Music of Changes
Encyclopedia
Music of Changes is a piece for solo piano
by John Cage
. Composed in 1951 for pianist and friend David Tudor
, it is Cage's earliest fully indeterminate
instrumental work. The process of composition involved applying decisions made using the I Ching
, a Chinese classic text that is commonly used as a divination
system. The I Ching was applied to large charts of sounds, durations
, dynamics
, tempi
and density.
work Cage composed (the first is Imaginary Landscape No. 4
, completed in April 1951, and the third movement of Concerto for prepared piano also used chance), and the first instrumental work that uses chance throughout. He was still using magic square
-like charts to introduce chance into composition, when, in early 1951, Christian Wolff
presented Cage with a copy of the I Ching
(Wolff's father published a translation of the book at around the same time). This Chinese classic text
is a symbol system used to identify order in chance events. For Cage it became a perfect tool to create chance-controlled compositions: he would "ask" the book questions about various aspects of the composition at hand, and use the answers to compose. In effect, the vast majority of pieces Cage completed after 1951 were created using the I Ching.
The title of Music of Changes is derived from the title sometimes given to the I Ching, "Book of Changes." Cage set to work on the piece almost immediately after receiving the book. The dates of composition are as follows: Book I completed on May 16, Book II on August 2, Book III on October 18 and Book IV on December 13. Cage's former mentor Henry Cowell
remarked that Cage had not freed himself from his tastes in the new work, and so for a short while Cage worked simultaneously on Music of Changes and Imaginary Landscape No. 4, which was to do what Cowell suggested.
The piece is dedicated to David Tudor
, a pianist and friend with whom Cage would have a lifelong association. The two met in 1950 through Morton Feldman
and Music of Changes was a sort of a collaboration between them. Tudor would learn parts of the score as soon as they were completed, although it was very hard for the pianist: Cage recalls that Tudor had to learn "a form of mathematics which he didn’t know before", and that this was "a very difficult process and very confusing for him." Music of Changes was premièred in its complete form by Tudor on 1 January 1952 (although the pianist had played Book I in public earlier, on 5 July 1951). Tudor also recorded Music of Changes in its complete form, in 1956.
Cage also composed several "spin-offs" of Music of Changes, shorter pieces using the same methods and even the same charts. These include Two Pastorales (1951–52), Seven Haiku (1951–52), For M.C. and D.T. (1952). The process Cage was using at the time to create music with the I Ching proved to be rather slow, so the composer would soon create a faster method in his Music for Piano
series.
and dynamics
charts. Thus, a short segment of music is composed. Silences are obtained from the sounds charts: these only contain sounds in the odd-numbered cells. To introduce new material, all charts alternate between mobile and immobile states (the alteration governed by the I Ching as well); in the latter the chart remains unchanged, but in the former, once a particular cell is used, its contents is immediately replaced by something new.
Furthermore, a density chart is used in the same way to add "polyphony
" to the piece. The above procedure results in a layer—a string of sound events—and then the I Ching is used to determine how many layers should there be in a given phrase. The layers are then simply combined with one another. There may be anywhere from one to eight layers in a phrase.
The structure of the piece is defined through the technique of nested proportions, just like in most of Cage's pieces from the 1940s. The proportion remains the same for the entire work: 3, 5, 6¾, 6¾, 5, 3⅛. So there are 29⅝ sections, each divided into phrases according to the overall proportion: 29⅝ by 29⅝. This is then divided into four large parts of one, two, one and two sections respectively. The tempo
is varied throughout the piece, using the I Ching and a tempo chart. The rhythmic proportion is expressed, then, not through changing time signatures as in earlier works, but through tempo changes.
The notation
of the piece is proportional: Cage standardized the horizontal distance between notes with the same rhythmic value. A quarter note
is equal to two and a half centimeters (almost exactly one inch) in the score. Each sound begins at a precise position indicated by the stem
of the note, rather than its note head
. The tempo is indicated using large numbers above the staves, accompanied with instructions: whether to accelerate from a given value or to slow down. Various other alterations to standard notation are used to indicate unconventional performance techniques: some notes are depressed but not sounded, some are played on the strings
rather than the keys, occasionally the pianist hits various parts of the instrument with specially provided beaters, or snaps the lid to produce a sharp percussive sound. Cage remarks in the foreword to the score that in many places "the notation is irrational; in such instances the performer is to employ his own discretion." The dynamics of the piece range from ffff to pppp.
Piano
The piano is a musical instrument played by means of a keyboard. It is one of the most popular instruments in the world. Widely used in classical and jazz music for solo performances, ensemble use, chamber music and accompaniment, the piano is also very popular as an aid to composing and rehearsal...
by John Cage
John Cage
John Milton Cage Jr. was an American composer, music theorist, writer, philosopher and artist. A pioneer of indeterminacy in music, electroacoustic music, and non-standard use of musical instruments, Cage was one of the leading figures of the post-war avant-garde...
. Composed in 1951 for pianist and friend David Tudor
David Tudor
David Eugene Tudor was an American pianist and composer of experimental music.- Biography :Tudor was born in Philadelphia, Pennsylvania. He studied piano with Irma Wolpe and composition with Stefan Wolpe and became known as one of the leading performers of avant garde piano music. He gave the...
, it is Cage's earliest fully indeterminate
Indeterminacy in music
Indeterminacy in music, which began early in the twentieth century in the music of Charles Ives, and was continued in the 1930s by Henry Cowell and carried on by his student, the experimental music composer John Cage beginning in 1951 , came to refer to the movement which grew up around Cage...
instrumental work. The process of composition involved applying decisions made using the I Ching
I Ching
The I Ching or "Yì Jīng" , also known as the Classic of Changes, Book of Changes and Zhouyi, is one of the oldest of the Chinese classic texts...
, a Chinese classic text that is commonly used as a divination
Divination
Divination is the attempt to gain insight into a question or situation by way of an occultic standardized process or ritual...
system. The I Ching was applied to large charts of sounds, durations
Note value
In music notation, a note value indicates the relative duration of a note, using the color or shape of the note head, the presence or absence of a stem, and the presence or absence of flags/beams/hooks/tails....
, dynamics
Dynamics (music)
In music, dynamics normally refers to the volume of a sound or note, but can also refer to every aspect of the execution of a given piece, either stylistic or functional . The term is also applied to the written or printed musical notation used to indicate dynamics...
, tempi
Tempo
In musical terminology, tempo is the speed or pace of a given piece. Tempo is a crucial element of any musical composition, as it can affect the mood and difficulty of a piece.-Measuring tempo:...
and density.
History of composition
Music of Changes was the second fully indeterminateIndeterminacy in music
Indeterminacy in music, which began early in the twentieth century in the music of Charles Ives, and was continued in the 1930s by Henry Cowell and carried on by his student, the experimental music composer John Cage beginning in 1951 , came to refer to the movement which grew up around Cage...
work Cage composed (the first is Imaginary Landscape No. 4
Imaginary Landscape
Imaginary Landscape is the title of several pieces by American composer John Cage. The series comprises the following works:* Imaginary Landscape No. 1 **for two variable-speed turntables, frequency recordings, muted piano, and cymbal...
, completed in April 1951, and the third movement of Concerto for prepared piano also used chance), and the first instrumental work that uses chance throughout. He was still using magic square
Magic square
In recreational mathematics, a magic square of order n is an arrangement of n2 numbers, usually distinct integers, in a square, such that the n numbers in all rows, all columns, and both diagonals sum to the same constant. A normal magic square contains the integers from 1 to n2...
-like charts to introduce chance into composition, when, in early 1951, Christian Wolff
Christian Wolff (composer)
Christian G. Wolff is an American composer of experimental classical music.-Biography:Wolff was born in Nice in France to German literary publishers Helen and Kurt Wolff, who had published works by Franz Kafka, Robert Musil, and Walter Benjamin. After relocating to the U.S...
presented Cage with a copy of the I Ching
I Ching
The I Ching or "Yì Jīng" , also known as the Classic of Changes, Book of Changes and Zhouyi, is one of the oldest of the Chinese classic texts...
(Wolff's father published a translation of the book at around the same time). This Chinese classic text
Chinese classic texts
Chinese classic texts, or Chinese canonical texts, today often refer to the pre-Qin Chinese texts, especially the Neo-Confucian titles of Four Books and Five Classics , a selection of short books and chapters from the voluminous collection called the Thirteen Classics. All of these pre-Qin texts...
is a symbol system used to identify order in chance events. For Cage it became a perfect tool to create chance-controlled compositions: he would "ask" the book questions about various aspects of the composition at hand, and use the answers to compose. In effect, the vast majority of pieces Cage completed after 1951 were created using the I Ching.
The title of Music of Changes is derived from the title sometimes given to the I Ching, "Book of Changes." Cage set to work on the piece almost immediately after receiving the book. The dates of composition are as follows: Book I completed on May 16, Book II on August 2, Book III on October 18 and Book IV on December 13. Cage's former mentor Henry Cowell
Henry Cowell
Henry Cowell was an American composer, music theorist, pianist, teacher, publisher, and impresario. His contribution to the world of music was summed up by Virgil Thomson, writing in the early 1950s:...
remarked that Cage had not freed himself from his tastes in the new work, and so for a short while Cage worked simultaneously on Music of Changes and Imaginary Landscape No. 4, which was to do what Cowell suggested.
The piece is dedicated to David Tudor
David Tudor
David Eugene Tudor was an American pianist and composer of experimental music.- Biography :Tudor was born in Philadelphia, Pennsylvania. He studied piano with Irma Wolpe and composition with Stefan Wolpe and became known as one of the leading performers of avant garde piano music. He gave the...
, a pianist and friend with whom Cage would have a lifelong association. The two met in 1950 through Morton Feldman
Morton Feldman
Morton Feldman was an American composer, born in New York City.A major figure in 20th century music, Feldman was a pioneer of indeterminate music, a development associated with the experimental New York School of composers also including John Cage, Christian Wolff, and Earle Brown...
and Music of Changes was a sort of a collaboration between them. Tudor would learn parts of the score as soon as they were completed, although it was very hard for the pianist: Cage recalls that Tudor had to learn "a form of mathematics which he didn’t know before", and that this was "a very difficult process and very confusing for him." Music of Changes was premièred in its complete form by Tudor on 1 January 1952 (although the pianist had played Book I in public earlier, on 5 July 1951). Tudor also recorded Music of Changes in its complete form, in 1956.
Cage also composed several "spin-offs" of Music of Changes, shorter pieces using the same methods and even the same charts. These include Two Pastorales (1951–52), Seven Haiku (1951–52), For M.C. and D.T. (1952). The process Cage was using at the time to create music with the I Ching proved to be rather slow, so the composer would soon create a faster method in his Music for Piano
Music for Piano (Cage)
Music for Piano is a series of 85 indeterminate musical compositions for piano by American avant-garde composer John Cage. All of these works were composed by making paper imperfections into sounds using various kinds of chance operations....
series.
Analysis
Music of Changes comprises four "books" of music. Cage used a heavily modified version of his chart system (previously used in Concerto for prepared piano). Every chart for Music of Changes is 8 by 8 cells, to facilitate working with the I Ching which has a total of 64 hexagrams. The I Ching is first consulted about which sound event to choose from a sounds chart, then a similar procedure is applied to durationsNote value
In music notation, a note value indicates the relative duration of a note, using the color or shape of the note head, the presence or absence of a stem, and the presence or absence of flags/beams/hooks/tails....
and dynamics
Dynamics (music)
In music, dynamics normally refers to the volume of a sound or note, but can also refer to every aspect of the execution of a given piece, either stylistic or functional . The term is also applied to the written or printed musical notation used to indicate dynamics...
charts. Thus, a short segment of music is composed. Silences are obtained from the sounds charts: these only contain sounds in the odd-numbered cells. To introduce new material, all charts alternate between mobile and immobile states (the alteration governed by the I Ching as well); in the latter the chart remains unchanged, but in the former, once a particular cell is used, its contents is immediately replaced by something new.
Furthermore, a density chart is used in the same way to add "polyphony
Polyphony
In music, polyphony is a texture consisting of two or more independent melodic voices, as opposed to music with just one voice or music with one dominant melodic voice accompanied by chords ....
" to the piece. The above procedure results in a layer—a string of sound events—and then the I Ching is used to determine how many layers should there be in a given phrase. The layers are then simply combined with one another. There may be anywhere from one to eight layers in a phrase.
The structure of the piece is defined through the technique of nested proportions, just like in most of Cage's pieces from the 1940s. The proportion remains the same for the entire work: 3, 5, 6¾, 6¾, 5, 3⅛. So there are 29⅝ sections, each divided into phrases according to the overall proportion: 29⅝ by 29⅝. This is then divided into four large parts of one, two, one and two sections respectively. The tempo
Tempo
In musical terminology, tempo is the speed or pace of a given piece. Tempo is a crucial element of any musical composition, as it can affect the mood and difficulty of a piece.-Measuring tempo:...
is varied throughout the piece, using the I Ching and a tempo chart. The rhythmic proportion is expressed, then, not through changing time signatures as in earlier works, but through tempo changes.
Musical notation
Music notation or musical notation is any system that represents aurally perceived music, through the use of written symbols.-History:...
of the piece is proportional: Cage standardized the horizontal distance between notes with the same rhythmic value. A quarter note
Quarter note
A quarter note or crotchet is a note played for one quarter of the duration of a whole note . Often people will say that a crotchet is one beat, however, this is not always correct, as the beat is indicated by the time signature of the music; a quarter note may or may not be the beat...
is equal to two and a half centimeters (almost exactly one inch) in the score. Each sound begins at a precise position indicated by the stem
Stem (music)
Stems can refer to two things in music, relating to music notation and production.-Notation:Stems are the lines which extend from the notehead. Stems may point up or down. Different-facing stems indicate the voice for polyphonic music written on the same staff...
of the note, rather than its note head
Note head
In music, a note head is the elliptical part of a note. Noteheads may be coloured completely black or white, indicating the note value . In a whole note, the note head is the only component of the note. Shorter note values attach a stem to the note head, and possibly beams or flags...
. The tempo is indicated using large numbers above the staves, accompanied with instructions: whether to accelerate from a given value or to slow down. Various other alterations to standard notation are used to indicate unconventional performance techniques: some notes are depressed but not sounded, some are played on the strings
String piano
String piano is a term coined by American composer-theorist Henry Cowell to collectively describe those pianistic extended techniques in which sound is produced by direct manipulation of the strings, instead of or in addition to striking the piano's keys...
rather than the keys, occasionally the pianist hits various parts of the instrument with specially provided beaters, or snaps the lid to produce a sharp percussive sound. Cage remarks in the foreword to the score that in many places "the notation is irrational; in such instances the performer is to employ his own discretion." The dynamics of the piece range from ffff to pppp.
Editions
- Edition Peters 6256-6259 (books 1-4). (c) 1961 Henmar Press. This is a facsimile of Cage's original, handwritten score. Each book is published separately.