Chance, indeterminacy and open form became popular in the 1950s, particularly in the music of the New York School. Demonstrate your understanding of these three terms with reference to appropriate scores and suggest reasons why composers adopted these styles.

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Submitted in partial fulfilment of the requirements ofEdinburgh Napier University forMUS09103Language and Structures of Music 3.2

The Ian TomlinAcademy of Music

May 2015

Chance, indeterminacy and open form became popular in the 1950s, particularly in the music of the New York School. Demonstrate your understanding of these three terms with reference to appropriate scores and suggest reasons why composers adopted these styles.

In the 1950s, particularly in New York, revolutionary new compositional techniques were developed, such as chance, indeterminacy and open form. These often overlapping techniques were referred to as experimentalism, whose main advocates were a group of composers based at the New School in New York. John Cage (1912-92), Morton Feldman (1926-87), Earle Brown (1926-2002) and Christian Wolff (1934-) pioneered this new system of composition and, along with some of their contemporaries, came up with some of the most innovative compositions seen up to this point. This essay will focus on chance and its use in Cages Music of Changes (1951); indeterminacy in Feldmans Projections (1950-1) and Wolffs For Pianist (1959); and open form in Browns 25 Pages (1953); and in all sections will discuss the reasons these techniques were employed.

Chance Chance music is where some form of chance outside composer control is used in the compositional process. This leads to a fixed performance, played as written- unless indeterminacy is also employed. Cage was the first major proponent of chance, often using a coin game he found in I Ching [see appendix for further explanation of game], the Chinese Book of Changes (Nyman, 1999). This worked to particularly good effect in Music of Changes (1951) for solo piano. Previously Cage had only used chance in particular aspects of his compositions, such as in Concerto for Prepared Piano and Orchestra (1950-1) where the pitch elements were determined by chance but the rhythmic and structural form were determined by Cage himself (Roeder, 1994). However, in Music of Changes, Cage applied chance to all areas of the music for the first time pitch, dynamics, rhythm, number of superpositions, all the things I could discern in a piece of music were subjected to chance operations (Kostelanetz, 1989 p59). He did this by creating 8x8 charts for each element, which therefore had 64 cells, corresponding exactly to the number of outcomes from the I Ching game (Pritchett, 1999).In the sound chart (fig. 1) only the odd numbered cells have values, the even numbered cells being options for silence, a technique which Cage continued through all his chart-based works (Thomson, 1970). Three coins would be tossed six times and the results read against the I Ching chart [see appendix] to give a numerical answer 1 64 which would then be read against the compositional chart. (Nyman, 1999). (Figure 1: Sound chart no. 2 from Music of Changes, even celled silences excluded [Pritchett, 1999 p80]) In the durations chart (fig. 2) all cells have values, and they were picked using the I Ching coin game as in the sound chart (Thomson, 1970). It was not only traditional note-lengths that were used, but also fifths, thirds and sevenths of notes, as seen by the numbers above the rhythms in figure 2.

(Figure 2: Excerpt from durations chart from Music of Changes, [Pritchett, 1999 p81])All elements of Music of Changes were determined by chance in this way. Figure 3 shows how the score was assembled from the multiple outcomes of the coin games. The six separate parts shown beneath the score are each complete results from the charts which were then superimposed upon each other to create the score shown on the top line. Essentially written in 4/4, every bar is divided into four crotchets each measuring 2.5cm on the score. It is within this 2.5cm that all the further, often highly complex rhythms are to be read- by their physical length on paper rather than note value (Iddon, 2013). For example, in figure 3 the first marking in the left hand of the score is written as a semiquaver rest, with 1/5 below it. This means that it is to last 1/5 of a beat, but as this cannot be written easily in standard musical notation a semiquaver is used to approximate, with the exact value written below, and its physical paper length will be 0.5cm, exactly 1/5 of the 2.5cm beat. While created entirely by chance, this is a fully realised score and thus purely a chance composition employing no performance indeterminacy (Cage, 1961; Griffiths, 1981; Kostelanetz, 1989). (Figure 3: First bar of the Music of Changes score and its constituent parts [Pritchett, 1999 p83])The piece was only able to be realised because of pianist, and later composer, David Tudor (1926-96), a friend of Cages. In this piece, Tudor had to evolve a complex mathematical system to play the score in the correct time. Music of Changes has an overall bar structure of 3:5:6:6:5:3 , each with a separate tempo associated, meaning that there were changes in tempo mid-bar, for example on beat 4 of bar 15, and there were also ritardandos and accelerandos in the score (Covell, 2006). This meant that complex mathematics was needed to work out precise note lengths due to the conflict between the traditional and metric notations. Tudor utilised complicated formulae to determine how long each note should last in seconds, sometimes up to two decimal points in accuracy (Iddon, 2013). Tudors incredible skill and willingness to learn new methods was the reason why the experimental composers wrote so many pieces for piano as they knew that in Tudor they had someone who was able and willing to perform whatever they asked, with Cage saying Whatever succeeds in the works I have done has been determined in relationship to him (Chase & Thomas, 2011 p53).Cage was probably the most prolific user of chance, and through this influenced many others to adopt it, although others influenced Cage too- it was Wolff who gave him a copy of the I Ching, leading to its use in Cages compositions and personal philosophy (Cage, 2011). Also influential to Cage were his lessons with Henry Cowell (1897-1965), who started and encouraged Cages fascination with non-Western ideas, having a far greater impact on Cages compositional development than his Western harmonic-focused teachings from Arnold Schoenberg (1874-1951) (Whittall, 1977). He was also influenced by proponents of non-Western principles such as painter Morris Graves (1910-2001) who had incorporated Asian ideas from living in Japan; composer Lou Harrison (1917-2003) and his use of Gamelan instruments; choreographer Merce Cunningham (1919-2009) who also used the I Ching to choreograph; and his marriage to the Russian Xenia Kashevaroff (m. 1935-45) (Cage, 1955; Silverman, 2010; Thomson, 1970).Cages Zen Buddhism obsession stemming from the I Ching was one of his main reasons for adopting chance, Cage admitting without my engagement with Zen I doubt whether I would have done what I have done (Nyman, 1999 p51). In Zen it is not important that things seem to make sense as opposites are seen as identical to each other, which shows in Cages use of chance, especially combined with the I Ching (Thomson, 1970). However, Zen Buddhism or similar philosophies were not the only ways to compose experimental music (Kostelanetz, 1989). Brown composed objectively based on the Schillinger System, a mathematical analysis of musical material which he expanded to include chance (Thomson, 1970). Feldman also had no Zen interest saying my whole debt to Oriental culture is Chinese food (Nyman, 1999 p51). Cage himself did not always use the I Ching- for example his Atlas Eclipticalis (1961-2) used a star map to determine the composition, and Music for Piano (1952-6) treated faults and marks on the paper as notes (Thomson, 1970). Other composers using chance include Iannis Xenakis (1922-2001) who used probability theories to decide individual sounds within his chosen structure in Pithoprakta (1955-6), literally meaning actions by means of probability (Jeongwon & Song, 2002 p265), and George Brecht (1926-2008) who used a deck of cards to create chance outcomes in Card Piece for Voices (1959) (Nyman, 1999). One of the main reasons composers chose to adopt compositional chance was to rid their music from the effect of individual bias and feelings. Cages aim was to let sounds be themselves rather than vehicles for man-made theories, or expression of human sentiments (Nyman, 1999 p50). The composers believed that music should be based on statement and logical sounds rather than human ideas, allowing sounds to exist as themselves, believing conscious composition forced relationships between sounds thus losing the natural ones (Nyman, 1999; Vinton, 1974). They also saw it as a way to show that music need not have a meaning- in Cages essay 45 for a Speaker (1954) he says the highest purpose is to have no purpose at all. This puts one in accord with nature (Whittall, 1977 p209) thus furthering the mentality of allowing sound to exist in itself. Cages interest in chance music was also highly down to his lack of a musical ear (Thomson, 1970). Cage himself said The whole pitch aspect of music eludes me (Kostelanetz, 1989 p74), resolving instead to focus on rhythm, which became a staple of his technique (Griffiths, 1981). What Cage lacked in musicality he certainly made up for in inventiveness, and due to his father being an inventor he held innovation in high regard (Thomson, 1970). Dick Higgins (1938-98) agreed that it was invention not music at the core of experimentalism, saying the real innovation lies in the emphasis on the creation of a system (Nyman, 1999 p5).

IndeterminacyAn indeterminate piece is a composition in which certain parts of the performance are decided by the performer. This could be decisions on pitch, rhythm or any aspect of the work, such as instructions to follow in certain situations (Vinton, 1974). This means that a performance of an indeterminate piece will be essentially unique (Kostelanetz, 1989). Composers wanted to free music from the idea that performances of a work should have a permanent outcome or be essentially identical, wanting to involve the performer and the audience in the creation and interpretation of the music in ways far beyond what would be possible if the composer had predetermined for himself exactly what he wanted to hear (Nyman, 1999; Whittall, 1977). Feldman was the first to produce proper indeterminate music with his Projections (1950-1) where his aim was not to compose but to project sound into time (Nyman, 1999 p53). He was highly influenced by Cage, who taught at New Yorks New School for Social Research and was described as the apostle of indeterminacy in music (Griffiths, 1989 p1). Feldman, along with Wolff and Brown, would meet with Cage, bringing new ideas to show each other (Vinton, 1974). Feldman explained that Cage liberated me in terms of self-permission to go on with what I had decided I was going to do (Nyman, 1999 p51) this fellowship, united by Cages strong spirit, was one of the many reasons that experimentalism progressed as it did (Nicholls, 1998). Figure 4 shows the first page of Feldmans Projection 1 (1950) for solo cello, with the three lines from top to bottom telling the performer whether to play harmonic, pizzicato or arco notes. The dotted lines indicate bars with the squares showing the timing of the note, but the pitch of the notes is chosen by the performer, with Feldman only indicating relative register; squares at the top of the stave are high, those in the middle are mid-register, and at the bottom low register notes (Welsh, 1996). For instance, the first note is a pizzicato mid-register note on beat 4 of the first bar.

(Figure 4: Page 1 of Feldmans Projection 1 [Welsh, 1996 p21])Feldman and his companions were influenced by other pioneers of experimental music, art and drama, whose art forms were following similar indeterminate discovery at the time. Feldman was inspired by Jackson Pollock (1912-1956) an abstract painter, and Alexander Calder (1898-1976) who was famous for his mobiles, admiring their willingness to be completely distinct from other art and feeling that he and his companions were the musical equivalents (Nyman, 1999; Whittall, 1977). Projection 1 was also the first use of graphic notation, which with its similarities in appearance to some of their abstract works, showed that Feldman was influenced by them to put greater emphasis on how his scores looked rather than merely how they sounded (Nicholls, 1998).

In 1959 Wolff wrote For Pianist, described as one of the most extreme instances of indeterminate music to have emerged (Thomas, 2014 p2), for David Tudor. Here Wolff explored the technique of giving choices to the performer that could only be determined during the performance by consequences of previous occurrences (Wolff, 1976). For example in figure 5 the pianist is instructed to pizzicato as hard as possible leading to three possible routes- the top route is taken if neighbouring string, of another pitch, hit (usually involves fingers slipping). The middle route is taken if neighbouring string, of same pitch, hit and the lowest route is taken if sound is clear (Thomas, 2014).

(Figure 5, p4 of For Pianist, [cms.philip-thomas.co.uk])This method of giving choice to the performer dependent on their performance is apparent throughout the piece. When the performer is asked to play as quietly as possible there are different routes depending on how successful they think they have been; at other points the direction the piece takes depends on whether a particular harmonic sounds, or how quickly a note dies away making it dependant on the venue acoustics as well (Chase & Thomas, 2013).

Wolff was only 16 when he met Cage, and having no previous opposing teaching was highly influenced by him (Whittall, 1977). Showing Cages influence, Wolff required that one note on the piano be prepared, and if this note is accidentally hit at any point then the performer must jump to page 6 immediately upon finishing the current system. Wolff allows the pianist to drop any of the systems that become too difficult at any point; and also leaves the performer the choice of which order to play the ten pages in, to repeat them at will, or indeed to not play them at all (Chase & Thomas, 2013). This means that every performance, while notated fully, will be unique and highly down to performer input (Pritchett, 1999).

For Pianist takes time-notation further than Cages Music of Changes, and is written completely in terms of time with no note rhythms given at all. Each sound lasts between 1/50s to 36s, decided from multiplications of fractions (Wolff, 1976). Further indeterminacy is employed as the sounds to be created within the designated time are performer-picked, either from a group of notes represented by a letter on the score, or given free choice, sometimes with extra instructions such as to transpose the chosen note a semitone either way (Chase & Thomas, 2013). For example in figure 5, if the top option is followed the first instruction is to play any 2 notes from group a, for 1/10 of a second, with one muted; followed by a 5/8s rest; then 1 1/8s to play a realisation of the shapes drawn in the box, crescendo-ing while tapping on the B7 key.

This piece was another example of Tudor being able to overcome performance practice issues- the use of prepared piano, unusual techniques such as different ways of playing on the pianos strings, and learning to read the unique notation style (Thomas, 2014). In a way though Wolff wrote this piece to tease Tudor who was known for always deciding, realizing and notating his chosen determinations before a performance, and here this was not possible as the choices were based on in-performance chances- although Tudor still tried to write out every potential outcome (Chase & Thomas, 2013).

Another reason experimental music developed was due to the focus on time and silences necessity. As seen here, basing a piece on time rather than notes made it truly possible to start or end at any point whereas under normal notation it would be impossible to specify all the points in time (Nyman, 1999). These composers also held silence as the opposite and necessary coexistent of sound (Nyman, 1999 p2), while acknowledging that true silence does not exist- most famously seen in Cages 433 (1952), believing that environmental sounds were not interruptions but important parts of a performance (Kostelanetz, 1989). Around this time, helped by Edgard Varse (1883-1965) it began to be accepted that all sounds could be musical material, allowing composers more variety such as using radios or computers to create new, unpredictable music (Vinton, 1974). It was momentary uniqueness rather than creating permanence that interested there composers they were more bothered with innovation that the sound of their pieces (Kostelanetz, 1989). Cage said that he composed to hear something he had never heard before, and as Wolff said, practically everythings been done now. There are just a few bizarre things that havent been thought of (Whittall, 1977, p210). This was why much emphasis was put on rhythm and time as it was an area where there was still the opportunity of innovation (Thomson, 1970).

Open FormOpen form is where the sections of a piece are able to be placed in an order chosen by the performer, meaning that performances will differ from each other although the musical material given is the same (Nyman, 1999). Open form pieces often also use other experimental techniques such as indeterminacy as can be seen in Wolffs For Pianist which we looked at previously where pages can be played in any order, repeated or not played. However, now we will look at Browns Twenty-Five Pages (fig. 6) a work where all the sound material is composed but the ultimate form, the organisation of the given material is left open (Nyman, 1999 p57).

(Figure 6, p1 of 25 Pages, http://www.earle-brown.org/works/view/40)This piece can be performed by one to twenty-five pianos, although it is unusual to hear it played with all twenty-five due to the logistics of requiring twenty-five grand pianos in one place and the same number of highly-skilled pianists to play them! The composition contains twenty-five pages, which can be ordered at the performers discretion. Further to this, they can choose to invert pages, can read the two line systems in either treble or bass clefs, and can set how long the piece will last for- from roughly 8 to 25 minutes (Welsh, 1994). Depending on which choices the performer makes some points in the score may not be physically playable. For example the highest note in system 3 of figure 5 would, if the page was inverted and played in bass clef, be too low for the piano and so would have to be left out. It is important to note that, while each performance of an open-form piece may be very different superficially, the identity of the material within the piece remains fairly constant (Didier & de Andrade, 2001).Brown, like Feldman, was highly inspired by the artists Calder and Pollock, especially Calders mobiles where Brown saw the creative function of non-control the integral but unpredictable floating variations (Nyman, 1999 p56), an idea which he carried over into his open form works. The composers were also influenced by Pierre Boulez (1925-), one of the first Europeans to embrace early experimentalism, using open form in works such as Third Piano Sonata (1957) (Goldman, 2011). Cage in particular admired and often corresponded with him, however his writing was still based upon serialism which limited Cages admiration as he saw Boulez as remaining trapped in old ways (Griffiths, 1981).

It would seem that inspiration for open form may have originated in classical Europe (as much as the New York School would have decried any suggestion of historical influence!) from the Musikalisches Wrfelspiel, a dice game often attributed to W. A. Mozart. Here, prewritten bars of waltz music could be selected according to chance dice rolls corresponding to tables of bar numbers to make a huge number of basic waltzes, which was very popular as it made it easy for music to be created by anyone (Hedges, 1978). Interestingly, in Cages HPSCHD (1967-9) he uses the Musikalisches Wrfelspiel as the basis of some of the harpsichord parts (Heinbecker, 2011; Thomson, 1970).Many of the reasons composers adopted open form are shared with the other forms of experimentalism, which is not surprising given the overlap of the different techniques within works. One of the main causes for the advent of open form and experimentalism was to break away from the historical traditions of Western music (Nyman, 1999). Cage was the most vocal opponent of traditional classical music, although there are differing opinions on his reasons. Cage called himself musics corrective (Thomson, 1970 p69) and believed removing music from traditions was the only way for it to regain its meaning. Some think that Cage, described as non-compliant and anti-authority, simply enjoyed being rebellious, backed up by Cages statement that Ive always been on the side of things one shouldnt do (Nyman, 1999 p61). Another view is that it was more of a commercial decision, done to gain attention by being fashionably novel (Thomson, 1970). No matter what his personal reasoning behind his rebellion though, where Cage went many followed.

The techniques of chance, indeterminacy and open form, either in combination or alone all serve to take some degree of control away from the composer, whether by compositional chance or performer input, and have all lead to highly interesting works. These techniques were used for a number of reasons including the belief that music should not be biased by composer feelings, the desire for complete originality, the influence of non-Western ideas, the advent of new performance techniques and skilled modern performers such as David Tudor, and hugely down to one person and his influence John Cage, who for many reasons started the experimental wave and who inspired many others.

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ReferencesCage, J. (1955) Experimental Music: Doctrine I. M. A. Magazine, London, accessed at http://ada.evergreen.edu/~arunc/texts/music/cage3/cage3.pdf April 2015.Chase, S. & Thomas, P. (2013) Changing the System: The Music of Christian Wolff Ashgate Publishing Limited, Farnham.Covell, G. C. (2006) 1951 and Cages Music of Changes accessed at http://www.lafolia.com/1951-and-cages-music-of-changes/ April 2015Didier, G. & de Andrade F. G. (2001) Earle Browns 25 pianos: a web interactive implementation Federal University of Paraiba, accessed at http://gsd.ime.usp.br/sbcm/2001/papers/rDidier_Guigue.pdf April 2015The Earl Brown Music Foundation (1953) Twenty-Five Pages Edition Peters, accessed at http://www.earle-brown.org/works/view/40 April 2015Edition Peters Group (1951) Imaginary Landscape No. 4 accessed at https://www.edition-peters.de/cms/deutsch/general/produkt.html?product_id=EP6718 April 2015Goldman, J. (2011) The Musical Language of Pierre Boulez: Writings and Compositions Cambridge University Press, Cambridge.Griffiths, P. (1981) Oxford Studies of Composers- Cage Oxford University Press, London.Hedges, S. A. (1978) Dice Music in the Eighteenth Century Music and Letters 59(2), Oxford.Heinbecker, S. J. (2011) John Cages HPSCHD University of Illinois, Illinois, accessed at http://hdl.handle.net/2142/24332Iddon, M. (2013) John Cage and David Tudor: Correspondence on Interpretation and Performance Cambridge University Press, Cambridge.Jeongwon, J & Song H.S. (2002) Roland Barthes Text and aleatoric music: Is The birth of the reader the birth of the listener? Muzikologija, 2 p263-281.Kostelanetz, R. (1989) Conversing with Cage Omnibus Press, New York.Nicholls, D. (1998) "The Cambridge History of American Music" Cambridge University Press, Cambridge.Nyman, M. (1999) Experimental Music- Cage and Beyond- Second Edition Cambridge University Press, Cambridge.Pritchett, J. (1999) The Music of John Cage Cambridge University Press, Cambridge.Roeder, M. T. (1994) A History of the Concerto Amadeus Press, Hong Kong.Silverman, K. (2010) Begin Again: A Biography of John Cage Knopf Doubleday Publishing Group, New York.Thomas, P. (2014) For Pianist accessed at http://cms.philip-thomas.co.uk/wp-content/uploads/2014/05/img008.jpgThomas, P. (2014) Pianist: Pieces CD Liner Notes Sub Rosa, Brussels, accessed at http://eprints.hud.ac.uk/22953/1/Pianist_Pieces_CD_liner_notes.pdf April 2015.Thomson, V. (1970) Twentieth Century Composers 1- American Music since 1910 Weidenfield and Nicolson, London.Vinton, J. (1974) Dictionary of 20th Century Music Thames and Hudson Limited, London.Welsh, J. P. (1994) Open Form and Earle Browns Modules I and II Perspectives of New Music 32(1) pp254-290.Welsh, J. P. (1996) Projection 1 (1950) in The Music of Morton Feldman ed. DeLio, T., Excelsior Music Publishing, New York.Whittall, A. (1977) Music since the First World War J.M Dent & Sons Ltd, London.Wolff, C. (1976) "Christian Wolff WER 60063" Composers Recordings Inc., New York

BibliographyAldridge, A. (2009) Music of Changes and I Ching accessed at http://www.ichingmeditations.com/2009/03/10/john-cage-music-of-changes-and-i-ching/Burton, K. (2015) The New York School accessed at http://moodle.napier.ac.uk/mod/resource/view.php?id=564939 April 2015Cage, J. (1955) Experimental Music: Doctrine I. M. A. Magazine, London, accessed at http://ada.evergreen.edu/~arunc/texts/music/cage3/cage3.pdf April 2015.Cage, J. (1937) The Future of Music: Credo transcript of lecture in Seattle, accessed at http://ciufo.org/classes/ae_sp14/reading/cage_future.pdf April 2015.Cage, J. (2011) Silence: Lectures and Writings, 50th Anniversary Edition Wesleyan University Press, Middletown Connecticut. Cage, J. (1985) A Year from Monday- Lectures and Writings Marion Boyars Publishing, London.Chase, S. & Thomas, P. (2013) Changing the System: The Music of Christian Wolff Ashgate Publishing Limited, Farnham.Covell, G. C. (2006) 1951 and Cages Music of Changes accessed at http://www.lafolia.com/1951-and-cages-music-of-changes/ April 2015Didier, G. & de Andrade F. G. (2001) Earle Browns 25 pianos: a web interactive implementation Federal University of Paraiba, accessed at http://gsd.ime.usp.br/sbcm/2001/papers/rDidier_Guigue.pdf April 2015The Earl Brown Music Foundation (1953) Twenty-Five Pages Edition Peters, accessed at http://www.earle-brown.org/works/view/40 April 2015Edition Peters Group (1951) Imaginary Landscape No. 4 accessed at https://www.edition-peters.de/cms/deutsch/general/produkt.html?product_id=EP6718 April 2015Goldman, J. (2011) The Musical Language of Pierre Boulez: Writings and Compositions Cambridge University Press, Cambridge.Griffiths, P. (1981) Oxford Studies of Composers- Cage Oxford University Press, London.Hedges, S. A. (1978) Dice Music in the Eighteenth Century Music and Letters 59(2), Oxford.Heinbecker, S. J. (2011) John Cages HPSCHD University of Illinois, Illinois, accessed at http://hdl.handle.net/2142/24332I Ching Online (2012) I Ching Online version 3.7 accessed at http://www.ichingonline.net/index.php April 2015Iddon, M. (2013) John Cage and David Tudor: Correspondence on Interpretation and Performance Cambridge University Press, Cambridge.Jeongwon, J & Song H.S. (2002) Roland Barthes Text and aleatoric music: Is The birth of the reader the birth of the listener? Muzikologija, 2 p263-281.Kostelanetz, R. (1989) Conversing with Cage Omnibus Press, New York.Menayan, J. (2012) I Ching Reading Step-by-step Guide accessed at http://hubpages.com/hub/I_Ching_divination April 2015Nicholls, D. (1998) "The Cambridge History of American Music" Cambridge University Press, Cambridge.Nyman, M. (1999) Experimental Music- Cage and Beyond- Second Edition Cambridge University Press, Cambridge.Petrucci Music Library (2008) Musikalisches Wrfelspiel, k.516f, Complete Score accessed at http://imslp.nl/imglnks/usimg/b/bc/IMSLP20432-PMLP47543-mozart_-_dice_waltz.pdfPritchett, J. (1999) The Music of John Cage Cambridge University Press, Cambridge.Roeder, M. T. (1994) A History of the Concerto Amadeus Press, Hong Kong.Silverman, K. (2010) Begin Again: A Biography of John Cage Knopf Doubleday Publishing Group, New York.Thomas, P. (2014) For Pianist accessed at http://cms.philip-thomas.co.uk/wp-content/uploads/2014/05/img008.jpgThomas, P. (2014) Pianist: Pieces CD Liner Notes Sub Rosa, Brussels, accessed at http://eprints.hud.ac.uk/22953/1/Pianist_Pieces_CD_liner_notes.pdf April 2015.Thomson, V. (1970) Twentieth Century Composers 1- American Music since 1910 Weidenfield and Nicolson, London.Vinton, J. (1974) Dictionary of 20th Century Music Thames and Hudson Limited, London.Welsh, J. P. (1994) Open Form and Earle Browns Modules I and II Perspectives of New Music 32(1) pp254-290.Welsh, J. P. (1996) Projection 1 (1950) in The Music of Morton Feldman ed. DeLio, T,, Excelsior Music Publishing, New York.Whittall, A. (1977) Music since the First World War J.M Dent & Sons Ltd, London.Wolff, C. (1976) "Christian Wolff WER 60063" Composers Recordings Inc., New York

Appendix 1I Ching HexagramEach red line represents one throwing of three coins. A broken line symbolises one coin of a different side from the other two. A complete line symbolises three identical sides. The Lower Trigram represents the first three throws from bottom up and the Upper Trigram represents the fourth to sixth throws from bottom up. The two trigrams are then interpreted together on the chart to give a numerical answer from 1 to 64.

(I Ching chart [Menayan, 2012, http://hubpages.com/hub/I_Ching_divination])