McCall (cello); Walter Trampler (viola), Alvin Bauman (piano); David Glazer (clarinet), Matthew Raimondi (violin), Assunta Dell'Aquila (harp); Robert Brink (violin), Daniel Pinkham (harpsichord). LP recording, 1 sound disc, 33⅓ rpm., 12 in. CRI 138. New York: Composers Recordings, 1960.

Contemporary American Chamber Music. Volume 9: Elliott Carter, Sonata for flute, oboe, cello, and harpsichord (1952); Milton Babbitt, Composition for Four Instruments, for flute, clarinet, violin, and cello; Igor Stravinsky, Fanfare for a New Theatre, for two trumpets; Henry Brant, Angels and Devils, concerto for flute and flute orchestra. New England Conservatory of Music Chamber Players (David Reskin, flute; Tom Hill, clarinet; Michael Levin, violin; Ronald Thomas, cello; John Heiss, cond.). New England Conservatory Series. LP recording, 1 sound disc, analog, 33⅓ rpm, stereo, 12 in. Golden Crest NEC 109. Huntington Station, New York: Golden Crest Records, 1975.

Slowly Expanding Milton Babbitt Album: Composition for Four Instruments (1948). Rachel Beetz (flute); Joshua Rubin (clarinet); Erik Carlson (violin); Michael Nicolas (cello), produced by Erik Carlson, 2018.

Sources

Arnold, Stephen, and Graham Hair. 1976. "An Introduction and a Study: String Quartet No. 3". Perspectives of New Music 14, no. 2 and 15, no. 1 (Spring-Summer/Fall-Winter): 155-186.

Babbitt, Milton. 1976. "Responses: A First Approximation". Perspectives of New Music 14, no. 2/15, no. 1 (Spring-Summer/Fall-Winter): 8-10.

Babbitt, Milton. 1987. Words about Music, edited by Stephen Dembski and Joseph N. Straus. Madison: University of Wisconsin Press.

Carlson, Erik (2018). "Composition for Four Instruments". erikcarlson.bandcamp.com.

Carter, Elliott. 1976. "To Think of Milton Babbitt". Perspectives of New Music 14, no. 2, and 15, no. 1 ("Sounds and Words. A Critical Celebration of Milton Babbitt at 60") (Spring-Summer/Fall-Winter): 29-31.

Cone, Edward T. 1967. "Beyond Analysis". Perspectives of New Music 6, no. 1 (Fall-Winter): 33-51.

Dubiel, Joseph. 1990. "Three Essays on Milton Babbitt" [Part 1]. Perspectives of New Music 28, no. 2 (Summer): 216-226.

Dubiel, Joseph. 1992. "Three Essays on Milton Babbitt (Part 3)". Perspectives of New Music 30, no. 1 (Winter): 82-131.

Howland, Patricia L. 2010. "Formal Processes in Post-Tonal Music: A Study of Selected Works by Babbitt, Stockhausen, and Carter". PhD diss. New York: City University of New York.

Mead, Andrew. 1983. "Detail and the Array in Milton Babbitt's My Complements to Roger". Music Theory Spectrum 5 (Spring): 89-109.

Pearsall, Edward. 1997. "Interpreting Music Durationally: A Set-Theory Approach to Rhythm". Perspectives of New Music 35, no. 1 (Winter): 205-230.

Perle, George. 1981. Serial Composition and Atonality: An Introduction to the Music of Schoenberg, Berg, and Webern, fifth edition. Berkeley and Los Angeles: University of California Press.

Sitsky, Larry (2002). Music of the Twentieth-Century Avant-Garde: A Biocritical Sourcebook. Greenwood Publishing. ISBN 9780313296895.

Swift, Richard. 1976. "Some Aspects of Aggregate Composition." Perspectives of New Music 14, no. 2 and 15, no. 1 ("Sounds and Words. A Critical Celebration of Milton Babbitt at 60") (Spring-Summer/Fall-Winter): 236-248.

Taruskin, Richard. 2009. Music in the Late Twentieth Century. Oxford and New York: Oxford University Press. ISBN 978-0-19-538485-7.

Whittall, Arnold. 2008. The Cambridge Introduction to Serialism. Cambridge Introductions to Music. Cambridge and New York: Cambridge University Press. ISBN 978-0-521-68200-8 (pbk).

Karpman, Laura, and Milton Babbitt. 1986. "An Interview with Milton Babbitt". Perspectives of New Music 24, no. 2 (Spring-Summer): 80-87.

Lewin, David. 1995. "Generalized Interval Systems for Babbitt's Lists, and for Schoenberg's String Trio". Music Theory Spectrum 17, no. 1: 81-118.

Mead, Andrew. 1994. An Introduction to the Music of Milton Babbitt. Princeton: Princeton University Press.

Morgan, Robert. 1991. Twentieth Century Music. New York: W. W. Norton.

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Composition for Four Instruments - Wikipedia

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Composition for Four Instruments (1948) is an early serial music composition written by American composer Milton Babbitt. It is Babbitt's first published ensemble work, following shortly after his Three Compositions for Piano (1947). In both these pieces, Babbitt expands upon the methods of twelve-tone composition developed by Arnold Schoenberg.

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Milton Babbitt - Composition for Four Instruments