Of Diagrammatology: Graphic Notations


This post explores the concept of notation developed in the 1960s by a diverse group of artists and composers including John Cage, Jackson Mac Low, LaMonte Young, George Brecht, Cornelius Cardew, and Anthony Braxton. In such collaborative collections as An Anthology (MacLow and Young), Notations (Cage, Treatise and Scratch Music (Cardew), these artist-composers developed a new medium of polysemiotic notation, mixing images or graphics with text instructions and musical notation, towards a utopian reconception of everyday experience in ordinary spaces. Anthony Braxton, similarly, beginning his career within the experimental jazz and avant-garde African-American musical tendencies of the 1960s, evolved an idiosyncratic graphic idiom for both his scoring and his titles. Although several of these figures, including Cage, Mac Low, and Cardew are now deceased, Braxton continues to compose utilizing an ever-more intricately interwoven texture of ideas, graphic symbols, and theatrical or operatic motives, showing the continued potential of this compositional thinking for innovative sound art.


Works of these sorts inevitably raise questions of the status of the score in relation to the “work”: Are the scores to be considered subordinate to performative interpretation? Or are performances primarily to be seen as partial, and problematic, attempts to realize in sound and motion a dense, suggestive work of visual and verbal art on the page? Are the scores independent sites of visual invention, and if so, by what standards should be judge them? In cases where interpretation is indeterminate and left up to performers’ choices, how do we understand the relations between score and performed instance of the work? And given the problems of translating graphic or diagrammatic figures that are not traditional means of notating music, how do we conceive of the relationships of visuality and aurality, reading and listening, simultaneous spatial apprehension and sequentiality as modes of experiencing the work? Finally, given the typical presentation of these works in anthology-like collections, as well as their more typical circulation as scores, to what extent does publication format play a role in their aesthetic status and effect? Can we discern generic effects of their being grouped, in a kind of montage, with other scores or analogous texts, thus highlighting their visual and verbal qualities at the expense of their relation to performed music and sound?


Given the diversity of these composers and their projects, there is no single answer that covers each case. Each work, with its concrete compositional features, implies a somewhat different configuration of score and work, visuality and aurality, simultaneity and sequentiality. However, it is possible to generalize that notations, as these conceived them, were not merely the abstract precursor form of a performed musical or sound work, but also themselves a medium of imaginative practice and experiment with the grammar, logic, and shape of holistic experiences and possible life-situations. Although actual performances might be based on notational scores, the scores also had an autonomous, intensive performative dimension as well, which might even predominate in some cases. As Cornelius Cardew notes in his Treatise Handbook about such works, “the sound should be a picture of the score, not vice versa.” Hence, these works often challenge the hierarchical relation of performance and score characteristic of traditional musical, dance, and theatre notation, in favor of a new dialectic of imagination, material practices of écriture and drawing, and performance.

Taking inspiration from the expanded notion of writing that Jacques Derrida advanced in his landmark book Of Grammatology, I have entitled my exploration of this topic, which spans a wide variety of artistic instances of notational practice, “of diagrammatology.” By this title, I mean to imply that both the indeterminate graphism of the score and the spatio-temporal topology of the performed sound event participate in in a common logic of the trace, which Derrida analyzed in his early essay “Differance.” Neither the notated score, I wish to suggest, nor the performance manifest the presence of the artwork, which has its paradoxical existence in being not-yet performance (as score) or as no-longer score (as performance). In other words, these works exist in the self-effacing interval between these two states, and can be said to exist as the differance, the spacing and delay between these two disjunct artistic conditions.

As Derrida writes, Insert

“The trace is not a presence but is rather the simulacrum of a presencethat dislocates,displaces, and refers beyond itself. The trace has, properly speaking, no place, for effacements belongs to the structure of the trace. Effacement must always be able to overtake the trace; otherwise it would not be a trace but an indestructible and monumental substance. In addition, and from the start, effacement constitutes it as a trace–effacement establishes the trace in a change of place and makes it disappear in its appearing. . . . [T]he present becomes the sign of signs, the trace of traces. It is no longer what every reference refers to in the last instance; it becomes a function in a generalized referential structure.”

The present becomes destabilized by the oscillation of the notational work between two states, which refer to one other, but with a gap of time and of space, indeed, of temporality (textual-graphic vs. enacted) and spatiality (virtual page space vs. three-dimensional, embodied space). as ontological dimensions of the work Both point to an underlying rhythmic articulation in terms of interval: at once spacing and temporal delay.




Before I go on to discuss some of the examples of avant-garde work, I want to define more closely the function of notation in its traditional sense. To begin with a fairly abstract philosophical definition, that of Nelson Goodman, we can see that the emphasis in traditional definition of notation falls on the identity and reproducibility of the structure of the work, as it passes into ciphering by the composer and emerges out of the deciphering process of the interpreter-performer. Goodman writes: “Symbols in a notation. . . are unambiguous and both syntactically and semantically distinct. A notational system must meet these requirements if it is to serve a primary function: preservation of work-identity in every chain of correct steps from score to performance and performance to score. A system violating these requirements will not guarantee that all performances in such a chain are of the same work.” Notations, in this sense, reduce structure to a set of unequivocal symbols that allow the piece to travel across time and space, while preserving its identity. By implication, then, notations that are “deficient” or deviant by Goodman’s standards–such as the graphic and verbal notations that I’m discussing–would lead to, or even actively encourage, mutation, difference, metamorphosis, or multiplication of identities as the score travels and endures.

In an address given in the new music center Darmstadt in 1960, “Time, Notation, and Coding,” composer Pierre Boulez analyzed and evaluated notation systems in terms of their rational, abstract ability to encode structure and especially to represent time. This presentation intervened into a context that was being shaped by the emergence of new notational practices, especially occasioned by electronic music and by the extension of serial composition to other parameters of music besides melody. Several important composers from Europeans such as Karlheinz Stockhausen and Boulez himself to Americans such as John Cage and Earle Brown were beginning to experiment with graphic scores. Boulez distinguishes between two historic means of notation, notations that simply represent the movement of music in time by a moving line (“neumatic”) and notations that represent music symbolically (for instance, the typical Western notational system of notes positioned on staff lines with pitch and duration represented by symbolic conventions). He argues for the superior abstraction and reliable codification that the move to symbolic notation involved, and therefore expresses skepticism that graphic notation represents any kind of advance in the compositional tools available to the New Music:

“[G]raphic notation does not completely cover the area covered by symbolic notation: it represents a regression from the general to the particular, and a return to the ideogram would be a further retreat. Any logical and coherent notation in the future will have to include what it replaces and will have to subsume our present symbols, the neumatic symbols and the ideograms. Until such a system is invented, any graphic notation will only constitute a regression, at best a literal, graphic transcription of a situation that can only be translated into symbols. It will be no more than a sheet of figured values.”

Although Boulez stresses that he does not reject all graphic solutions to notational problems, graphic and figural means, for him, are only progessive if they are subsumed into a larger, more powerful, more abstract and comprehensive symbolic system that would allow the composer greater control over the various sound dimensions that constitute his composition.

Cornelius Cardew, whose graphic composition collections Treatise and Scratch Music form two of the key examples I will discuss later on, offered an analogous view in an essay from the mid-1970s entitled “Wiggly Lines and Wobbly Music,” published in the art journal Studio International. He distinguished between graphic notation, which he acknowledged as an element in the technical progress of musical composition, and “graphic music,” in which “the graphic element has become dominant” and which “tends to be conceptual rather than pragmatic.” Graphic notation, Cardew writes: “is a perfectly justifiable expansion of normal notation in cases where the composer has an imprecise conception. . . . For example, if a composer wants a string orchestra to sound like a shower of sparks, he can interrupt his 5-line staves and scatter a host of dots in the relevant space, give a rough estimate of the proportion of plucked notes to harmonics, and let the players get on with it. This is graphic notation in the best sense of the work–vivid and clear.”


In contrast, Cardew understands graphic music as a relinquishing of musical discipline and a transferral of musical skill over to, at best, a graphic discipline that makes musical scores into aesthetic artifacts in their own right. Graphic music “leaks out into various areas that have nothing to do with music notation.” Thus, for Cardew, as for Boulez and Goodman, the identity of the work is at issue in the problem of graphic notation: both the identity of the individual artwork and its distinct placement within a medium-based artistic practice clearly identified as music or sound art. At the same time, however, Cardew, who primarily wishes to defend the value of composition as a specifically skilled social and communicative practice, admits the value of graphic music as a pivot around which a transformation of the artistic world took place, beginning in the 1950s:

“In the crisis of extreme formalism that occurred in the post-war avant-garde . . . a reaction was inevitable. Catchwords like “Open Form” and “Indeterminacy” that drifted over from the States in the mid-1950s were eagerly welcomed by young avant-gardists who felt stifled by the dominant determinism of the European scene. Under these catchwords the genre of graphic music flourished. It not only reinstated the interpreter as an active participant in a non-mechanical way in the musical process, but also enabled improvising musicians (who often have not learned traditional notation) and amateurs to participate in the production of avant-garde music.” DSC_0041

Though Anthony Braxton is adept with a range of traditional and non-traditional notations, this last remark of Cardew roughly describes his situation. Coming out of the free jazz and African-American musical experimentalism of the 1960s, but also eclectically assimilating in an auto-didactic blend a range of European avant-garde and experimental influences, Braxton has developed an idiosyncratic graphic musical compositional practice that finds its location in this looser space between notation, drawing, music, and narrative or drama.


An Anthology (La Monte Young and Jackson Mac Low)

In 1961, as a special issue of the West Coast magazine Beatitude West, composer La Monte Young and poet Jackson Mac Low gathered together a number of scores, scripts for Fluxus events and experimental dance pieces, essays, and poetry. The collection was published in 1963, under the title An Anthology, and was republished, in a slightly expanded form in 1971. This work became extremely influential, as it publicized and generalized the interdisciplinary collaboration of artists working across media of visual arts, film, music, literature, dance, and theater, with their work converging not only in common performances in certain gallery spaces and venues, but also in a new interest in scripts and scores requiring substantial interpretation and choice from the performers. Although its genesis was only partially connected to the influence of John Cage, An Anthology can nevertheless be legitimately seen as significant evidence of the generalized impact of Cage’s aesthetic on the art world, and not just on composers.


The book itself is designed as a sort of montage work, not only insofar as it juxtaposes work in different media by a range of artists, but also materially: it uses a number of non-standard typographical formats, incorporates colored construction paper pages and folded inserts, and even contains envelopes holding further formats such as note cards (as in Composition 1960 #9 by La Monte Young, an event score composition). The suggestion is both whimsical and multidimensional, making the book appealing surprising to page through, when one suddenly comes across an unexpected insert or fold-out or enigmatically formatted page. In one sense, the work is a paradigmatic, early example of conceptual art.

In fact, in keeping with this genealogy, although graphics and drawing are certainly not absent from An Anthology, and while the typography tends to lend its words an ideogrammic, figurative quality, verbal language actually predominates here over the visual. In some cases, the verbal scripting emphasizes the conceptual nature of the work, while in other cases, it highlights the gap between the verbal instructions of the composer of the script and its embodied interpretation by the performers. The abstract, even paradoxical or absurd, character of the instructions stands in a productive, ambiguous tension with the need to realize the script in concrete bodily gestures and actions.

The book, too, might be seen as a kind of analogue of a space of artistic activity or an artistic community. Visual artists, musicians, poets, dancers communicate and intermingle, taking inspiration from one another and from their commonalities, which the abstraction of language allows to come to the fore in the virtuality of the anthology, before it is differentiated and concretized by different artistic practitioners working in their media and disciplines. It prefigures a utopian community to come, a community of an aesthetically transfigured life practice typical of the avant-garde. Yet this passage through language also suggests that this community is traversed by the paradoxical trace, as the utopian community to come will have already happened as an event of language and graphic signs, opening an ontological interval of spacing and deferral between the text on the page and sounds, movements, and objects occupying real space and duration.


Notations (John Cage)

In 1969, John Cage published an anthology of music manuscripts entitled Notations; it appeared with the Something Else Press, directed by Fluxus artist and intermedia theorist Dick Higgins. The collection of the manuscripts was inspired by the Mac Low and Young anthology and was a benefit for the Foundation for Contemporary Performance Arts. In format, it is more uniform materially–it has none of the collage aspects of An Anthology–but it more consistently represents the textual aesthetic that Cage developed in his own books such as his influential volume Silence. He attempted to allow the book to respond to the contingencies of circumstance and helped this process along with injections of arbitrary, non-hierarchical criteria of arrangements such as alphabetics and through the use of chance methods.

Thus, the manuscripts are not grouped according to notational type, style, or other technical or aesthetic criteria, but solely according to the alphabetic position of the composer’s name. The works appear without further informational text other than composer’s name, title, and sometimes date. There are, however, brief texts that accompany the manuscript scores, but these texts are arbitrarily selected and arranged according to chance methods. Hence, they are not commentary on the score, but fragments of a larger discourse about notation and composition, which is of equivalent status with the scores, fragments of the total musical discourse of the present. To emphasize this independence of the text from any direct, intended commentary function, Cage even subjected typography and other elements of graphic design to chance selection: “Not only the number of words and the author, but the typography too–letter size, intensity, and typeface–were all determined by chance operations. This process was followed in order to lessen the difference between text and illustrations.”


Mac Low’s and Young’s An Anthology had played between presenting its individual scores and texts as individual works and presenting itself as a composite montage work whose medium was print and paper, text and graphics. Its use of different papers and heterogeneous inserts underscore the potential detachability of the individual work. Indeed, one can imagine someone performing a selection of events out of An Anthology. Cage’s Notations, in contrast, tends to become an autonomous work of printed, published art: a book composed of graphics and texts, arranged in a consistent way by chance methods. It is more unified, and in a way, more traditional than An Anthology, which has more of the anarchic energy of the avant-garde.

Nevertheless, Cage’s work also gains by this greater coherence as a vehicle of his social thinking, which emphasized creativity and interaction of individuals within an anarchist cooperative relationship. One catches a glimpse of this sidelong reference to a social order in the preface, where Cage offers the following metaphor to explain the lack of explanatory text: “A precedent for the absence of information which characterizes the book is the contemporary aquarium (no longer a dark hallway with each species in its own illuminated tank separated from the others and named in Latin): a large glass house with all the fish in it swimming as in an ocean.” Cage combines here, in a witty image, and one particularly appealing to a Californian who lives near the great Monterey National Aquarium, the idea of community (having overcome their isolation, which derived from their being displayed as individual cases of precious beauty, all the species swim together and create a more open, fluctuating beauty) and the idea of unconstrained freedom (they swim without bumping into glass walls, as in an ocean).

Cage even draws upon the imagery of the architectural utopia that excited the dreams of modernists from Ludwig Mies van der Rowe to Walter Benjamin to André Breton: the glass house. The book Notations, then, presents itself as a work of utopian architecture where all the beautiful fish of musical creativity can be housed: the blank covers, almost untainted by text, figure the transparent walls that contain this rich fauna, yet allow it to intermingle freely.


Treatise and Scratch Music (Cornelius Cardew)

Concurrently with this activity around graphic notation in the United States, the British composer and virtuoso pianist Cornelius Cardew was at work on what would become one of the most spectacular and extended works of graphic music, Treatise, composed between 1963 and 1967. The original drafts involved a mixture of musical and graphic composition, first with sixty-seven, then ninety-nine pages. Both extended and rewritten over several years, the composition eventually extended to one-hundred ninety-three “elements,” each comprising a page of scored graphics. As with Cage’s presentation of the manuscripts in Notations without textual commentary, so too Cardew wrote Treatise “with the definite intention that it should entirely on its own, without any form of introduction or instruction to mislead prospective performers into the slavish practice of ‘doing what they are told’.”

Unlike Cage’s book, however, Cardew’s was intended not simply as an anthology, but rather as a unitary work, for which actual performance was envisioned. In fact, as Cardew documents, the work was already performed in part in June 1964 and May 1965, and many times subsequently. Treatise thus not only raises general questions about the relationship of graphics and performances; it poses performers with specific problems of how to translate its unconventional graphic notation into sounds on particular instruments, none of which is specified in the score. It is clear from Cardew’s various notes–which he collected in a subsequent volume entitled Treatise Handbook–that he saw Treatise as a problem-piece that should occasion reflection and action on the part of its reader-interpreters.

For example, in a note to himself early in the process of composing the work, he wrote: “The test: Devote time not to writing on in the treatise, but studying it and trying to realise what exactly is at work in it. How does it keep my imagination at work? What actually am I manipulating in the way of material? Do I assume some material that is not explicit (eg. real sounds)?” (May 1963) But along with this philosophical aspect, he also from the beginning had in mind the social aspect of the piece, as a spur to collective action, for which both traditional and non-conventional notations are problematic means: “Notation is a way of making people move. If you lack others, like aggression or persuasion. The notation should do it. This is the most rewarding aspect of work on a notation. Trouble is: Just as you find your sounds are too alien, intended ‘for a different culture,’ you make the same discovery about your beautiful notation: no-one is willing to understand it. No-one moves.” (8 Feb 1963)


In subsequent years, he emphasized what was also suggested by its title, its quasi-discursivity and   even narrativity, writing in December 1966, for example, that “Treatise is a long continuous drawing–in form rather similar to a novel.” In April 1967, he would state: “It is comparable to a lengthy work of prose treating exhaustively of a number of topics. In Treatise the topics are graphic elements.” Treatise remained a kind of device for exploring the borderlines between music and graphic art, musical education and visual education, discursivity and non-discursive experience, seeing and reading, and so on. Cardew’s revisions and shifting commentaries on it suggest that its real value was precisely its problematic, paradoxical nature, its production of exemplary problems, reflection upon which could occasion deeper levels of artistic, existential, and social understanding.

In the late 1960s, Cardew had gone even more radically in the direction of an improvisatory aesthetic, having helped constitute the Scratch Orchestra, which was composed of amateur and untrained musicians. Since the Scratch Orchestra was a large, anarchic bunch that was notoriously unpunctual, members of the Orchestra were encouraged to keep notebooks and make sketches for improvisation by a smaller group; these could be played while waiting for the Orchestra members to show up. This music was called “Scratch Music,” and the collection, which includes work by Cardew, the visual artist Tom Phillips, composer Michael Parsons, and others was published in 1972. These notebook pieces were intentionally whimsical, rapidly jotted or sketched pieces meant to capture inspiration from the flow of everyday experience. As Cardew wrote in a note in 1970, “Rites and Scratch Music are vessels that catch ideas that would in the normal course of events be thrown away and forgotten, sometimes definitely rejected. So should they be discontinued? Does this depend only on their usefulness?”

Again, one can see their function as instruments of reflection: putting a magnifying glass onto the flow of everyday experience, they interrupted that flow, extracting a piece and rendering in a mixed graphic-verbal ideogram that could be elaborated socially in an improvisatory setting. To refer again to Derrida’s conception of the trace, these works revealed the complexity of the present, which was a composite of embedded time-frames, some instantaneous, some enduring, some intermittent and recurrent, but this complexity was effaced in the normal flow of experience. Similarly, the question of usefulness raises Derrida’s trace-structure to a question of social dimensionality as well, questioning the unity and identity of individual experience in the present: the use of these sketches was a way of submitting the ideograms of lived experience to a kind of laboratory social analysis, in which some elements were revealed to have immediate potentials to connect a larger collective in artistic action, while others might prove isolating or worthless.

Such analysis is only possible in practice with others, and in this sense, the Scratch Music project a kind of anarchist social model of small group activity. They are not, however, themselves so much proposals of social structures, as a kind of training for the sort of social communication that could lead to freer structures and modes of interaction. As Cardew wrote in 1970, “A square musician (like myself) might use Treatise as a path to the ocean of spontaneity. Whether it will equip him for survival in that ocean is another question altogether.”


Anthony Braxton

I’d like to conclude with some brief references to the African-American experimental composer Anthony Braxton. Over the years since his emergence as a young saxophonist and composer in Chicago in the late 1960s, Braxton has evolved as an idiosyncratic, eclectic, visionary, and auto-didactic artistic intellectual, whose musical works synthetically incorporate composition and improvisation, jazz and European new music influences, and visual, verbal, and musical elements. Braxton’s music is characterized by a signature use of symbolic, increasingly ideogrammic graphic titles, as well as graphic elements within the scores proper. His graphic means range from abstract, structural diagrams, resembling the language of circuit diagrams, to a shorthand for expressive elements, to full-scale ideogrammic representations of narrative or dramatic situations.


The best critics of Braxton’s work remark that his notation draws on references that can be situated in a range of cultural spaces, from black folk art, to science and technology, to popular culture, gathered together into an idiosyncratic code of avant-garde compositonal practice. Ronald Radano, for example, suggests that Braxton’s graphic practice revises European modernist and contemporary compositional technique, lending it a kind of postmodern playfulness: “by replacing the serial rows and chance procedures with a mix of squiggly lines, starlike asterisks, and connect-the-dot directions, Braxton appropriates a modernist forum for a kind of pop-culture stylistic play. These symbols orient the image of popular script–comic books, adolescent doodling– into the context of “serious” musical composition. They are Braxton’s way of refiguring formal methods, notations, and compositional techniques according to the whims of personal taste.”


Again, as with Cardew and Cage, Braxton’s compositions also have a utopian social dimension. They are increasingly tied in with ideas of reshaping fields of ideas and orientations of energies, which in turn find their context in a larger tradition of African-American utopian thinking. Graham Lock, in his recent study Blutopia, traced this lineage, for example, in the work of three jazz artists, Duke Ellington, Sun Ra, and Braxton, and in recognition of the end of my speaking time, I will conclude with a quote from his book that suggests this social significance of Braxton’s practice:

“It is no surprise. . . that Braxton has said one intention behind his use of colleage forms is “to aid understanding and unification,” the idea being that people learn how to listen to, and share the space with, others, while maintaining their independence. . . . The history of jazz in particular is the history of continuing attempts to effect and negotiate. . . an equable balance between the individual and the collective, freedom of expression and responsibility to the group. One reason why Braxton’s work embraces so many different structural forms is because he is keen to explore every facet of such relationships (and, perhaps, to demonstrate in a variety of contexts that people working together, supporting each other, can be both effective and fun).”

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