indeterminacy: music in which some aspects are not pre-determined or are obtained by chance

Cope distinguishes 3 types:

    1. composer indeterminate: performance is determinate; chance operations produces a fixed score

    2. performer indeterminate: composed events; performer determines order, etc.

    3. both composer & performer indeterminate

Europeans: 1 & 2

Americans: 3 (2)rise in early ‘50’s

"aleatoric" alea=dice: European practice [Boulez]


issues: improvisation, tool vs. aesthetic, "alea", ego

1. Historical precedents

earlier efforts: Cowell, Harrison, [Partch]

    • Cowell studied non-European musics in Europe under a Guggenheim grant

    • interest in new sounds shifted to an investigation of ethnic music: sound, forms; "elastic
        form"-notion of indeterminacy-performer takes role in determining order of performed segments

2. Composers, repertoire

John Cage

    • studied with top teachers of ‘30’s, including Cowell, Shoenberg: discovered his deficiency with
        harmony; accepted it; initially a serial composer, but extended the idea to explore ways of
        organizing rhythm [time]

    • early works are percussion/prepared piano works, often to accompany dance; structures are
        modeled on eastern rhythmic [time] cycles

    • approach towards indeterinacy grew out of approach to form: organizing sounds [determinate pitch,
        indeterminate pitch], silences

    • 1951-took eastern concept to heart: Magic square, tossing coins, dice, I Ching; explored
        indeterminate techniques for generating material, structures

    • new phase of composing career brought on by a life crisis: personal & creative anxieties; exchanged
        knowledge with an Indian woman

    • believed purpose of music was to quiet and sober the mind, thus making it susceptable to divine
        influences; felt this to be proper purpose of music, comparing -pre Renaissance and Oriental
        aesthetics as sharing the same basis; self-expression in art [music] was heretical; cycled back into
        communal attitudes

    • wanted to remove expression [purpose] from art: "My purpose is to eliminate purpose" [intention
        into non-intention]; took logic out of music-felt logic restricts our apprehension of the world

    • I Ching: oracle style for consulting, divination; cast yarow sticks, chance operation

    • structure is perceived by the individual: perception of listener more important [as opposed to
        Western approach, re: Beethoven’s aesthetic]

    • equated openness in aesthetic to architecture of Mies van der Rohe, others

    • lectured in Darmstadt, 1958; met Stockhausen

    • associated with Earle Brown, Morton Feldman, Christian Wolff

    Music of Changes (1951)

        • prepared piano; every detail of score determined by toss of three coins six times, directed him to a
            specific number in I Ching; sent him to a numbered position on one of 26 pre-arranged charts:
            procedure repeated to determine pitch, duration, timbre, etc. Resulted in a precisely notated with
            ultra specific instructions for the performer; performance is fixed

    Imaginary Landscapes #4 (1951)

        • 12 radios, 24 players, conductor

        • frees choice of materials, maintains control over form by directing performers’ actions according
            to a precisely determined schedule of duration and dynamics

        • 2 layers of indeterminacy

            1) operation of radios

            2) random events broadcast over airwaves

    4’33" (1952)

        • emphasized role of silence as a frame for sound

        • ambient sounds

    Concert (1957-58)

        • prepared piano, chamber orchestra

        • each part written in detail; no master score; piano part is book of 84 kinds of material that may be
            played in whole or in part, in any sequence; orchestra may involve any number of players; work
            may be of any length, determination is made by conductor


    • introduced to piano music of Cage and Feldman-David Tudor’s European tour; Klavierstucke V-X
        reflect the influence

    • Klavierstucke XI -19 groups on a single sheet that can be played in any order

Gesang der Junglinge (1956)

    • explores redundancy in randomly created texts, aleatoric manipulatoin of electronic controls
        according to various curves: results in "an aleatoric layer of individual pulses which, in general,
        speeded up statistically."

    • insisted that attempts to trace European approaches to ‘open forms’ to American influences were
        incorrect; insisted that approach was linked to contemporary European investigations in statistics
        of Meyer-Eppler

Kontakte (1959-60)

    • moves from interdependent "group" to autonomous "moment": each moment is to be experienced
        individually, non is more important than any other, listener’s attention may bary without
        detriment to the whole [each "moment" is dispensable]

        • rejects anticedent/consequent concept

Pierre Boulez

    • initially impressed with rhythmic structures and gamelan sounds of Cage’s First Construction (In
        Metal), became estranged in 1952 after New York trip; correspondence stopped

    • Boulez attacked Cage for adopting "a philosophy tinged with Orientalism that masks a basic
        weakness in compositional techniques"; two composers assesment of Music of Changes widened
        gap between them

    • further distanced himself from Cage and Stockhausen, criticized Klavierstucke XI as a sort of
        automatism, only lets in element of risk inimical to the integrity of the work

Livres pour quatuor (1948-49) freedom to choose which movements to perform

Third Piano Sonata (1956-7)

    • "mobile" form with 8 possibilities of ordering the five movements

    • third movement is fixed in its ordering: some performance options with respect to segment
        ordering, but choice is limited; formal coherency is assured

Aléa (dice) article: acknowledges chance in composition, states need for compser to absorb and control it