Indeterminacy/ Chance/ Aleatory Music

• Music in which the composer introduces elements of chance or unpredictably with regards to the composition and/ or its performance
• the terms aleatory, chance music, indeterminacy, have been applied to many works created since 1945 by composers who differ widely as to the concepts, methods, and rigor with which they employ procedures of random selection

Aleatory

• European: Meyer-Eppler, Darmstadt (1957) ~ "its course is determined in general but depends on chance in detail"

Indeterminacy

• American: Cage, early Ives, Cowell ~ an aesthetic that strives for a fluid process that eliminates traditional control of the composer over the material

In the composition process:

• pitches, durations, degrees of intensity and other elements may be chosen or distributed in time by dice throwing, interpretation of abstract designs, or according to certain mathematical laws of chance (Xenakis, stochastic music)

In Performance

• Chance is allowed to operated by leaving the choice or order of appearance of some elements to the performer's discretion (Earl Brown, Pierre Boulez, Karlheinz Stockhausen, Henri Pousseur)

Examples

Projections for Solo Cello ~ Morton Feldman
(1950)

• timbre indicated
• relative pitch is indicated as a square or oblong written in one of three boxes which represent either high, medium of low registers
• Duration is indicated by the amount of space taken up by the square or rectangle within the dotted lines
• dotted lines represent four pulses at tempo 72 "or therabouts"
• Indeterminate parameters

1. pitch within each of the three registers
2. dynamics
3. expression
   

Zeitmasze ~ Stockhausen
(1956)

• Wind Quintet
• Indeterminacy in time - flute and bassoon playing in exact time quarter note 112, set against oboe playing "as slow as possible", english horn "slow quickening"; clarinet begins after a pause of imprecise duration
• Imprecision is made part of the structure in the overall tempo and in the relative tempos of the five players. The tempos are dependent less on notational precision than on limitations of techniques and feasibility
• "is an elastic play of five time-strands, each of which mixes passages in strict tempo with others whose speed is determined by the musician's capacity to play as fast as possible or as slow as possible

Music of Changes ~ John Cage
(1951)

• solo piano
• Based off the I-Ching, a chinese classical text used to identify order in chance events
• four "books" of music
• Chart system used with 8x8 cells to accommodate the 64 hexagrams
• charts for sounds, durations and dynamics

Folio "December 1952" ~ Earle Brown

• Expansive palate of cultural influences, especially abstract-expressionism and jazz
• immediacy of what comes next
• single notes
• "music is my material but art is my subject"

Corroboree ~ Earle Brown
(1964)

• for 3 pianos

Four Instruments ~ Morton Feldman
(1965)

• A sound world where coordinates are staked out by extremely reduced dynamics and "glassy" timbres
• piano, tubular bells, string harmonics
• slow tempos
• minimal density of events
• Indeterminate parameters

1. duration open (typically 12 minutes)
2. coordination of parts
3. Some coordinated vertical events
4. player must enter before the previous event from another performer has died away - forming a continuity of surface

• silence used to anticipate events