Number Pieces

Two time brackets from Five (1988), the first one flexible, the second fixed

The term Number Pieces refers to a body of late compositions (40, or 41 if Seventeen was actually composed) by John Cage. Each piece is named after the number of performers involved: for instance, Seven is a piece for seven performers, One⁹ (read "One Nine") is the ninth work for one performer, and 1O1 is a piece for an orchestra of 101 musicians. The vast majority of these works were composed using Cage's time bracket technique: the score consists of short fragments (frequently just one note, with or without dynamics) and indications, in minutes and seconds, of when the fragment should start and when it should end. Time brackets can be fixed (e.g. from 1.15 to 2.00) or flexible (e.g. from anywhere between 1.15 and 1.45, and to anywhere from 2.00 to 2.30).

All of the Number Pieces were composed during the last six years of Cage's life, 1987–1992. Most are for traditional instruments, with six exceptions that range from works for the Japanese aerophone shō and conch shells to an electronically amplified version of 4′33″. This article lists all Number Pieces, organized by number of performers.

List of Number Pieces

One

Title	Instrumentation	Date of composition	Dedicatee(s)	Details
One	piano	December 1987	Juan Allende-Blin	10 time brackets, all flexible except for the ninth. Each contains music written on two staves, but the content of one staff can be played in any relation with that of the other staff.
One^2	1–4 pianos	Summer 1989	Margaret Leng Tan	The pianist moves between several pianos (in 1992 Cage advised Margaret Leng Tan to use the I Ching to coordinate her movements). All instruments have their damper pedals wedged, so that the strings vibrate freely throughout the piece.
One^3	unspecified (amplified ambient sound)	late 1989		Full title: One^3 = 4′33″ (0′00″) + . There are no time brackets. The performer is to arrange a sound system so that "the whole hall is on the edge of feedback, without actually feeding back." Thus the composition consists entirely of electronically amplified sound of the hall and the audience.
One^4	percussion	1990	Fritz Hauser	6 time brackets for the left hand and 8 for the right. Each contains a numeral on a stave, referring to an instrument — the piece is to be performed on "cymbals and/or drums chosen by the drummer." Cage adds that the sounds produced should be either very long or very short.
One^5	piano	May 1990	Ellsworth Snyder	21 time brackets for the left hand and 24 for the right. Each contains a single chord or a single note. The performer is instructed to either hold the pedal throughout, or make as many overlappings as possible (again, using the pedal if necessary).
One^6	violin	June 1990	János Négyesy	The time brackets are extremely long in this piece, up to 7 minutes, many overlap, and all contain just a single tone. Performances of the piece can be accompanied by a sound sculpture by Mineko Grimmer, which is made of ice with pebbles in it. When the ice melts, the pebbles fall and strike wires, producing sound, and then fall into a pool of water. One^6 was initially intended for Paul Zukofsky.
One^7	unspecified	Fall 1990	Pauline Oliveros	This piece is the first part from Four^6. The performer chooses 12 different sounds and plays within flexible time brackets.
One^8	cello with curved bow	April 1991	Michael Bach	There are 53 time brackets, each with a single sound produced on one, two, three or four strings. This Number Piece is microtonal. It may be performed with 108.
One^9	shō	July 1991	Mayumi Miyata	Ten movements, amounting to maximum total duration of 121 minutes. Any three movements of this piece may be performed with 108.
One^10	violin	February 1992		Each time bracket contains a single sound. Like One^6, this piece can be performed simultaneously with a sound sculpture by Mineko Grimmer; the sculpture is essentially the same as in the earlier piece, but in a different configuration.
One^11	unspecified (film)	1992		This Number Piece is a film that consists of chance-determined play of electric light. It is scored for "solo cameraman." It may be performed with 103.
One^12	voice	1992	Alfonso Fratteggiani Bianchi and the Quaderni Perugini di Musica Contemporanea	Possibly not a separate work, but a performing score for One^7. The score contains instructions for creating a chance-determined series of 640 numbers between 1 and 12. The numbers are then interpreted as vowels or consonants (numbers 2–11), words (12) or "empty words" (1; pronouns, articles, etc.). The choice of words is left to the performer.
One^13	cello with curved bow 1 live and 3 recorded cellos	July–August 1992	co-author is Michael Bach Bachtischa[1]	The work remained incomplete at the time of John Cage's death but was published in 2009 as a collaborative composition with Michael Bach Bachtischa. The work has four voices, all playing the same note, but with various differences.

Two

Title	Instrumentation	Date of composition	Dedicatee(s)	Details
Two	flute and piano	December 1987	Roberto Fabbriciani and Carlo Neri	This was the first Number Piece. Both parts contain 9 flexible time brackets and one fixed. Originally devised for flute and vibraphone,[2] the flute part has only three different pitches and is quiet throughout, dynamics ranging from mp to pp. The piano part is notated on two staves, with the content of one played in any relation to that of the other. Each piano time bracket consists of 7 to 10 sounds.
Two^2	2 pianos	Summer 1989	For "Double Edge": Edmund Niemann and Nurit Tilles	This piece does not use time brackets. The score consists of 36 lines of music, 5 bars each. There are 31 sound events per each line, divided 5, 7, 5; 7, 7 as in Renga poetry. The pianists play one bar at a time in different tempi, both have to finish playing the bar at hand before moving to the next one.
Two^3	shō and five conch shells	July 1991		The shō part is the solo shō Number Piece, One^9. There are 10 movements in this work, amounting to 121 minutes total duration. The conch shell parts contain only fixed time brackets. Within each time bracket there are two numbers: the first refers to the conch, the second, in superscript, refers to the intended number of bubbles to be produced (the shells are filled with water and "played" by carefully tipping them until a bubble forms inside, producing a sound). Any three movements of this piece may be performed with 108.
Two^4	violin and piano or shō	July 1991	Commissioned by the McKim Fund of the Library of Congress	Only flexible time brackets are used. The violin part is microtonal and consists for the most part of long sounds. It is divided into three movements. The piano/shō part contains mostly short sounds and is in four movements.
Two^5	tenor trombone and piano	October 1991	Hildegard Kleeb and Roland Dahinden	The trombone part is microtonal. Both parts include silences (up to 5 minutes).
Two^6	violin and piano	April 1992	Ami Flammer and Martine Joste	The time brackets of Two^6 are empty and the performers have to fill them themselves. The pianist's material consists of parts of Extended Lullaby (chance-determined variations of Erik Satie's Vexations) and sequences of ascending pitches. The violinist chooses between silence, microtonal passages, or dyads from chance-determined pitches.

Three

Title	Instrumentation	Date of composition	Dedicatee(s)	Details
Three	a variety of recorders	July 1989	Trio Dolce	The three performers all use several instruments: the first uses sopranino, soprano, alto and tenor recorders, the second sopranino, soprano, alto, basset, tenor and bass, the third soprano, alto, basset, tenor and double bass. The outer movements are to be performed "as legato as possible."
Three^2	unspecified percussion	May 1991	Michael Pugliese and the Talking Drums

Four

Title	Instrumentation	Date of composition	Dedicatee(s)	Details
Four	string quartet	1989, before May 9	Arditti Quartet	There are three five-minute sections: A, B, and C. All parts contain 10 time brackets, 9 flexible and one fixed. The structure of the piece varies depending on how long the desired duration is. For a 10-minute performance, section B is played once, then the performers exchange their parts according to the instructions in the score, and then section B is played again. For a 20-minute performance, only sections A and C are played, without pause, but again with the performers exchanging parts between sections. Finally, a complete 30-minute performance requires the sections played in the ABC order twice. Time brackets contain only single tones at low dynamics (p to ppp).
Four^2	SATB chorus	October 1990	Madrigal Choir of the Hood River Valley High School	There are 3 time brackets for sopranos, 4 for altos, 6 for tenors, and 6 for the basses. The score also supplies a pronunciation table. Each section of the chorus (sopranos, altos, etc.) may be divided into two or more groups, so that one group started the sound and the other continued it.
Four^3	1–2 pianos, violin or oscillator, 12 rainsticks (three for each performer)	May 1991	Merce Cunningham Dance Company	There are 24 empty flexible time brackets, to be filled by the performers. The piano part is to be constructed from Extended Lullaby, 48 chance-determined variations on Erik Satie's Vexations. Each of these consists of 12 eighth notes. Sounds other than the piano are silence, a high frequency sine wave played on an oscillator or on a violin (without vibrato), and the sound of rainsticks (played by tilting them).
Four^4	percussion	October 1991	Amadinda Percussion Group	The four performers have 22, 16, 10 and 15 time brackets respectively. Instruments are chosen by the performers; the time brackets only contain numerals to refer to different instruments.
Four^5	four saxophones	October 1991	John Sampen
Four^6	unspecified	March 1992	Pauline Oliveros, Joan La Barbara, William Winant and Leonard Stein	Each performer chooses 12 different sounds and plays within flexible time brackets. The sounds must have fixed amplitude, overtone structure, etc. The first performer's part may be performed solo, as One^7.

Five

Title	Instrumentation	Date of composition	Dedicatee(s)	Details
Five	unspecified instruments or voices	January 1988	Wilfried Brennecke and the Wittener Tage für neue Kammermusik	One of the earliest number pieces. Although the instruments are unspecified, pitches and dynamics are provided. Each part contains five time brackets, and each time bracket contains one, two, or three sounds.
Five^2	English horn, 2 clarinets, bass clarinet, timpani	May 1991	Mauricio Kagel	A birthday present for Mauricio Kagel. Every part contains five time brackets; the parts are nearly identical in the durations of the brackets (except for time bracket no. 3). The first two brackets for timpani and the last two for English horn are silences; all others contains one, two, or three sounds.
Five^3	trombone and string quartet	October 1991	James Fulkerson and the Mondriaan Quartet
Five^4	two saxophones and percussion	October 1991	In Memoriam Stefan Wolpe
Five^5	flute, 2 clarinets, bass clarinet and percussion	October 1991	Thomas Nee	Every time bracket contains a single sound.

Six to Twenty

Title	Instrumentation	Date of composition	Dedicatee(s)	Details
Six	percussion	September 1991	Slagwerk Den Haag (Percussion The Hague)	Time brackets contain single sounds. Long sounds should be played softly, using tremolo and/or with brushes.
Seven	flute, clarinet, percussion, piano, violin, viola and cello	May 1988	Boston "Musica Viva", "The Voices of Change" in Dallas, and the San Francisco Contemporary Music Players	Each part contains 20 time brackets, all but one flexible. The duration of the brackets is the same, but again, always with one exception. Flute, clarinet, and percussion play single sounds, brackets for strings contain from one to three sounds, and the piano part has three to five sounds per bracket.
Seven^2	bass flute, bass clarinet, bass trombone, unspecified percussion, cello and contrabass	1990, before July 23	Heinz-Klaus Metzger and Rainer Riehn	Percussionists should use "any very resonant instruments."
Eight	flute, oboe, clarinet, bassoon, horn, trumpet, tenor trombone and tuba	1991	Trisha Brown Dance Company	This large (more than 80 time brackets per each part) piece was choreographed by Trisha Brown as Astral Converted.
Ten	flute, oboe, clarinet, trombone, percussion, piano, 2 violins, viola and cello	October–November, 1991	Ives Ensemble	The percussionist uses any ten different instruments, which should be able to produce both long and short sounds. The piano is played both normally and using extended techniques, i.e. on the strings, or hitting parts of the instrument, etc. All other instruments play microtonal passages.
Thirteen	flute, oboe, clarinet in B-flat, bassoon, trumpet in C, tenor trombone, tuba, percussion, 2 violins, viola and cello	May 1992	Manfred Reichert and the Ensemble 13, commissioned by the City of Gütersloh	The number of time brackets per part ranges from 39 (clarinet) to 89 (xylophones). The piece is some 30 minutes long. Long sounds should be played softly.
Fourteen	flute/piccolo, bass flute, clarinet, bass clarinet, horn, trumpet, percussion, bowed piano, 2 violins, viola, cello and double bass	1990	Commissioned by the Zürcher Oberland for Werner Bärtschi and René Müller	The number of time brackets per part ranges from 5 (bass flute) to 22 (piano). The piece is some 20 minutes long. Percussionists use "any very resonant instruments."
Sixteen	flute, oboe, clarinet, bassoon, horn, trumpet, trombone, bass trombone, piano, percussion, 2 violins, viola, cello and double bass	Spring 1992		Unfinished. Manfred Reichert reported that this was the original version of Thirteen.
Seventeen	N/A	N/A	N/A	No score known. Mentioned by Cage in an interview; possibly a mistake on his part. See Sixteen.

Twenty to 108

Cage's late orchestral works are to be performed without a conductor.

Title	Instrumentation	Date of composition	Dedicatee(s)	Details
Twenty-Three	upper strings (13-5-5-0)	1988, before June 21	Commissioned by the Yellow Barn Music Festival	Each performer has their own chronometer, and decides when to start.
Twenty-Six	26 violins	December 1991	Sinfonieorchester des Saarländischen Rundfunks and the Alte Opera	This piece may be performed with Twenty-Eight (Fifty-Four), Twenty-Nine (Fifty-Five), or both (Eighty-Three). All time brackets contain a single sound. The first violin starts the videoclock.
Twenty-Eight	3 flutes, 1 alto flute, 4 clarinets, 3 oboes, 1 English horn, 3 bassoons, 1 contrabassoon, 4 trumpets, 4 horns, 2 trombones, 1 bass trombone, 1 tuba	December 1991	Sinfonieorchester des Saarländischen Rundfunks and the Alte Opera	This piece may be performed with Twenty-Six (Fifty-Four), Twenty-Nine (Fifty-Seven), or both (Eighty-Three). All time brackets contain a single sound. The first flute starts the videoclock.
Twenty-Nine	2 timpani, 2 percussionists, bowed piano, lower strings (0-10-8-6)	December 1991	Sinfonieorchester des Saarländischen Rundfunks and the Alte Opera	This piece may be performed with Twenty-Six (Fifty-Five), Twenty-Eight (Fifty-Seven), or both (Eighty-Three). All time brackets contain a single sound. The first viola starts the videoclock.
Fifty-Eight	3 piccolos, 4 flutes, 3 alto flutes, 4 oboes, 3 English horns, 4 B-flat clarinets, 3 bass clarinets, 4 bassoons, 3 contrabassoons, 3 soprano saxophones, 3 alto saxophones, 3 tenor saxophones, 3 baritone saxophones, 4 horns, 4 trumpets, 4 tenor trombones and 3 tubas	March 1992	Solf Schaefer and the Österreichische Rundfunk (Pannonisches Blasorchester)	This large work (some 60–70 time brackets per part) was composed to be performed at The Landhaus in Graz, a 16th-century Renaissance building. The Landhaus has 58 arches, in which the performers were to be positioned.
Sixty-Eight	3 alto flutes, 3 Cor Anglais, 5 clarinets, 5 trumpets, 4 percussionists, 2 pianos, strings (14-12-10-10-0)	February 1992	Ernstalbrecht Stiebler and the Sinfonieorchester des Hessischer Rundfunks	Each part has 15 time brackets, each with a single sound. The sequence of pitches is always the same, but time bracket durations are different.
Seventy-Four	3333–4331, 2 pianos, 2 percussionists, harp and strings (14-10-8-8-6)	March 1992	Francis Thorne, Dennis Russell Davies and the American Composers Orchestra	There are just two parts: one for high instruments, another for low. Performance notes suggest slight exaggeration of the usual imperfection of tuning, to give the impression of a microtonal work.
Eighty	7 alto flutes, 7 English horns, 7 clarinets, 7 trumpets, upper strings (16-14-12-10-0)	February 1992	András Wilheim	All parts are identical, only transposed for each instrument. Premiered on 28 October 2011 at Munich's Herkulessaal, with the Symphonieorchester des Bayerischen Rundfunks conducted by David Robertson.
1O1	4 (picc, alto) 4 (2 cor anglais) 4 (bass clarinet) 4 (contrabassoon) – 6431, timpani, 4 percussionists, piano, harp, strings (18-16-11-11-8)	1988, before November 13	Boston Symphony Orchestra	The title is to be spelled with capital "O" (unlike 103 and 108). The instrumentation includes bullroarers and angklungs. Although the piece is scored for a large orchestra, the duration is approximately 12 minutes, and the maximum number of time brackets per part is 12.
103	4 (+picc, +alto) 4 (+2 cor anglais) 4 (+bass clarinet) 4 (+contrabassoon) - 4441, 2 timpani, 2 percussion and strings	September 1991	Henning Lohner, Wolfgang Becker-Carsten and the Kölner Rundfunk-Sinfonieorchester	All parts consist of series of single tones. The piece may be performed together with One^11 (which is an abstract film).
108	4 (+piccolo, +alto flute), 5 (+2 English horns), 5 (+2 Bass clarinets), 5 (+2 Contrabassoons) - 7551, 5 percussionists and strings (18-16-12-12-8)	April 1991	Süddeutscher Rundfunk Orchestra	Similar in structure to a symphony, the work is in four movements (A, B, C, D) with silence occurring at the start, between each movement, and at the end. The percussion instruments are "distinguished from one another but not named" and should be "very resonant." The piece may also be performed as a cello concerto with One^8 (109a), as a shō concerto with any three movements of One^9 (109b), and as a double concerto for shō and five conch shells with any three movements of Two^3 (110). The first performance of One^8 and 108 (109a) was performed by the Radio Symphony Orchestra Stuttgart, Nov. 30, 1991 with Michael Bach, cello soloist with curved bow.[3]

Notes

1. http://bach.bogen.pagespro-orange.fr/html/one13.htm
2. Faralli, Jonathan (2012). Cage: Music for an Aquatic Ballet · Music for Carillon No.6 - Roberto Fabbriciani · Jonathan Faralli (Liner Notes of Brilliant Classics CD 9284). Brilliant Classics. pp. 5—6.
3. http://www.youtube.com/watch?v=3H5WfJJ7LVs

References

• Emmerik, Paul van (in collaboration with Herbert Henck and András Wilheim). A John Cage Compendium
• Haskins, Rob. 2004. "An Anarchic Society of Sounds": The Number Pieces of John Cage. Ph.D. Diss., Eastman School of Music, University of Rochester.
• Popoff, A. 2010. John Cage’s Number Pieces: The Meta-Structure of Time-Brackets and the Notion of Time. Perspectives of New Music, pp. 65–84, 48/1.
• Popoff, A. 2011. Indeterminate music and probability spaces: The case of John Cage's number pieces, Springer Lecture Notes in Computer Science, Volume 6726 LNAI, pp. 220–229
• Popoff, A. 2015. A Statistical Approach to the Global Structure of John Cage’s Number Piece Five5, Springer Lecture Notes in Artificial Intelligence, Volume 9110 LNAI, pp. 231-236
• Weisser, B. 2003. "... the whole paper would potentially be sound": Time-Brackets and the Number Pieces. Perspectives of New Music, pp.  176-225, 41/2.
• "MUSICAGE", editor: Joan Retallack, Wesleyan University Press 1996, ISBN 0-8195-5285-2

External links

• John Cage Database - Worklist - includes a complete catalogue of Cage's music, details and lists of recordings for all pieces.
• John Cage Complete Works - hosted and developed by the John Cage Trust
• Rob Haskins: Program and Liner Notes, includes a number of essays on Number Pieces in general, One⁴, One⁹, Two², Two³, Two⁴, Four, Four⁴, Twenty-Nine and 108.
• James Pritchett: Liner Notes: One⁸ for cello and curved bow
• Publication Release Notice by the C.F. Peters Corp. New York: One¹³ for cello with curved bow and 3 loud-speakers