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 101 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, during which the fragment can start and by what time 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 between 2.00 and 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 rainsticks, 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.
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.
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.
One3
unspecified (amplified ambient sound)
late 1989
Full title: One3 = 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.
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.
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).
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. One6 was initially intended for Paul Zukofsky.
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.
Ten movements, amounting to maximum total duration of 121 minutes. Any three movements of this piece may be performed with 108.
One10
violin
February 1992
Each time bracket contains a single sound. Like One6, 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.
One11
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.
One12
voice
1992
Alfonso Fratteggiani Bianchi and the Quaderni Perugini di Musica Contemporanea
Possibly not a separate work, but a performing score for One7. 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.
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.
Two2
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.
Two3
shō and five conch shells
July 1991
The shō part is the solo shō Number Piece, One9. 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.
Two4
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.
The trombone part is microtonal. Both parts include silences (up to 5 minutes).
Two6
violin and piano
April 1992
Ami Flammer and Martine Joste
The time brackets of Two6 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: Christine Brelowski, Geesche Geddert, and Dorothea Winter
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."
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).
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.
Four3
1–2 pianos, violin or oscillator, 12 rainsticks (three for each performer)
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).
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.
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 One7.
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.
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.
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.
The percussionist uses any ten different instruments, which must 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, two percussionists, 2 violins, viola and cello
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, two percussionists, 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."
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.
Rundfunk-Sinfonieorchester Saarbrücken and the Alte Oper
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.
Rundfunk-Sinfonieorchester Saarbrücken and the Alte Oper
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.
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.
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.
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.
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 One8 (109a), as a shō concerto with any three movements of One9 (109b), and as a double concerto for shō and five conch shells with any three movements of Two3 (110).
^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.
Further reading
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.
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.
