Variations (Cage)
Encyclopedia
Variations is a series of works by American
avant-garde
composer
John Cage
. Some of the pieces in the series are seminal examples of indeterminate music
, others are happening
s: performance pieces executed according to the score.
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
avant-garde
Avant-garde
Avant-garde means "advance guard" or "vanguard". The adjective form is used in English to refer to people or works that are experimental or innovative, particularly with respect to art, culture, and politics....
composer
Composer
A composer is a person who creates music, either by musical notation or oral tradition, for interpretation and performance, or through direct manipulation of sonic material through electronic media...
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...
. Some of the pieces in the series are seminal examples of indeterminate music
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...
, others are happening
Happening
A happening is a performance, event or situation meant to be considered art, usually as performance art. Happenings take place anywhere , are often multi-disciplinary, with a nonlinear narrative and the active participation of the audience...
s: performance pieces executed according to the score.
- Variations I (1958)
- The first piece in the series is dedicated to David Tudor and was a belated birthday present. The score consists of six transparent squares: one with 27 pointsPoint (geometry)In geometry, topology and related branches of mathematics a spatial point is a primitive notion upon which other concepts may be defined. In geometry, points are zero-dimensional; i.e., they do not have volume, area, length, or any other higher-dimensional analogue. In branches of mathematics...
of four different sizes, five with five lines each. The squares are to be combined in any way, with points representing sounds, and lines used as axesCartesian coordinate systemA Cartesian coordinate system specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances from the point to two fixed perpendicular directed lines, measured in the same unit of length...
of various characteristics of these sounds: lowest frequency, simplest overtone structure, etc. Said characteristics are obtained by dropping perpendicularsPerpendicularIn geometry, two lines or planes are considered perpendicular to each other if they form congruent adjacent angles . The term may be used as a noun or adjective...
from points and measuring these perpendiculars. The piece is to be performed by any number of performers on any kind and number of instruments.- Variations II (1961)
- This work is intended "for any number of players and any sound producing means." The score consists of eleven transparent sheets: six lines and five points. The mechanism is the same as in Variations I: perpendiculars are dropped from points to lines to determine sound characteristics, except that the list of characteristics is different: frequency, amplitude, timbre, etc.
- Variations III (1962)
- Intended "for one or any number of people performing any actions", this is the first entry in the series that does not make any references to music, musical instruments or sounds. The score consists of two sheets of transparent plastic: one is blank, the other has 42 identical circles on it. Cage instructs the performers to cut the sheet with circles so that they end up with 42 small sheets, a full circle on each. These should then be dropped on a sheet of paper. Isolated circles are then removed, and the rest are interpreted according to complex rules explained in the score. The information derived includes the number of actions and the number of variables that characterize an action. Cage does not specify the performers' actions, but notes that these can include noticing or responding to "environmental changes". He also states that although some of the factors of a performance may be planned in advance, the performers should "leave room for unforeseen eventualities"; and that "any other activities are going on at the same time" as the work is performed.
- Variations IV (1963)
- This piece is the second in a group that included Atlas Eclipticalis as the first piece and 0'00" as the third. Variations IV is intended for any number of players producing any sounds by any means, "with or without other activities." It is dedicated to Peter Pesic. The score consists of seven points and two circles on a transparent sheet. The sheet is cut into nine small sheets. One of the circles is then placed anywhere on a map of the area where the performance is to take place. Then the rest of the sheets are dropped anywhere on the same map, and straight lines are drawn from the first circle to the seven points; if a line intersects or is tangent to another circle, the same procedure is applied to that circle. The explanatory note in the score gives instructions on how to interpret the results; Cage also mentions that performers do not need to confine themselves to a performance of the piece during the entire performance and are free to engage in any other activities at any time.
- Variations V (1965)
- Variations VI (1966)
- Variations VII (1966)
- Variations VIII (1967, revised 1978)