cage concerto prepared piano - james pritchett

From Choice to Chance: John Cage's Concerto for Prepared PianoAuthor(s): James PritchettSource: Perspectives of New Music, Vol. 26, No. 1 (Winter, 1988), pp. 50-81Published by: Perspectives of New MusicStable URL: http://www.jstor.org/stable/833316 .Accessed: 09/06/2011 12:22

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FROM CHOICE TO CHANCE: JOHN CAGE'S CONCERTO FOR

PREPARED PIANO

JAMES PRITCHETT

THE YEAR 1951 stands out as the single most important milepost in John Cage's long musical career. It was at that time that Cage made the step

for which he is most known today: the inclusion of chance operations in his compositional process. But what Paul Griffiths refers to as "the revolution of 1951"' was not a sudden or even a radical change in Cage's outlook. As Michael Nyman notes:2

Cage's adoption of chance and random procedures... [was] as much the logical outcome of his earlier methods as [it was] evidence of his deepening attachment to the Zen philosophy of non-involvement.

The pivotal work in Cage's development of chance techniques was the Concerto for Prepared Piano and Chamber Orchestra (1950-51). Griffiths

Cage's Concerto for Prepared Piano

sees the Concerto as both the culmination of Cage's early work, and as an

important step towards his later style,3 and William Brooks describes it as both a summary of Cage's work of the 1940s and a "small step" away from his chance-composed works of the 1950s.4 It would seem, then, that any musicological assessment of Cage's use of chance, and hence of Cage's work as a whole, would include a thorough study of the Concerto. Unfortu-

nately, such a study has yet to appear. Though Cage has written an entire article about the Music of Changes (1951), he has devoted only a few passing sentences to the subject of the Concerto.5 Cage's remarks about the Con- certo have revealed only that he used charts of sounds, and that "the method of composition involved moves on these charts analogous to those used in constructing a magic square. "6 The nature of these charts and the

technique of using them has remained unclear, although Cage has said that in the second movement he used "large concentric moves on the chart. "7

This scanty information has formed the basis of all further discussions of the Concerto. Paul Griffiths, in his monograph on Cage, devotes barely a

page to the Concerto, summarizing Cage's comments, supplemented by a

pair of examples from the score.8 Monika Fiirst-Heidtmann, in her work on Cage's music for prepared piano, presents a fuller description of the Concerto, but still relies on Cage's few comments and the published score.9

Finally, while Deborah Campana presents important new information about the Concerto in her recent dissertation, she never actually deals with the score itself, and her description of the chart techniques involved is nei- ther complete, nor completely accurate.10

In this paper, I will present the first complete account of the composition of this Concerto. This study is made possible by the recent identification of the following original compositional materials, all currently in the

possession of David Tudor:1

1. Three pages of worksheets for the second movement.

2. Two pages of sketches of orchestral music, second movement.

3. One page of sketches of piano music, second movement.

4. A draft of the orchestra part, second movement, in piano reduction.

5. Four pages of worksheets for the third movement.

These manuscripts, together with Cage's own commentary, allow a docu- mentation of the compositional process used in the creation of the Con- certo. For each movement of the Concerto, I will give a detailed description of the compositional method used, along with an analysis of its musical results. From this description and analysis, we can better explore the role of

51

Perspectives of New Music

the Concerto as a bridge between Cage's traditional and chance-composed works. I will show how aspects of Cage's earlier works, in particular rhythmic structure and sound gamuts, are extended in the Concerto to accom- modate a more systematic approach to composition. In addition, several important devices and principles of Cage's later style are found to be already present in the Concerto, among them the use of sound charts, chance operations involving the I Ching, and the equivalence of sound and silence.

Two aspects of Cage's compositional style of the 1940s can be seen as keys to his adoption of chance techniques. The first of these is his use of"rhythmic structure." This sort of structure was initially used in his First Con- struction for percussion (1939), and was developed as a result of his work in the late 1930s with percussion ensembles. Cage recognized the inadequacy of traditional musical forms with regards to percussion music:12

Since Arnold Schoenberg had impressed upon me the structural func- tion of tonality, I felt the need of finding some structural means ade- quate to composing for percussion.

The result of this search was rhythmic structure, which:13

In contrast to a structure based on the frequency aspect of sound ... was as hospitable to non-musical sounds, noises, as it was to those of the conventional scales and instruments.

A rhythmic structure is based on a single set of proportions that govern durations at two different levels.14 A given structure is expressed as a series of numbers; these represent, at the small scale, the length of phrases in terms of measures. One complete set of phrases (that is, one complete expression of the proportions at the small-scale level) constitutes a phrase group, which in Cage's scores is usually marked by a double barline. At the large scale, the same proportion numbers represent the lengths of sections of the work in terms of these groups. Hence, the proportions of the large sections of the work, made up of phrase groups, are equivalent to the proportions of the phrases making up each of those groups.15

In First Construction, for example, the structural proportions are {4,3,2,3,4}. The structure of the work at both the large- and small-scale levels is shown in Example 1. Each phrase group of the piece contains sixteen measures divided into five phrases with lengths of four, three, two, three, and four measures, respectively. The overall work contains sixteen of these groups, divided into five sections whose lengths (in groups) are given

52


M V V V

3

c )

el

U

3

.g

ro

S

.I t

.E . .

A A A I I I

u:i~ :z m-

53


by the same number series. The equivalence of measures, at the small scale, with groups at the large scale, means that a given work will always have as many measures in one group as there are groups in the whole work. This explains why Cage, referring to a piece such as First Construction, describes the structure as being "16 units of 16 measures each" or "16 times 16 measures of 4/4. "16 It also explains his rather oblique explanation of rhythmic structure as "based on a number of measures having a square root"'7 since it insures that the length of one phrase group will always be the square root of the total length. Virtually all of Cage's concert works from 1939 to 1956 use this sort of structure.

The second aspect of Cage's work in the 1940s that bears upon our cur- rent discussion is the use of sound collections or "gamuts." The concept was derived from his work with the prepared piano:18

On depressing a key, sometimes a single frequency was heard. In other cases depressing a key produced an interval; in still others an

aggregate of pitches and timbres.

A single key on the prepared piano, then, was associated not with a note, but with a sonority, one that could be quite complex. These were classified by Cage as tones (single notes), intervals (simultaneous pairs of notes), agfre- gates (a simultaneity of three or more notes), and constellations (collections of tones, intervals, and/or aggregates distributed in time).19 In composing for the prepared piano, Cage would select a collection of such sonorities "as one chooses shells while walking along a beach."20 This collection of single tones, intervals, and aggregates would become the universe of sound within which the work would move.

In the late 1940s, Cage extended the idea of a gamut of sounds to media other than the prepared piano. In the String Quartet in Four Parts (1949-50), for example, there is a gamut of "single tones, intervals, triads, and aggregates requiring one or more of the instruments for their produc- tion. '21 The scoring for each sonority in the gamut is fixed throughout the work (see Example 2a). The top note of each sonority in the gamut is treated as its primary note, these top notes then forming the "melodic line without accompaniment" that Cage refers to in his description of this piece.22

Examples 2a-c give an example of the gamut technique in the String Quartet. Example 2a shows the gamut of sonorities associated with the range of pitches C5 to C6, and Example 2b is the melody of the first five bars of the last movement of the Quartet. Example 2c, then, is the actual music of the Quartet (in reduction), showing how the sonorities of the gamut are used to "play" the melody. While working on the Quartet, Cage described it as being:23

54


(a)

TO i L -fF -a I I IF Ir

41e'.';] 5+9 finaA ~

p) V : V I a- * * _ * E . _ ,, t~~~~~~~~~-1

4ii^FMi , " F' KT 4 1 -1 ~ ~~~~~~~~~~~~~~~~I f I I

EXAMPLE 2: STRING QUARTET, FOURTH MVT., MEASURES 1-5: GAMUT TECHNIQUE

Like the opening of another door; the possibilities implied are unlimited and without the rhythmic structure I found by working with percussion and the newness, freshness of sound I found in the

prepared piano, it would be impossible.

It was after this "opening of another door" that Cage composed his Con- certo for Prepared Piano and Chamber Orchestra. The Concerto was begun in the summer of 1950 and completed in February of 1951.24 In addition to the prepared piano solo, it is scored for flute (doubling on piccolo), oboe, English horn, two clarinets, bassoon, horn, trumpet, tenor and bass trombones, tuba, piano (doubling on celeste), harp, solo strings, and four per- cussionists playing a variety of instruments and electronic devices (the latter

(b)

(c) t.-

55

I I fI I I


including a radio, an amplified coil of wire, a buzzer, and a recording of a generator).

The piano preparation is quite extensive, involving fifty-three notes cov- ering the entire range of the piano. The materials used are the usual bolts, screws, strips of plastic and rubber, as well as a new object, referred to in the table of preparations as a "plastic bridge." Cage describes this object:25

The piano preparation has many microtonal pitch relations, brought about by an object, the height of which can be controlled, that rests on the sounding board and becomes a bridge (making the strings other and similar lengths).

The Concerto is constructed according to the principles of rhythmic structures discussed above, as used in Cage's other works. In this case, the structural proportions are [3,2,4; 4,2,3; 5}. The symmetry of the first six numbers is reminiscent of the structure of First Construction, {4,3,2,3,4), and this symmetry is of compositional significance in the last movement, as we shall see. Adding the numbers, we can see that the Concerto consists of twenty-three groups of twenty-three measures each, arranged into seven sections of varying lengths. Cage has imposed a three-movement structure on top of the basic rhythmic structure: the first movement consists of the first three sections (3,2,4), the second movement encompasses the next three (4,2,3), and the third movement consists of the last section only (5). The tempo (half note = 54) is constant throughout all three movements.

Cage conceived of the Concerto as a portrayal of the opposition and reconciliation of piano and orchestra:26

I made it [the Concerto] into a drama between the piano, which remains romantic, expressive, and the orchestra, which itself follows the principles of oriental philosophy. And the third movement sig- nifies the coming together of things which were opposed to one another in the first movement.

This dramatic plan mirrored an inner conflict:27

The Concerto for Prepared Piano and Chamber Orchestra is an example of the lack of resolution I felt... between letting the aggregates of sounds emerge by themselves ... and continuing to experiment with my own personal tastes. These are the two poles of that Concerto.

Cage found the means of "letting the aggregates of sounds emerge by themselves" in the use of a sound chart: a two-dimensional representation of the gamut. He described the principle in a letter to Boulez:28

56


A new idea entered which is this: to arrange the agregates [sic] not in a

gamut (linearly) but rather in a chart formation. In this case the size of the chart was 14 by 16. That is to say: 14 different sounds produced by any number of instruments (sometimes only one) (and often

including percussion integrally) constitute the top row of the chart and favor (quantitatively speaking) the flute. The second row in the chart favors the oboe and so on. Four rows favor the percussion divided: metal, wood, friction, and miscellaneous (characterized by mechanical means, e.g., the radio). The last four favor the strings. Each sound is minutely described in the chart: e.g., a particular tone, sul pont. on the 2nd string of the first violin with a particular flute tone and, for example, a woodblock. I then made moves on this chart of a "thematic nature" but, as you may easily see, with an athe- matic result.

Unfortunately, the sound charts used in composing the Concerto no

longer survive, although they can be at least partially reconstructed from the other compositional materials that do exist. Example 3 shows a diagram of the chart layout Cage described to Boulez: sixteen rows of fourteen columns each, with each row favoring one or more instruments. Cage numbered the columns 1 to 14 and lettered the rows A to Q (skipping P), so that each cell in the chart could be identified by a letter-number pair (e.g., G7), as is shown in the diagram. In the course of composing the Concerto, Cage would notate the sequences of chart moves as a series of these cell names, which thus provided a convenient shorthand form for manipulating the sound charts. Worksheets with such notations survive for the second and third movements of the Concerto, and allow us to identify certain sounds and to associate them with their appropriate cells in the chart.

The chart of sounds for the orchestra contains a rich variety of material.

Many sounds are simply single notes played by a single instrument or a dyad played by two. The sonorities formed of three or more notes are constructed of various intervals (see Example 4): seconds, sometimes forming clusters (C9), thirds, sometimes forming triads (C7), fourths or fifths (L1), or a mixture of intervals(H9). Although most are chordal, some sounds consist of short flourishes (A14), or include grace notes (13). The notations in the chart must have specified no durations, since the same sound may recur in the piece with different rhythmic values. There is a differentiation in a large number of the chordal sounds, however, between very short notes and held notes (e.g., A2).

Cage offers the following description of the first movement:29

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.

57

Flute, piccolo Al A2 A3 A4 A5 A6 A7 A8 A9 AIO All A12 A13 A14

Oboe Bi B2 B3 B4 B5 B6 B7 B8 B9 BlO Bli Bi2 B13 B14

Clarinet Cl C2 C3 C4 CS C6 C7 C8 C9 CIO CliI C12 C13 C14

Bassoon Dl D2 D3 D4 D5 D6 D7 D8 D9 DIO Dli D12 D13 D14

Trumpet El E2 E3 E4 E5 E6 E7 E8 E9 EIO Eli E12 E13 E14

Horn Fl F2 F3 F4 F5 F6 F7 F8 F9 FIO Fll F12 F13 F14

Trombones Gi G2 G3 G4 G5 G6 G7 G8 G9 GIO GIl G12 G13 G14

Tuba HI H2 H3 H4 H5 H6 H7 HR H9 HIO HiI H12 H13 H14

Percussion (wood) Ii 12 13 14 15 16 17 18 19 110 ill 112 113 114

Percussion (metal) Ji J2 J3 J4 J5 J6 J7 J8 J9 Jl0 Jil J12 J13 J14

Percussion (friction) KI K2 K3 K4 K5 K6 K7 K8 K9 KIO Kll K12 K13 K14

Percussion (mechanical) LI L2 L3 L4 L5 L6 L7 L8 L9 LIO Lii1 L12 L13 L14

ViolinlI Ml M2 M3 M4 M5 M6 M7 M8 M9 MIO Mll M12 M13 M14

Violin II Ni N2 N3 N4 N5 N6 N7 N8 N9 NIO NIl N12 N13 N14

Viola 01 02 03 04 05 06 07 08 09 010 011 012 013 014

Celolo, Doublebass Ql Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 QIO Qll Q12 Q13 Q14

EXAMPLE 3: souND--CHART LAYOUT

U, co

-o

(r,

CD~

0 (AC


C9 C7 L1 H9 A14 13 A2

Fk o bb $, &

9: C'S

F1,Cl;Hp;Str Ob,Cl;Db BTr,Tba;Vc Fl;Tpt,Tba;Vn Vn Vn,Vc F1;Tpt;Hp

EXAMPLE 4:ORCHESTRA SOUNDS (SAMPLE)

The piano solo in this movement, unlike the orchestra, does not use any predefined gamuts of sounds other than those implied by the preparation of the piano. In it, we find the same sort of forms and gestures common to

Cage's prepared piano music of the 1940s. Much of the solo is composed in a quasi-improvised way using only a few notes in simple, repetitive patterns. Example 5 shows a typical passage from the solo (measures 52-56), in which the motion from Eb6 through El5 to C#4 in the right hand is set against "chromatic" meanderings within a limited range in the left hand.30

t I __?

I/i t

A ._-

e i

mm ...'' mm -

-L -" 1, s;r *

Y ,wI r^* , , -j ^-^ ^

^Vr/rf^- ^ ^^'-r^

EXAMPLE 5: FIRST MOVEMENT, MEASURES 52-56

Perhaps the most expressive part of the first movement is the extended solo passage near the end (Example 6, measures 177-204). This serves as a cadenza for the soloist, and is the longest extended solo in the first movement. It is based on another "chromatic" pattern in the left hand together with sustained tones in the right. The left hand gestures begin slowly at first, then intensify rhythmically, leading to the climax at measure 198. Here, the acceleration of the pattern rhythm to every half bar, the strin- gendo, the crescendo, and the swiftly rising right-hand line all combine to push forward to the dramatic high point at measure 198.

59

kLitb 't

Perspectives of New Music 60

.4 I? F


tl-

tl-

\ij

V)

61


In contrast to the definable contours and drama of the piano solo, the sounds of the orchestra seem almost stoic in their assertion of independence and disconnectedness. According to Cage:31

The entire first movement uses only 2 moves [on the chart], e.g. down 2, over 3, up 4, etc. This move can be varied from a given spot on the chart by going in any of the directions.

Since no compositional materials survive for this movement, it is not possible to further describe the method used to produce it. Since most of the sounds consist of single attacks, and are rarely overlapped, it is possible to isolate individual sounds, and, in some cases, to positively identify them by cross-referencing with the better-documented second and third movements. What we can determine is that, whatever these moves were, they were such that they formed sequences of two, five, or eight sounds each. Without a complete identification of the sounds and without a more detailed description of the system of moves used, we cannot arrive at a full explanation of the selection of sounds in this movement.

Whatever the method used to produce them, Cage created one such sequence for each phrase of the orchestra part, and composed the rhythms for each phrase so that the required number of sounds would fit within the length allotted by the rhythmic structure. The rhythms used are fairly simple, consisting mainly of half and whole notes (see Example 7). Despite the appearance of disconnectedness, therefore, the technique used in the Con- certo is far from one in which Cage had little control over the results once the system was set in motion. True, the order of sounds was entirely the product of an autonomous system, but the placement of the resulting sounds in time within phrases was entirely left to Cage's musical sense.

21 J J|44J J J IJ JiJ JJ4JJJ J JJ4 J. JJ4 I

EXAMPLE 7: FIRST MOVEMENT, MEASURES 24-36, ORCHESTRA RHYTHM

If we look at the opening of the Concerto (see Example 8), we might note, for example, the way Cage has handled the glissandi in the tenor and bass trombones and harp in measures 6-7. Nothing in the chart or the method of ordering sounds caused Cage to overlap the two "sliding" sounds; it does make perfect musical sense, however. A similar effect

62

Cage's Concerto for Prepared Piano 63

Fl t

Ob/EH 44j 2jCfDm -

ci_--- - - - -,

Bn J - - Th- -

Hn v - ff.- - j.

Tpt - - J

--

Perc 41 0 I p I- I I i l I

Hp

Str


64 Perspectives of New Music

occurs in measures 123-25 (see Example 9), where this time the water-gong glissando is overlapped with that of the tenor trombone. Sounds rarely overlap one another in this movement, but when they do, it is always for some such musical reason.

Where two or more adjacent sounds contain the same instrument, Cage takes the opportunity, if possible, to bind the adjacent notes in a phrase rather than separate them. At measure 17, for example, the two trumpet notes A4 and G4 are phrased, and the connection enhanced by the dimin- uendo. Similar two-note phrases occur at measure 78 (horn and trumpet), measure 130 (horn), and measure 133 (trumpet), as well as at other points. More striking examples are the four-note flute line at measure 42, and another four-note line in the tenor trombone at measure 127, both of which are carefully phrased by Cage in the score.

Ob

EH

Cl

Tpt

TTr

Gong

Str

~J

-')

NW*1

^sbr "- O __- i - b2. J 2

AIa - -^- --- -

r

- .



In the second movement of the Concerto, the conflict between piano and orchestra is resolved somewhat. For this movement, Cage maintained the same orchestral sound chart, but drew up a sound chart for the piano as well, structured in the same way as the orchestral chart. The sounds in the piano's gamut (a sampling of which appears in Example 10) are of a greater variety than those in the orchestra's. In addition to single tones and aggregates, the gamut of sounds for the piano include a wide variety of trills, flourishes, and quasi-motivic gestures. The types of sounds are similar to those found in the first movement (although there are no exact corres- pondences), but taken out of context and given new, independent identities.

F1r b Trb ; ?

EXAMPLE 10: PIANO SOUNDS (SAMPLE)

The chart technique used in the second movement involved concentric

squares and circles on the charts. Examples lla-c are diagrams of the method used. Given a square of cells drawn on the chart (see Example ila), circles can be drawn that intersect this square. As shown in Example llb, the largest such circle is the one connecting the four corners of the square, while the smallest is the one connecting the midpoints of the four sides. All circles between these two extremes intersect the square in eight places, two on each side (see Example 11c). These intersections of squares and circles produced sequences of chart cells.

Having worked out the geometry of this technique in the abstract, Cage was able to notate the sound sequences produced. Using the cell D9 as the center, Cage began with the smallest square and circle and moved gradually outwards, producing the sound lists excerpted in Example 12. Each phrase of the second movement was matched with one sound list. Each phrase was then assigned, arbitrarily, to either piano or orchestra. For example, in the first phrase, the sounds, {C9,D10,E9,D8}, are drawn from the orchestra chart, while the sounds of the following phrase, {C10,E10,E8,C8}, are drawn from the piano chart.32 Then, he would distribute the sounds rhythmically within the phrase in a manner similar to that used in composing the orchestra music of the first movement.

65


(a) 6 7 8 9 10 11 12 A ' I

B .

C -

D -

E -

F .

G

(b) A6 A12

D6 D12,

G6t G12

(c) -^ TI _ 7 / : -"--l

EXAMPLE 11: SECOND MOVEMENT, CHART TECHNIQUE

66


C9 D10 E9 D8 C10 E10 E8 C8 B9 D11 F9 D7 B10 Cll Ell F10 F8 E7 C7 B8 Bll Fll F7 B7 A9 D12 G9 D6 A10 C12 E12 G10 G8 E6 C6 A8 All B12 F12 G11 G7 F6 B6 A7 A12 G12 G6 A6

EXAMPLE 12: SECOND MOVEMENT SOUND LISTS (EXCERPT)

Although he wrote the sound lists going from the center cell out, Cage actually used them in the reverse order: he began with the outermost circle of the outermost square and proceeded inwards (so that the examples given in the preceding paragraph, while being the first two sequences in the list, actually occur at the end of the movement). By the end of the movement, the piano and orchestra have followed each other along the inward spiral of sounds to the center point of the circles and squares-which, however, never actually sounds. The chart technique in this movement, therefore, serves poetic as well as technical ends; the gradual coming together of piano and orchestra is simply expressed by the motion to a center, a still silent

point where the opposition of the two forces is negated. Cage has com-

pared the technique of the second movement to the way "a disciple follows his master, in a sort of antiphony, then comes to join the latter in his

impersonality. "33

In the orchestral phrases of the second movement, the technique produces music similar to that of the first movement, and the comments made about that movement apply here as well. The only difference is that since most phrases contain eight sounds here, as opposed to five sounds in the first movement, the prevailing density of events is higher, and the predomi- nant sound durations shorter. Cage produces a certain amount of con-

tinuity in the piano solo, as well. Example 13a shows the sounds selected for use in measures 93-100. Given this sequence of sounds, Cage then added rhythms, dynamics, phrasing, and pedaling to produce the music

given in Example 13b. Note, for example, measures 96-97, where the sound sequence {J2,K3,K1,J2,N2} is linked by rhythm, dynamics, and pedaling to form a single gesture. Or again, in measures 99-100, where the

proximity of the top notes of sounds 12 and K14 form the basis of a per- fectly "logical" cadential figure.

67


M2 K2 K2 M2 M3 N2 J2 K3 K1 J2 N2 M1 M4 02 12 K4 K14 I2 K4 K1

^-' 4 . 0 boO o ' & bo &,D &V o 4, t ,o a's - o

#0oo x? 0

#co #40~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~,

EXAMPLE 13: SECOND MOVEMENT, MEASURES 93-100

The third movement of the concerto was to represent the resolution of the dualism of expression and nonexpression, and for it, Cage for the first time used chance as a compositional tool. He had recently been given a copy of the I Ching, or "Book of Changes" by his student Christian Wolff, and was struck by the similarity of its chart of hexagrams to his own sound charts.34 Cage no doubt also saw in its philosophy of mutually-embracing opposites a parallel to his concerto in progress, and so, for the last movement, he adapted his chart technique to include the use of the I Ching.

The I Ching is based on the interpretation of figures made of six solid or broken lines, which represent the basic principles of weak and strong, yin and yang. There are sixty-four such hexagrams, which are numbered 1 to 64, and which are said to represent various situations in life. To consult the I Ching, one throws three coins to determine each individual line of a hexagram. If the coins come up two tails and a heads, then a strong (yang) line

(a)

68


is obtained, while two heads and a tails results in a weak (yin) line. If the coins come up all heads or all tails, then a "moving" yang or yin line is obtained. Moving lines are considered to be in the process of changing into their opposites. If the hexagram obtained in consulting the book contains any moving lines, a second hexagram is formed in addition to the first by changing all the moving lines into their opposites.

Cage applied this concept of strong and weak forces either remaining constant or changing into one another to create a new sound chart for the third movement. Whereas in the second movement there had been two charts, one for piano and one for orchestra, Cage felt the resolution of the two players in his drama necessitated the use of a single chart with a mixture of piano and orchestral sounds to be prepared from the separate orchestra and piano charts. This chart was exactly like the others with sixteen rows and fourteen columns. For each cell in the chart, three coins were tossed to obtain an I Ching hexagram line. For the purposes of constructing the chart, the orchestra was associated with the strong or yang, and the piano with the weak or yin. If a stable yang or yin line was obtained by the coin toss, that cell of the new chart would be filled by the corresponding cell from the orchestra or piano chart, respectively. If a moving line was thrown, a new sound combining piano and orchestra would be composed and placed in the chart. If the line was a yang moving to a yin, the sound would begin with the orchestra and end with the piano, while if it was a yin moving to a yang, the sound would begin with the piano and "move" to the orchestra. Examples 14a and 14b are examples of the new combination sounds used in the third movement.

(a) (b)

Vla r| Fl

Tpt TTr

Gong I ; -

Piano

Pi?an

EXAMPLE 14: THIRD MOVEMENT, NEW SOUNDS

69


Two additional charts were constructed to govern the moves made on the new sound chart.35 Cage decided to limit these to a set of simple two- part moves: a move down followed by a move to the right. The move down was in a range of zero to seven cells (eight possibilities), and the move to the right was in a range of zero to three cells (four possibilities), thus resulting in a total of thirty-two possible moves, each expressed as a pair of numbers. Two charts, both with sixty-four cells, were used to control these moves: one contained moves only in the even-numbered cells, the other only in odd-numbered cells (see Example 15).

0,0 0,1 0,2 0,3

1,0 1,1 1,2 1,3

2,0 2,1 2,2 2,3

3,0 3,1 3,2 3,3

4,0 4,1 4,2 4,3

5,0 5,1 5,2 5,3

6,0 6,1 6,2 6,3

7,0 7,1 7,2 7,3

0,0 0,1 0,2 0,3

1,0 1,1 1,2 1,3

2,0 2,1 2,2 2,3

3,0 3,1 3,2 3,3

4,0 4,1 4,2 4,3

5,0 5,1 5,2 5,3

6,0 6,1 6,2 6,3

7,0 7,1 7,2 7,3

EXAMPLE 15: THIRD MOVEMENT, CHARTS OF MOVES

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Cage composed the third movement of the concerto one phrase group at a time. To illustrate the method used, I will refer to Example 16, a dia-

grammatic representation of the fourth group (measures 70-92) of the third movement. In this diagram, each of the seven phrases is represented by a separate "timeline" divided into measures and half measures. Cage divided each group into three subgroups in the same way the concerto was divided into three movements: a subgroup of three phrases (3,2,4), followed by a subgroup of three more phrases (4,2,3), followed by the single remaining phrase (5) (the divisions marked by dotted lines in Example 16). The final phrase of five bars (phrase D of Example 16) was to be silent in

every group. Note that the first two subgroups are symmetrical in terms of

phrase lengths. For this reason, the equivalent phrases of each subgroup have been given the same letter designation in the diagram.

A G1,H4 17, L9 10-16 16-,51 30

B Q11,All 38--10 9-,5

C , , , G11,G12 47- 17 23-,35 43- 19 50-+4

C' H5, J5 L8, Q9 E10, G 11 47- 17 23-,35 43- 19 50-,4

B' , Hll,H13 38-,10 9- 5

A' , ,N14 10- 16 16-,51 30

D

EXAMPLE 16: THIRD MOVEMENT, DIAGRAM OF MEASURES 70-92

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In each group, Cage consulted the I Ching once for each measure of the first subgroup, and noted the hexagram numbers obtained. Because of the

possibility of moving lines, each measure could be assigned either one or two numbers. These numbers are shown below the timelines in Example 16, where an arrow between numbers represents a pair of hexagrams result-

ing from one or more moving lines. Once the numbers for the first sub-

group were obtained, Cage, following the symmetry of the first two sub-

groups, used the same numbers for the equivalent phrases of the second

subgroup. These hexagram numbers were applied to the two charts of moves Cage

had constructed. The chart with even-numbered cells filled was used for the first subgroup, while the second subgroup used the odd-filled chart. For each hexagram number, if the corresponding cell in the chart was filled, then the move contained in that cell would be made on the sound-chart, and the resulting sound used. If an empty cell was referenced by the number, then a silence occurred at that point in the subgroup. In the dia-

gram, the sound-chart cells used are given above the timelines, with blank

spaces representing silences. Durations were kept simple; if only one number had been obtained for a measure, then the sound or silence filled the measure. If two numbers were used in a measure, the two sounds or silences were each assigned a half bar's duration. Since the same numbers were used for the two subgroups, and since the two charts of moves were complementary with regards to sounds and silences, the patterns of sounds and silences in the corresponding phrases of each subgroup were also complementary.

Example 17 shows this system in action, depicting the conversion of hexagram numbers via the charts of moves into actual sound cells in the first phrase of the fourth group. In the case of the second sound of that phrase, the hexagram number thrown was 16, indicating a move of down one row, over three columns. When this move is executed from the previous cell (G1), the cell H4 is arrived at. The same number (16) is obtained for the next sound in the phrase, and hence the same move (down one, over three) is used, resulting in cell 17. Thus Cage proceeded, moving from cell to cell on the chart, throughout the movement. Actually, there are two such strands going in parallel, as demonstrated graphically in Example 18, in which the phrases are lettered as in Example 16. The sequence of random moves found in the first three phrases of a group (ABC) continue with the first three phrases of the next group, and so on, through to the end of the movement. Similarly, the moves of the last three phrases of each group (C'B'A ) form an unbroken chain of moves through the movement. When either the right or bottom edge of the sound chart was reached, Cage simply "folded" around to the left or top edge.

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1 2 3 4 5 6 7 8 9 10 11 12 13 14

G1 I > H4

' > 17

-> L9

EXAMPLE 17: THIRD MOVEMENT, CHART MOVES, MEASURES 70-92

A B C .........>

C' B' A'..

(D)

A B C .........

..... > C' B' A' . ..

(D)

EXAMPLE 18: THIRD MOVEMENT, CONNECTION OF PHRASES

The use of a combined piano and orchestra chart, the extensive use of silences, and the simple rhythms combine to give the third movement of the concerto a substantially different sound from the rest of the work. The piano is no longer a solo, alternating with the orchestra on a phrase-by- phrase basis, but is an equal member of the ensemble. The individual sounds tend to be isolated from one another by the silences, and the restricted rhythmic technique prevented Cage from producing the sort of continuity found in the first two movements.

* * *X

A

B C D E F G H I

J K L

M N 0

Q

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10-*16; 16 - 51; 30; = 0,0), 0,3); 0,3), (S); (3,2);


With this account of the composition of the Concerto for Prepared Piano and Chamber Orchestra, we may now see more clearly the strands which pass through this piece, connecting Cage's pre- and post-chance works. First, we find that although Cage continues to use rhythmic structure, he treats it in a significantly different way. In Cage's work up through the String Quartet, rhythmic structure was a means of regulating the phrase- ology of the work. This structure was understood at the phrase level through the medium of melody, and at the larger level by the division of the work into movements or sections. Interest in music, Cage felt, was caused by hearing "the laws of rhythmic structure now observed and now ignored" by the melodic phrases.36

In the "Lecture on Nothing," written early in 1950 as he was on the verge of composing the Concerto, Cage presents a new conception of rhythmic structure based on his realization that such structure exists in complete independence from the sounds that occur within it. Rhythmic structure is fundamentally empty, implying nothing at all in the way of musical content: "It is like an empty glass into which at any moment anything may be poured."37 In the Concerto, the various units of the structure are no longer expressed by melodic phrases, but exist solely as lengths of time in which sounds may occur. The "nothing" of the lecture's title is in fact this emptiness of structure, an emptiness that Cage sees as necessary for the "emergence" of all sounds:38

[Structure] is a discipline which, accepted, in return accepts whatever, even those rare moments of ecstasy, which, as sugar loaves train horses, train us to make what we make.

In describing his new work to Boulez, Cage compares the nature of rhythmic structure to that of physical space:39

I keep, of course, the means of rhythmic structure, feeling that that is the "espace sonore" in which these sounds may exist and change. Composition becomes "throwing sound into silence" ...

Rhythmic structure, in the Concerto, is thus a series of silences, empty compartments into which Cage has "thrown" his sounds. Without this approach to the structure and its inherent emptiness, the method of arbitrarily selecting sounds from the charts could not work well-Cage realized in the Concerto that structure could be a means of regulating a process that would otherwise have had no clear boundaries. To a certain degree, the importance of the phrase in the Concerto is less "musical" than in earlier works, in that it is not a wholly audible one, particularly in the last movement. In the Music of Changes, Cage was to remove all audible traces

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of the structure through the use of shifting tempi. The phrase and section structure remains, as it does in other works through 1956, but it serves only as a convenient means of producing time frames for the distribution of sound materials and also to trigger various compositonal decisions, such as when to change the texture of a work.

The second stylistic thread woven through these works is the use of sound gamuts, now transformed into charts. In previous pieces using gamuts, although the collection of sonorities was strictly determined, their use in the work was left free. The sounds of the gamut in a work like the

String Quartet served to delineate traditional melodic gestures and forms, and hence did not "emerge by themselves," in Cage's view. In other words, although the sounds of the gamut were composed outside of any context, with no connections to one another, they had been placed in a melodic context, so that they acquired relationships to one another by means of Cage's melodic invention. Hence, a dissimilarity exists between the conception of the sounds and their use; the composition of a gamut emphasizes the uniqueness of each sound, but this uniqueness is obscured

through the "false" melodic relations that are introduced. With the Concerto, the chart provided Cage with a means of manipulat-

ing the sounds of the gamut without regard to harmonic or melodic implications. Rather than bind the sounds together in a melodic or harmonic gesture, Cage used the arbitrary moves on the rows and columns of the chart to determine which sounds to use at any given point in the piece. The ordering of the sounds thus had nothing to do with any perceived or

composed relations between them, but rather was dependent only on the coincidence of their positions in the chart with the pattern of moves, both of which were arbitrary. The chart technique of the Concerto produced a parallelism between the fragmentary way in which the gamut was composed and the way in which it was used. The occurrence of a given sound was no longer the result of an imposed melodic or harmonic idea, but was now the result of nothing at all but geometry; the sounds simply "happen."

The "Lecture on Something," written in early 1951 while Cage was still working on the Concerto, deals extensively with the aesthetics of arbitrary sound orders. In the "Lecture on Nothing," Cage had called continuity:40

A demonstration of disinterestedness. That is, it is a proof that our delight lies in not possessing anything. Each moment presents what happens.

In the new lecture, Cage refers to this as "no-continuity" :4

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No-continuity simply means accepting that continuity that happens. Continuity means the opposite: making that continuity that excludes all others.

For Cage, a continuity is the product of an artist's mind-it is an abstraction, something that the artist feels he may "securely possess." With "no- continuity," on the other hand:42

The essential underlying idea is that each thing is itself, that its relations with other things spring up naturally rather than being imposed by any abstraction on an artist's part.

While the use of charts in the Concerto made "no-continuity" possible in the selection of sounds, rhythms and dynamics are still totally under Cage's control. The sequences of sounds produced by the moves on the charts serve as sonorous objets trouvees that are molded by Cage via rhythm and dynamics. Thus, the chart technique only prevents the exercise of Cage's "tastes" in terms of pitch relations (melody and harmony). Cage at that time felt that basing music on pitch relations was wrong and "deadening to the art of music, "43 and so it is not surprising to find that the Concerto, his first foray into "nonintention," would use extra-personal controls only over pitch succession. In the Music of Changes, Cage extended the chart technique to other aspects of the music: tempo, texture, rhythm, and dynamic.

In addition to the extension of old concepts and techniques, there are important new ideas found in the Concerto, as well. The most obvious is the use of chance, and, in particular, the I Ching. Considering the development of Cage's ideas about the emptiness of rhythmic structure and the acceptance of no-continuity, that the Concerto should include his first use of chance is no surprise. Cage himself realized as he wrote the Concerto that his use of arbitrary moves on the charts "brings me closer to a 'chance' or if you like an un-aesthetic choice."44 While the time was ripe for Cage to take on chance as a compositional tool, his introduction to the I Ching by Christian Wolff may have been the impetus for its actual use in the Con- certo. The third movement represented the resolution of the dualisms of piano and orchestra, sound and silence. Cage's use of the I Ching as a model and method for the composition of this movement makes perfect poetic sense; the book's philosophy of strong and weak forces in constant flux directly parallels the interchange of piano and orchestra sounds in the charts, as well as the interchanging of sound and silence between phrases. In later works, the I Ching would become more or less a faceless device in the compositional process, but Cage's attraction to the book may be traced to its singular appropriateness to the message of the Concerto.

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The sound orders produced in the last movement are free of pitch relations to no greater degree than those of the first two movements, which, although not strictly chance-composed, are nevertheless completely arbi-

trary. What makes the third movement sound so different from the others is Cage's arrival at the single most important new discovery of the Con- certo: the interchangeability of sound and silence.

The significance of Cage's treatment of silence can be seen if we articulate the compositional questions implied by his working methods. In his work of the 1940s, rhythmic structure determined phrase lengths, so that the compositional question was: "Given a time length, what phrase shall fill it?" Cage then composed a melodic phrase (using whatever materials were in his total sound gamut) to fill the space. Silences (if present at all) were used to subdivide the phrase into subphrases, or to fill out an unused

portion of the duration. In the first two movements of the Concerto, the compositional

"givens" were somewhat different. In addition to a phrase length, Cage was given a particular succession of sounds to work with, so that the question becomes "Given a time length and a series of sounds, how will the sounds be shaped rhythmically?" Cage no longer has control of the selection of particular sounds, but his tastes are still active in the rhythmic and

dynamic shaping of the sounds. Silences, as we find them in these two movements, are used to articulate the groupings of sounds.

It is with the last movement that Cage discovers a radically new formula- tion of the compositional question. The phrase has given way to the measure (or half measure) as the fundamental compositional unit, and the question becomes "Will there be sound or silence here, and if sound, what particular sound?" Here, for the first time, sound and silence become musical equals, as they have remained in Cage's work through the Music of Changes and beyond.

Cage has himself noted the importance of the treatment of silence in the Concerto:45

Cage: [In the third movement of the Concerto] I had decided to accept rather than seek to control.... At the same time I grant more and more space to silences. Which may signify that I ceased being a composer. The silences speak for me, they demonstrate quite well that I am no longer there.

Daniel Charles: They are no longer expressive silences?

Cage: No. They say nothing. Or, if you prefer, they are beginning to speak Nothingness!

When composition becomes simply the determination of one sound or

77


silence at a time, the fragmentation of continuity into no-continuity is complete; each sound is totally independent of all others:46

Listening to this music one takes as a springboard the first sound that comes along; the first something springs us into nothing and out of that nothing arises the next something; etc. like an alternating cur- rent. Not one sound fears the silence that extinguishes it. And no silence exists that is not pregnant with sound.

The sounds of the Concerto's final movement come of themselves, as a Tibetan poem says, "as from the surface of a clear lake there leaps suddenly a fish. "47

NOTES

1. Paul Griffiths, Cage, Oxford Studies of Composers, no. 18 (London: Oxford University Press, 1981), 1.

2. Michael Nyman, Experimental Music: Cage and Beyond, (New York: Schirmer Books, 1974), 43.

3. Griffiths, Cage, 22.

4. William Brooks, "Choice and Change in Cage's Recent Music," in A John Cage Reader, ed. Peter Gena and Jonathan Brent (New York: C. F. Peters, 1982), 85.

5. John Cage, "Composition as Process: Changes" (1958), Silence (Mid- dletown, Conn.: Wesleyan University Press, 1961), 25. John Cage, For the Birds (Boston: Marion Boyars, 1981), 41, 43,104. Bernard Jacobson, liner notes to sound recording, Nonesuch H-71202.

6. Cage, "Composition as Process," 25.

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7. Jacobson, Liner notes.

8. Griffiths, Cage, 22-24.

9. Monika Furst-Heidtmann, Das prdparierte Klavier des John Cage, Kolner

Beitrage zur Musikforschung, 97 (Regensburg: Gustav Bosse, 1978), 212-28.

10. Deborah Campana, "Form and Structure in the Music of John Cage" (Ph.D. dissertation, Northwestern University, 1985), 75-78, 82-83.

11. I wish to express my deep gratitude to Mr. Tudor for allowing me full access to the documents in his possession, and for his most helpful assistance in my research.

12. John Cage, "On Earlier Pieces" (1958), in John Cage, ed. Richard Kostelanetz (New York: Praeger Publishers, 1970), 127.


14. Cage, "On Earlier Pieces," 127.

15. Cage generally refers to phrases, groups, and sections simply as small, medium, and large "units." To clarify the distinctions between the various structural units, I have adopted a more traditional musical

terminology.

16. Cage, "On Earlier Pieces," 127.

17. John Cage, "To Describe the Process of Composition Used in Music of Changes and Imaginary Landscape No. 4" (1952), Silence, 57.


19. Cage, "To Describe the Process of Composition," 58.


21. John Cage: Catalog of Works (New York: Henmar Press, 1962), 23.

22. Ibid.

23. John Cage, letter to Milton and Crete Cage (20 August 1949), John Cage Archive, Northwestern University.

24. The completion dates for the three movements (according to the published score) are August 1950, 3 October 1950, and February 1951.

25. John Cage, Letter to Pierre Boulez, n.d. [1 September 1950?], John Cage Archive, no. 5.

26. Cage, For the Birds, 41.

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28. John Cage, letter to Pierre Boulez, 22 May 1951, John Cage Archive, no. 18.

29. Jacobsen, liner notes.

30. Because of the preparations, the notated pitches are not indicative of the actual sound produced. What I wish to draw attention to in these

examples is not precise pitch relations, but the presence of simple lin- ear patterns.

31. John Cage, Letter to Pierre Boulez, 22 May 1951, John Cage Archive, no. 18.

32. There are three cases of chart sequences, ultimately assigned to the

piano, for which there are versions sketched out using the corresponding orchestra sounds. Apparently Cage, in these cases, was uncertain as to which chart to use, and thus sketched out both possibilities, choos-

ing whichever he preferred.



35. Although these charts do not survive among the manuscripts for the

Concerto, their existence is necessary to explain the contents of the

surviving worksheets.

36. John Cage, "Grace and Clarity" (1944), Silence, 92.

37. Cage, "Lecture on Nothing" (1950), Silence, 110.

38. Cage, "Lecture on Nothing," 111.

39. John Cage, letter to Pierre Boulez, n.d. [18 December 1950?], John

Cage Archive, no. 15.

40. Cage, "Lecture on Nothing," 111.

41. Cage, "Lecture on Something" (1951), Silence, 132.

42. John Cage, letter to Pierre Boulez, 22 May 1951, John Cage Archive, no. 18.

43. John Cage, "Defense of Satie" (1948), John Cage, ed. Richard Kostelanetz (New York: Praeger Publishers, 1970), 81.

44. John Cage, letter to Pierre Boulez, n.d. [18 December 1950?], John Cage Archive, no. 15.


30

Cage's Concerto for Prepared Piano 81

46. Cage, "Lecture on Something," 135.

47. Quoted in Alan Watts, The Way of Zen (New York: Vintage Books, 1957), 132.

cage concerto prepared piano - james pritchett

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