Introduction
The structural importance of time in John Cage's music is well recognized. As Cage himself has stated, "What is the most important element of music? The element of time."1 This concern with time can be traced back to his early works from the 1930s and 1940s, where he first formulated his concept of musical structure. In his 1949 essay Forerunners of Modern Music, Cage explains, "Of the four characteristics of sound, only duration involves both sound and silence. Therefore, a structure based on durations (rhythmic: phrase, time lengths) is correct (corresponds with the nature of the material), whereas harmonic structure is incorrect (derived from pitch, which has no being in silence)."2
This conclusion was formed, according to Cage, through his association with modern dance and percussion music. In many instances Cage was writing music for completed dances, forcing him to compose to pre-existing phrase lengths given by the dance. Also, because many percussion instruments lack pitch, harmony or melody could not be used to create structure for these works. Cage succinctly sums up the influences when he states, "Two facts that led to structural rhythm: the physical nature of the materials with which I was dealing [percussion], and the experience I had in writing within the lengths of time prescribed for me by modern dancers."3
Recent studies have revealed hierarchies of micro and macro rhythmic structure operating in Cage's early works.4 While many of these analyses also stress the importance these rhythmic structures had on his later pieces, little has been offered detailing the specific temporal relations between his early and later works.5 What are the specific ways in which Cage structured musical time in diverse works from different periods, and are there relationships?
Through analyses of A Room for solo prepared piano from 19436, and Ryoanji for solo parts with percussion from 1983-84,7 I argue there are two specific and related ways Cage uses time in early and late works. First, both A Room and Ryoanji project multiple temporal layers simultaneously. A temporal layer is defined as musical material that has a distinct temporal identity created through rhythm, meter, repetition, or accent. Second, regularity of pattern is often de-emphasized and irregularity emphasized through both the superimposition of multiple temporal layers and anomalies within each layer.8 Although I will focus on only two pieces, these temporal characteristics exist in many other pieces by Cage from his early, middle and late periods including Sonatas and Interludes (1946-1948) for prepared piano, HPSCHD (1969) for a variety of sound sources, Apartment House 1776 (1976) a "musicircus" for any number of musicians, and Europera I-V (1987-1991) a type of opera. In his later works like Apartment House 1776 and Europera, Cage extends the idea of simultaneous multiple temporal layers operating within a single piece, to multiple pieces operating simultaneously that project multiple temporal layers. For example, Apartment House 1776 has four vocal soloists each singing a different type of American spiritual song; Protestant songs, Sephardic songs, African-American calls and hollers, and Native American songs.9 For his Europera works, this idea was extended beyond sound to include aspects of theater such as lighting, costumes and stage action.
I begin with an analysis of A Room followed by Ryoanji, defining and discussing the temporal layers for each, and the irregularity of pattern achieved through both the superimposition of these layers and anomalies within each layer. Despite their sonic and even conceptual differences, both pieces show striking temporal parallels.
A Room
The immediate background to the early experimental music needs to be traced back no further than the rhythmic structures that Cage used in the thirties and forties.10
A Room is a revealing example from these innovative years. Originally intended as the third movement of a nine-movement suite, only four movements were completed. The first two movements were published as She is Asleep, the third movement as A Room, and the eighth movement remains unpublished.11A Room creates four distinct temporal layers created through surface rhythm, duration expressed by measure number, repetition of musical material, and timbre differences made by the piano preparations.
Surface Temporal Layer
The surface temporal layer for A Room, defined by the surface attack rhythm, is composed of even eighth notes. Although different pitches have different durations throughout the piece, this surface rhythm never changes until the ending whole note on e'. Thinking in terms of Kramer's "linear" and "nonlinear" categories for musical time, this surface layer could be viewed as "nonlinear" in the sense that it does not progress, remaining the same for the entire piece.12 This surface layer is the only temporal layer in the piece with a consistently regular pulse. Bubbling underneath this static surface layer, however, is a rich world of temporal activity filled with a variety of pulsating rhythmic layers.
Durational Temporal Layer
In the score for A Room Cage states the "rhythmic structure is 2 (4, 7, 2, 5, 4, 7, 2, 3, 5)."13 This rhythmic structure or durational temporal layer is defined by the number of measures used for each melodic pattern. The numbers in parentheses refer to the number of measures used for each repeating melodic pattern, and the two outside the parentheses means this measure number sequence is stated twice, dividing the piece into two sections. For instance, as shown by examples 1a and 1b the first melodic pattern takes place in four measures, and the second, distinguished from the first by the addition of d", takes place in seven measures.
Example 1a. First duration of four measures, mm. 1-4.
Example 1b. Second duration of seven measures, mm. 5-11.
On the macro level, the work's durational temporal layer is duplicated exactly (by being repeated); on the micro level, note the near-exact internal duplication embedded in the durational structure—only the 3 that occurs before the final value of 5 inflects the structure's internal symmetry (4, 7, 2, 5 - 4, 7, 2, 3, 5). This added 3 both extends and adds irregularity to the second section of the piece. The pattern of surface repetition that results, however, is not as clear as this scheme seems to indicate. Cage does not realize his durational layer as four repetitions of a melodic pattern followed by seven repetitions of a different pattern, followed by two of another, and so on; an entirely different temporal layer emerges as a result of a separate pattern of melodic repetition superimposed on this durational temporal scheme.
Repetitive Temporal Layer
The repetitive temporal layer is defined by the number of times each melodic pattern is repeated. As shown by example 2, the number of actual melodic repetitions creates its own numerical sequence.
Example 2. Repetitive temporal layer numerical sequence.
While the durational temporal layer is identical for both sections, example 2 reveals that the repetitive temporal layer for each section is more unique. The number of repetitions for each melodic pattern coincides only four times between sections. In the first part the first and third 4 and first and second 2 coincide with the second part (highlighted by the rectangles). Every other repetition of material between sections is unique. Also, the total number of repetitions expands from 26 in the first section to 28 1/2 in the second section. This repetitive expansion can be viewed as paralleling the durational expansion mentioned earlier with the insertion of the added 3 before the final 5.
Example 3 shows the repetitive temporal layer compared to the durational temporal layer. The numbers on the outside show the number of measures or durational layer, the inside numbers with the "x" show the number of actual melodic pattern repetitions or repetitive layer, and the parentheses show variations in repetition either at the end or beginning of the pattern.
Example 3. Repetitive temporal layer compared to the durational temporal layer.
Outer number = durational layer
Inner number = repetitive layer
( ) = variations in melodic pattern
Because the durational and repetitive temporal layers are often unequal, there is a constant shifting of repetitive patterns in relation to the measure, subverting any clear sense of meter and increasing irregularity for the piece. For example, in the first section the pattern in the first durational layer 5 begins on the downbeat of beat one, but because the repeated sequence is one beat longer than the measure, it begins again on the downbeat of beat two in the second measure. The next repeat begins on the third beat of the third measure, and the fourth and final repeat of the pattern starts on the fourth beat of the fourth measure and ends on the last beat of measure five. This type of displacement, however, does not occur in durational layers 4 and 2 for both sections, and in the second durational layer 7 of the second section. In addition to the surface, durational, and repetitive temporal layers, there is a fourth temporal layer based upon timbre, which is created through the preparations.
Timbral Temporal Layer
Timbre can be used to form distinct temporal identities. Borrowing from "Gestalt" psychology, Deutsch and Shepard discuss ideas of "proximity" and "similarity" in relation to timbre, as well as other musical elements such as dynamics, register and time.14 As they demonstrate, sounds that are similar in timbre, dynamics, register, and close in time, tend to be grouped together. As Deutsch states, "Tones can also be grouped together on the basis of sound quality, or timbre. This is an instantiation of the principle of similarity...when different instruments play in parallel, we may form groupings based on their timbres even when their pitch ranges overlap heavily."15
The preparations indicated for A Room create three specific timbres that are intimately linked with pitch and register, resulting in distinct rhythmic pulsations. These distinct pulsations based on timbre create what I call a timbral temporal layer. Example 4 shows the three types of timbres created by the preparations in relation to pitch.
Example 4. Three types of timbre created by preparations.
The first timbre, constantly heard throughout the piece, is associated with the pitches d', eb', e', and f', which are all prepared by bolts creating a gamelan-like sound. The second timbre is associated with the pitch d", which is not prepared at all, and g", which is prepared using rubber, creating a slightly muted piano sound. Because the preparation for g" does not alter the sound of the piano pitch dramatically, the piano-like sounds of d" and g" are grouped together. The lowest pitch d is used for the third timbre, which is prepared using a penny and weather stripping resulting in a buzz-like sound.
While the first timbre created by the middle group of pitches (d'-f') projects the even eighth note surface layer, the second (d" and g") and third timbres (d) create their own unique pulsations that result in distinct timbral rhythmic layers. For instance as shown by example 5, in mm. 5-13 the piano timbre of d" (highlighted by the beamed stems) is played periodically with a total of ten attacks.
Example 5. Timbral layer on d", mm. 5-13.
Timbrally distinct from the gamelan-like timbre of the middle pitches (d'-F), these ten piano sound attacks result in a discrete temporal layer. This timbral layer (example 6a), as well as every other timbral layer for the piece, is shown by examples 6a-g.Example 6a shows a repeating oscillating pattern of a single d" attack followed by five eighth-note rests, and then another single d" attack followed 7 eighth-note rests. Only between mm. 11-12, where this timbral layer overlaps with the repetitive layer, does the pattern change, shifting to three eighth-note rests instead of five. Like the durational and repetitive layers, Cage overlaps timbral and repetitive layers, and thus increases the amount of irregularity in the pattern.
As shown by example 7 and example 6b, another timbral layer occurs at m. 19 with the introduction of the buzz-like timbre on d, which is attacked twice.
Example 6a-g. Timbral layers showing eighth note durations between each attack.
Number = number of eighth note durations between each pitch
a. mm. 5 - 13
d" d" d" d" d" d" d" d" d" d" 5 7 5 7 5 7 5 3 7
b. mm. 19 - 21
d d 15
c. mm. 30 - 34
d" d" d" d" 7 10 11
d. mm. 44 - 52
d d" d d d" d d" d d d" g" d" d" g" d" d" 7 5 7 4 7 5 7 4 1 4
e. mm. 59 - 61
d" d" d" 15 2
f. mm. 62 - 68
d d d d 15 15 15
g. mm. 69 - 73
d" g" d" d" g" d" d" d" d" d" 4 1 4 4 10
Example 7. Timbral layer at mm. 19-22.
The pitch d is notated as a whole note and sounds on the downbeat of m. 19 and m. 21. This results in a two beat rhythmic layer separated by 15 eighth-note rests. Because the buzz-like timbre of d is unique and is emphasized through a whole note duration, a distinct temporal layer emerges. Notice, however, that d' at m. 20 and m. 22 is also notated as a whole note, but is not part of the d temporal layer due to the homogeneity of sound with the other pitches eb', e' and f'. This moment highlights the critical difference between the unprepared and prepared piano versions of the piece. If played without preparations the piano sound and whole-note duration of d would more easily merge into the piano sound and whole-note duration of d', creating a composite temporal layer. Rather than two attacks of d separated by 15 eighth-note rests, this alternate layer would consist of d, seven eighth-note rests, d', seven eighth-note rests, d, seven eighth-note rests, and d'.
Finally, as shown by example 8 and example 6d the timbral layer at mm. 44-52 is an exciting, climactic moment for the piece.
Example 8. Timbral layer at mm. 44-52.
This is the only time both the piano sound of d" and the buzz-like sound of d are combined within the same repetitive layer, and the piano-like sound of g" is introduced for the first time. The simultaneous interplay of all three timbres creates a unique, constantly shifting mosaic of pulse and sound. Unlike the surface, durational and repetitive layers, all of the seven timbral layers shown in example 6a-g are completely unique, further increasing the amount of irregularity within the timbral temporal layer.
A Room, therefore, exhibits a rich temporal life that projects two distinct characteristics. First, multiple temporal layers (surface, durational, repetitive, and timbral) are played simultaneously, sometimes coinciding and sometimes overlapping with one another. Second, irregularity is emphasized through these juxtaposed temporal layers, but also through irregularities within the temporal layers themselves. For example the durational layer has an added 3 measures at the micro level for each section, the repetitive layer shows only four correspondences between sections, and every timbral layer is completely unique. Moving from durational to repetitive to timbral layers, the number of irregularities within each layer increases. Ryoanji, a later work by Cage that is radically different from A Room in both sound and concept, exhibits similar temporal characteristics.
Ryoanji
Ryoanji written four decades after A Room takes its' name from the Ryoanji Zen Buddhist rock garden in Kyoto, Japan, which consists of fifteen stones placed in a rectangular bed of raked sand. These basic elements of the garden, the raked sand and stones, find their musical analogies in Ryoanji through the percussion and solo parts. The percussion part represents the sand of the garden and the solo parts represent the stones.16 Whereas the percussion part must always be played in performance, the solo parts can be mixed and matched in any combination.
Ryoanji creates two distinct temporal layers. The first, which I call the pulse layer, is defined by the percussion part consisting of a rhythmic pulse composed entirely of traditionally notated quarter beat attacks and rests. The second, which I call the glissandi layer, is defined by the solo parts consisting solely of proportionally notated glissandi lines. The solo instruments enter and exit depending on where their parts fall relative to the visual score. Unlike A Room, therefore, Ryoanji uses both traditional and proportional notation to enhance temporal difference for each layer.
Pulse Layer
What I wanted to do, was to find a way not to know what the beat was, even though what I'd written would be measured.17
The pulse temporal layer, which is played by "At least two only slightly resonant instruments of different material," begins and ends the piece.18Ryoanji represents the first time in thirty years Cage uses a prominent pulse in his music. This pulse is conventionally notated as measures lasting 12, 13, 14, or 15 quarter beats, is played slowly, and the players can begin anywhere in the part. Example 9 shows a measure lasting 12 quarter-note beats.
Example 9. Measure lasting 12 quarter-note beats.
The pulse layer creates a sense of stasis and irregularity, both of which appear to exist simultaneously. Although the specific order in which attacks and rests appear is never predictable (in other words, no clear repeating patterns emerge), there is subtle repetition within the pulse layer. Based on my own hearings I would describe the pulse layer as a sonic illusion—an auditory experience that would seem impossible.19 How does Cage achieve this affect? In order to try and answer this question I have calculated the frequency of occurrence for each of the four types of measures (12/4, 13/4, 14/4, or 15/4) and individual attacks and rests.
Example 10 lists every attack and rest pattern in the pulse layer (* = quarter note attack and number = quarter note rests) along with specific totals. In order to more easily compare the content of each measure, however, they are listed out of their actual temporal order. In other words, example 10 is simply a tabulation and is not related to the order in which they appear in the part. Each measure (12/4, 13/4, 14/4, 15/4) is listed horizontally above, and the attack and rest patterns for each are below. As shown by example 10, there is a virtual absence of repetition of measure patterns. Out of seventy-seven total measures only three repeat, indicated by brackets. Along with the slow tempo for the part, this contributes to the overall sense of irregularity in these attack and rest patterns for the pulse layer.
Looking at these patterns of attack and rest more closely, however, certain commonalities emerge. For example, the most frequent type of attack in the pulse layer, occurring 255 times, is a single quarter beat surrounded on each side by at least one rest. The next most frequent, occurring 58 times, is a successive attack of two beats, and the least frequent is a successive attack of three beats, occurring only three times. Interestingly, each time there are three successive attacks, they occur between measures, i.e., the attacks at the end of one measure carry over to the beginning of the next measure. Example 11 shows the most frequent attack patterns.
Example 11. Most frequent attack patterns.
|
One attack |
255 |
Two successive rests, occurring 107 times, is the most frequent rest pattern followed by one rest occurring 99 times and three successive rests occurring 94 times. With the appearance of four, five and six successive rests the frequency drops dramatically. Example 12 shows the most frequent rest patterns.
Example 12. Most frequent rest patterns.
|
Two successive rests |
107 |
The pulse layer, therefore, is dominated by single attacks separated by one, two or three successive rests, but when and where these single attacks occur is still irregular and unpredictable, not based upon any obviously perceivable pattern. The first measure in the pulse layer, shown in example 13, displays these governing details.
Example 13. The first measure displaying the most frequent surface rhythms.
Due to the predominance of single attacks and one, two or three successive rests, the remaining attack and rest patterns become anomalies within the pulse layer. With the addition of two or three attacks in a row, and four, five or six successive rests, irregularity is enhanced. Example 14 shows where these anomalies occur within the pulse layer.
Example 14. Anomalies within the pulse layer.
The horizontal line of numbers, read from left to right, represent the quarter beat measures (either 12, 13, 14, or 15) in the order they appear in the score. The three repeated quarter beat measures, and the less frequent attack (two or three) and rest (four, five or six) patterns are indicated above and below. Notice the relatively even distribution of the anomalies within the pulse layer—a paradoxical situation—but one that helps explain why this temporal layer is both static and dynamic, predictable and yet unpredictable, simultaneously.
Glissandi Layer
. . . as much as is possible like sound events in nature rather than sounds in music.20
The glissandi layer, played by the solo parts, is written using proportional notation and the soloists play according to the visual placement of their part in the score. (attack/duration/release).21 Cage wrote five solo parts for Ryoanji including ones for flute, oboe, trombone, bass, and voice. Each soloist has eight pages of four rectangles, within which their notation appears (the Ryoanji garden is also in the shape of a rectangle). The vertical axis of each rectangle represents pitch and the horizontal axis represents time. The soloists enter and exit the piece depending upon the proportional notation.
Due to the relatively long sustained glissandi, lack of repetition and the use of proportional notation, the solo parts sound non-pulsed, resulting in a unique temporal layer distinct from the pulse layer (the obvious timbral differences also contribute to temporal distinction between layers). In addition, density can also be viewed as an important factor that contributes to the uniqueness of the glissandi layer.22
Example 15 shows the totals for high (H), medium (M) and low (L) density levels.
Example 15. Density totals for each solo part.
Number = number of rectangular boxes of the score for each density level
| Oboe | Flute | Voice | Bass | |
| L | 16 | 22 | 19 | 15 |
| M | 13 | 5 | 12 | 9 |
| H | 3 | 5 | 5 | 8 |
Low density is defined as glissandi that appear in less than one-third of the notation rectangle, medium density as between one-third and one-half of the rectangle, and high density as more than one-half of the rectangle. I determined the density level by visually examining each notational rectangle for each part.
Like the commonalities of attacks and rests in the pulse layer, common traits in relation to density persist for the solo parts. The predominant density for each part is low, followed by medium and then high density (except for the flute, which has equal medium and high density). Low density levels for each solo part reduces the amount of attack rhythm per rectangle, which increases the difference between the glissandi and pulse layer. Whereas the pulse layer emphasizes attack rhythm or rather is defined by it, the glissandi layer de-emphasizes attack rhythm. This de-emphasis of attack rhythm, in conjunction with the sustained sounds, lack of repetition and proportional notation, creates for the solo parts a distinct temporal layer—one that Cage describes as "sound events in nature rather than sounds in music."23
In a manner similar to A Room, Ryoanji projects temporal activity with two distinct characteristics. One is the simultaneous playing of temporal layers; the pulse layer and the glissandi layer, which never intentionally coincide. The other is the emphasis on irregularity created through both the simultaneous playing of multiple temporal layers and irregularities within each layer. For example, there is virtually no repetition of measure patterns (12, 13, 14, and 15) and specific anomalies of attack and rest patterns are evenly distributed throughout the piece. Also, the glissandi layer has no discernable repetition of pattern.
Unlike A Room, however, Ryoanji extends beyond the confines of physical sound to embrace the conceptual meaning of the Ryoanji garden. The pulse layer, representing the raked sand is omnipresent, expressing both stasis and irregularity. The glissandi layer, representing the stones, weave their lines in and out of the sonic fabric like gently placed stones on sand. Both Ryoanji the Zen garden and Ryoanji the musical work can be experienced as places for contemplation.
In this sense, an evolution (or even shift) in Cage's compositional approach can be seen. Unlike his earlier works, his later works tend to focus with almost equal intensity on both the sonic and conceptual experience. With Ryonaji Cage is equally concerned with creating a sonic "image" of the Ryonaji garden as well as an abstract musical work. This idea of sonic representation is so important to him that he explicitly details these connections in the preface to each instrumental and vocal part. Other works from this same period also show sensitivity to extra-musical concepts. In his Freeman Etudes (1977-80/1989-90) written for solo violin, Cage relates their performance to solutions for societies in general. The Freeman Etudes are intentionally written to be as difficult as possible in order to demonstrate the possibility of achieving the impossible when one is serious and committed to the task at hand.24 Cage draws out of the virtuosic Etude not only extreme technical demands, but also optimistic social encouragement.
Conclusion
As a way of concluding I would like to re-visit one of the opening quotes by Cage that began this paper, "Of the four characteristics of sound, only duration involves both sound and silence. Therefore, a structure based on durations (rhythmic: phrase, time lengths) is correct (corresponds with the nature of the material), whereas harmonic structure is incorrect (derived from pitch, which has no being in silence)."25 This simple (almost naïve) yet profound statement provides the clue to understanding the primary connections that bridge Cage's early and late works—from his pre-chance prepared piano pieces to his chance derived later compositions. Rather than a simplistic compositional technique used to create similar sounding pieces, "duration (rhythmic: phrase, time lengths)" is used as a multiplier of possibilities and variation, generating radically divergent works in both sound and concept.
A Room and Ryoanji provide clear instances of this dynamic approach to composition, revealing how time operates on both the macro and micro level in often bewilderingly complex arrangements. A Room uses four distinct temporal layers including surface, durational, repetitive, and timbral, and Ryoanji uses two temporal layers including a pulse layer expressed through conventional notation and a glissandi layer expressed through proportional notation. Through the simultaneous interaction of these temporal layers and emphasis on irregularity, Cage brings the element of time to the forefront, providing not only structure and design, but also a methodology for future exploration. These fascinating temporal parallels link the works of John Cage both in and through time.
List of References
Bernstein, David W. "Music I: to the late 1940's." In The Cambridge Companion to John Cage. David Nicholls ed. Cambridge: Cambridge University Press, 2002, 63-84.
Cage, John. "Interview with Roger Reynolds." Contemporary Composers on Contemporary Music. E. Schwartz and B. Childs eds. New York: Da Capo Press, 1998, 335-348.
______. Ryoanji for Trombone Solo. New York, NY: Henmar Press Inc, 1985.
______. Ryoanji for Flute. New York, NY: Henmar Press Inc, 1984a.
______. Ryoanji for Bass. New York, NY: Henmar Press Inc, 1984b.
______. Ryoanji for Percussion. New York, NY: Henmar Press Inc, 1983a.
______. Ryoanji for Solo Voice. New York, NY: Henmar Press Inc, 1983b.
______. Ryoanji for Oboe. New York, NY: Henmar Press Inc, 1983c.
______. "An Interview [with John Cage]." [interview with Laura Fletcher and Thomas Moore] Sonus 3/2 (1983d), 16-23.
______. Silence. Cambridge MA: Massachusetts Institute of Technology Press, 1971.
______. A Room: for piano (with or without preparations) solo. New York: Henmar Press, 1968.
Campana, Deborah. "Sound, Rhythm and Structure: John Cage's Compositional Process Before Chance." Interface 18 (1989): 223-41.
Deutsch, Diana. "Grouping Mechanisms in Music." The Psychology of Music. Diana Deutsch ed., San Diego: Academic Press, 1999, 299-48.
______. Musical Illusions and Paradoxes. Philomel. 001, 1995.
Emmerik, Paul van. "An Imaginary Grid: Rhythmic Structure in Cage's Music Up to circa 1950." In John Cage: Music, Philosophy, and Intention, 1933-1950. David W. Patterson ed., New York: Routledge Publishing Inc, 2002, 217-38.
Jenkins, Chadwick. "Structure vs. Form in The Sonatas and Interludes for Prepared Piano." In John Cage: Music, Philosophy, and Intention, 1933-1950. David W. Patterson ed., New York: Routledge Publishing Inc, 2002, 239-61.
Kostelanetz, Richard. "A Composer's Confessions." [1948]. John Cage: Writer. New York, 1993, 27-44.
Kramer, Jonathan. The Time of Music: New Meanings, New Temporalities, New Listening Strategies. New York: Schirmer Books, 1988.
Miller, Allan. John Cage: I Have Nothing to Say and I am Saying It. The Music Project for Television, Inc. and American Masters. VHS. Kulter, 1990.
Nyman, Michael. Experimental Music: Cage and Beyond. New York: Schirmer Books, 1981.
Perry, Jeffrey. "Cage's Sonatas and Interludes for Prepared Piano: Performance, Hearing and Analysis." Music Theory Spectrum 27/1 (2005): 35-66.
Pritchett, James. The Music of John Cage. Cambridge: Cambridge University Press, 1994.
Revill, David. The Roaring Silence, John Cage: A Life. Arcade Publishing: New York, 1992.
Shepard, Roger. "Cognitive Psychology and Music." In Music, Cognition, and Computerized Sound: An Introduction to Psychoacoustics. Perry Cook ed., Cambridge MA: MIT Press, 2001a., 21-35.
Shepard, Roger. "Stream Segregation and Ambiguity in Audition." In Music, Cognition, and Computerized Sound: An Introduction to Psychoacoustics. Perry Cook ed., Cambridge MA: MIT Press, 2001b., 117-27.
Endnotes
1Cage, "Interview with Roger Reynolds," 340.
2Cage, Silence, 63.
3Kostelanetz, "A Composer's Confessions," 27-44. I would also add that his studies with Schoenberg were critical for his durational conception of musical structure. In a famous dialogue often described by Cage, Schoenberg tells Cage that he can never become a composer because he has no feeling for harmony. Schoenberg explains to Cage that he would reach a wall that he will not be able to get through, to which Cage replies that he will then beat his head against that wall. This conversation certainly troubled Cage but did not deter him, and could be viewed as another impetus that encouraged his search for structural determinants other than harmony.
4These studies include Pritchett, The Music of John Cage, 6-35; Bernstein, "Music I: To the Late 1940's," 63-84; Emmerik, "An Imaginary Grid: Rhythmic Structure in Cage's Music up to circa 1950," 217-238; Jenkins, "Structure vs Form in the Sonatas and Interludes for Prepared Piano," 239-261; and Perry, "Cage's Sonatas and Interludes for Prepared Piano: Performance, Hearing and Analysis," 35-66.
5Emmerik is the most specific about these connections when he states in "An Imaginary Grid," on p. 234, "In spite of the numerous and drastic metamorphoses that composition using rhythmic structures underwent in the course of time, especially after the 1940s, its basic principle—the manipulation of temporal units and subsequent affixing of musical functions to them—is a constant factor in Cage's music." Emmerik defines three basic types of functions for rhythmic structures. These functions can regulate motifs, dictate density, and/or determine texture. In "Sound, Rhythm and Structure: John Cage's Compositional Process Before Chance," Campana takes a unique approach when she argues that pre-compositional temporal frameworks, among other pre-compositional decisions, "predicted the application of chance operations."
6See Cage, A Room: for piano (with or without preparations). As the title indicates, A Room can be played with or without preparations. My temporal analysis of A Room is valid for either version except for the timbral rhythmic layer section. While the pitches and pitch regions of d, d'-f' and d", g" without preparations still encourage a layered hearing based on register (Deutsch 1999), the unique timbres created by the preparations create more definite separations based on timbre, resulting in more clearly defined layers.
7Cage, Ryoanji for Percussion, Ryoanji for Solo Voice, Ryoanji for Oboe, Ryoanji for Flute, Ryoanji for Bass, Ryoanji for Trombone Solo.
8I would like to thank Jeff Perry for his helpful comments on an earlier draft of this paper that greatly improved its clarity.
9Cage also began to combine different pieces of his own that were written separately. Apartment House 1776 was performed simultaneously with Renga (1976) at the 50th Festival of the International Society for Contemporary Music in Boston on October 27, 1976. This is discussed in Revill, The Roaring Silence, John Cage: A Life, 253.
10Nyman, Experimental Music: Cage and Beyond, 27.
11Emmerik, "An Imaginary Grid," 223.
12In The Time of Music: New Meanings, New Temporalities, New Listening Strategies, Kramer defines linearity on p. 20 as "the determination of some characteristic(s) of music in accordance with implications that arise from earlier events of the piece." He defines non-linearity as "the determination of some characteristic(s) of music in accordance with implications that arise from principles or tendencies governing as entire piece or section."
13Cage, A Room: for piano (with or without preparations) solo.
14See Deutsch, "Grouping Mechanisms in Music," 299-348 and Shepard, "Cognitive Psychology and Music," 21-35 and "Stream Segregation and Ambiguity in Audition," 117-27.
15Deutsch, "Grouping Mechanisms in Music," 318. In his article, "Cage's Sonatas and Interludes for Prepared Piano: Performance, Analysis and Hearing," Perry also discusses relationships based upon timbre, using the term "pitchedness" to define the degree of original pitch preservation, and reveals connections between pitches that have the same "pitchedness". I agree with Perry when he states on p. 43, "When one listens to these pieces [Sonatas and Interludes for Prepared Piano], notes that posses similar degrees of pitchedness seem to stream together . . . ." and follow the same type of hearing for A Room.
16Cage, Ryoanji for Percussion.
17Revill, The Roaring Silence, John Cage: A Life, 279.
18Cage, Ryoanji for Percussion.
19Deutsch's Musical Illusions and Paradoxes CD recording provides a number of fascinating musical illusions as well as extended liner notes explaining each illusion.
20Cage, Ryoanji for Flute.
21The solo parts for Ryoanji demonstrate ways composers have allowed the visual arts to influence their musical scores. This was especially true for John Cage who, throughout his life, created visual art as well.
22In earlier pieces such as She is Asleep, Cage uses density as a structural compositional component. See Emmerik, "An Imaginary Grid," 228.
23Cage, Ryoanji for Flute.
24As Cage (1983d) states in an interview on p. 19, "These [Etudes] are intentionally as difficult as I can make them, because I think we're now surrounded by very serious problems in the society, and we tend to think that the situation is hopeless and that it's just impossible to do something that will make everything turn out properly. So I think that this music, which is almost impossible, gives an instance of the practicality of the impossible." This quote is reprinted in Pritchett, The Music of John Cage, 198.
25Cage, Silence, 63.