Time space synthesis: the relationship of the grid to twentieth century music

6/19/15, 8:14 AMTime-Space Synthesis: The Relationship of the Grid to Twentieth- Century Music

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Time-Space Synthesis: The Relationship of the Grid to Twentieth- Century Music Paul Paccione

"The grid is an emblem of modernity by being just that: the form that is ubiquitous in the art of our century....."[1]

Thus art critic and historian Rosalind Krauss describes the importance of the grid as a structure within thevisual arts of the twentieth century. Krauss goes on to state that: "In the flatness that results from itscoordinates, the grid is the means of crowding out the dimensions of the real and replacing them with the lateral

spread of a single surface."[2]

The foregoing observations about the grid and its relationship to twentieth-century visual arts could beapplied to the temporal arts as well, particularly music. It is in the synthesis of musical time and space that thegrid and its geometricized order operates. In modern music, the grid allows for the concept of equivalence ofmusical space and contributes to the abolishment of the opposition between the horizontal and the verticalaspects of this space.

In the visual arts the grid acts as a "mapping of the space inside the frame onto itself."[3]

The mapping ofthe musical space first begins to make its appearance in twentieth-century music in the late serial works ofAnton Webern. In these works the unification of all the elements of a composition is regarded as ideal. As a visual structure, the grid is anti-narrative and rejects sequential reading. This absence of discourse,and rejection of both thematicism and hierarchical order, is explored in music in the works of the so-calledMinimalist composers (Riley, Reich, Glass, Feldman, Young). A number of these composers have eitheremployed grids as a concrete element of their music (for example, Feldman's early graphic music scores) orhave worked with visual artists whose motif is the grid (for example, Philip Glass and Sol Le Witt). In the work ofthese composers time has ceased to be ordered according to what composer Philip Glass describes as the

"traditional concepts of recollection and anticipation."[4]

It is the ambiguity of metric accent (strong-weak) and the absence of the traditional dependency onperiodicity in this music that contributes to this loss of directionality. (Again, this characteristic can be traced backto the music of Webern, where the barline begins to serve more as a frame for the structuring of the musicalspace than a metrical division.) Finally, it is the repetitiousness and unity of the grid that exerts strong influence on the musical space. This paper will explore the grid as a spatial model in twentieth-century music. It will trace the development of thisrelationship beginning with the music of Anton Webern and extending through present-day minimalistcomposers. Grids have become important modes of organization for recent art. Rosalind Krauss writes that: "Bydiscovering the grid, Cubism, de Stijl, Mondrian, Malevich ... landed in a place that was out of reach ofeverything that went before. Which is to say, they landed in the present and everything else was declared the

past."[5]

For these painters the grid emphasized a drawing style that stressed the materialness of the physical

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qualities of the painting's surface, thereby affirming the space of art as self-contained. Igor Stravinsky takes aninterestingly similar stance in regard to the autonomous nature of music when he states: "Music expresses

nothing but itself."[6]

Yet, while the grid does focus on the material nature of art, it has become so ingrained inmodernist sensibility that it has also come to stand as an aesthetic symbol, what Rosalind Krauss describes as

an "emblem of modernity."[7]

Considered this way, Rosalind Krauss notes how the grid can be viewed as a mapping of the physicalqualities of the surface onto the aesthetic dimensions of the same surface. It is the dual nature of the grid(material and aesthetic) that partly accounts for its power. As a symbolic representation of contradiction(material/aesthetic) embodying well-contained forces (horizontal/vertical), the grid has `burrowed down' into our

culture.[8]

In its capacity to emblematize the Modern, the grid's presence emerges not only in the pictorial arts but in

music as well - "the result not of imitation but of aesthetic decree."[9]

Art critic John Elderfield writes that: "Whileit is satisfying to recognize what look like formal continuities, what we really need to distinguish is what belongs

to the established traditions of a genre and what special ways its topics perform in special situations."[10]

Theexamination and justification of function and character of the grid within both the fields of modern music and artis an attempt to decipher meaningful structural functions and directions that lay behind the music and art of thetwentieth century. The basic principle underlying the present analysis is recognition of what English sociologist Michael Lane

describes as "the logical priority of the whole over the parts."[11]

This happens to be a structuralist approach. Lane writes "Probably the most distinctive feature of the structuralist method is the emphasis it gives to wholes,to totalities ...The essential quality of the structuralist method, and its fundamental tenet, lies in its attempt tostudy not the elements of a whole, but the complex network of relationships that link and unite those elements ...structuralism seeks its structures not on the surface, at the level of the observed, but below or behind empirical

reality."[12]

A distinguishing feature of structural analysis is the rearrangement of the sequential features of a story(particularly myths) to form a spatial organization that represents the temporal dimension of the story. In theapplication of this method, features of the story are arranged into vertical columns. In this way the diachronicand synchronic dimensions of time are represented by the horizontal and vertical axes of the grid. Thehorizontal axis indicates temporal succession, the vertical axis indicates the non-temporal relations ofcomparison and contradiction. In this sense the structuralist approach bears a relationship to the formalstructure and character of the grid. Distinguishing features of this relationship include:

1) the priority given to the whole over the parts;2) the priority given to relationships among the parts;3) the rejection of narrative or sequential reading;4) the attempt to deal with contradiction, and5) the basic organization of the horizontal/vertical grid as the matrix of order.

Thus, in order to compare the parallel structures and functions of the grid in the diverse disciplines of art andmusic it will be useful to take a structuralist approach. Suzi Gablik, in Progress in Art states that "parallel developments in two completely different fields ofculture allow one to suspect the existence of a general principle which has operated on the entire evolution of

culture; this concerns the unfolding of `laws of development' within the cognitive processes.[13]

Certain conditions (`laws of development') have combined to bring about the grid as the modern











paradigm. One of these is the concept of equivalence. For Mondrian and the de Stijl, the straight line, the planeand the angle were the primary elements of art. Ultimately for Mondrian, the right angle, consisting of anequivalent but unequal opposition of vertical and horizontal lines, was the purest of relationships. In 1926Mondrian drew up a list of general principles in which he states: "There must be an equivalence of plasticmeans. The duality of opposing elements in the plastic medium is also required in the composition. Constantequilibrium is achieved through opposition and is expressed by the straight line (line of the plastic means) in its

principal opposition in the right angle."[14]

The de Stijl development in Holland parallels the musical developments in the Second Viennese School inGermany. Between 1920-23 Schoenberg composed his first twelve-tone work governed by the `total system of

relations of the sounds with one another."[15]

In an essay which appears in Style and Idea entitled "Composition with Twelve Tones," Schoenberg discussesthe essence of the musical idea and its disposition:

A musical idea though consisting of melody, rhythm and harmony, is neither the one nor the other alone, but all three together. Theelements of a musical idea are partly incorporated in the horizontal plane as successive sounds and partly in the vertical plane assimultaneous sounds ... The mutual relation of tones regulates the succession of intervals as well as their association with harmonies; the rhythm regulates the succession of tones as well as the succession of harmonies and organizing phrases. The unity of musicalspace demands an absolute and unitary perception. In this space ... there is no absolute down, no right or left, movement of tones has

to be comprehended primarily as a mutual relation of sounds, of oscillatory vibrations, appearing at different places and times.[16]

For Schoenberg musical space has no limits or boundaries. The musical work is a relational structure thatthe composer applies to limitless space. Interestingly, the concept of fixed space as only one in an unendingseries of spaces appeared in the art of the Cubists at approximately the same time. The cubists recognized theequivalence of a multitude of perspectives, spatial frames, and points of view that can be applied to an object. The equivalence and relativity of a number of points of view in space is best represented by what art criticClement Greenberg describes as the "all-over, decentralized" or "polyphonic" picture. It is a picture that

dispenses apparently with beginning, middle, and end."[17]

The use of the musical term "polyphonic" is noaccident for Greenberg, who believes there is a specific parallel between Mondrian's term "equivalence" andSchoenberg's twelve-tone composition. Greenberg observes: "Just as Schoenberg makes every element, every sound in the composition of equalimportance - different but equivalent - so the àll-over' painter renders every element and area of the pictureequivalent in accent and emphasis. Like the twelve-tone composer, the àll-over' painter weaves his work of art

into a tight mesh whose scheme of unity is recapitulated at every point."[18]

The grid itself is a synthesis of this àll-over' extension in space. Its appearance in the modern period as amodel for spatial relationships has been concisely summarized by Suzi Gablik:

The geometric grid which the Renaissance, with its Euclidean turn of mind, imposed on the process of representation wassystematically dismantled and `de-constructed'by the cubists:the tendency since then, in the twentieth century has been to use the

elements of geometry abstractly, in the manner of a ùniversal grammar'; exploring and permuting its internal relationships.[19]

Charles Rosen speaks of a similar dismantling that took place in music, of the harmonic and tonalconception of large form:

The renunciation of the symmetrical use of block elements (i.e. cadential formulas) in working out musical proportions places the

weight on the smallest units, single intervals, short motifs.[20]










The unequal but equivalent opposition of the horizontal and vertical aspects of pictorial space that Mondrianspeaks of is similarly addressed by Pierre Boulez in regard to the twelve-tone series and its effect on musicalspace; "The series dilutes the opposition between the horizontal and vertical, just as it creates a universe where

consonance and dissonance are abolished." [21]

Each piece of music possesses its own special form of coherence and is a unique presentation of therelationship (part to part and to whole) of musical time and space. The examination and juxtaposition of thefunction and character of the grid within both the fields of modern art and music is an attempt to deciphermeaningful structural functions and directions. In order to show the connection and continuity that exist betweenboth pictorial and musical conceptions of space in the modern period, some detailed analysis is necessary.

Both Mondrian's Composition With Lines,1917[22]

and Webern's Symphony op.21, 1927, are milestonesin their creators' individual development. In the paintings that culminate in the entirely abstract CompositionWith Lines, Mondrian's style moves from an impressionistic and analytical representation of nature to pureabstraction. And in the Symphony op.21, Webern's serial technique reaches full development and stylisticcohesion. Both works have had an enormous influence on later generations of artists, who have used theinherent ideas as points of departure for their own works. In Composition With Lines Mondrian creates an àll-over', `polyphonic' picture, (similar to lateimpressionism) entirely from short horizontal and vertical lines (and a few squares) of varying size that fill thecanvas with almost uniform density. Some lines occur singly or are paired as equal parallels. Some touch orcross one or two others; in these places, asymmetric clusters of up to six bars are formed. In all cases, thesemodular units stand in contrast to and are surrounded by a white background. In this way, variations on a basicunit result in a decentralized unified texture. The particular disposition of the individual units appears at first to behighly irregular. However, this apparently random disposition of elements on closer examination yields a numberof surprising consistencies:

1. The greater the degree of density of the units the less frequent their occurrence. 2. A certain degree of formal symmetry is achieved by the series of single vertical lines that runparallel to both the left and right edges of the painting. 3. The weight of the composition seems to lean towards the lower, denser half of the surface asopposed to a slight decrease in density towards the upper half.

Thus in Composition With Lines Mondrian seems to have combined both a systematic and intuitive approach inorder to produce a unified composition. Meyer Schapiro notes of this painting how "the simple and regular

compose a surprisingly irregular design."[23]

(The reader is referred to Meyer Shapiro's discussion ofComposition With Lines in the previously cited volume.) This can also be said to be true of the Checkerboard paintings of 1919. In these paintings, the grid isexplicit; in fact, it seems to have been produced almost mechanically. However, the placement of colors seemsto defy analysis except on the basis of intuition. The use of intersecting bars as a means of creating varyingdensities in Composition With Lines is replaced in the Checkerboard paintings by areas of the same color thattouch horizontally or vertically (sometimes even diagonally). In a manner similar to Composition With Lines, thegreater the density of colored boxes, the more limited their occurrence tends to be. An important difference liesin how they are comprised. Composition With Lines is produced through an additive or cumulative process. Thegrid of the Checkerboard paintings is subtractive; that is, the lines are a method of dividing the pre-existentsurface. However, the use of color fields in this painting adds another dimension and it is this element that mustbe applied additively. (It is interesting to note how the horizontal and vertical bars of Composition With Linesrepresent plus and minus signs and, as a result, these paintings are often referred to as such.) The additive andsubtractive nature of the grid has been particularly influential in the methods and concepts of both






painter/sculptor Sol Le Witt and composer Philip Glass. The methods of repetition and modification employed by Mondrian in these works find their parallel inmusic in the techniques of imitation and variation. In both Webern and Mondrian's cases, these principles areapplied as a means of achieving limitless results from limited means. For Webern, the grid had symbolic meaning and illustrates his ideas of balance, symmetry and theequality of horizontal and vertical musical space. To illustrate these ideas Webern used the Latin palindrome("The sower Arepo keeps the work circling.") SATOR AREPO TENET OPERA ROTAS In the analysis of the op.21 which follows, it becomes clear that both the horizontal (duration) and thevertical (registral) dimension receive the most careful attention, and it is clear that Webern is seeking to equalizetheir structural importance. In fact, the strongest aural impression of Webern's music is that everything is ofequal importance. The Symphony in this sense must be viewed whole. Through octave displacement, carefulmeasurement of durations and rests and the compression of lines, the Symphony takes on an àll-over' texture. Contributing to this àll-over' effect particularly in the first movement of the Symphony is the absence of anysolo/accompaniment function - each instrument in the ensemble is equal. In the same way, each pitch receivesits own dynamic and articulation. Twelve-tone compositional technique gave Webern the means to deepen and clarify the unity he wasstriving for. Through the use of contrapuntal techniques, primarily canon, Webern maintains his equality ofvoices and the àll-over' quality of his music. Webern thought of canon as representing the vertical presentationof themes (themes heard simultaneously) and sonata and variation forms as representing the horizontalpresentation (themes heard successively). It was through the use of such traditional techniques and practicesthat Webern achieved thematic unity in his twelve-tone compositions. The Symphony is Webern's crowningachievement in his personal synthesis of the horizontal and vertical dimensions of music. (See example 1.) In Composition With Lines the exposed untouched surface of the white canvas is as actively important anelement of the composition as the pointillistic bars. In a similar way, silence, both contextual and absolute, playsan active role in Webern's Symphony. In the Symphony, motives are reduced to an extremely limited number ofpitches surrounded by rests. Webern's consistent use of disjunct intervals further serves to isolate the individualsounds. The pointillistic texture is further reinforced by the continual use of Klangfarben, where each note ormotive is given a new timbre. As a result, each sound becomes a unique phenomenon in itself. This is similar toDebussy's (and later Varese's more radicalized) view of the chord as a moment in itself. The totality of the registral space receives equal emphasis, and by the unique positioning of sounds, bothregistrally and temporally the individual areas remain unique. Areas of varying density are created by the piling

up of the individual parts or by what Boulez terms "a constellation of events."[24]

An important aspect ofComposition With Lines is the frequent intersection of the bars. In the Symphony the intersection of lines (voicecrossings) is a frequent occurrence that reinforces the autonomy of the individual lines. Similar to Mondrian's use of restricted and divided color areas in the Checkerboard paintings, theorchestration of the Symphony can best be described as pure. That is, the simultaneous orchestral doubling ormix of a sound is rare. Webern is concerned with exploring the way a pitch sounds in a specific instrument, in aspecific register. When the same pitch is transferred among instruments, the aim is the distinctiveness of eachsound. As in Mondrian, beneath what initially may appear in the Symphony as a random disposition of sounds,




is a highly systematized approach. In the opening of the Symphony the serial flow is mainly carried out linearly, in four-part texture, as adouble canon in contrary motion. What is interesting is how Webern chooses to subvert both of the rigidsystems he has adopted for the opening. The row for the Symphony consists of two equal asymmetric six-notesubsets, of which the second half is a transposition in retrograde of the first half (A-F#-G-A flat-E-F/B-Bflat-D-C#-C-E flat). This limits the number of transpositions to 24. In the canon of the first movement, four forms of therow always appear simultaneously. The result of this vertical alignment is the frequent repetition of pitches. Actually, the twelve-note chromatic does not complete itself until the 24th note is reached. In this sense,Webern uses the twelve-note system as a means of defeating itself. In addition, the canon is completelymasked by the frequent voice crossings, uses of Klangfarben and pitch repetition. Thus, Webern's methodproves to be rich enough in implication to encompass this contradiction between the technique and its means ofapplication.

Example 1: Anton Webern, Symphony op.21, I, mm. 1-14.

Copyright 1929 by Universal Edition. Copyright renewed. All rights reserved. Used by permission of European American Music Distributors Corporation, sole U.S. and Canadian agent for Universal Editions.

In the unfolding of the different row forms the registral placement of the individual notes is fixed and isbased on a six-note rotational chord of five perfect fourths and its mirror form, revolving symmetrically aroundthe axis pitch of A natural. The opening of the Symphony therefore can be viewed as one of the most extremeexamples of minimalist technique. That is, the first 26 measures are nothing but the arpeggiation of a single



registrally fixed twelve-note chord! Traditionally, in tonal music, the arpeggio served primarily as anaccompaniment figure and as such was treated not in note-by-note fashion but as a unit (i.e. the triad). In theSymphony, the arpeggio's role is no longer that of accompaniment; rather, it is all that is displayed. Here thearpeggio receives an àll-over' distribution of emphasis and it is the means by which Webern can make coherentthe note-by-note unfolding of the series. It is the arpeggiation of this chord that unifies the various techniques that are applied to the opening. It cantherefore be considered as the composite harmonic field of the piece.

Example 2: 12-note rotational chord from Webern's op.21.

The rhythmic flow of the opening can be viewed in the same way. From measures 1-14, each of theindividual parts, when taken as a composite, yield but one single rhythmic pattern: quarter, half, quarter. Thesecond half of the opening (mm.13-26) yields another pattern of four quarter notes. Thus, though the individualparts seem highly disjunct rhythmically, the composite rhythm takes a highly singular and conjunct approach. The context or mode of organization in Webern's Symphony is both systematic and repetitive. ForWebern, the concept of the grid acts as the invisible means of organization and coherence. In Mondrian, theconcept of the grid is the intentionally visible means of organization. In the works examined thus far, bothsymmetry and repetition play an important role, and, in Webern in particular, symmetry is the predominant formof repetition. In fact, the second section of the first movement of the Symphony consists solely of two mirror-likehalves (mm. 26-44). A similar use of symmetry as a form of repetition occurs in the opening measures of the Variations, op.27(1936). Here the musical gesture or motive is treated as a repeatable modular structure. As in the Symphony,beat and meter act as a scaffolding or frame on which to construct symmetries of pitch and rhythm.

Example 3: Anton Webern Variations op.27, I mm.1-6.Copyright 1937 by Universal Edition. Copyright revewed. All rights reserved. Used by permission of European American Music Distributors

Corporation, sole U.S. and Canadian agent for Universal Editions.



George Rochberg writes: "Although metric uniformity was still characteristic of Webern's style, the loss ofan evident melodic shape took its toll on the directional force inherent in rhythmic periodicity. For the first timesince the beginning of non-tonal pitch orders (atonality and twelve-tone) periodicity and the phrase were broughtto a state of near equilibrium. One of the techniques that reinforced this condition of virtually suspending

rhythmic motion was structural symmetry, for which Webern had a strong penchant."[25]

The beats that make up each measure are of equal value and are referential points in the mapping oftime. This approach is similar to Mondrian's almost mechanical mapping of space in the Checkerboard paintings. The àll-over' distribution of emphasis that both musical time and space and painterly space now receiveis often characterized as being non-relational in effect. That is, individual entities, forms or motives are notpresented against any background and are not related to each other in a hierarchical sense. In clarifying theformal difference between non-relational (non-hierarchical) and relational (hierarchical) art, Lawrence Alloway,former curator of the Guggenheim museum, notes that, although relationships, in fact, still do persist in non-

relational art: "the relations are those of continuity and repetition rather than of contrast and interplay."[26]

Although both Mondrian and Webern eventually moved away from the non-relational surface structure intheir works (for example, Mondrian's use of asymmetry and Webern's use of stratified harmonic areas, alreadypresent in the second movement of the Symphony, it is this aspect of their work that has had the greatestinfluence on a younger generation of individual artists in diverse media who are often referred to as"minimalists." Indeed, repetitive, self-contained, modular structures now permeate modern art and music alike. And thegrid itself has surfaced as the prototypical mode of organization. John Elderfield writes: "For the minimalistsensibility, the grid system supports the flatness and delimitation of the flatness in the painting in question, its

`minimal conditions' for being a painting."[27]

Although much has been written concerning the presence of thegrid as both structure and symbol in the work of minimalist sculptors and painters (i.e. Sol Le Witt, Agnes Martin,Carl Andre, Jasper Johns, Philip Guston) little has been said concerning the presence of the grid concept in themusic of the composers most closely associated with these artists (i.e. Morton Feldman/Abstract Expressionismand Philip Glass, Steve Reich/Minimalism). Indeed, initially their music met with the most interest andunderstanding among visual artists. My examination of a sampling of these composers' works will be more concerned with the music's overallimplications and Gestalt than with note-by-note analysis. Through this I hope to emphasize, in relation to thegrid, the important relationship that exists between what Pierre Boulez calls "the expression of a form and the

content of the composer's thought."[28]

In the late 1940's Jackson Pollock and the Abstract Expressionist New York School of painters (MarkRothko, Philip Guston,Ad Reinhardt) began to develop their own form of painting that was based on the àll-over'and decentralized drawing style of Mondrian's non-relational paintings. The Abstract Expressionists were verymuch concerned with preserving the flatness of the canvas - its surface - and, for these painters, the grid servedas a means of emphasizing both the materialness of the surface and the "all-over" drawing style. The ideas andworks of these artists had an enormous influence on the musical attitudes and methods of composer MortonFeldman. In a similar way, the early non-relational paintings of Mondrian also served as stimuli for Feldman'smusic, particularly his graphic music (Projections 1-4, Out of Last Pieces, Intersections). Clearly one of the moststriking qualities about these works is their resemblance, in terms of sheer visual composition, to the paintings ofMondrian. Indeed, the title "Intersections" is meant to suggest the grid-like character of New York City's streets,where Feldman was living. Feldman's concept of composition as a way of generating ideas and asking questions embraces both







graphic and precise notation and, although he stopped composing graphic scores, his musical intentions andconcerns remained highly singular and consistent. Because it is in his graphic pieces that Feldman began toformulate his central aesthetic tenet, this discussion is limited to these works. In contrast to Earle Brown's graphs of the same period, which are clearly based on the grid structure, forexample, December, 1952, Feldman's graphic scores are not meant as visual stimuli for the performer, but aremore exacting in their demands. John Cage observed that: "On paper, of course, the graph pieces are as heroicas ever, but in rehearsal Feldman does not permit the freedom he invites, to become the occasion for license."[29]

In the Projections series, the parameters of register, number of sounds to be played, timbre and duration arespecified. In the same way an action painter such as Pollock literally `projects' his paint onto a canvas, Morton

Feldman's aim in the Projection pieces was "not to compose but to project sounds into time."[30]

Feldman's use of the word "sound" instead of pitch is important in that, traditionally, "pitch" impliesrelationships with other pitches, whereas sound is not associated with a traditional context. This stance is

similar to Varèse's stated compositional goal of the "liberation of sound."[31]

In the Projections, register andtimbre, being determined by the notation, are the real differentiating structural factors - pitch itself is secondary.

According to Feldman: "What I did was break down the whole notion of close passage work."[32]

These worksare clearly non-relational, that is, there are no identifiable motives and the music is a continuous process,beginning and ending without a particular goal being reached. Michael Nyman observes that: "each note, eachchord, is a separate weight, composed and heard separately, having no priority over the one coming before or

after."[33]

Feldman is also concerned with the surface of his music. He has remarked: "My obsession with surface is

the subject of my music."[34]

As the Abstract Expressionists sought not to disturb the flatness of the canvas (the

space) Feldman wishes to present "time undisturbed in its unstructured existence."[35]

Feldman's approach isclearly a more radicalized version of Webern's non-hierarchical treatment of musical time and space. Thesurface of Feldman's music could certainly be described as flat. The graph is without dynamics or expressivemarks. There are no "solo" or "accompaniment" passages and nothing stands out in relief. Indeed, the graphitself lays flat on the page, unlike the graphs of other composers (for example, the graphs of Sylvano Busotti). An unusual aspect of listening to Feldman's music has always been that individual events are not remembered; each event cancels out the one that came before. And although compositional systems are contrary toFeldman's beliefs, he is so singular in his approach to his materials that this consistency can be viewed asconstituting a system in itself. Feldman writes: "It is not a matter of a controlled or a de-controlled methodology. In both cases, it is a

methodology. Something is being made. And to make something is to constrain it."[36]

Feldman has observed

that an important word for his generation was "ambivalence"[37]

In describing his music, Feldman has said "Mycompositions are really not compositions at all: one might call them time canvases in which I more or less primethe canvas with an overall hue of the music,. I prefer to think of my work as: between categories. Between time

and space. Between painting and music. Between the music's construction and its surfaces."[38]

For Feldman, the grid, and its many implications, are not only present figuratively in the score andconceptually in the music, but symbolically as well, in terms of his relationship to his work. Feldman writes: "Themoment a composer notates musical thought to an ongoing ictus, a grid of sorts is already in operation, as with

a ruler."[39]

The influence of Abstract Expressionism on Feldman is similar in many respects to the reciprocalrelationship that developed between Minimalist painters, sculptors and composers in the 1960's, particularly in













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New York City. It is by way of what Rosalind Krauss describes as the "mutually accessible space of the grid"[40]

that this relationship can best be explored. John Elderfield notes how the emergence of grids and grid structures in the Minimalist art and sculpture ofthe '60s (Sol Le Witt, Carl Andre, Anges Martin, Don Lewallen, Kenneth Nolland) objectified Pollock's previous

approach. In this sense they no longer serviced other pictorial components, for none existed.[41]

Lawrence Alloway writes: "The field and the module (with its serial potential as an extendable grid) have incommon a level of organization that precludes breaking the system. This organization does not function as theinvisible servicing of the work of art, but it is the visible skin. It is not, as that is to say, an underlying

composition, but a factual display."[42]

A distinguishing characteristic of the Minimalist Music which emerged in the '60s (Steve Reich, PhilipGlass, Terry Riley, La Monte Young) lies in its emphasis on musical process. This concern with musical processhas led many to refer to this music as "systematic." However, unlike serial music, wherein the process actsmore as a hidden structural device, the Minimalist emphasis on process is an audible aspect of the music.Replacing the more traditional models of composition, the concern of these artists is with discovering the rightprocess or operation for generating the structural and organizational principles used in the building of the work. The process or system acts not as the simple arrangement of independent elements but as the structuring ofconcepts. The aim of much Minimalist music and art is to project modular sound objects within a given piece bymeans of a continuous and repetitive process. Lawrance Alloway writes "Here form becomes meaningful, not

because of ingenuity and surprise, but because of repetition and extension.".[43]

The process itself is oftenserial in nature, based on additive or subtractive methods (Philip Glass) or some other type of serialmethodology (permutation, rotation). However, between the Serialists in music (Babbit, Boulez) and theMinimalists, the emphasis placed on process (the system) has extended itself from a purely underlying structuralfunction to a perceptual one as well. This emphasis on the perceptual necessitates that the material beingprocessed be minimal in nature, that is, clearly defined, explicit, and ponderable. The intention that the process of the work be perceivable does not necessarily contribute to a loss incomplexity or richness of content. The repeated motive is subject to continuous change. This repeatedtransformation of a configuration (the process) results in a profusion of surface changes that elicit a continuousmultiple number of possible readings. Therefore presupposing, as stated by Lawrence Alloway, "a situation ofmultiplicity (John Cage's continually apt phrase) in which the extension of the module elicits variable readings

but without sacrifice of a consistent structure."[44]

Precedents for this type of formulation or mode of reduction in music can be found in the music of AntonWebern, particularly in the Concerto for Nine Instruments op. 24. This work is based entirely on a three-notemotive. Through intervallic rotation and transposition this modular unit appears in the twelve-note pitch series inall four possible modes of transformation: prime, retrograde, inversion, retrograde-inversion, and is clearlypresented in the opening six-measure introduction. In addition, in the total of 48 row forms, there exist four transformations (P,R,I,RI) of the 4 x 3, twelve-notegrouping that each contain, at the identical pitch level, four different rotations of the three-note modular unit. Inthat it appears four times at the same pitch level, the available material for the composition is reduced to 24distinct three tone groups (and their retrogrades).








Example 4: Anton Webern Concerto for Nine instruments op.24 No.1, mm.1-5.Copyright 1948 by Universal Edition. Copyright revewed. All rights reserved. Used by permission of European American Music Distributors

Corporation, sole U.S. and Canadian agent for Universal Editions.

A. FOUR BASIC KINDS OF STRAIGHT LINES: 1. Vertical 2. Horizontal 3. Diagonal left to right

4. Diagonal right to left

B. SUPERPOSITION: 1. Vertical is the same as in A. 2. is 1 + 2 3. is 1 + 2 + 3 4. is 1 + 2 + 3 + 4



While A is flat, B in tonal.

Example 5: Anton Webern, Op.24 I rotational row forms. Sol Le Witt, plan for Wall Drawing IA & B, IIA& B, 1969. The rotational process at work here is strikingly similar to that presented by Sol Le Witt in his Wall

Markings (1968) [45]

in which the motif is a square divided into four quarters, each one inflected by straight linesrunning across, down and on left and right angles diagonally. Rotation is also an important basis for Steve Reich's Piano Phase (1968). Example 8 shows the first ofthree motivic modules which constitute the piece. One pianist repeats the motive while the other slowlyaccelerates until he is one 16th-note ahead. This process is continued until both players are back in unison. The different alignments of the module against itself result in a continuously shifting accentual scheme. Clearlythe principle that underlies this phase shifting is that of rotation. This is made even more apparent in the verynature of the opening motive itself with its numerous pitch repetitions. Motive one is composed of twelve notes using five different pitches. The left hand notes repeat every six16th notes, the right hand notes every four. In this motive, pitch repetition is generated from the rotation ofdyads within the motive, every six 16th notes. This rotation generates not only the repetition of the five pitcheswithin the motive but the repetition of the motive itself.

Example 6: Steve Reich Piano Phase, 1967, opening module. Copyright 1980 by Universal Edition. Copyright renewed. All rights reserved. Used by permission of European American Music Distributors Corporation, sole U.S. and Canadian agent for Universal Editions. Both the Webern and Reich works make use of this rotational process. However, in Piano Phase, theprocess is gradual, literally slowed down and exposed over an extended time span. This process is all that isdisplayed. It is the essence of the work and as such does not service other musical components. The processis literally the only audible structure of the work. It is the empirical and material means by which we approach thesound. In Opus 24, aspects other than the rotational process are necessary to the work's substance. Theprocess is thus used as a framework to be departed from. It is the underlying organization, the invisibleframework on which to place the more crucially dramatic forms of music (phrase, form, dynamic, melodicdirection, articulation, orchestration). In notes for Music in Twelve Parts, Philip Glass discusses what he sees as the essence of the Minimalist




work; he writes :"It is that one would be able to perceive the music as a presence freed from dramatic structure,

a medium of pure sound."[46]

In its ability to signify the antidramatic, the antinarrative, the antidevelopmental, the antihierarchical, theantirepresentational, the grid has conferred precisely this sense of presence on twentieth-century art. And it isthe grid's capacity to foreclose accepted conventions, to function as an emblem of the minimal, the essential, theirreducible, that has compelled so many twentieth-century artists. List of Available Reproductions Kermit Swiller Champa, Mondrian Studies (Chicago: The University of Chicago Press, 1985). Hans L.C. Jaffe, Piet Mondrian (New York: Harrny N. Abrams, Inc., 1985). Sol Le Witt, Sol Le Witt, ed., Alicia Legg, essays by Lucy Lippard, Bernice Rose, and Robert Rosenblum (NewYork: The Museum of Modern Art, 1978).

[1]

Rosalind E. Krauss, The Originality of the Avant-Garde and Other Modernist Myths (Cambridge: The M.I.T. Press,1985), p.10.

[2]

Krauss, op.cit. pg.9.

[3]


[4]

Wim Mertens, American Minimal Music, trans., J. Hautekeit (New York: Alexander Braude Inc., 1983) pg.88.

[5]

Krauss, op. cit. pg.10.

[6]

Igor Stravinsky and Robert Craft, Expositions and Developments (New York: Doubleday and Company, Inc., 1962)pg.114-115.

[7]


[8]


[9]


[10]

John Elderfield, "Mondrian, Newman, Noland: Two Notes on Change of Style," Artforum December 1971: pg.49.

[11]

Michael Lane, ed., Introduction to Structuralism (New York: Basic Books, 1970) pg.14.




[12]

Lane, op. cit. pg.12.

[13]

Suzi Gablik, Progress in Art (New York: Rizzoli International Publications, Inc., 1977) pg.82.

[14]

Frank Elgar, Mondrian (New York: Frederick A. Praeger, Inc., 1968) pg. 114.

[15]

Arnold Schoenberg, Style and Idea (New York: Philosophical Library Inc., 1950) pg.107.

[16]

Schoenberg, op.cit. pg. 109.

[17]

Clement Greenberg, Art and Culture (Boston: Beaton Press, 1961) pg.155.

[18]

Greenberg, op.cit. pg.156.

[19]

Gablik, op,cit. pg.69.

[20]

Charles Rosen, Arnold Schoenberg (New York: The Viking Press, 1975) pg.21.

[21]

Pierre Boulez, Boulez on Music Today, trans., Susan Bradshaw and Richard Rodney Bennett (London: Faber andFaber, 1975) pg.132.

[22]

The reader is referred to the list of available reproductions at the conclusion of the article.

[23]

Meyer Shapiro, Modern Art: 19th and 20th Centuries (New York: George Braziller, Inc., 1978) pg. 249.

[24]

Boulez, op.cit. pg.132.

[25]

George Rochberg, The Aesthetics of Survival: A Composer's View of Twentieth-Century Music, ed., WilliamBolcom (Ann Arbor: The University of Michigan Press, 1984) pg.111.

[26]

Larence Alloway, "Systematic Painting," Minimal Art: A Critical Anthology, ed. Gregory Battcock (New York: E.P.Dutton and Co., Inc., 1968) pg.45.

[27]

John Elderfield, "Grids," Artforum May 1972: pg.53.

[28]

Pierre Boulez, Orientations, ed. Jean-Jacques Nattiez, trans. Martin Cooper (Cambridge: Harvard University Press,1968) pg.116.

[29]

John Cage, Silence (Middletown: Wesleyan University Press, 1961) pg.128.

[30]

Morton Feldman, notes from record jacket, Durations, Time 58007.



[31]

Edgard Varese, "The Liberation of Sound," Contemporary Composers on Contemporary Music, eds. ElliotSchwartz and Barney Childs (New York: Holt, Rinehart and winston, 1967) pg.196.

[32]

Fred Orton and Gavin Bryars, "Morton Feldman: Interview," Studio International November/December 1976)pg.196.

[33]

Michael Nyman, Experimental Music (London: Studio Vista, 1974) pg.45.

[34]

Morton Feldman, "Between Categories," Composer September 1969: pg.76.

[35]

Feldman, op.cit. pg.75.

[36]


[37]

Orton, op.cit. pg.245.

[38]


[39]

Morton Feldman, Essays (West Germany, Beginner Press. 1985) pg.125.

[40]


[41]

Elderfield, Grids pg.54.

[42]

Alloway, op.cit. pg.58.

[43]

Alloway op.cit. pg.56.

[44]

Lawrence Alloway, "Sol Le Witt: Modules, Walls, Books," Artforum April 1975: pg.41.

[45]

Philip Glass, notes form record jacket, Music in Twelve Parts Virgin Records Ltd. 1974.

[46]

Philip Glass, notes from record jacket, Music in Twelve Parts Virgin Records Ltd., 1974.

Documents

Time space synthesis: the relationship of the grid to twentieth century music