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Composing By Numbers

by James Fulkerson

The following notes were written to accompany recordings by The Barton Workshop of 13 of Feldman's 17 graph pieces. These recordings are to appear in two volumes under the title Composing by Numbers: The Graph Scores of Morton Feldman on the Mode Records label.

Perhaps only because it's been this way for me, it seems that the strongest artists have their 'why' before they have their 'how'. It certainly was that way for Pollock, for Reinhardt, for Judd, for Flavin. It's about having one's 'why' and realizing that everyone else's 'how' won't do; and the continuing search for a personal 'how' that directly answers and relates to his 'why'.[1]

(Joseph Kosuth)

Perhaps the unifying characteristic of the four composers of the New York School (John Cage, Earle Brown, Morton Feldman and Christian Wolff) was their search for an ideal - freedom. Freedom ... but from what or for what? Overall, the 1950's were a time of exploration and re-definition within society and the arts. American composers (and artists) were unfettered by the bonds of tradition - unless it was a tradition which demanded change and innovation. World War II had ended and new world orders were being cemented. Americans had a newfound confidence and were less isolationist than usual. Einstein's theories of relativity had broken the paradigms of Newtonian physics and the ramifications of this new understanding were filtering through into the arts and society demanding a re-examination of how the world might actually work. In place of predictable systems governed by the laws of cause and effect, the world was beginning to consider that it was perhaps a world of chance and indeterminacy. What did this mean for the world as a whole, within the world of an individual and how should this be reflected in a work of art?

On a completely opposite tack, modernists were posing the question "What is the fundamental nature of this art form?"[2] The work of Cage and his associates can of course be understood as a continuation of the modernist's examination of the arts: a stripping away, a paring down of materials - until one had defined the absolute essence of an art form.

However, the greatest single change within Cage's work came about with his acceptance of Zen Buddhism. He began to ask the question, "What might be possible?" instead of trying to express himself through his musical compositions. He sought not to impose his ideas but to set up a system which could create the mechanisms necessary to make the requisite decisions to bring about a musical performance. His intentions were to devise a system wherein he could become educated/enlightened/entertained by learning what might be possible instead of imposing his thoughts on musical materials. This process of working led him to expand what was previously defined as music and to include much of the world at large including the act of performing music (theatre) as the proper materials of music itself.[3]

When Feldman met Cage, they quickly established a friendship based upon a similarity of intent and a mutual respect for the work each was doing. What exactly was that music like at the time and what were the aesthetic aspirations of these composers? Feldman has spoken of the first meeting between himself and Cage after the performance of Webern's Symphony in Carnegie Hall during the winter of 1949-50. Soon thereafter, Feldman showed a string quartet he had been writing to Cage. Cage's enthusiasm for this work and his delight in Feldman's being unable to explain "how" he had written it gave Feldman an all important "permission" to follow his intuition. In any case this period of time marks the beginning of Feldman's "graph music" or graphic notation - so named because it was written on graph paper. As a term, graphic notation signifies within 20th century music, the practice wherein which music notation has departed from the traditional staff notation. This departure was necessary for many composers as they tried to express different aspects of music making which they considered to be very important but which they felt were not conveyed within the conventions of staff notation.[4]

What were some of the aesthetic aspirations of Cage, Wolff, Brown and Feldman? They sought a music free from gesture or musical rhetoric, allowing sounds to be heard as individual entities. They sought a plasticity of musical materials which would correspond to the freedom which the abstract expressionist painters were achieving on their canvases.

"...in connection with musical continuity, Cowell remarked at the New School before a concert of works by Christian Wolff, Earle Brown, Morton Feldman and myself, that here were four composers who were getting rid of glue. That is: Where people had felt the necessity to stick sounds together to make a continuity, we four felt the opposite necessity to get rid of the glue so that sounds would be themselves."[5]

In so far as these composers were trying to "unglue" their music, trying to allow the sounds to be themselves, the Projection scores of Feldman were important conceptual breakthroughs for him (and the others of the New York School). Rather than dealing with a musical rhetoric, Feldman was able to "project" sounds in space. The time dimension of music was a canvas upon which he could "paint/paint" his sound palette.

"'Art should come from within; then it is profound.' But it seems to me Art goes within, and I don't see the need for "should" or "then" or "it" or "profound." When Art comes from within, which is what it was for so long doing, it became a thing which seemed to elevate the man who made it above those who observed it or heard it and the artist was considered a genius or given a rating: First, Second, No Good, until finally riding a bus or subway: so proudly he signs his work like a manufacturer.
But since everything's changing, art's now going in and it is of the utmost importance not to make a thing but rather to make nothing. And how is this done? Done by making something which then goes in and reminds us of nothing. It is important that this something be just something, finitely something; then very simply it goes in and becomes infinitely nothing.
It seems we are living. Understanding of what is nourishing is changing. Of course, it is always changing, but now it is very clearly changing, so that the people either agree or they don't and the differences of opinion are clearer. Just a year or so ago everything seemed to be an individual matter. But now there are two sides. On one side it is that the individual matter going on, and on the other side it is more not an individual but everyone which is not to say it's all the same, - on the contrary there are more differences. That is: starting finitely everything's different but in going in it all becomes the same. H.C.E.
[6] Which is what Morton Feldman had in mind when he called the music he's now writing Intersection. Feldman speaks of no sounds, and takes within broad limits the first ones that come along. He has changed the responsibility of the composer from making to accepting. To accept whatever comes regardless of the consequences is to be unafraid or to be full of that love which comes from a sense of at-one-ness with whatever."[7]

Feldman composed Projection I (thru) V, Intersection I-IV, Marginal Intersection, Ixion, Atlantis, ...Out of 'Last Pieces', The Straits of Magellan, The King of Denmark and In Search of An Orchestration using his graph notation between 1950 and 1967. For 17 years during the 41 years in which he composed what he considered to be his "work" he used both graph notation and conventional stave notation. Feldman moved away from these graphic scores - noting that he had not achieved the freedom from gesture that he had truly sought.[8] It should be noted that he never abandoned staff notation while he employed the graph notation. The freedom from gesture to which Feldman refers was his own freedom from gesture rather than the performer's.

"Between 1953 and 1958, the graph was abandoned. I felt if the means were to be imprecise the result must be terribly clear. And I lacked that sense of clarity to go on. I hoped to find it in precise notation; i.e. "Extensions for Three Pianos", etc. But precision did not work for me either. It was too one-dimensional. It was like painting a picture where at some place there is always a horizon. Working precisely, one always had to "generate" the movement - there was still not enough plasticity for me. I returned to the graph with two orchestral works: Atlantis (1959) and "...Out of 'Last Pieces'" (1961), using now a more vertical structure where soloistic passages would be at a minimum."[9]

In these 17 works, Feldman was searching for a plasticity and freedom that he never seems to have fully captured. Yet, when he began to compose these graphic scores, he seemed to be further along his envisioned path than even Cage. In addition, one hears in these works, many musical attributes which other composers were later to embrace as essential trademarks within their compositional styles but which were nevertheless rejected by Feldman in his own later works: the micro-polyphony of later Ligeti, noise, ferocity in the sound or performance gesture.

How should one hear these works? Early, unimportant works, interesting early studies, works which showed him the way forward (the 'how') to an originally sensed vision (the 'why')?

One often hears that Feldman's music never changes/changed - which we see is clearly not true. I suggest that these works all exist within an original "why" as defined by Kosuth. I suggest that they are simply works within the entire output of Feldman - more original perhaps than later work in some respects - but most importantly, simply part of the output of one of the 20th century's remarkable composers, works we need to know to understand the aspirations of Feldman. Of the 17 'graph pieces' (18 if one considers the score to his tape composition as a score which someone might realize), this recording offers a total of 13 of them. They appear on the CD in their order of composition to assist the listener in comprehending the development of Feldman's compositional thinking:

1Projection I (1950)solo cello
2Projection II (1951)flute, trumpet, piano, violin, cello
3Projection III (1951)2 pianos
4Projection IV (1951)violin and piano
5Projection V (1951)3 flutes, trumpet, 2 pianos, 3 cellos
6Intersection I (1951)orchestra
7Marginal Intersection (1951)orchestra
8Intersection II (1951)solo piano
9Intersection III (1953)solo piano
10Intersection IV (1953)solo cello
11Out of 'Last Pieces' (1961)orchestra
12The Straits of Magellan (1961)flute, horn, trumpet, amplified guitar, harp, piano, bass
13In Search of An Orchestration (1967)orchestra

Other quotes from John Cage with resonances to Composing By Numbers:

"... The idea, consequences, suggests the musical term continuity and that produced a discussion last week for Feldman spoke of no continuity, whereas it was argued from a rational point of view that no matter what there is continuity. This is again a matter of disinterest and acceptance. No-continuity simply means accepting that continuity that happens. Continuity means the opposite: making that a particular continuity that excludes all others... [10]
"...at the root of all this is the idea that this work is a thing separate from the rest of life, which is not the case with Feldman's music. We are in the presence not of a work of art which is a thing but of an action which is implicitly nothing. Nothing has been said. Nothing is communicated. And there is no use of symbols or intellectual references. No thing in life requires a symbol since it is clearly what it is: a visible manifestation of an invisible nothing. All somethings equally partake of that life-giving nothing."[11]

© James Fulkerson, 2002


  1. Joseph Kosuth Art after Philosophy and After: Collected Writings 1966-1990, pg 82
  2. This is, of course, at odds with the ideas of indeterminacy which by their definition suggest that nothing can be completely known because of its indeterminate nature.
  3. Once, when being pressed by a journalist over the people who had influenced his work, he replied, "Stravinsky and Schoenberg. Stravinsky because I chose not to study with him and Schoenberg because I did study with him. Furthermore, while Schoenberg said that all twelve sounds were equally acceptable, I said by extension, that all sounds were equally acceptable."
  4. Graphic scores are scores that have departed, for various reasons, away from the stave notation that has served musicians for several centuries. While Feldman's graphic scores in fact utilize graph paper, more often the term refers to the use of various graphic symbols appearing within a space = time continuum. The vertical space represents pitch and the horizontal line represents time. The size of a symbol or thickness of a line represents dynamics. Such notation has an inherent ambiguity as to whether the thickness of a line drawn within such a continuum represents a cluster or a single, loud sound. Earle Brown's December 1952 - often labeled a black and white Mondriaan (painting) - is probably the prototype for this approach. However, his instructions for December 1952 could just as easily be understood as the score for the piece while the graphic page itself is only a possible representation of any one moment.
    In Feldman's graphic scores, he used the unit of a box as being equal to a given slice of time and indicated the number of notes to be played on or within this given unit. In solo pieces, he tended to use three boxes to indicate the high, middle or low ranges of a given instrument but in ensemble pieces, he tended to specify that the notes were free with respect to range or were exclusively high (most often) or low. Unlike his later work, the dynamics were often freely chosen by the player. In performing these early graphic works, I feel it is important to perform them using the freedoms and restrictions which he enumerates - rather than using a revisionist approach in which one plays them using the hindsight of how Feldman developed to make them sound like later Feldman. While as a performer, it would be more satisfying to get all the brass players (or woodwinds or string players) to simultaneously begin what amounts to a cluster at the beginning of a beat - a precise beginning! - this is not what Feldman allowed in these scores. One must let the performers make their individual choices as to when they will play within this given unit of time. A precise beginning within the ensemble pieces is a rarity! Yet, some scores such as Intersection 2, 3 and 4 require so many notes to be played within a short amount of time, performers have had to make some sort of "sub-score" or pre-realized part in order to do more than just slap at fistfuls of notes. These works demand extreme virtuosity from the soloists - both physically and aesthetically!
    Sometime ago Arthur Weisberg said that a fully notated score contained about 30% of the information one needed in order to perform it - his implication being that what is not there must be added by performers based upon their personal training and experiences. The working assumption today is that, given the small amount of information which a score can convey, composers are creating roadmaps in which they indicate the most important points necessary in order to create their music. Some composers moved to graphic scores because they felt what they needed was not being conveyed by traditional stave notation. Currently composers view scores as a communication system in which one tries to communicate as efficiently and clearly as possible and chooses the best notational system to achieve this.
  5. John Cage, Silence : History of Experimental Music in the United States, pg 71
  6. H.C.E. = Here Comes Everybody
  7. John Cage, Silence: Lecture on Something (1959) - actually written earlier but was printed in 1959, pg 129
  8. Morton Feldman: Morton Feldman: Essays - Autobiography edited by Walter Zimmermann, pgs 38-39:
    "After several years of writing graph music, I discovered its most important flaw. I was not only allowing the sounds to be free - I was also liberating the performer. I had never thought of the graph as an art of improvisation, but more as a totally abstract sonic adventure. This realization was important because I now understood that if the performers sounded bad it was less because of their lapses of taste than because I was still involved with passages and continuity that allowed their presence to be felt."
  9. ibid
  10. John Cage, Silence: Lecture on Something (1959) pg 132
  11. ibid, pg 136

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