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.