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class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Technique in musical composition</div> <p><b>Indeterminacy</b> is a composing approach in which some aspects of a musical work are left open to chance or to the interpreter's free choice. <a href="/wiki/John_Cage" title="John Cage">John Cage</a>, a pioneer of indeterminacy, defined it as "the ability of a piece to be performed in substantially different ways". </p><p>The earliest significant use of music indeterminacy features is found in many of the compositions of American composer <a href="/wiki/Charles_Ives" title="Charles Ives">Charles Ives</a> in the early 20th century. <a href="/wiki/Henry_Cowell" title="Henry Cowell">Henry Cowell</a> adopted Ives's ideas during the 1930s, in works allowing players to arrange the fragments of music in a number of different possible sequences. Beginning in the early 1950s, the term came to refer to the (mostly American) movement which grew up around Cage. This group included the other members of the <a href="/wiki/New_York_School_(art)#Music" title="New York School (art)">New York School</a>. In Europe, following the introduction of the expression "<a href="/wiki/Aleatory_music" class="mw-redirect" title="Aleatory music">aleatory music</a>" by <a href="/wiki/Werner_Meyer-Eppler" title="Werner Meyer-Eppler">Werner Meyer-Eppler</a>, the French composer <a href="/wiki/Pierre_Boulez" title="Pierre Boulez">Pierre Boulez</a> was largely responsible for popularizing the term. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Definition">Definition</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Indeterminacy_(music)&action=edit&section=1" title="Edit section: Definition"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Describing indeterminacy, composer John Cage said: "My intention is to let things be themselves." Cage initially defined indeterminacy as "the ability of a piece to be performed in substantially different ways".<sup id="cite_ref-FOOTNOTEPritchett1993108_1-0" class="reference"><a href="#cite_note-FOOTNOTEPritchett1993108-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Bryan Simms thus conflates indeterminacy with what Cage called chance composition when he claims that "Any part of a musical work is indeterminate if it is chosen by chance, or if its performance is not precisely specified. The former case is called 'indeterminacy of composition'; the latter is called 'indeterminacy of performance'."<sup id="cite_ref-FOOTNOTESimms1986357_2-0" class="reference"><a href="#cite_note-FOOTNOTESimms1986357-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Indeterminacy_(music)&action=edit&section=2" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The earliest significant use of music indeterminacy features is found in many of the compositions of American composer <a href="/wiki/Charles_Ives" title="Charles Ives">Charles Ives</a> in the early 20th century. <a href="/wiki/Henry_Cowell" title="Henry Cowell">Henry Cowell</a> adopted Ives's ideas during the 1930s, in such works as the <i>Mosaic Quartet</i> (String Quartet No. 3, 1934), which allows the players to arrange the fragments of music in a number of different possible sequences. Cowell also used specially devised notations to introduce variability into the performance of a work, sometimes instructing the performers to improvise a short passage or play <i>ad libitum.</i> <a href="/wiki/John_Cage" title="John Cage">John Cage</a> is regarded as a pioneer of indeterminacy in music. Beginning in the early 1950s, the term came to refer to the (mostly American) movement which grew up around Cage. This group included the other members of the so-called <a href="/wiki/New_York_School_(art)#Music" title="New York School (art)">New York School</a>: <a href="/wiki/Earle_Brown" title="Earle Brown">Earle Brown</a>, <a href="/wiki/Morton_Feldman" title="Morton Feldman">Morton Feldman</a> and <a href="/wiki/Christian_Wolff_(composer)" title="Christian Wolff (composer)">Christian Wolff</a>. Others working in this way included the <a href="/wiki/Scratch_Orchestra" title="Scratch Orchestra">Scratch Orchestra</a> in the United Kingdom (1968 until the early 1970s) and the Japanese composer <a href="/wiki/Toshi_Ichiyanagi" title="Toshi Ichiyanagi">Toshi Ichiyanagi</a> (born 1933). In Europe, following the introduction of the expression "<a href="/wiki/Aleatory_music" class="mw-redirect" title="Aleatory music">aleatory music</a>" by <a href="/wiki/Werner_Meyer-Eppler" title="Werner Meyer-Eppler">Werner Meyer-Eppler</a>, the French composer <a href="/wiki/Pierre_Boulez" title="Pierre Boulez">Pierre Boulez</a> was largely responsible for popularizing the term.<sup id="cite_ref-FOOTNOTEPeyser2008193_3-0" class="reference"><a href="#cite_note-FOOTNOTEPeyser2008193-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-FOOTNOTEBoulez1957_4-0" class="reference"><a href="#cite_note-FOOTNOTEBoulez1957-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p>In 1958 Cage gave two lectures in Europe, the first at Darmstadt, titled simply "Indeterminacy",<sup id="cite_ref-FOOTNOTECage196135–40_5-0" class="reference"><a href="#cite_note-FOOTNOTECage196135–40-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> the second in Brussels called "Indeterminacy: New Aspect of Form in Instrumental and Electronic Music" (given again in an expanded form in 1959 at Teacher's College, Columbia). This second lecture consisted of a number of short stories (originally 30, expanded to ninety in the second version), each story read by Cage in exactly one minute; because of this time limit, the speed of Cage's delivery varied enormously.<sup id="cite_ref-FOOTNOTECage1961260_6-0" class="reference"><a href="#cite_note-FOOTNOTECage1961260-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> The second performance and a subsequent recording<sup id="cite_ref-FOOTNOTECage1959_7-0" class="reference"><a href="#cite_note-FOOTNOTECage1959-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> contained music, also by Cage, played by <a href="/wiki/David_Tudor" title="David Tudor">David Tudor</a> at the same time. Subsequently, Cage added still more stories, and published a selection of them, partly as an article, "Indeterminacy",<sup id="cite_ref-FOOTNOTECage1961260–273_8-0" class="reference"><a href="#cite_note-FOOTNOTECage1961260–273-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> and partly as scattered interludes throughout his first collection of writings, <i>Silence</i>.<sup id="cite_ref-FOOTNOTECage1961_9-0" class="reference"><a href="#cite_note-FOOTNOTECage1961-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p><p>Between 2007 and 2013, the Dutch artist <a href="/w/index.php?title=Iebele_Abel&action=edit&redlink=1" class="new" title="Iebele Abel (page does not exist)">Iebele Abel</a> developed an electronic instrument called <i>Real-time Indeterminate Synthetic Music Feedback</i> (RT-ISMF). The instrument was designed for empirical research on subjective experiences induced by real-time synthesized music, based on the output of electronic random number generators. The basic idea of this approach was that indeterminate music might evoke unique and exceptional human experience.<sup id="cite_ref-FOOTNOTEAbel201326,_117–119_10-0" class="reference"><a href="#cite_note-FOOTNOTEAbel201326,_117–119-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Classification">Classification</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Indeterminacy_(music)&action=edit&section=3" title="Edit section: Classification"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Indeterminate or chance music can be divided into three groups: (1) the use of random procedures to produce a determinate, fixed score, (2) mobile form, and (3) indeterminate notation, including graphic notation and texts. The first group includes scores in which the chance element is involved only in the process of composition, so that every parameter is fixed before their performance. In John Cage's <i><a href="/wiki/Music_of_Changes" title="Music of Changes">Music of Changes</a></i> (1951), the process of composition involved applying decisions made using the <i><a href="/wiki/I_Ching" title="I Ching">I Ching</a></i>, a Chinese classic text that is commonly used as a divination system. The <i>I Ching</i> was applied to large charts of sounds, durations, dynamics, tempo and densities. Cage himself, however, regarded <i>Music of Changes</i> as a determinate work, because it is completely fixed from one performance to another.<sup id="cite_ref-FOOTNOTEPritchett1993108_1-1" class="reference"><a href="#cite_note-FOOTNOTEPritchett1993108-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Iannis_Xenakis" title="Iannis Xenakis">Iannis Xenakis</a> used probability theories to define some microscopic aspects of <i><a href="/wiki/Pithoprakta" title="Pithoprakta">Pithoprakta</a></i> (1955–56), that is the Greek for "actions by means of probability". This work contains four sections, characterized by textural and timbral attributes, such as glissandi and pizzicati. At the macroscopic level, the sections are designed and controlled by the composer, but the single components of sound are generated by mathematical theories.<sup id="cite_ref-FOOTNOTEJoe_and_Song2002268_11-0" class="reference"><a href="#cite_note-FOOTNOTEJoe_and_Song2002268-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> See: <a href="/wiki/Stochastic_music" class="mw-redirect" title="Stochastic music">stochastic music</a>. </p><p>In the second type of indeterminate music (the only type of indeterminate music according to Cage's definition), chance elements involve the performance. Notated events are provided by the composer, but their arrangement is left to the determination of the performer. According to Cage, examples include <a href="/wiki/Johann_Sebastian_Bach" title="Johann Sebastian Bach">Johann Sebastian Bach</a>'s <i><a href="/wiki/The_Art_of_Fugue" title="The Art of Fugue">The Art of Fugue</a></i>, Morton Feldman's <i>Intersection 3</i>, Earle Brown's <i>Four Systems</i>, and Christian Wolff's <i>Duo for Pianists II</i>.<sup id="cite_ref-FOOTNOTECage196135–39_12-0" class="reference"><a href="#cite_note-FOOTNOTECage196135–39-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> A form of limited indeterminacy was used by <a href="/wiki/Witold_Lutos%C5%82awski" title="Witold Lutosławski">Witold Lutosławski</a> (beginning with <i><a href="/wiki/Jeux_v%C3%A9nitiens" title="Jeux vénitiens">Jeux vénitiens</a></i> in 1960–61),<sup id="cite_ref-FOOTNOTERae2001_13-0" class="reference"><a href="#cite_note-FOOTNOTERae2001-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> where extensive passages of pitches and rhythms are fully specified, but the rhythmic coordination of parts within the ensemble is subject to an element of chance. Earle Brown's <i>Twenty-Five Pages</i>, uses 25 unbound pages, and called for anywhere between one and 25 pianists. The score allowed the performers to arrange the pages in whatever order they saw fit. Also, the pages were notated symmetrically and without clefs so that the top and bottom orientation is reversible. </p><p>"Open form" is a term sometimes used for "mobile" or "polyvalent" musical forms, where the order of movements or sections is indeterminate or left up to the performer. <a href="/wiki/Roman_Haubenstock-Ramati" title="Roman Haubenstock-Ramati">Roman Haubenstock-Ramati</a> composed a series of influential "mobiles" such as <i>Interpolation</i> (1958). </p><p>However, "open form" in music is also used in the sense defined by the art historian Heinrich Wölfflin (1915) to mean a work which is fundamentally incomplete, represents an unfinished activity, or points outside of itself. In this sense, a "mobile form" can be either "open" or "closed". An example of a "dynamic, closed" mobile musical composition is <a href="/wiki/Karlheinz_Stockhausen" title="Karlheinz Stockhausen">Karlheinz Stockhausen</a>'s <i><a href="/wiki/Zyklus" title="Zyklus">Zyklus</a></i> (1959),<sup id="cite_ref-FOOTNOTEMaconie2005185_14-0" class="reference"><a href="#cite_note-FOOTNOTEMaconie2005185-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Terry_Riley" title="Terry Riley">Terry Riley</a>'s <i><a href="/wiki/In_C" title="In C">In C</a></i> (1964) was composed of 53 short sequences; each member of the ensemble can repeat a given sequence as many times as desired before going on to the next, making the details of each performance of <i>In C</i> unique. However, because the overall course is fixed, it is a closed form.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (June 2018)">citation needed</span></a></i>]</sup> </p><p>The greatest degree of indeterminacy is reached by the third type of indeterminate music, in <a href="/wiki/Graphic_notation_(music)" title="Graphic notation (music)">graphic score</a> pieces, in which the music is represented using symbols and illustrations suggesting how a work can be performed. Hans-Christoph Steiner's score for <i>Solitude</i>, created using Pure Data's data structures. This notation may be, like music on traditional staves, a time-pitch graph system. <a href="/wiki/Earle_Brown" title="Earle Brown">Earle Brown</a>'s <i>December 1952</i> consists purely of horizontal and vertical lines varying in width, spread out over the page; it is a landmark piece in the history of graphic notation of music. The role of the performer is to interpret the score visually and translate the graphical information to music. In Brown's notes on the work he even suggests that one consider this 2D space as 3D and imagine moving through it. <a href="/wiki/Cornelius_Cardew" title="Cornelius Cardew">Cornelius Cardew</a>'s <i><a href="/wiki/Treatise_(music)" title="Treatise (music)">Treatise</a></i> is a graphic musical score comprising 193 pages of lines, symbols, and various geometric or abstract shapes that generally eschew conventional musical notation. Although the score allows for absolute interpretive freedom (no one interpretation will sound like another), the work is not normally played spontaneously, as Cardew had previously suggested that performers devise in advance their own rules and methods for interpreting and performing the work. There are, however, infinite possibilities for the interpretation of <i>Treatise</i> that fall within the implications of the piece and general principles of experimental music performance in the late 1960s, including presentation as visual art and map-reading <sup id="cite_ref-FOOTNOTEAnderson291–317_15-0" class="reference"><a href="#cite_note-FOOTNOTEAnderson291–317-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Discography">Discography</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Indeterminacy_(music)&action=edit&section=4" title="Edit section: Discography"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><style data-mw-deduplicate="TemplateStyles:r1041539562">.mw-parser-output .citation{word-wrap:break-word}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}</style><cite class="citation wikicite" id="CITEREFCage1959">Cage, John. 1959. <i>Indeterminacy: New Aspects of Form in Instrumental and Electronic Music</i>. Ninety Stories by John Cage, with Music. John Cage, reading; David Tudor, music (Cage, <i>Solo for Piano</i> from <i>Concert for Piano and Orchestra</i>, with <i>Fontana Mix</i>). Folkways FT 3704 (2 LPs). Reissued 1992 on Smithsonian/Folkways CD DF 40804/5 (2 CDs).</cite></li></ul> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Indeterminacy_(music)&action=edit&section=5" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Process_music" title="Process music">Process music</a></li> <li><a href="/wiki/Aleatoric_music" title="Aleatoric music">Aleatoric music</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Indeterminacy_(music)&action=edit&section=6" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-columns references-column-width" style="column-width: 18em;"> <ol class="references"> <li id="cite_note-FOOTNOTEPritchett1993108-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-FOOTNOTEPritchett1993108_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-FOOTNOTEPritchett1993108_1-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFPritchett1993">Pritchett 1993</a>, 108.</span> </li> <li id="cite_note-FOOTNOTESimms1986357-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTESimms1986357_2-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFSimms1986">Simms 1986</a>, 357.</span> </li> <li id="cite_note-FOOTNOTEPeyser2008193-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEPeyser2008193_3-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFPeyser2008">Peyser 2008</a>, 193.</span> </li> <li id="cite_note-FOOTNOTEBoulez1957-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEBoulez1957_4-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFBoulez1957">Boulez 1957</a>.</span> </li> <li id="cite_note-FOOTNOTECage196135–40-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTECage196135–40_5-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFCage1961">Cage 1961</a>, 35–40.</span> </li> <li id="cite_note-FOOTNOTECage1961260-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTECage1961260_6-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFCage1961">Cage 1961</a>, 260.</span> </li> <li id="cite_note-FOOTNOTECage1959-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTECage1959_7-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFCage1959">Cage 1959</a>.</span> </li> <li id="cite_note-FOOTNOTECage1961260–273-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTECage1961260–273_8-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFCage1961">Cage 1961</a>, 260–273.</span> </li> <li id="cite_note-FOOTNOTECage1961-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTECage1961_9-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFCage1961">Cage 1961</a>.</span> </li> <li id="cite_note-FOOTNOTEAbel201326,_117–119-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEAbel201326,_117–119_10-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFAbel2013">Abel 2013</a>, 26, 117–119.</span> </li> <li id="cite_note-FOOTNOTEJoe_and_Song2002268-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEJoe_and_Song2002268_11-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFJoe_and_Song2002">Joe and Song 2002</a>, 268.</span> </li> <li id="cite_note-FOOTNOTECage196135–39-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTECage196135–39_12-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFCage1961">Cage 1961</a>, 35–39.</span> </li> <li id="cite_note-FOOTNOTERae2001-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTERae2001_13-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFRae2001">Rae 2001</a>.</span> </li> <li id="cite_note-FOOTNOTEMaconie2005185-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEMaconie2005185_14-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFMaconie2005">Maconie 2005</a>, 185.</span> </li> <li id="cite_note-FOOTNOTEAnderson291–317-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEAnderson291–317_15-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFAnderson">Anderson</a>, 291–317.</span> </li> </ol></div> <p><b>Sources</b> </p> <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col" style="column-width: 45em;"> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFAbel2013">Abel, Iebele. 2013. <i>Manifestations of Mind in Matter</i>. Princeton: ICRL Press. <style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-936033-07-2" title="Special:BookSources/978-1-936033-07-2">978-1-936033-07-2</a>.</cite></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFAnderson">Anderson, Virginia. 2006. <i>"Well, It's a Vertebrate …": Performer Choice in Cardew's Treatise</i>. <i>Journal of Musicological Research</i>. <b>5</b>, (3-4): 291-317. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1080%2F01411890600840578">10.1080/01411890600840578</a></cite>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFBoulez1957"><a href="/wiki/Pierre_Boulez" title="Pierre Boulez">Boulez, Pierre</a>. 1957. "Aléa". <i><a href="/wiki/La_Nouvelle_Revue_fran%C3%A7aise" class="mw-redirect" title="La Nouvelle Revue française">La Nouvelle Revue française</a></i>, no. 59 (1 November): 839–857.</cite></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFCage1961"><a href="/wiki/John_Cage" title="John Cage">Cage, John</a>. 1961. <i>Silence: Lectures and Writings</i>. Middletown, Connecticut: Wesleyan University Press.</cite></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFJoe_and_Song2002">Joe, Jeongwon, and S. Hoon Song. 2002. "<a href="/wiki/Roland_Barthes" title="Roland Barthes">Roland Barthes</a>' 'Text' and Aleatoric Music: Is the Birth of the Reader the Birth of the Listener?". <i>Muzikologija</i> 2:263–281.</cite></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFMaconie2005"><a href="/wiki/Robin_Maconie" title="Robin Maconie">Maconie, Robin</a>. 2005. <i><a rel="nofollow" class="external text" href="https://books.google.com/books?id=iuJP2gIDDJkC&pg=185">Other Planets: The Music of Karlheinz Stockhausen</a></i>. Lanham, Maryland, Toronto, and Oxford: The Scarecrow Press. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-8108-5356-6" title="Special:BookSources/0-8108-5356-6">0-8108-5356-6</a>.</cite></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFPeyser2008"><a href="/wiki/Joan_Peyser" title="Joan Peyser">Peyser, Joan</a>. 2008. <i>To Boulez and Beyond</i>, revised edition. Lanham, Maryland: Scarecrow Press. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-8108-5877-0" title="Special:BookSources/978-0-8108-5877-0">978-0-8108-5877-0</a>.</cite></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFPritchett1993">Pritchett, James. 1993. <i>The Music of John Cage</i>. Music in the 20th Century. Cambridge, New York, Melbourne: Cambridge University Press. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-521-41621-3" title="Special:BookSources/0-521-41621-3">0-521-41621-3</a> (cloth); <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-521-56544-8" title="Special:BookSources/0-521-56544-8">0-521-56544-8</a> (pbk).</cite></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFRae2001">Rae, Charles Bodman. 2001. "Lutosławski, Witold (Roman)". <i><a href="/wiki/The_New_Grove_Dictionary_of_Music_and_Musicians" title="The New Grove Dictionary of Music and Musicians">The New Grove Dictionary of Music and Musicians</a></i>, second edition, edited by <a href="/wiki/Stanley_Sadie" title="Stanley Sadie">Stanley Sadie</a> and <a href="/wiki/John_Tyrrell_(musicologist)" title="John Tyrrell (musicologist)">John Tyrrell</a>. London: Macmillan</cite></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFSimms1986">Simms, Bryan R. 1986. <i>Music of the Twentieth Century: Style and Structure</i>. New York: Schirmer Books; London: Collier Macmillan. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-02-872580-8" title="Special:BookSources/0-02-872580-8">0-02-872580-8</a>.</cite></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Indeterminacy_(music)&action=edit&section=7" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1184024115"><div class="div-col" style="column-width: 45em;"> <ul><li><a href="/wiki/Barney_Childs" title="Barney Childs">Childs, Barney</a>. 1974. "Indeterminacy". <i>Dictionary of Twentieth-Century Music</i>, edited by John Vinton. London: Thames and Hudson. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-500-01100-1" title="Special:BookSources/0-500-01100-1">0-500-01100-1</a> American edition published under title <i>Dictionary of Contemporary Music</i> (New York: E. P. Dutton, 1974) <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-525-09125-4" title="Special:BookSources/0-525-09125-4">0-525-09125-4</a>.</li> <li><a href="/wiki/Paul_Griffiths_(writer)" title="Paul Griffiths (writer)">Griffiths, Paul</a>. 2001. "Aleatory". <i><a href="/wiki/The_New_Grove_Dictionary_of_Music_and_Musicians" title="The New Grove Dictionary of Music and Musicians">The New Grove Dictionary of Music and Musicians</a></i>, second edition, edited by <a href="/wiki/Stanley_Sadie" title="Stanley Sadie">Stanley Sadie</a> and <a href="/wiki/John_Tyrrell_(musicologist)" title="John Tyrrell (musicologist)">John Tyrrell</a>. London: Macmillan.</li> <li><a href="/wiki/Michael_Nyman" title="Michael Nyman">Nyman, Michael</a>. 1974. <i>Experimental Music: Cage and Beyond</i>. London: Studio Vista; New York: Schirmer Books. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-02-871200-5" title="Special:BookSources/0-02-871200-5">0-02-871200-5</a> Second edition 1999, Cambridge and New York: Cambridge University Press. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-521-65297-9" title="Special:BookSources/0-521-65297-9">0-521-65297-9</a> (cloth) <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-521-65383-5" title="Special:BookSources/0-521-65383-5">0-521-65383-5</a> (pbk).</li> <li><a href="/wiki/Miguel_Roig-Francol%C3%AD" title="Miguel Roig-Francolí">Roig-Francolí, Miguel A.</a> 2008. <i>Understanding Post-Tonal Music</i>. Boston: McGraw-Hill. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-07-293624-X" title="Special:BookSources/0-07-293624-X">0-07-293624-X</a>.</li> <li>Sutherland, Roger. 1994. <i>New Perspectives in Music</i>. London: Sun Tavern Fields. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-9517012-6-6" title="Special:BookSources/0-9517012-6-6">0-9517012-6-6</a>.</li></ul> </div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Indeterminacy_(music)&oldid=1233329578">https://en.wikipedia.org/w/index.php?title=Indeterminacy_(music)&oldid=1233329578</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Categories</a>: <ul><li><a href="/wiki/Category:Experimental_music" title="Category:Experimental music">Experimental music</a></li><li><a href="/wiki/Category:Musical_composition" title="Category:Musical composition">Musical composition</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Hidden categories: <ul><li><a href="/wiki/Category:Articles_with_short_description" title="Category:Articles with short description">Articles with short description</a></li><li><a href="/wiki/Category:Short_description_is_different_from_Wikidata" title="Category:Short description is different from Wikidata">Short description is different from Wikidata</a></li><li><a href="/wiki/Category:All_articles_with_unsourced_statements" title="Category:All articles with unsourced statements">All articles with unsourced statements</a></li><li><a href="/wiki/Category:Articles_with_unsourced_statements_from_June_2018" title="Category:Articles with unsourced statements from June 2018">Articles with unsourced statements from June 2018</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> This page was last edited on 8 July 2024, at 14:15<span class="anonymous-show"> (UTC)</span>.</li> <li id="footer-info-copyright">Text is available under the <a href="/wiki/Wikipedia:Text_of_the_Creative_Commons_Attribution-ShareAlike_4.0_International_License" title="Wikipedia:Text of the Creative Commons Attribution-ShareAlike 4.0 International License">Creative Commons Attribution-ShareAlike 4.0 License</a>; additional terms may apply. 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