John Cage's "Trio" from Amores (1943): A Study of Rhythmic Structure and Density1

John Welsh

  John Cage's percussion music of the late 1930s and 1940s is striking with regard to its structure and unique sonic identity. Toward this end, Cage sustains a high level of compositional craftsmanship. Consistency and balance are integral to the organization and composition of such works as his Imaginary Landscape series (1939-1952), Credo in Us (1942), She Is Asleep (1943) and Amores (1943) - among others. Deeply rooted in numerical procedures and containing an economy of sonic materials, these works reveal a carefully calculated sense of dramatic growth.


Cage's Amores (1943), for percussion trio and prepared piano, contains a third movement - "Trio" - scored for seven woodblocks (see Appendix A). The woodblocks are distributed as follows:




Thus, three different registers/pitches are notated. In this work of limited resources, Cage creates a remarkably rich level of activity and a clear formal design. The score for the "Trio" has been reprinted on the next pages. The formal and dynamic design is supported by the entrance of different rhythmic modules. It begins "piano" with the next change of dynamics "pianissimo" appearing in measure 23 followed by a diminuendo beginning in measure 28. Measure 13 begins in the same manner as the opening except for the metric displacement of the rhythmic modules. This design is illustrated in Figure 1.



Figure 1: Sectional dynamic scheme of Cage's "Trio" from Amores.

            More significant in this formal design, however, is the interplay of two basic modules (now called Module A and B, see Example 1 below) and their variants, from which the entire "Trio" is composed.



Example 1: Rhythmic modules in Cage's "Trio" from Amores

            Module A is really three repetitions of a basic cell. Because the three repetitions appear in a single rhythm during the course of the work, it is the author's decision to label Module A as cited. (The first three measures of the "Trio" clearly illustrate this grouping.) The exact combinations of these two modules can be observed in the resultant rhythm of the entire movement.

Figure 2: Resultant rhythm of the "Trio" from Cage's Amores


            Each section has been marked off in the above chart with a dotted line. Within each section, phrases have been identified as well. These phrases reveal the formation of activity. In fact, Cage's "Trio" is concerned, on the micro- and macro- levels, with a consistent increase in the level of activity. On the micro level, the A and B modules themselves gain in activity, while, despite the decreasing dynamic level, the entire work slowly generates more and more energy.


            The resultant rhythm will be examined with regard to the increase in activity (i.e. increases in attacks.) Consider Section I which divides into three phrases, each, four measures in duration: phrase 1 (mm. 1-4), phrase 2 (mm. 5-8), and phrase 3 (mm. 9-12). The patterns of fluctuation in activity determines this division. Each begins slowly and then speeds up. This aspect is significant and forms the basis for the entire "Trio". Furthermore, the two modules themselves are rhythmically distinctive -module A features  e values and module B featuresx values. A shift from the A module to the B module produces a new rhythmic identity and a more dense texture as can be observed in phrase 1 of Section I (Figure 3).



Figure 3: Section I, phrase #1 (mm. 1-4)


The increase in attacks in the resultant rhythm can be examined further. A determination can be made regarding the rate of attacks per  e ; in this way, both modules can be observed either together or independently as they unfold during the course of the work. For  example, in phrase 1, Module A contains 3 attacks, 3 attacks and 3 attacks, a total of nine attacks spanning a duration of 18 e ) s. Consequently, for Module A there are 0.5 attacks per e.  For Module B, there are 9 attacks spanning 6 e  s; the rate of attacks per e is

1.5. In moving from the A to the B Module, the rate of attacks per e is tripled. A clear pattern of activity formation has been drawn, and Cage is consistent in his utilization of this technique throughout the work.


The rate of attacks per e for the resultant rhythm of the entire work is summarized in Figure 4 (below). In this chart, which describes the activity of the resultant rhythm, the attacks listed under Module A are those that are clearly variants of Module A and/or feature the characteristic eighth values. The same is true for Module B, and its characteristic sixteenth and triplet values. The totals on the right display a steady increase in attacks per e in three of the four sections. There is a gradual increase in attacks culminating in Section III. Section IV balances the ending with the opening section.


            With regard to Section I, Module A steadily increases in attacks per  (from .50 to .78) while these attacks are occurring within decreasing time frames (from 18 e s to 14 e s). For the B Modules, the rate of attacks per e decreases (while the duration increases); however, 1.25 and 1.10 attacks per  e are still far above those of the A Module. Compared to the A Modules (horizontally in the chart), the B Modules show a substantial increase in activity. In phrase 1 alone there are 1.50 attacks per e and that is three times greater than that of the A Module. The rate of attack is nearly doubled in phrase 2 when moving from Module A to Module B. In phrase 3, the same comparison reveals a slight increase in the attack rate.


Section II consumes less time (ten measures) with only two phrases. Remarkably, phrase 1 is consistent with phrase 1 of Section I. Module A contains .50 attacks per e; while, Module B has 1.42 attacks per e ). The  only significant change here is that Module B maintains its high attack level over an extended time period (12 e opposed to 6 eearlier.) Phrase 2 shows a dramatic increase in the attack rate per e for Module A. In a 10 e duration, there are .70 attacks per e , while Module B nearly maintains its high level of activity (1.40 attacks per e over 20 e).


The intensification for each module occurs separately. Module B is highlighted in Section III, Module A in Section IV. In Section III, the A Module appears briefly. Nearly the entire section involves the B Module (1.47 attacks per maintained over 30 es) while Module A sounds only 0.50 attacks per e . Therefore, with regard to the rate of attacks in the resultant rhythm, for Module A there is a precise and consistent increase in the formation of activity culminating in Section IV (its highest rate maintained over its longest duration/appearance). Likewise, Module B increases its activity level by spanning out and slowly assuming more time, yet very nearly maintains 1.50 attacks per e) . Module B reaches its zenith in Section III.


 Figure 4: Rate of Attacks Per Eighth


The Interaction of Rhythmic Modules


The next area to be addressed concerns the modules themselves. ;How are they juxtaposed? How do they relate to one another? Taken 'together, do the modules reflect the formal design and do they support the activity gain that was so prominent in the resultant rhythm?


Figure 5 reveals the entrance and duration of each module during the course of the work. As the piece unfolds, the sections grow shorter while the space or time between module entrances decreases. With regard to the balanced proportions displayed in Cage's early music, the A Module enters in the order: Player 1, 2, and 3; the B module enters in reverse fashion. In addition, each B Module entrance is 16 e s apart (mm. 4, 7, and 11).


If the succession of entrances is traced through the entire "Trio," the increase in activity will clearly be discerned. With reference to the preceding chart, each section has been divided where appropriate to reflect the opening series of entrances (dotted, line in Figure 5 below ): that is, an A Module followed by an A and B Module (simultaneously) then succeeded by an A Module. (This is the first portion of Section I). The second half of Section I begins with an A Module displaced to the second beat. This displacement is one of the primary vehicles for development in Amores. In Section I (first half), the time of 18 es  passed before any new entrance. In the second half, after the displaced A Module appears, a denser texture emerges when a B Module enters after only 2 es. Next, Players 2 and 3 enter with A Modules; however, this occurs earlier than in the first half, thus creating an overlap of three A Modules. Player 1 concludes the section with a B module which creates a balance in this section: each player performs two A Modules and one B Module (each appearing at a regular time interval of 16 es).


Section II begins in the same manner as Section I, with an unaccompanied statement of Module A now displaced to the upbeat of one. Recall that in Section I, Players 2 and 3 entered after 18 e s with an A and B Module respectively. Consistent with the acceleration of activity that is the hallmark of Cage's "Trio," in Section II (m.1,6) the A Module enters at the expected time (after 18 e s) to parallel the opening, but the B Module (Player 3, m. 16) enters early: an eighth-note's duration exactly. This is the first time the B Module has entered before the A Module. To reinforce this acceleration there are two consecutive statements of the B Module. This increase in activity can be seen as well in the second half of Section II. After the A Module enters displaced (Player 2, m. 16), there is another A Module sounded by Player 3. This statement enters after 17 e s) or one eighth sooner than usual. The third A Module enters after just 4 es. Finally, Player 1 sounds three B Modules in succession, now propelling the work into Section III.

Figure 5: Entrances and Durations of the Modules


Section III includes a series of five repetitions of the B module (four successive and one overlapping) which has now completely overtaken in predominance from the A Module. (Section I had only one statement of the B module at a time; Section II had two and three in succession.) In Section III, the B Module reaches intensification with five statements: four (Player 3) and one (Player 1) with the only overlap of B Modules occurring in measure 27. The rests between B Modules in mm. 25 and 26 begin to decrease the attack rate and thin the texture of the work in preparation for the ending.


In Section III, Player 1 (m. 23) sounds an A Module followed by Player 2 (with an A Module) only nine eighth notes later. This is the smallest amount of time yet between first and second soundings of an A  Module. To elicit the intensification for the A Module, Cage utilized the technique of elision. The first elision appears with Player 2 in measure 27 as illustrated in Example 2.

Example 2: Rhythmic Elision in m. 27


Along with this significant departure from the techniques of the earlier part of the work, the elision is combined with melodic inversion, thereby signaling even greater activity in the A Module. These successive statements produce longer phrases constructed from the A Module and its melodic variant. The focus in Section IV (mm. 28-33) shifts to the A Module and functions as a final exclusive intensification of this idea. A second elision displays the intertwining of A Modules and sounds with Player 3 (mm. 28-31, see Example 3.)



Example 3: Rhythmic Elision in m. 28-31


The Structuring of Coincidental Attacks


Now consider a count of the multiple attacks (i.e. 2, 3, and 4 simultaneous attacks). This is charted in Figure 6.




Figure 6: Simultaneous Attacks


An important observation can be made regarding the rate of multiple attacks per  e . The rate increases through Sections III and IV, creating the most dense textures in the "Trio." This runs parallel with the intensification of Modules A and B. These totals are summarized in Figure 7.

Section I           0.333

Section II         0.383

Section III         0.437

Section IV         0.500

Figure 7: Rate of Multiple Attacks per e


Now consider a detailed look at these multiple attacks. While there seems to be an equal distribution among all the players, the number of tutti attacks (i.e. 3 or 4 attacks) is significant. In Section I, the only tutti attack occurs in measure 11, where the cadence for the entire first section takes place. All three players simultaneously strike the lowest woodblock, thereby punctuating the increased activity rate. A slight increase in the rate of multiple attacks per e occurs in Section II. This acceleration is further enhanced in Section III with three tutti attacks. In measure 25, beat 3, a significant tutti attack occurs - Player 1 with its two attacks and Players 2 and 3 with one apiece. This is the only such tutti in the "Trio". In Section IV, while the rate of multiple attacks is its highest, only one triple attack /appears. At this point in the composition, Cage begins to prepare a final cadence - here there is a gradual thinning of the texture and exclusive emphasis on the eighth-note rhythmic values. Along with the non-sustaining quality of the woodblock, this introduces silence near the final cadence, balancing the sound and silence interaction of the opening few measures.


The conclusion of the work is prepared with great care. Until measure 31-33, the multiple attacks have avoided the downbeats, occurring only four times previous to mm. 31-33. At the downbeat of measure 31, Players 2 and 3 simultaneously strike their lowest woodblock, again at the downbeat of measure 32, and a third time in measure 33, thus emphasizing and stabilizing the triple meter for the first time in the "Trio."


The final chart to be considered (Figure 8) is of a more globally statistical nature, containing attack points in all voices and their distribution throughout the "Trio."


Figure 8: Attack Points



Players 1 and 3 have the most attacks; they also sound the B Module more times. Player two performs Module B only once (in Section I). The only significant number with regard to attacks per section can be observed in Section I, where each of the players has 26 attacks, creating an initial state of balanced distribution between the players., More important, however, is the number of total attacks per section per e (the right side of the chart). The rate of attack points per e ) rises until Section III, coinciding with the high level of multiple attacks and soundings of the B Module. Thus, the most dense texture of the work is formed. The final cadence is prepared by the dramatic decrease in attacks in Section IV.


In conclusion, Cage's "Trio" is a classic example of a clear unfolding of activity and formal design through the juxtaposition of two distinct modules. This is supported by the resultant rhythm, the intensification and movement of each module, the multiple attack rate, and the attack points. The statistical calculations reveal with great clarity the compositional precision of John Cage which is especially evident in his percussion music of the 1930s and 1940s. Consistency, balance, and an economy of means are the mind-set for Cage's early music. This can be further witnessed in a statement by the composer himself:


Patsy Davenport heard my Folkways record. She said, 'When the story came about my asking you how you felt about Bach, I could remember everything perfectly clearly, sharply, as though I were living through it again. Tell me, what did you answer? How do you feel about Bach?' I said I didn't remember what I'd said -that I'd been nonplused. Then, as usual, when the next day came, I got thinking. Giving up Beethoven, the emotional climaxes and all, is fairly simple for an American. But giving up Bach is more difficult. Bach's music suggests order and glorifies for those who hear it their regard for order . . . . Some people say that art should be an instance of order so that it will save them momentarily from the chaos that they know is just around the corner. Jazz is equivalent to Bach (steady beat, dependable motor) and the love of Bach is generally coupled with the love of jazz . . . . Giving up Bach, jazz, and order is difficult. Patsy Davenport is right. It's a very serious question. For if we do it give them up, that is - what do we have left?2



1 With permission from Peters Edition. The recording of the "Trio" from Amores reproduced on the accompanying sound cassette for this issue features Edmund Fay as Player I, James Pugliese as Player II and Charles Descarfino as Player III, recording engineer Manfred Knoop, recorded at Mohawk Recording Studio, River Edge, New Jersey.


2 John Cage, Silence, Weslayan University press, Middletown, 1973, pp. 262-263.