Camille Gunter

The Music of John Cage: Exploring Liminal Space through Algorithmic Composition

9 December 2019

Algorithms, used in a variety of ways ranging from algebra to musical composition, are useful in reducing something down to its formal and structural elements. Algorithms allow composers to hold aesthetics and organization in tension. While it’s true that forms and structures are essential in music across cultures and genres, the term algorithmic composition seems to imply a diversion from traditional compositional technique. Traditionally, across musical eras, structures are used to express certain aesthetic decisions and narratives. Algorithms in mid-20th-century music, such as in the music of John Cage, are employed in order to reject a sequential narrative and instead focus on structural elements to expose a different side of music.

Cage sought to explore the results when the ‘story’ is removed and only the structure remains, in order to understand compositional processes and challenge the expectations of audiences. Cage harnessed the power of the algorithm to relinquish the control that any composer works hard to tightly grasp.

John Cage explored the algorithmic techniques scattered across the Medieval, Baroque, and Classical eras and applied them to his own 20th-century compositions to create structures and leave the sonic landscape up to chance. Using grids; ones he created, ones found in divination books and ones computer-generated, Cage was able to explore musical territory that other composers dared not traverse. Examining Cage’s music, we can begin to understand algorithms through a contemporary lens in relationship to structures of music and their evolution over time. Examining how the grid, a means of spatial organization, is used across musical eras to organize music into linear structures is important in understanding how structures in music are used and developed. John Cage used the grid, aleatoricism, and algorithmic composition in order to understand the processes involved in the creation of music. Cage used the grid; a solid,

1 logical, and clearly defined medium to create and explore undefined liminal spaces. A liminal space can be thought of as “a place of transition, waiting, and not knowing. Liminal space is where all transformation takes place, if we learn to wait and let it form us” (“What Is A Liminal ​ Space?”). John Cage sought to explore the vast musical unknown in every way possible. In his ​ 1948 lecture, “A Composer’s Confessions”, he speaks on the unknown: “before we know the unknown, it inflames our hearts. When we know it, the flame dies down, only to burst forth again at the thought of a new unknown” (Cage “A Composer’s Confessions” 67). Not only does ​ ​ he acknowledge the importance of entering a liminal space, he describes the uniquely human need to have faith “not in the peaceful center of the spirit but in an ever-hopeful projection onto things of our own desire for completion” (Cage “A Composer’s Confessions” 67). He ​ ​ understands the human desire to enter an unknown realm in hopes of clawing one’s way out of it, perhaps even shrieking Eureka! By creating liminal spaces in his compositions in which ​ ​ anything can happen, Cage sought to expose the musical unknown and uncharted world for himself and his audiences. He understood the importance of entering liminal spaces and used his music to create these spaces for his listeners; one which granted them the opportunity to question not only the nature of music but also their role and their expectations as the audience of performative music. Because the use of algorithms to explore the unknown allows for composers to explore ideas that tend to reach beyond common practice tonality, and (especially in Cage’s case) give up compositional control, contemporary music tends to be misunderstood and often becomes the punchline of a joke. To understand why John Cage and contemporary music are controversial and tend to receive negative critique from those both in and outside the music world, one must first challenge their own expectations when it comes to musical performances.

2 Cage, through his music, sought to work through liminal spaces, or the unknown, and create a space for his audiences that allowed them to reevaluate their expectations of musical performances. The state of questioning the unknown that he created for his audiences allowed them the opportunity to view music in a new and refreshing way.

The Isorhythmic Motet: Late Medieval and Early Renaissance

Understanding the Medieval isorhythmic motet and its development into the Renaissance period is essential in understanding the development of structures in music. Isorhythm, a celebrated 13th-century technique, employed a linear representation of time and space in music.

This early example of the use of an algorithm in music used a talea; a repeating rhythmic pattern ​ ​ to organize a color; a sequence of pitches (Cope 3). Isorhythm (“iso” Greek for same, meaning ​ ​ literally, “same rhythm”), was originally defined by Friedrich Ludwig in 1904 to describe a repetitive rhythm in the tenor voices of French polyphonic motets originating in the 13th-century

(Lanford 1). This technique became more elaborate in the following century, and the use of the technique in the 13th-century can be viewed as a primitive foreshadowing of the compositions of the ars nova (Harbinson 100). The main difference between the 13th (ars antiqua) and 14th ​ ​ ​ ​ century (ars nova) versions of the isorhythm lie in their complexity and rigidity. The ars nova ​ ​ ​ version tends to possess a wider, more elaborate rhythmic pattern; and appears to abandon the stricter rhythmic modes of ars antiqua (Harbinson 101). ​ ​ French composers of the ars nova, notably Philippe de Vitry (1291–1361) and ​ ​ Guillaume de Machaut (1300–1377) played significant roles in further developing the isorhythm as a means of unification for their compositions (Simoni). In Philippe de Vitry’s treatise documenting the musical development of the ars nova, he developed musical notation and the ​ ​

3 motet in a revolutionary way that allowed for more rhythmic complexity (Bent), and thus, more freedom of expression in music. de Vitry’s most significant contribution to common practice was the concept of time signature; simple and compound, as well as a new method of measuring rhythm, which allowed for more complexity and the implementation of syncopation (Bent). The concept of rhythm as a result of a heightened awareness of time in the Medieval period must be considered. The invention of the mechanical clock, an otherwise nonmusical event, triggered new compositional techniques that focused more on time in music. The division of notes into smaller parts allowed for imperfect rhythmic patterns and combinations, sparking the rise of an emphasis on the second and fourth beats (Higgins 114). Thus, rhythm became more independent of scripture, opening the door for the development of secular music and its potential to be adapted to Church music (Higgins 114). This, unsurprisingly, made the Church and Pope John

XXII uneasy; the prospect of secular and sacred music intertwining prompted a scathing response from the Pope which claimed that “instead of promoting devotion, [composers] prevent it” (Higgins 114). Composer and church official Guillaume de Machaut played an important role in the development of isorhythm and is known for his use of a “staggered effect” in his compositions (Higgins 115). In this case, the melody and meter do not coincide. If a melody exceeds the number of beats in the rhythmic mode, the melody must repeat a number of times until it catches up with the rhythmic mode, only to exceed it again (Higgins 115). Each time they repeat, they coincide at different places; which not only organized the music and gave the tenor line shape but also allowed for the equality of the musical elements. No longer was the focus solely on the melodic line; the rhythm was of equal significance to the music (especially since isorhythms began to expand to other voices beyond the tenor in the 14th century) (“Isorhythm”).

4 20th-century composers Igor Stravinsky and Steve Reich, contemporaries of John Cage, were known to have used this particular isorhythmic technique (Higgins 115). Cage is known for his belief in the equality of musical elements; a system that was heavily emphasized in his compositions. The appeal of isorhythmic technique is understandable. Before the development of rhythmic modes and time signatures, when rhythm was dependent on scripture alone, musical expression was limited. The use of isorhythms allowed for composers to organize music into a linear structure; a talea, to support a color, or a sequential narrative. The idea of a structure ​ ​ ​ ​ supporting a narrative is far from novelty, however examining this early use of an algorithm in music aids in the understanding of algorithmic composition as used by John Cage in the twentieth century.

Bach’s Preludes and Fugues: Baroque

Johann Sebastian Bach (1635-1750) played a significant role in developing contrapuntal styles of music during the Baroque period (1600– circ.1750), such as fugues and canons. Bach’s collection of preludes and fugues, titled The Well-Tempered Clavier, contains two sets of ​ ​ preludes and fugues in every major and minor key. Bach used this particular style of composition which consists of creating a definite, predetermined structure before the piece is written.

Elements such as form, phrase lengths, patterns, and harmonic progression are determined prior to composition (Muscutt & Cope 11). The first prelude in the collection in C major is curious ​ ​ considering its lack of conventional melody and rhythmic differentiation; the repeating pattern only breaking in the last two measures of the piece. The same rhythmic figure is repeated throughout, while the pitches are changed in order to create a solid harmonic progression; which is somewhat reminiscent of the aforementioned isorhythmic motet technique. This prelude, in

5 particular, demonstrates the use of a predetermined rhythmic pattern to give a linear structure to the piece. This quasi-algorithmic technique allowed the composer to master the art of tonality while following a strict and consistent structure. It is also noteworthy that Bach left no performance instructions in reference to musical nuances such as dynamics, tempo, etc. in this prelude. What appears to be a steady, uninterrupted stream of repeating rhythms can be varied in many ways by the performer; in terms of tempo, dynamics, dramatic swells, and rubato. Leaving these important musical elements up to the performer was a forward way of composing; perhaps foreshadowing the mid-twentieth century technique of devising a structure and allowing the performer to take some of the compositional control to make aesthetic decisions that Karlheinz

Stockhausen and John Cage employed (Cook 257). ​ ​ Bach’s fugues and canons also follow predetermined algorithms. Both begin with a melody called the leader, which is followed by another voice at a delayed time interval, called the follower (Simoni). The follower also may vary the melody of the leader through transposition or inversion (Simoni). The difference between the two forms is that a canon’s followers are exact repetitions of the melody; it must be written so that the melody may harmonize with itself, while the follower in a fugue can contain differing themes. The use of harmonic layering using a sole melody in canons may seem contrived, however, it is a fine example of how strict and specific structure can be used to organize a piece of music. The development of bar lines toward the end of the seventeenth century allowed for more rhythmic complexity (Higgins 116). The use of these vertical lines can be thought of as a way of dividing the musical grid to provide a clear visual structure and to show which voices were to sound together. It was not necessarily developed in order to divide the melody equally into measures, which of course it did (Higgins

6 116). Measures and bar lines allowed for division of the beat as well as naturally occurring strong and weak beats in a measure. Bach used this as a tool in his favor; it allowed him more control over the contrapuntal texture of his pieces (Higgins 118). Bach was able to achieve unity in his fugues because of the bar line, without it the interlocking voices would not line up and would make little sense.

The use of the grid in Bach’s works can be understood using a visual representation of the grid, which one cannot easily observe just by looking at his scores. Mid-twentieth century artist Sol Lewitt and his Well-Tempered Grid, named for Bach’s ​ ​ collection of preludes and fugues, had a similar vision to Bach’s. He sought to use the simplest of elements; the grid, to create complex structures. Like Bach, LeWitt “found extraordinary richness in systematic formal logic” (“Sol LeWitt”). Looking at LeWitt’s grids, ​ ​ one can easily observe the connection between the two great artists' work. LeWitt uses the grid to assign each “voice” (represented as lines by Lewitt) has a predetermined course. Each voice (or line) tends to have an assigned color, and one can follow its course and examine its relationship to the other lines. It is important to understand Bach’s grid in a visual sense in order to understand the music of John Cage. Cage’s use of the grid in his music is not unlike Bach’s methods, both composers used this medium to unify and organize music using linear structures. Although Cage would use the grid to abandon tonality and reject a narrative, the connection to Bach’s use of the grid is far too significant to be overlooked.

7 Mozart’s Dice Game: Classical

Algorithms are proven useful in the creation of music and musical structures to support or unify a composition. Algorithms can also be used to create aleatoric composition, which is composition by chance. Wolfgang Amadeus

Mozart (1756–1791), one of the many greats of the Classical period

(1750-1827), explicitly used algorithmic methods in his

Musikalisches Würfelspiel (translates to: “Musical Dice Game”). ​ Mozart developed a system of using dice to randomly generate music from options that he composed, referring to a table containing different (yet related) musical excerpts (Edwards 60). These fragments would be combined randomly according to the sum of the dice throw (Edwards 60). It is important to take note of the visual grid which guides the assembly of the fragments to create the composition. The row of letters A–H refer to the eight precomposed parts of the waltz, the numbers 2–12 in the left-hand column denoting the potential sums of the thrown dice, and the numbers in the matrix are in reference to the individual measure numbers of the excerpts (Edwards 60). The resulting “algorithmic waltz” (Edwards 60), although it has prefabricated elements, is entirely left up to chance. Mozart developed an algorithmic structure, with the help of a grid, in order to explore different precomposed possibilities determined by thrown dice. This is a significant event in the development of algorithmic music since chance compositions were a fairly new idea (although becoming increasingly more popular in the 18th and 19th centuries) (Hedges 180). Mozart may have intended for this composition to be a game, however, it paved the way for a more serious and perhaps more deliberate

8 contemporary art form of aleatoric composition, which John Cage and his contemporaries developed extensively in the mid-20th-century.

John Cage and Algorithmic Composition: Mid-Twentieth

John Cage (1912–1992), one of the most adventurous and controversial American composers, was at the forefront of the avant-garde movement of the fine arts in the mid-twentieth century. In the late 1930s, Cage began to structure all his compositions around time as a result of his early work composing for dancers (Pritchett “What Silence Taught John Cage” 168). His ​ ​ great interest in rhythmic, percussive music also influenced him to devote most of his focus to time and durational structures, since melody and harmony are not an essential part of percussion music of the non-pitched variety (Pritchett “What Silence Taught John Cage” 168). His reliance ​ ​ on and devotion to time in musical structure in his early career helped pave the way for his more ambitious and avant-garde compositions which relied heavily on silence in relation to time

(Pritchett “What Silence Taught John Cage” 168). Much like the shift of focus to time and ​ ​ duration in the Medieval period, Cage’s heightened awareness of time influenced his musical decisions going forward. After experiencing some dissatisfaction with his career and personal life, Cage began to look inward for answers (Pritchett “What Silence Taught John Cage” 169), as ​ ​ many twentieth-century artists did. He became friends with musician Gita Sarabhai, who taught

Cage about aesthetics and practice of Indian music (Pritchett “What Silence Taught John Cage” ​ 169). She famously taught him; “the purpose of music is to quiet and sober the mind, making it susceptible to divine influences,” (Pritchett “What Silence Taught John Cage” 169). Silence and ​ ​ spirituality consequently became significant cornerstones of Cage’s work. In Cage’s lecture, “A

Composer’s Confessions” (1948), he reflects on his time in a new Lower Manhattan apartment

9 which faced away from the city and toward the water; “the quietness of this retreat brought me finally to face the question: to what end does one write music?” (Cage “A Composer’s ​ Confessions” 65). He began to ponder the role of silence in music. During his early career, ​ Cage’s experimentation with percussion instruments in order to create as many sounds as possible resulted in durations of time that were full of sound (Pritchett “What Silence Taught ​ John Cage” 168). Leading into 1951 however, Cage began to focus on the antithesis of noise– ​ silence. Using the same time structures used in his earlier career, he began to think of music being built out of blocks of time, in which sound or silence could occur (Pritchett “What Silence ​ Taught John Cage” 171). Cage’s 1950 “Lecture on Nothing” speaks on time as a structure for ​ music; “this space of time is organized. We need not fear these silences, we may love them”

(Cage “Lecture on Nothing” 109). He also notes that in the duration of the lecture, “I can say anything. It makes very little difference what I say or even how I say it.” (Cage “Lecture on

Nothing” 112). Cage implies that in composition, (much like in this lecture) the content is far less significant than the structure itself. Like Bach, Cage understood the importance of comprehensive structures and algorithms in music. Unlike Bach, Cage used these algorithms to reach beyond standard tonality and gradually abandon compositional control. Like Mozart, Cage used algorithms to create aleatoric music. Unlike Mozart, Cage saw this as a legitimate compositional form and developed upon this concept throughout his career. His increasing interest in Zen Buddhism is evident here; the belief that significance lies not in what something represents, but instead in what it is. One of his main goals was also to rid his compositions of his own tastes and ego; which is undeniably Buddhist in principle. Cage’s newfound devotion to time structures for their ability to allow anything to happen also facilitated his belief of the

10 equality of sound and silence (Pritchett “What Silence Taught John Cage” 172). Cage was a firm ​ ​ believer in the importance of silence in music and its equality to sound.

In John Cage’s String Quartet in Four Parts (1950), he began to experiment with silence ​ ​ ​ ​ in a different sense while exploring Indian philosophy in this four-movement piece. With this piece, he set out to use chords without a harmonic progression, this being one of his first steps towards non-sequential music. This departure from traditional common practice is deliberate as it is forward-thinking. Cage’s String Quartet contained chords without relation to one another, ​ ​ while the pitches of the melody are defined by a particular chord (Pritchett “What Silence Taught ​ John Cage” 172). This means that chords are always defined by a certain pitch (or pitches) which ​ he called gamuts; the outlining gamut serving as the structure, while the chord in the middle was chosen more freely. Cage experimented with the idea of “letting sounds appear freely within the silence of his time structures” (Pritchett “What Silence Taught John Cage” 173). The ‘silence’ of ​ ​ this piece was not silence itself (he would explore and develop true silence in later works) but within the lack of harmonic progression, which can be thought of as a narrative. If a chord progression tells a sequential story, Cage sought to reject the use of a story. In Cage’s own words to his parents, he sought to “praise silence” (Pritchett “What Silence Taught John Cage” 172) ​ ​ without actually using it yet. Because he is rejecting a cohesive, sequential narrative in favor of a spatially organized musical algorithm, he is expressing silence as the antithesis of a story. The harmonies of the String Quartet praise silence because “they have nothing to say about harmonic ​ ​ theory” (Pritchett “What Silence Taught John Cage” 172). This piece is a form of commentary ​ ​ on traditional practice that allows the listener to hear sonorities and harmonies in a new way, as individual entities, and not just in relationship to one another. Rather than express his own

11 internal emotions through his music, Cage’s goal circled back to the idea of quieting the mind, perhaps for the susceptibility to divinity. Cage uses his medium of music as a means of going inward to explore an unseen world. This particular quartet indeed sobers the mind, and it seems to float peacefully by with no sense of time whatsoever. Herein lies Cage’s genius; he in fact deliberately created blocks of time with extra attention to duration, as time was in the front of his mind in 1951 and beyond. This piece deceptively seems lackadaisical in terms of the passage of time, when in reality it is quite the opposite.

John Cage’s use of a strict algorithm to create indeterminate music continued to develop throughout the decade. A pioneer of indeterminacy, Cage sought to explore possibilities of music that would be performed differently every time as a result of aleatoric compositional technique.

He began to understand that building structures on silence produced different and exhilarating results; his discovery of silence gave him exciting newfound freedom in his compositions. 1951, arguably the most important and pivotal in his career, was the year Cage began including chance operations in his music. The first notable example of this is his Concerto for Prepared Piano and ​ ​ ​ Chamber Orchestra (1950–51). Cage’s prepared piano (his own 1940 invention) consisted of a ​ variety of objects inserted in between the strings; such as bolts, screws, strips of plastic, rubber, and more (Pritchett “From Choice to Chance” 56). This piece marks the first time Cage explicitly ​ ​ used a grid to organize the sounds. He described the chart he created and used in the compositional process in these terms: “14 by 16. That is to say, 14 different sounds produced by any number of instruments. . . each sound is minutely described in the chart: e.g., a particular tone. . . I then made moves on this chart of a ‘thematic nature’ but, as you may easily see, with an athematic result” (Pritchett “From Choice to Chance” 57). Geometric patterns would be traced ​ ​

12 along this rectangular chart to compose the music, using a quasi-aleatoric technique. This piece ​ also marked his first use of the I Ching, also known as the Book of Changes. This Chinese oracle ​ ​ book, to help guide his compositional process. The musical events could be chosen by tossing a coin to consult the I Ching to decide if sound or silence was to be placed in the measure in ​ ​ question (Pritchett “What Silence Taught John Cage” 173). If sound was chosen, Cage would then consult to book to see which of the predetermined musical events/sounds were to be entered, notate it, then move onto the next musical event and repeat this randomized process.

His belief in the equality of sounds and his wish to separate the artist’s personal touch from the art is also evident in this piece. Cage’s athematic methods using this grid allowed him to reject a sequential narrative. The first movement contains free composition techniques in the piano part, which Cage spoke on: “I let the pianist express the opinion that music should be improvised or felt, while the orchestra expressed only the chart, with no personal taste involved”

(Pritchett “From Choice to Chance” 57). Much like in Mozart’s dice game, Cage uses this grid to ​ ​ relinquish compositional control. Unlike the orchestra, the piano part has no predefined gamuts of sound. Besides the preparation of the piano, the part is entirely improvised around a few repetitive patterns of notes (Pritchett “From Choice to Chance” 58), not unlike those found in ​ ​ isorhythmic motets of the Medieval era. Using a two-dimensional grid to represent the gamut not only allowed Cage to spatially organize sonic possibilities, but also provided an adequate structure to allow for chance technique in the piano part.

John Cage’s Imaginary Landscape No. 4 (1951), the fourth piece in a series of five, is a ​ ​ fine example of chance operations in his music, and one of his first explorations of electronics in music. This is an important landmark in Cage’s career, considering his experimentation with and

13 usage of computer music later in that decade. Imaginary Landscape contains parts for twelve ​ ​ radios and twenty-four performers, two performers stationed at each radio. One performer controls the dial for different stations, while the other controls volume and timbre. The score contains indications for tuning, amplitude, and tone color (“Imaginary Landscape No. 4”). ​ ​ Because radios will create an unpredictable sonic landscape, Cage’s intention was achieved perfectly. The structure of this piece lies in the numbers 3–15 which indicate volume (3 being on ​ but inaudible, 15 being loudest possible volume) (“Imaginary Landscape No. 4”). Devising this ​ ​ ​ algorithm to create a structure and leaving the entire rest up to chance was a considerable step forward in Cage’s career as he began to widen the liminal space that he worked through. With extensive use of the I Ching, Cage composed Music of Changes in 1951 (“Music of Changes”). It ​ ​ ​ ​ ​ ​ was named for the oracle book, and the title aptly chronicles the changes in his compositional language in 1951 onward. Again using this book to derive charts for chance operations, Cage created a piece using chance entirely for the first time. This book contains sixty-four hexagrams represent results of coin tosses, which provided random numbers which helped Cage derive said charts (Husarik 2). The structural elements are similar to his preceding aleatoric compositions, again using the charts as parameters that would decide musical events of sound and silence; dynamics, tempi, durations, superimpositions, and other musical events (“Music of Changes”). ​ ​ Using the grid and conventional notation in full detail, Cage developed on his experimentation with different sonic possibilities. The pianist would produce sounds reaching far beyond just the keys; such as by plucking the strings, striking and slamming the lid, and using various beaters meant for percussion instruments to strike the strings (“Music of Changes”). Once again, Cage ​ ​ used the grid and a chance algorithm to eliminate a narrative. If Concerto for Prepared Piano is ​ ​

14 Cage’s toe-dip into chance composition, Imaginary Landscape No. 4 and Music of Changes ​ ​ ​ serve as a complete head-first dive into a vast and liminal world. Music of Changes helped Cage ​ ​ develop his goal of abandoning traditional creative processes and incorporation of individual touch in music. Although the piece is composed using chance the actual performance is entirely determined and fixed, unlike in Imaginary Landscape No. 4, which lets the unpredictable nature ​ ​ of radios determine the performance of the composition within the allotted time structure.

In subsequent compositions, John Cage would further explore and develop liminal space in composition. Later in his career, Cage worked with Lejaren Hiller, a contemporary and friend, to create HPSCHD (1967-69) (computer abbreviation of harpsichord and pronounced ​ ​ accordingly). A monumental piece in his exploration of computer music, this piece also documents Cage’s interest in Zen Buddhism. Cage describes this piece and his method of composition: “after studying the philosophy of Zen Buddhism with Diasetz Suzuki, I became interested in finding ways of composing that would free the music, free the sound from my memory and my likes and dislikes.” (Husarik 2). Cage speaks on Buddhist philosophy which is

“completely free of hierarchy” and so “the octave, then, has no more reason being divided into 5,

6, 7, 8, or 9 equal intervals than it has to be divided into 34, 43, or 56 parts, and it’s just a question of establishing limits. I can’t see the idea of superimposing all those various divisions of the octave (as I did in HPSCHD) arising in a structure influenced by our (Western) way of ​ ​ thinking” (Husarik 2). Cage set out to explore computer-generated algorithms in order to understand compositional processes, he once said; "it is the machine that will help us to know ​ whether we understand our own thinking processes”. Although he was indeed a pioneer in the emerging medium of computer music, Cage may have also understood algorithms used across

15 musical eras as “machines”, ones that could be used to structure music and thus develop what we have come to expect of music. Using the concept of microtonal gamuts, Cage would develop ​ upon algorithms to create randomly generated music, this time with the aid of computers. The

University of Illinois invited Cage to compose chance music using their highly advanced computer music facilities, which he first used to devise a system of 6,000 hexagrams from the I ​ Ching which would randomly generate numbers for him as well as microtonal gamuts (Husarik ​ 2). This program, named ICHING, randomized gamuts, pitch details, musical events in solo ​ ​ parts; and the printouts created visual portions of HPSCHD (Husarik 2). The resulting ​ ​ composition, seven solo pieces for one to seven harpsichords and fifty-one computer-generated tapes, created the ultimate indeterminate concert (“Music of Changes”). Said tapes were created ​ ​ ​ from randomly computer-processed pieces by Mozart, Beethoven, Chopin, Schumann,

Gottschalk, Busoni, and Schoenberg; as well as Cage and Hiller themselves (“Music of ​ ​ Changes”). The references to Mozart in the first solo pieces are derived from his Musikalisches ​ ​ ​ Würfelspiel in a program Cage named DICEGAME (Husarik 7), a deliberate nod and Cage’s way ​ ​ ​ ​ ​ ​ ​ of paying homage to Mozart’s classical-era algorithmic chance composition. The epitome of indeterminate music; HPSCHD, allowed Cage to explore algorithms in a new way. Using ​ ​ computers, which in this decade still took up the square footage of several large living rooms,

Cage was able to create music that was left entirely up to random chance, and was thus objective and completely separate from his own ideas, memory, and ego. Using the grid, computerized this time, Cage continued to explore the liminal world of indeterminate music and brought audiences a new and futuristic version of chance composition.

16 This brings us to 4’33” (1952), a piece for which John Cage is most famous (or perhaps ​ ​ infamous is a more accurate word). Though it was composed before he was invited to utilize

Illinois’ computer music programs, the creation of this piece marks his most important encounter with silence. Consisting of four minutes and thirty-three seconds of utter silence, Cage created liminal spaces for his audiences like never before. As an audience member, one may encounter this piece with apprehension, or perhaps newfound awareness of the ambiance and a multitude of previously unnoticed sounds. One may also consider the philosophical and political statements behind this performance, or grapple with the meaning behind the piece and what the composer meant to say. However, we must again consider Cage’s deliberate rejection of a statement or story in the previously discussed cases. Forcing a statement onto this piece would be to defeat its purpose. Critics, audiences, and music students in circle discussions tend to grossly misinterpret

Cage’s music when they begin by asking questions such as What is music? Can this be ​ considered music? Viewing Cage’s compositions from this philosophy of aesthetics point of ​ view may be the wrong place to begin. His music diverges from traditional practice deliberately in order to explore music’s unanswered questions; What does music look like when the story is removed and only the structure remains, or when the structure creates conditions for chance operations? What happens when the ‘stuff’ in a piece of music is left up to the performer, or left up to chance entirely? To look at Cage’s works from the superficial lens that it often is viewed through is to ignore his intention and perhaps turn a blind eye to the unseen world that Cage attempted to expose for his audiences. The authority of Cage’s music tends to be questioned as well, since from 1951 onward, his music contains elements of chance, sometimes entirely left up to chance. This, in consideration with the removal of the composer’s personal influence and

17 personality, causes audiences to argue against Cage’s authorship of his own music. In the introduction to The Music of John Cage (1993) by James Pritchett (a scholar of John Cage), he disagrees yet sympathizes with this approach, and asks “how does one judge the toss of a coin?”

(Pritchett The Music of John Cage). Pritchett argues that since the composer originated these ​ ​ ​ ideas, he is indeed the composer. However, they must be evaluated independently of traditional and conventional music practices, since his works using chance and silence, especially 4’33”, ​ ​ were never meant to be viewed as aesthetic products. Doing so would only take away from the opportunity Cage is allowing us to experience silence. 4’33” can be thought of as a reminder of ​ ​ the existence of silence, perhaps a question of whether silence exists; however Pritchett also argues that that the fundamental flaw with this piece is that it implies someone else can provide one with the experience of silence. Cage is giving his audience a small block of time consisting of silence, throwing them into an uncomfortable, yet, liminal space. Cage recognized the importance of entering this space, one which he delved into deeply, as evidenced by the aforementioned compositional case studies; because to ask questions or be uncomfortable is the first step in understanding a new truth. He also caused his audiences to question their expectations when entering the concert hall; why do we expect to receive information in the form of a narrative in musical performances? What happens when these expectations are not met? In

Cage’s case, he sought to allow people a small window (AKA, block of time) to experience silence and his liminal world. This experience would not end at four minutes and thirty-three seconds however, or so he hoped; perhaps the audience would become aware of Cage’s unseen, unknown, and sonically beautiful world.

18 Works Cited

Alsop, Roger. “Exploring the Self Through Algorithmic Composition.” Leonardo Music Journal, ​ ​ vol. 9, 1999, pp. 89–94. JSTOR ​ Bent, Margaret and Andrew Wathey. "Vitry, Philippe de." Oxford Music Online. 2 Feb. 2009 ​ ​ Cage, John. “A Composer’s Confessions” (1948), MusikTexte Nos. 40/41, August 1991, p. 65.

Cage, John “Lecture on Nothing,” Silence, pp. 109–10. ​ ​ Cook, Nicholas. “Structure and Performance Timing in Bach's C Major Prelude (WTCI): An

Empirical Study.” Music Analysis, vol. 6, no. 3, 1987, pp. 257–272. JSTOR/ ​ ​ ​ ​ Cope, David. The Algorithmic Composer. A-R Editions, 2000. ​ ​

Edwards, Michael. “Algorithmic Composition.” Communications of the ACM, vol. 54, no. 7, Jan. ​ ​

2011, p. 58., doi:10.1145/1965724.1965742.

Fowler, John W. “Algorithmic Composition.” Computer Music Journal, vol. 18, no. 3, 1994, pp. ​ ​ 8–9. JSTOR ​ Haskins, Rob. "Aspects of Zen Buddhism as an Analytical Context for John Cage's Chance

Music." Contemporary Music Review 33.5-6 (2014): 616-29. Web

Harbinson, Denis. “Isorhythmic Technique In The Early Motet.” Music and Letters, vol. 47, no. ​ ​

2, 1966, pp. 100–109., doi:10.1093/ml/47.2.100.

Hedges, Stephen A. “Dice Music In The Eighteenth Century.” Music and Letters, vol. 59, no. 2, ​ ​

1978, pp. 180–187., doi:10.1093/ml/59.2.180.

Higgins, Hannah. The Grid Book. MIT Press, 2009. ​ ​

Husarik, Stephen. “John Cage and LeJaren Hiller: HPSCHD, 1969.” American Music, vol. 1, no. ​ ​

19 2, 1983, pp. 1–21. JSTOR, www.jstor.org/stable/3051496. ​ ​

“Imaginary Landscape No. 4” (March No. 2).” John Cage Complete Works, ​ ​ ​ ​

https://johncage.org/pp/John-Cage-Work-Detail.cfm?work_ID=104.

“Isorhythm.” Ars Novita, 22 Sept. 2012, https://arsnovita.wordpress.com/medieval/isorhythm/. ​ ​

Muscutt, Keith, and David Cope. “Composing with Algorithms: An Interview with David Cope.”

Computer Music Journal, vol. 31, no. 3, 2007, pp. 10–22. JSTOR. ​ ​ ​ “Music of Changes.” John Cage Complete Works, https://www.johncage.org ​ ​ ​ ​

/pp/John-Cage-Work-Detail.cfm?work_ID=134.

Pritchett, James. The Music of John Cage. Cambridge Univ. Press, 2009. ​ ​

Pritchett, James. “From Choice to Chance: John Cage's Concerto for Prepared Piano.”

Perspectives of New Music, vol. 26, no. 1, 1988, pp. 50–81. JSTOR. ​ ​ ​ Pritchett, James. “What Silence Taught John Cage: The Story of 4’33”.’’ 2009. pp. 166-177 ​ ​

Simoni, Mary. “Algorithmic Composition: A Gentle Introduction to Music Composition Using

Common LISP and Common Music.” Scholarly Monograph Series, 2003. Michigan ​ ​ ​

Publishing, doi:10.3998/spobooks.bbv9810.0001.001. ​

“Sol LeWitt: The Well-Tempered Grid.” Williams College Museum of Art, ​ ​

https://wcma.williams.edu/sol-lewitt-the-well-tempered-grid/.

“What Is A Liminal Space?” Liminal Space, ​ ​ https://inaliminalspace.org/about-us/what-is-a-liminal-space/.

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