SA12: The Treatise Issue
Composition is the attempt to either assimilate a pre-existing set of symbols or to create your own language or semiology to communicate the sound in your head to other people.
This is the kind of simple discursive starting point that one comes to at a party then immediately abandons when someone suggests getting pizza. That simplicity though, when soberly followed, gets you into all kinds of magnificent and joyous trouble.
Take Ludwig Wittgenstein’s Tractatus Logico-Philosophicus as a somewhat left-field example. Its conceit is simple if strained through the “party” type of thinking: there is a relationship between language and things (reality).
However it is obvious that, when following this line of reasoning, someone working in the rigorous fashion and at the level of Wittgenstein finds the pathways of ideas to be endless, varied, and magnificently complex. If you don’t believe me, read the first proposition – a scant seven terse lines – and see how long it takes you before you begin drawing diagrams to envision and understand the structure of his logic.
This digression into Wittgenstein does have a purpose beyond my own self-satisfaction as it relates to the idea of composing as the attempt to create a set of symbols for communication of an idea and, specifically, to the composition that is at the center of this twelfth issue of Sound American.
Most composers and performers of any music have agreed upon some sort of traditional notation or collectively interpreted and understood set of symbols that relate the ideas of the composer to the performers, who then “read” the symbols as sound. There are some composers, however, who have spent at least part of their lives traveling down a musical analogue of Wittgenstein’s magnificently complex pathway, finding new ways of expressing their logic and questioning the way composers notate music, as well as the way performers perceive and make it “sound”.
Probably the most fascinating example of such an artist is Cornelius Cardew. Inspired by Wittgenstein’s Tractatus, Cardew spent a significant portion of his short life working on a 193 page graphic score called Treatise (the English translation of the Latin Tractatus) that would call into question the simple concept of composition as semiology for performance.
Cornelius Cardew’s Treatise
Treatise is one of the most stunningly beautiful graphic scores of the 20th century. It’s a mix of lines, circles, numbers, and objects derived from traditional music notation, all drawn with an expert draftsman’s eye and hand – Cardew supported his family for some years as a graphic designer for Aldus Books publishing in London – and arranged around a thick black line that runs through the vast majority of the piece. Each page has its own character and charm. Some give an intuitive feeling of space and expansiveness, while others are cluttered or claustrophobic. The use of the thick line and symbols derived from musical notation add a level of consistency and identification that almost feels narrative.
And, if this was all there was to Treatise there is a good chance that we wouldn’t be spending an entire issue exploring its meaning. But, what makes this specific work of Cardew’s special and unique is what it lacks.
Cardew did not include a key to his symbols. He purposely was ambiguous when writing about Treatise and left very little by way of instructions for its performance – essentially leaving the “reading” part of the equation elucidated above entirely up to the performers. This makes for a very dangerous and unique moment in musical history. Even at the apex of John Cage’s profession of freeing composition from the ego of the composer, there still existed an element of a sanctioned “correct” performance of his work. With Treatise as much of this last vestige of the composer was removed from the field of play and the piece, if treated respectfully and with the rigor it demanded, forced the musicians to take part in a social atmosphere of collective creation.
For the idealist, this means that each reading of the composition can be a distillation of the performer’s history and knowledge by using the composition as a framework for discussion and collective decision-making. It is this idealist point of view that we’d like to maintain to the best of our ability for this issue of Sound American.
About This Issue
A solid point of reference is necessary for any investigation, even when the subject is as pluralist as Treatise. The point of reference for all things Cornelius Cardew is British pianist, composer, improviser and author John Tilbury. Over the next weeks, Sound American will feature serialized excerpts from Tilbury’s epic biography: Cornelius Cardew (1936-1981) a life unfinished. The first portion of this excerpt is featured in our opening articles along with what could be considered a quintessential (if such a thing could theoretically exist) excerpt of his performance of Treatise (with Michael Duch and Rhodri Davies).
John Tilbury on Treatise
Treatise Excerpt by Tilbury, Michael Duch, Rhodri Davies
‘It is impossible for me to say one word in my book about all that music has meant in my life. How then can I hope to be understood?’ 
My age of romanticism is over. Sensations, moments, drop away. My desire is to experience long-term continuities as beautiful. In the Treatise to create the coherent code which expresses the truths we do not know and cannot live up to. To dismiss Bodmin Moor and the girl around the corner as beings without future. To pursue the lonely adventure of the spirit, to draw nourishment from the life of the land and the continuity of family life. To be aware of the psychological groundings of your musical strivings (being timid, physically, as a boy, I became bold in spirit), and still leave the ground. (When did I write that it is only possible to leave the ground if you are on it?) 
In a Journal entry in 18 November 1966, when he was in Buffalo, Cardew describes the genesis of Treatise:
Treatise. I’ve always been preoccupied with huge abstractions. I was 23 when I first came across Wittgenstein’s Tractatus; right from the first sentence, handwritten by Slad (David Sladen) as a foretaste before he gave me the book, ‘The world is everything that is the case’, it made a deep impression on me. The name Treatise (from Tractatus): - a thorough investigation. Of what? Of everything, of nothing, like the whole world  of philosophy. I started work on it in 1963 and have worked on it inconsistently ever since. In that time it has lost some of its abstract quality; autobiographical aspects have crept in. But then there are autobiographical wisps to be read into Wittgenstein’s Tractatus – the whole takes on a slight autobiographical slant in view of his later rejection of parts of it.
Cardew began working on Treatise during the first months of 1963, ‘on the basis of an elaborate scheme involving 67 elements, some musical, some graphic; the fusion of two professions’.  In its final version, drawn and measured on a grid, it clearly owes much to the fact that for much of the time he was employed as a design assistant at Aldus Books. In a BBC talk preceding a broadcast of a part of Treatise on 15 January 1966 he acknowledges the important influence that working at Aldus exerted upon him:
While there I came to be occupied more and more with designing diagrams and charts and in the course of this work I became aware of the potential eloquence of simple black lines in a diagram. Thin, thick, curving, broken, and then the varying tones of grey made up of equally spaced parallel lines, and then the type – numbers, words, short sentences like ornate, literary, art-nouveauish, visual interlopers in the purely graphic context of the diagram.
Yet for a work which displays such virtuosity and panache, it emerged tentatively; Cardew confessed to having no idea, initially, as to the outcome, and progress was fitful. Paradoxically, it was the musical elements and their integration which created the greatest obstacles; it was the ‘apparent musicality’ of p.99, for example, which he described as “a stumbling block that impeded my way for some time to come.”  Somehow these ‘idiosyncratic’ musical signs, these ‘interlopers’, seem to have been a source of equivocalness, even embarrassment, to him: they impinged on the visual content disproportionately to their relative importance as indices for many of the basic elements. Yet such traditional indicators as treble clef and forte were considered indispensable and they litter the score; in relation to conventional musical notation Treatise is an act of de-construction rather than rejection. There is historical and stylistic sedimentation scattered throughout the score as well as expressive, visual gestures of an immediate, inspirational or suggestive nature. In other words, the notation is an attempt to embody the way people actually experience structure in music. And the way a composer notates delimits his creative imagination; the force of Cardew’s creative imagination broke the fetters of a musical language which for him had become obsolete and supressive. Perhaps he felt that the superabundance of traditional symbols on page 99 were in some way threatening, that they might assume a dominant role, forcing a more referential, less creative mode of interpretation, upon the performer. Be that as it may, the consequent on page 100 is a master-stroke; rather than an arbitrary cessation of these signs Cardew simply allows them to wither and dissolve into new shapes of similar dimension, so that there is no feeling of dislocation – a brilliant exercise in damage limitation.
Whatever the problems presented by page 99, they do not appear to have been exaggerated. Around eighteen months elapsed between the first ninety-nine pages and their continuation as late as December 1964, when seven separate, that is non-consecutive, pages were put into freehand fair copy. And it was at this juncture that Cardew decided to abandon freehand drawing in favour of the drawing instruments with which he had become familiar and adept at Aldus Books. By October 1966, when Cardew arrived in Buffalo, he had completed pages 45-143 and the piece was beginning to assume its final shape, although the first forty-four pages were still to be revised. During the early months of 1967, still in Buffalo, Cardew drew the final fifty pages and Treatise was submitted to the Gallery Upstairs Press for publication.  Some years later he was to recall his execution of those last pages:
It was surprisingly poignant coming to Buffalo again, really golden in the sunset. The sun sets over Lake Erie and has to struggle with all the smoke of Bethlehem Steel, which makes it red as red. Especially my old favourite the phallic library, its tip gleaming with coloured mosaics that I don’t remember being there before. I remember sitting on the lakeside in freezing sunshine sketching out the last 40 pages or so of Treatise. Then I put the library in when I was re-doing the beginning, but for some reason I laid it on its side! 
The Gallery owner, Ed Budowski, showing both foresight and alacrity, published Treatise before the year was out and it appeared in accordance with Cardew’s wishes without any introductory material or instruction 'to mislead prospective performers into the slavish practice of “doing what they are told”’.  In fact it was the sheer length of Treatise as much as anything else that militated against the provision of an interpretative system; and because of the exhaustive manner in which the signs are treated it was assumed, at least by a sanguine and trusting composer, that performers would devise their own methods of interpretation, as their study of the work progressed.
Ideally, then, we should while composing strive to eliminate all mere interpretation, and concentrate on the notation itself, which should be as new and as fresh as possible (hence less likely to arouse preconceptions in the interpreter – though if you have a good interpreter isn’t it likely that his preconceptions will be good too?) and should contain implicit in its internal structure, without any need of any instruction, all the implications necessary for a live interpretation. 
Several years later, in 1971, the publication by Peters Edition of the Treatise Handbook did not really compromise his earlier position in relation to performer instruction, although the Journal of Working Notes, with which it begins, and the numerous aphorisms which spice it, provide a fascinating insight into Cardew’s developing ideas on musical notation – as well as an indication of the extent to which these were influenced by his on-going study of Wittgenstein’s writings.
The Graphic Material of Treatise
The topography of Treatise may be divided into four distinct categories: abstract shapes (of which circles, squares, rectangles are the most prominent), signs associated with conventional musical notation, numbers, and a horizontal middle line which divides each page into two equal parts. Nearly all the symbols are draw with either of two pen-widths, the thicker width being used throughout for the middle line. 
I posit four categories; yet even this most general description may be regarded as contentious: for example, by including the two empty staves which Cardew provides at the bottom of each page underneath the graphic material, Brian Dennis insisted that there are five categories. Dennis’s view is strengthened by the fact that at one point these prosaic and seemingly functional staves are themselves subjected to idiosyncratic treatment. In the middle of page 25 the graphic symbols actually encroach upon the upper stave and for two inches the top two lines of (of the stave) are missing. Furthermore, in the Handbook, p.v, Cardew himself proposes that the two staves be read as part of the score, ‘as being suggestive for beginners’. But even if we acknowledge an arcane quality in the presence of the two lower staves, in practice they have been regarded either as an irrelevance (by non-readers) or at best as a useful space (for experienced readers) where material can be traditionally notated as and when required; for example, where specific tones are to be featured on a page. (This in fact is how Cardew uses it in his own annotated copy of the score.)
The symbols constituting the (four) categories are deployed throughout the one hundred and ninety-three pages hierarchically; that is, a specific stretch of the score will feature a particular symbol, or a combination of symbols will predominate, while other symbols will appear only spasmodically, playing a more dominant role in another section; or a symbol, having fallen into desuetude, will be marked by its absence. It is a method of structuring material which Cardew employs in a number of works through which the form of the work falls naturally and conveniently into sections which in turn sub-divide into smaller units, into short pieces perhaps, and into phrases and tropes which can be regarded as self-contained and yet belonging, fitting within a context. In Cardew’s indeterminate works, as we have already seen, the originality of the notation serves to bring the question of musical ‘structure’ to the surface and the listener is aware of the resulting music ‘as a token of something that exists in some sense independently of the sound; it means not so much hearing the sound as hearing the composition through the sound.’  Conversely, as readers we may ‘hear’ Treatise through the notation; as Richard Barrett has observed, an involvement with Treatise, as performer or simply as reader, leaves us with the strong impression ‘that there is a sonic analogue to what is on the page, that it will remain forever just out of reach, but that something about Treatise consistently makes musical sense.’  In so far as it ‘provides a unique context within which sound can be heard as musically meaningful’  Treatise is a composition. But can our concept of ‘composition’ accommodate the perpetual tension which Treatise creates between the presumption of a form (‘compositional’) representation of sounds, and the desire to unleash sounds, to give them free rein, and to reveal a latent aspiration to sing of other worlds?
I have broken Treatise down into eight sections on the basis of the frequency, scope and visual presence of the particular symbols which characterize them:
Section 1: pages 1-19.
Section 2: 20-44.
Section 3: 45-88.
Section 4: 89-126.
Section 5: 127-144.
Section 6: 145-164.
Section 7: 165-178.
Section 8: 179-193.
Not that I am underestimating the roles of other symbols whose appearances are more fitful; it is simply that to me their functions within a particular section appear to be of lesser significance. In other words I am interpreting, rather than describing, the form of Treatise. The exercise is a subjective one – just as an initial classification of the graphic material depends as much on the visual awareness and imaginativeness of the reader as on the objective features of the signs themselves. Nor am I concerned with the far-reaching modifications and transformations which a symbol undergoes; for example, there is an extraordinary range of graphics under the generic heading ‘stave’. At this initial stage what I am trying to do is to build up a knowledge and understanding of the score by adopting a simple, perhaps over-simplified, system of classification.
Of course, it is tempting, and would be reassuring, to analyse Treatise into seven sections, which would conveniently correspond to the seven sections of Wittgenstein’s Tractatus. In fact, it would not be a difficult undertaking, although I suspect that it would be no less arbitrary than my own interpretation, with the crucial difference that I am not seeking a particular outcome. However, the attraction is undeniable and one could argue persuasively that the final two and a half pages of Treatise are a perfect notational exemplification of the famous seventh section of the Tractatus: ‘Whereof one cannot speak, thereof one must be silent.’  Brian Dennis drew attention to this ‘final cadence’ of Treatise:
On p. 191 the ‘lifeline’ stops and after two beautifully drawn loop designs the staves emerge as shown: the top stave is hand-drawn (apart from line 2), the bottom is ruled (apart from line 2) and the process continues for two more pages of empty staves, identical except for the minute fluctuations of the composer’s unguided hand (Ex. 6.3).’ 
Keith Rowe and myself took advantage of a succession of long flights in North American to try and identify the ‘sixty-seven’ elements, some musical, some graphic, which, according to Cardew in the Handbook, constitute the score of Treatise. The problem was compounded by the extraordinary fecundity of the score and the elusiveness of the signs which constantly combine and change in bewildering fashion, contribution to an exhilarating and vivifying impression of movement in the notation. So it was partly in desperation that we agreed that an approximate figure, say between sixty and seventy, would be acceptable. However, our first count was far too general and amounted to less than thirty. It was clear that what we had included in the ‘circle’ category, for example – say a crescent shape or incomplete circle – needed to be grouped separately; our problem was a conceptual one. So we had to redefine the limits for each group of elements – that is, to decide what to include, what to exclude, in order to achieve an appropriate taxonomy. For example, the elements [appearing close to*] L V could be subsumed either into one category, or each could belong to a separate category; the target figure of around sixty-seven indicated that the latter would be the most expedient choice. Similarly, and more obviously, the nine (and only nine) numbers which Cardew uses in Treatise – 1,2,3,4,5,6,8,10,34 – needed to be categorized separately into ones, twos, threes, etc. Thus the target figure itself became a key, determining factor in our method of taxonomic classification. Conversely, the practicalities of interpretation may subsequently demand that it is precisely the interrelatedness of categories, rather than their separation, that is of consequence, and they may then be grouped under a single, generic heading – say ‘circle derivatives’, or ‘numbers’. 
Like Wittgenstein, his private mentor, Cardew was concerned with the nature and limitations of language and logic and with the relationship between the structure of language and the structure of reality. Musically, or more specifically, in terms of musical composition, these concerns were expressed in the correlation between the way music is notated and the nature of the actions and sounds it generates. In Treatise Cardew created a notation which embodied his needs and aspirations at that time, freeing him from the cramping disability which, in the light of his own experience, the system of traditional notation seemed to impose on compositional thought. There seemed to be no limits to Cardew’s musical horizons or, if there were, they extended outside and beyond the locus of compositional theory and practice (and the imagination) of his peers and colleagues. At the time of Treatise tensions had already begun to show and Cardew’s relation to the avant-garde, both the European and the American, had reached a breaking-point. Whatever similarities seemed to exist between Cardew’s indeterminate compositions and those of his peers, on both sides of the Atlantic, they were in essence superficial, or at least inconsequential. Significantly, neither the European nor the American musical avant-garde, with very few exceptions, had sought to subvert, or even to question, the prevailing composer/performer relationship of Western art music, which reached its most extreme expression in post-1945 serialism – a relationship marked by an increasing dominance in the role of the composer, whilst the compliant performer assumed a ‘technocratic’ role, as a kind of ‘systems-expert’. Even Cage, for all his radicalism, could not relinquish it. By contrast, what was of primary concern to Cardew was to evolve a way – rather than a method – of notation music which could express the subtleties and nuances, the indeterminacies, and above all the mutuality, of the composer/performer relation.
Treatise was the culmination of a trilogy of works (with Autumn 60 and Octet ’61) in which this essential, human dialogue was re-opened, explored and refined. Rather than prescribing sounds Cardew sought to stimulate, provoke and inspire through a visual score of astonishing scope and imagination which sometimes subtly, sometimes flagrantly impinges on the performer’s sensibilities, serving not simply as a measure of the performer’s intellectual capacity, digital dexterity and viability, but also of his probity, of his virtuosity, courage, tenacity, alertness and so on. And for Cardew, drawing Treatise was an integral part of the compositional process; he was aware of the psychological drama generated through the performer’s relation to the (drawn) notation in the act of interpretation.
A composer who hears sounds will try to find a notation for sounds. One who has ideas will find one that expresses ideas, leaving their interpreatation free, in confidence that his ideas have been accurately and concisely notated. 
Cage’s notations, too concern themselves with ideas but I would baulk at describing their interpretation as ‘free’ in the sense that Cardew meant ’free’. Certainly Cardew’s admiration for Cage’s scores was unstinting and he would frequently cite Cage’s Winter Music and Variations as works where the notation is a consummate expression of the ideas – where there is no element of ‘blur’. Howard Skempton shares Cardew’s enthusiasm for Variations I:
That a score so starkly pure and simple is capable of yielding results of extraordinary richness and complexity is proof that Cage’s work, at its best, is successful in its aim of imitating nature in the manner of its operation. 
Yet in the light of Cage’s own musical philosophy such enthusiasm begs the question. From the performer’s point of view isn’t Cage treading the same familiar ground? Isn’t it the case that Cage is providing specific instructions for the performer to follow: the procedural rules which accompany the score – in this instance a sequence of mechanically-derived readings and measurements? At a certain point the performer’s artistic creativity and ingenuity is engaged, but it is too late, and his sense of alienation from the score is undiminished. Variations I belongs to the composer, it is leased to the performer under certain conditions. Certainly, Cage was not a man to claim proprietorial rights over anything, and yet in terms of his own philosophical credo might it not be argued that his compositions under-achieved – for all their exhilarating iconoclasm? And might it not also be argued that his oft-cited objection to ‘idiosyncratic’ performances of his works was somehow a derogation from the moral teachings and the idealism embodied in his writings? By his insisting on the criteria for making judgments of performances, in the ‘freedom’ which Cage championed severely compromised?
The importance of Cage’s involvement with Eastern philosophies have been comprehensively documented, by himself and others, and cannot be overstated; but equally important it seems to me, is the fact that Cage was also a product and exemplary model of American individualism. Seminal, indeterminate works such as the Variations I-VI and 4’33”, in which he ignored artistic taboos and boldly crossed frontiers into outlawed territory are strikingly emblematic of the American pioneering spirit. These prodigious and audacious works owe at least as much to the ethos of individualism – individual risk, individual discovery – as they do to Zen, and it is the indispensable quality, together with patronage, marketing and availability, which has ensured that Cage’s compositions have remained essentially with the mores of Western musical practice and has helped his music to compete successfully in the perennial quest for sponsorship and exposure.
Treatise, I submit, embodies a different set of relations; most importantly it is a negation of the egocentricity that lies at the heart of Western artistic orthodoxy. Treatise does not wholly belong, either to Cardew or to those whose lives it nourishes and inspires; it is offered and shared unconditionally, untethered to any rules or laws of musical composition or any other ‘figments of the musicological imagination.’ What Cardew proposes to the performer in Treatise is no less than a voyage of ‘self-invention’ (to borrow from Eddie Prévost): ‘What I hope is that in playing this piece each musician will give of his own music – he will give it as his response to my music, which is the score itself.’  And it was the ethos of ‘self-invention’ which became the categorical imperative of Cardew’s revolutionary musical though and practice in those heady years of the late sixties – with AMM and with the Scratch Orchestra.
1 Ludwig Wittgenstein. From Recollections of Wittgenstein, ed. Rush Rhees (Oxford, 1984), p. 160
2 Jml. 4 September 1963.
3 The word ‘white’, in brackets and with a question mark, is written above ‘whole world’, with a different pen and presumably at a later date.
4 Treatise Handbook p.i. (CCR).
5 Ibid, p.i. (CCR).
6 In November 1966, just a few months before its completion, Cardew was the recipient of an Arts Council grant of 600 GBP for his Treatise project.
7 Letter from CC to SK, dated 11 January 1975.
8 Treatise Handbook p.i. (CCR).
9 From ‘On the Role of the Instructions in the Interpretation of Indeterminate Music’, ibid. p.xv. (CCR).
10 Keith Rowe recalls that in drawing Treatise Cardew used the early German rapidograph which had two widths and was capable of extreme precision.
11 Nicholas Cook: Music, Imagination and Culture, (Oxford: Clarendon Press, 1990), p. 35.
12 New Music 87, ed. by Michael Finnissy and Roger Wright (Oxford University Press), p.24. (CCR).
13 Nicholas Cook: Music, Imagination and Culture, p. 41.
14 Ludwig Wittgenstein: Tractatus Logico-Philosophicus (London: Routledge, 1990), p. 189.
15 Brian Dennis, ‘Cardew’s Treatise (mainly the visual aspects)’, Tempo Magazine no. 177, June 1991, pp. 10-16. (CCR)
16 Brian Dennis pointed out the hierarchic ratio of the tally of numbers: 1 (96), 2 (27), 3 (19), 4 (9), 5 (7), 6 (1), 8 (1). 34 is the first number and 10 the last, and both occur only once; he detected the possible influence of Stockhausen here. But Cardew’s fascination with numbers was broad-based; the work of Jasper Johns and Wittgenstein, whose Remarks on the Foundations of Mathematics Cardew had studied, could also have been reference points for the particular use of numbers in Treatise.
Some Remarks on the relation of Treatise to Wittgenstein’s philosophy
Cardew had been acquainted with Wittgenstein’s philosophy for over three years before he embarked on Treatise and although Wittgenstein’s name is rarely mentioned there is a freight of oblique references to Wittgensteinian thought both in his writings (Notation – Interpretation, etc.) and in his compositions (Autumn 60 and Octet ’61) during the period 1959-62. Yet it is unlikely that the extent of Wittgenstein’s influence on Cardew and the debt which his musical and compositional practice owes to Wittgenstein can ever be accurately measured; those of us who have taken the first tentative steps have floundered in a sea of speculation, observing connections where probably none exist and overlooking the obvious and the significant. This is certainly the case with the present writer, but of this I am certain: that the plot will thicken and the discoveries by people more knowledgeable, more perspicacious, both about music and about philosophy, than myself, will create lines of enquiry which will yield results of far-reaching and unimaginable consequences.
Rather than plunging headlong into the analytical fray let us begin modestly with a broad and intuitive, if unremarkable impression which several commentators have entertained; it is, after all, largely on the basis of intuition that the performer proceeds with Treatise. Let us take the imposing, middle line of Treatise – the ‘lifeline’ which runs throughout the piece and whose occasional distortions and absences are as meaningful as its majestic presence – and suggest an analogy to the single, sweeping line, metaphorically speaking, of Wittgenstein’s Tractatus. In fact, the analogy is too pat; track the middle line of Treatise and by the time we reach page 30 the comparison begins to jar; Cardew’s ‘lifeline’, for all its qualities, shows a vulnerability which is entirely absent in the Tractatus, with its continuity and clarity of purpose. Cardew’s middle line occasionally falters, deviates, and even disappears – and with it our analogy. Let us therefore broaden our perspective and cite other, less contentious correspondences – not least, the striking coherence which both works exhibit. For Cardew this meant a kind of graphic logic in which each and every sign was appropriate to the context in which it appears (this he described as ‘diagrammatic writing’), a stylistic imperative which determines the process of refinement which they undergo; in Treatise the presence and characterization of a sign in a given context never Cardew had been acquainted with Wittgenstein’s philosophy for over three years before he embarked on Treatise and although Wittgenstein’s name is rarely mentioned there is a freight of oblique references to Wittgensteinian thought both in his writings (Notation – Interpretation, etc.) and in his compositions (Autumn 60 and Octet ’61) during the period 1959-62. Yet it is unlikely that the extent of Wittgenstein’s influence on Cardew and the debt which his musical and compositional practice owes to Wittgenstein can ever be accurately measured; those of us who have taken the first tentative steps have floundered in a sea of speculation, observing connections where probably none exist and overlooking the obvious and the significant. This is certainly the case with the present writer, but of this I am certain: that the plot will thicken and the discoveries by people more knowledgeable, more perspicacious, both about music and about philosophy, than myself, will create lines of enquiry which will yield results of far-reaching and unimaginable consequences.
Rather than plunging headlong into the analytical fray let us begin modestly with a broad and intuitive, if unremarkable impression which several commentators have entertained; it is, after all, largely on the basis of intuition that the performer proceeds with Treatise. Let us take the imposing, middle line of Treatise – the ‘lifeline’ which runs throughout the piece and whose occasional distortions and absences are as meaningful as its majestic presence – and suggest an analogy to the single, sweeping line, metaphorically speaking, of Wittgenstein’s Tractatus. In fact, the analogy is too pat; track the middle line of Treatise and by the time we reach page 30 the comparison begins to jar; Cardew’s ‘lifeline’, for all its qualities, shows a vulnerability which is entirely absent in the Tractatus, with its continuity and clarity of purpose. Cardew’s middle line occasionally falters, deviates, and even disappears – and with it our analogy. Let us therefore broaden our perspective and cite other, less contentious correspondences – not least, the striking coherence which both works exhibit. For Cardew this meant a kind of graphic logic in which each and every sign was appropriate to the context in which it appears (this he described as ‘diagrammatic writing’), a stylistic imperative which determines the process of refinement which they undergo; in Treatise the presence and characterization of a sign in a given context never seems arbitrary. Treatise is informed with an organicity both of motion and structure.
Yet we should not get carried away with the idea of the pre-eminent role of ‘logic’ in Treatise; an important (contradictory?) feature of the graphics is precisely its non-homogeneity; compare, for example, the precise shape and connotation of the neatly-drawn bass clef signs, notes and accidentals just four pages earlier on page 186 with the wild, impulsive gestures – like missiles propelled into the air causing two birds to take evasive action – which dramatise page 190. And signs are often juxtaposed with other signs; or signs are fused, as we saw in Octet ’61 (Ex. 6.4a)
seems arbitrary. Treatise is informed with an organicity both of motion and structure.
Yet we should not get carried away with the idea of the pre-eminent role of ‘logic’ in Treatise; an important (contradictory?) feature of the graphics is precisely its non-homogeneity; compare, for example, the precise shape and connotation of the neatly-drawn bass clef signs, notes and accidentals just four pages earlier on page 186 with the wild, impulsive gestures – like missiles propelled into the air causing two birds to take evasive action – which dramatise page 190. And signs are often juxtaposed with other signs; or signs are fused, as we saw in Octet ’61 (Ex. 6.4a)
What is significant is that these spontaneous gestures which characterize page 190 appear towards the end of Treatise, and it was in 1966, when Treatise was nearing completion, and when he was already a fully-fledged member of AMM, that Cardew expressed the view that an improvisatory character was essential to Treatise. This was a clear shift in his thinking for which a newly-discovered, serious commitment to free improvisation was a key, contributory factor. Initially, he had insisted that the score must govern the music; it was not an arbitrary jumping off point for improvisation, although this, in fact, is what it became for most interpreters; the majority found it simply more practical, and less daunting, to adopt an impressionistic attitude towards Treatise. Yet as late as 1970 Cardew still seemed unsure as to the precise nature of this ‘improvisatory quality’. On the one hand he did not consider Treatise ‘improvisatory’, and yet ‘it does seem (using hindsight) to have pointed in the direction of improvisation. A square musician (like myself) might use Treatise as a path to the ocean of spontaneity’.  Michael Parsons has drawn an interesting comparison between Cardew’s change of heart in relation to Treatise and Wittgenstein’s earlier and later views on musical notation. In the Tractatus Wittgenstein talks of the notation as being an exact analogue of the sound: the idea that for every element in the notation there is an aural correspondence. Thus the structure of the musical notation corresponds exactly to the structure of the sounds which it represents. This representational theory is perfectly exemplified in the theory and practice of serialism, where the score is expected to represent an exact picture of the sound. (And there is a broader relationship in the way that the elaborate formal structures of the serial works of the fifties express both the purity and the artificiality of the Tractatus.)
Despite his insistence, initially, on the authority of the score – something which he stresses several times in the Working Notes in the Treatise Handbook – Cardew recognized that Wittgenstein’s representational theory, at least in respect of the musical score and its realization, was flawed. In the Tempo article there is a reference to it dated as early as July 1959, which would have been around the time that David Sladen presented him with a copy of the Tractatus:
Suppose the player to behave as follows: he reads the notation and makes himself a picture of the sound (in his mind – the hypothetically imagined sound). He then attempts to reproduce this picture in sound; he plays, and then listens to the sound he has made; he compares it with the picture of the sound he had in his mind beforehand, and he may make a few changes, reducing the most glaring discrepancies, releasing wrong notes quickly, reducing the notes he finds too loud, etc. etc. 
And just as Wittgenstein later objected that the picture theory was deficient because it did not take into account the way language is actually used, so for Cardew the concept of the ‘hypothetically imagined sound’ was ‘dubious’. ‘On what basis does the player imagine the sound?’ he asked. ‘On the basis of his understanding of the notation? But the process of imagining cannot be included in the notation!’  Could a notation be devised which at least took into account the way instruments ‘actually are played’? This in turn raises the question: what mental and physical processes are actually involved in playing?
In an earlier note in the Tempo article he had identified 5 stages in the production of music: 1. What is written. 2. Information gleaned by the player from (1). 3. The player. 4. The action to produce the sound. 5. The sound. What strikes one immediately here is the world of distance which exists between stage 1 and stage 5, both of which are referred to as the ‘composition’. Significantly, the player is found mid-way between the two – the midwife who delivers the notation into the world of sound – and there are myriads of uncertainties (indeterminacies) between conception and birth. So the role of the notation in determining the ‘sound’ may be crucial, but it is also limited.
In many cases we do not imagine the sound on the basis of the notation, but on the basis of our previous experience, that is, (too) while practicing the piece, and therefore the ‘imagined’ sound has no particular claim to correctness at all, and therefore a comparison of the actual sound with it has no sense whatever. 
[…] in February Piece 1 Cardew attempted to circumvent the problem of the performer’s ‘imagining’ by excluding it – just as the European serialists had: ‘He (the performer) should not interpret in a particular way (e.g. how he imagines the composer intended) but should be engaged in the act of interpretation.’  But is the performer really ‘engaged in the act of interpretation’ – or is he simply engaged in doing what he is told? Despite its efficacy and sophistication the prescriptive nature of his notation for February Piece 1 belonged to a compositional mode which he had found wanting, and in the Tempo article, some three years before he embarked on Treatise, he already expresses a deepening skepticism of the role which the representational apparatus of traditional notation is still expected to play in contemporary music. Cardew was more aware than most of the limitations which the constraints of the western notational system imposed on compositional thought – not least by the mere fact of sitting at a desk with a sheet of manuscript paper impressing its image on the mind’s eye.
But to return to Michael Parsons’ comparison: around 1929-30, when he was beginning to reconsider his earlier theory, Wittgenstein’s view of musical notation had begun to shift:
Later (in MS107, p.243) [this refers to the unpublished MS of 1929] Wittgenstein notes that musical notation can be thought of as a set of instructions for acting in a certain way:
‘Die Sprache der Notenschrift [ist] eine Anweisung für das Spielen eines Instruments’.
Thus musical notation provided Wittgenstein with an interesting example of how a symbolism can be part of a complex which includes human activities guided by his notation. 
And right at the outset of Treatise, in February 1963, (Handbook, p. iii) Cardew had expressed the same idea: ‘Notation is a way of making people move.’ So in both cases a fairly rigid, representational relationship is dismantled. Rather than representing a reality, the notation intervenes; its role is dynamic, creative, and the way notation is actually used becomes the crucial factor, just as the use of language became central to Wittgenstein’s later philosophy. In the later work Wittgenstein regards language as a part of human life; this is the context in which language should be examined – in the way that it ‘meshes with life’. Its complexities of form and function have no independent basis outside themselves; their justification can only be met within language and its place in our lives. He refused to construct systemic philosophical theories and he rejected the pseudo-scientific treatment of non-factual modes of thought, defending their claim to independence. His aim was simply to assemble the facts about language and to wage a continuous war against what he saw as the bewitchment of the intellect.
If we can posit an analogy with Wittgenstein’s repudiation of his earlier work, it would reside, I believe, in Cardew’s rejections of serialism (the representational theory) in favour of graphic notation, or even in his abandonment of notation altogether in favour of improvisation. Here are where the most profound correspondences can be sited, rather than in his politically motivated position during the seventies. During his apprenticeship in Cologne Cardew, too, had concluded that to theorize was to falsify, and throughout the seventies he was to pour scorn on what he regarded as the pseudo-science which had permeated theoretical discussion in Darmstadt during the fifties.  For Cardew it was not the scientific ‘validity’ of musical theories that was of importance or relevance; it was the way in which any musical manifestation affected the lives of those who practiced and listened to it. He was skeptical of the usefulness of ‘science’ when we try, for example, to describe the impression a piece of music makes on us; it might be necessary to enter other areas of discourse, but rarely science. Like Wittgenstein he held the view, at that time, that the aesthetic creations of the human mind enjoy a precious immunity from scientific analysis.
Notwithstanding its title Treatise clearly reflects Cardew’s simultaneous preoccupation with both the earlier and the later Wittgenstein. Moreover, it can be argued that Treatise does express their chronology: the forward trajectory, the flow and continuity of the graphics, the more abstract, pristine quality of the geometrical shapes of the first two sections (pages 1-44) suggest the bold, majestic sweep of the Tractatus; by contrast, the later sections of Treatise, with their ‘autobiographical wisps’, correspond more to the anthropocentrism of the Philosophical Investigations, with its ‘short, sharp observations, interspersed with arresting questions, and startling dialectical volte-faces.’  In the latter pages of Treatise, in particular, copious musical equivalents are to be found, and to the sensitive and perceptive interpreter a recognition of these correlations will have meaningful consequences. By the time Treatise was nearing completion Cardew’s attitude towards it was decidedly anthropocentric:
Each player interprets the score according to his own acumen and sensibility. He may be guided by many things – by the internal structure of the score itself, by his personal experience of music-making, by reference to the various traditions growing up around this and other indeterminate works, by the action of the other musicians working on the piece, and – failing these – by conversation with the composer during rehearsal. 
For Cardew insight into the way of (musical) life of musicians was crucial to any understanding of the art they practice. He was deeply interested in the ‘stream of life’ within which musical utterances found expression, just as Wittgenstein would try to draw us away from words and sentences to consider rather the occasions on which we use them, the context which gives them a particular meaning.  Despite his frequent references in the earlier pages of the Handbook to the supremacy of the notation, Cardew now seemed to be suggesting that in the act of making music the score has no more ‘authority’ than any other parameter. For in Treatise the notation does not depict, or attempt to depict, an existing sound ‘reality’; it is there to inspire, even incite the performer in order to bring about a music which does not yet exist. In fact, this was a view he had reflected upon even in the early months; on 28 September 1963 he remarked that in Treatise ‘the score seems not representational. No rules of representation. Except the central line represents perhaps the performer or a single line of thought’.  Notation could not be simply a representation of sounds any more than linguistic forms comprise solely statements of facts.
Rules and Rule-making 
‘I tell you, no virtue can exist without breaking these ten commandments. Jesus was all virtue, and acted from impulse, not from rules.’ 
In Treatise by prescribing no rules at all, Cardew brings the question of ‘rules’ to the surface; the performer is invited, by implication, or by default, to provide his own. Of course, different modes of procedure presuppose different perceptions, but even in the most spontaneous and wayward of interpretations (for example, where the performer responds to perceived changes in audience behavior) rules and attitudes towards rules are invariably involved. It is the absence of prescribed rules which makes Treatise such a radical departure.
The rules which we are therefore obliged to invent for Treatise, sometimes as we go along, rarely provide a fixed and immutable point of reference. Even in group realisations, where it may be desirable for some kind of consensus to be reached, our collectively-agreed rules allow for divergent, individual interpretations; paradoxically, what gives such musical practices their stability is a consciousness of the limitations of whatever rules are applied, and of the need for flexibility. Some interpreters set great store by the rules they adopt and try to hold to them systematically; others, whilst adopting rules, cannot resist flouting them – sometimes for the sake of convenience, sometimes through mental laziness, sometimes through a fiercely-held conviction that rules (even homemade ones) are meant to be broken – interpreters such as Janice Tilbury to whom a return date stamped on a library book is an intolerable act of authoritarianism. ‘Rules and regulations ruin our true appreciation of nature and our powers to express it’, Goethe opined in The Sorrows of Young Werther. 
In one way or another the rules we adopt, whether purposefully or half-heartedly, and their application, reflect our perception, our understanding, of Treatise; more broadly, they relate to and are determined by our practice, by the way we lead our lives; they are not plucked randomly out of the air. Through his creation of a notation which was about ‘making people move’ Cardew had to address the fundamental issues of why and how people humanize sounds, just as Wittgenstein had brought all the great philosophical questions which have arisen out of the various discourses to the same level from which philosophy started – ordinary human life. One may even conceptualize a musical language which has no rules at all, an internalized language embedded in life, in human activity.
In the early sections of Treatise, in particular, there is a lucidity and explicitness, which invites, if not demands, the application of a system of rules. In the Handbook, in an elaborate interpretation of the various triangles which appear in the score, Cardew shows how precise information relating to the morphology of a sound can be derived by the systematic application of rules.  There is also a detailed description of a method he devised for determining tones from each appearance of the 5-line musical stave. This was for a Swedish trombone quartet who were to have taken part in a performance with the composer and other musicians in the Warsaw Autumn Festival in September 1966; for some reason their appearance did not materialise. Some performers would regard this process as intolerably pedantic but it does demonstrate the detailed extent to which Cardew felt it was possible to interpret the signs and thereby to determine the minutiae of sound production.
Flexibility in the interpretation of rules was something which Cardew admired in the music of Christian Wolff. In Wolff’s scores the signs do not represent sounds; they create situations in which the performer act, and the instructions consist mainly of suggestions as to how the players interact. Rules have to be modified, altered, or simply jettisoned in order to deal with the ‘impossible’ situations which arise from time to time during the course of a Wolff piece: playing five tones in zero seconds, for example! ‘One can establish a hierarchy among rules and make general decisions about which rule takes precedence (where two rules seem mutually exclusive). Alternatively one can decide for each particular situation which rules are binding.’  Thus, mutatis mutandis, the rules are obeyed differently according to the circumstances. With the music of Christian Wolff it is as if one is interpreting the rules, rather than the notation; rules and notation coalesce.
Cardew clearly enjoyed these problems, not least because logic seemed to be under threat from art. In the following quote from the Tempo article he seems to be expressing the same anthropological attitude to logic which had impressed him in the Philosophical Investigations: ‘Compare “that seems natural” with “that seems logical” with “there is a sort of severe logic in it” meaning it’s not natural but it’s “right”.’  In the context of human affairs logic appears less intractable, even vulnerable. For Cardew the source of all rules and rule-making, of all necessities, is in ourselves; rules and their application are derived from our practice, our modus vivendi. In music they are derived from the requirements, the needs, of our music-making, not according to some external musicological canon. At the same time he warned against what he described as ‘lapses into constant evasions’: when the going gets tough we simple abandon the prevailing method of interpretation and adopt another. Yet he did not condemn these ‘evasions’ out of hand; they must be ‘watched and conscious’. As a last resort consistency – that is a self-imposed, unbending rule or set of rules – may be jettisoned, but not in a cavalier fashion, and certainly not as a recipe for anarchy. For it is assumed that new rules, perhaps rules that contradict the deposed rules, are substituted. Cardew recognized the necessity of rules – but not their supremacy’; rules are dispensable.  The subtleties of the notation/performance relation in Treatise, for example, transcend the rules:
The notation should put the player on the right road. He can rise above the notation if he works through the notation. Interpreting according to the rules should lead him to the identity of the piece; this grasped, he may slough off the rules and interpret freely, secure in the fact that he knows what he is doing – he knows the piece. 
On Interpreting Treatise
As we have seen, several years before he embarked upon Treatise Cardew had already turned his back on what he dismissed as the coercive formalism of serialism in favour of the nuances of the particular case, or indeterminacy; indeed, some of the ideas which were developed during the Treatise years, 1963-7, had been anticipated as early as 1959 in the Tempo article:
One point is, that every sign should be active (compare the barlines in [Morton] Feldman and [Pierre] Boulez). Here are openings for indeterminacy, or freedom for the player: he must decide which signs he will give activity to, or allow to act. The composer can bring this about in a variety of ways: by overloading the player with so many rules that they begin to contradict each other; or by using the same sign in a variety of contexts where it cannot mean the same (paradoxical notation); or by giving no rules whatever and obliging the player to seek out just such rules as he needs or as will make sense of the notation. (This last is very important, and often seems the case with Feldman.) All these are psychological obscurities directed at the player in the hope of waking him up. 
Of course, the indeterminacies which Cardew lists here are associated only with the interpretation of signs: the signs themselves should not be indeterminate: his view at that time was that a notation was not a drawing, even though a drawing might suggest an interpretation.  Significantly, in the latter stages of Treatise, in particular, the notation does become more impressionistic; I have already touched upon the importance of AMM with respect both to the transformation of the graphic content, and to Cardew’s own attitude toward the work.
It is worth reminding ourselves that when Cardew joined AMM, in January 1966, Treatise was still a year before completion; dramatically, he was plunged headlong into a situation in which the making of music would reach an unparalleled level of intensity and would inspire a depth of personal commitment which he had previously never experienced. In the Handbook, on p. xi, he refers to the influence of his music-making with AMM on Treatise and identifies this change of perception:
Before that [joining AMM], Treatise had been an elaborate attempt at graphic notation of music; after that time it became simply graphic music (which I can only define as a graphic score that produces in the reader, without any sound, something analogous to the experience of music), a network of nameless lines and spaces pursuing their own geometry untethered to themes and modulations, 12-note series and their transformations, the rules or laws of musical composition and all other figments of the musicological imagination.
In fact, the ‘untetheredness’ of the network produces more than ‘something analogous to the experience of music’; it launches the reader/interpreter into the unknown, into speculative realms hitherto deemed unimaginable, into metaphysical abstractions – all far beyond the province of mere personal experience. In a lecture (untitled) at the University of Illinois on 25 February 1967, just at the point of the completion of Treatise, Cardew refers to the ‘infinite variety of possible sounds’, and their notation:
Like vectors – space filled with lines going in all possible directions, each extending to infinity at both ends. One line is for instance piano sounds. This would rather be a big cluster of parallel lines representing all the pianos so far. Intersecting these are the lines of the millions of people who plays all these pianos. Other clusters of lines are the other instruments. Along the lines are the infinite gradations of loud and soft, and the infinite subdivisions of pitch. Amidst the maze of infinite lines there are infinite intersections, or points of identity – the sound of this pen striking the table is identical with the sound of the table being struck by the pen. All lines also extend as planes in time (since time of occurrence can also be a significant variation – e.g. the horn player entering a bar late is a very different sound from when he enters at the right time). And so on and so on. Finally it seems as though there must be almost an infinity of dimensions in which sounds can vary. Timbre, pitch, loudness, duration, time of occurrence, place of origin, orientation of hearer, acoustical environment, etc. etc.
Here Cardew seems to be positing a kind of science-fiction notation, a musical space journey for the intrepid musician-traveller across vast expanses of space-time; the multi-lined staves of Treatise, which notate a calculus of piano sounds across the whole keyboard, representing the idea of ‘all the pianos so far’ and the infinite number of pianists that played them. A truly intoxicating projection.
‘Sounds – ideas; reading Treatise is a twilight experience where the two cannot be clearly distinguished’.  Cardew proffered diverse descriptions of Treatise (‘a travelogue in the land of composition’), as if he were seeking to establish an identity for the work in his own mind. For the would-be interpreter some are particularly useful: ‘an articulated network’, for example, implies that something, say the interpreters’ performance material, should be referable to the network of signs which constitutes the whole work. Like a grid Treatise is placed over the material and allowed to ‘work’ on the sounds. The sounds are placed at the mercy, as it were, of the signs, which act both upon each other and on the sound material: interfering with, modifying, changing, distorting. And however much one attempts to ‘control’ this relationship, the signs insist on assuming a certain autonomy – or what Cardew calls ‘authority’.
So the interpreter devises and freely connects up his musical language with this pre-existing structure, this ‘articulated network’. In making these connections he has certain options, but the structure itself is permanent and unchangeable. And whatever signification it is decided that an individual symbol should bear – and the meaning of a sign is the role it plays (the role assigned to it by the interpreter) – its interpretation is contextually dependent, as is the case, of course, with all notated music.  Moreover, since the rules which connect interpretation to score can never be described exhaustively, the information they embody is often transmuted beyond the point of recognition.
Yet assigning ‘meaning’ to each and every sign can become a tiresome, cramping exercise; its intellectualism stultifying. Sometimes an obdurate hieroglyph refuses either to yield a sound or to relate in some way to one; the reader must remain patient in the hope that eventually he/she will be able to coax it into an intelligible response. Often it is the context which will suggest an interpretation, a point Cardew makes in the notes for Octet ’61. Pedantry, however well-meaning and incorruptible, soon leads the reader into one cul-de-sac after another, forcing him to abandon his interpretation in a state of moral crisis. Perhaps what Cardew wanted to demonstrate in Treatise was the incompatibility of the permanent symbolism of notation and the transience of sound.
The relationship between the signs and the ‘resulting’ music cannot, in my view, be described in purely symbolic terms; one can prepare oneself for Treatise but one cannot sit and work it all out. What one can do is to react emotionally, spontaneously, irreverently to the notation while still following, or rather observing, a set of rules which one has devised, none of which necessarily involve a specific symbolism. This corresponds to the way in which improvising musician Eddie Prévost (of AMM) approaches a group performance of Treatise:
Without having any preconceived ideas about what I will play – except by virtue of the instrumentation I will apply – I immerse myself within the sounds of the music unfolding, reading the score as if it were a visual representation of the music. I then engage in a dialogue with the other players, using the inspiration of sounds and symbols to add my own voice. These are, of course, simultaneous readings (they always are). 
In Treatise the reader is swept along, sometimes at breath-taking speed, by the visual expression of ‘long-term continuities’; for example the stave, free of traditional constraints, will take off in unpredictable, vertiginous flight, now contracting, now expanding, twisting and turning, disintegrating, fragmenting, now orderly and undemonstrative, now riotous and violent, exploding into fragments like a display of fireworks. Then, suddenly, a particular element catches our eye; we follow it, it seems to offer a temporary stability, an orientation. Or it incites us to extravagancies; the pulse quickens, and we are driven, page after page, towards a climactic expression. And then it disappears, leaving us marooned in unfamiliar territory. And yet, by following it, using it, by your commitment, we have validated it. Through it we have been moved to make music. For many performers it is the morphology of the signs in Treatise and their broad trajectories as much as any symbolic meaning which is attached to them that governs and stimulates interpretation. Like living forms they grow, expand, metamorphose, splinter, vanish, are revitalized – just as real sounds behave. As if Treatise were a kind of notational naturalism which resists symbolic representation, or renders it, at least in part, superfluous.
To read and act upon a notation can be a liberating experience; a notation can posit the unthinkable, the unimaginable, the unplayable, the unperformable, just as Cage’s and Wolff’s notations sometimes do. In Treatise, too, the signs expand the normal field of reference of traditional notation beyond the received definitions of ‘music’. Treatise cannot be circumscribed by purely musical references; Treatise invites us, irresistibly, to play, to sing – but also to dance (dancers have been inspired to choreograph their readings of Treatise), to perform, to act, to move; ultimately, to self-invent.  With Treatise Cardew wanted to incite the performer to risk to transgress, not through an ‘accident thrown up by the score, as in Cage, but through the re-definition, the re-invention, of her own consciousness.
To ‘sight-read’ through Treatise is an exhilarating experience (John White described reading through Treatise more soberly as ‘a music lesson’); for there is no time to think, to imagine, to prepare the sound beforehand. The relation is kinaesthetic, the notation more an incitement to act than to imagine – or rather, action and imagination coalesce to defy notational control, however subtle and persuasive. Thus, and here reservations surface, sight-reading through Treatise the sound is created less on the basis of the notation, more on the basis of the player’s previous (playing) experience; the performance is thereby closer to improvisation. But as source material the past is always treacherous; it can turn the tables on the indulgent performer, hold him hostage; the bedrock of past experience is too easily accessible, too comforting, dissuades the performer from leaving the ground, from flying and discovering. So although in the more spontaneous context of ‘sight-reading’ the signs enjoy less authority, their mere presence is crucial; intervening, checking, moderating, reducing/subverting the insidious purchase of subconscious habit – their influence recorded instantaneously, or not at all.
If Cardew did not completely abandon notation, he had nevertheless, with AMM in 1966, discovered a way of making music where the question of notation was simply bypassed. (‘But one cannot “write” sound; the best one could do would be to “sound” the sound’.  Rather than creating an elaborate metaphor, Cardew chose to illustrate, just as Wittgenstein ‘abandoned theory, and all the glory that theory can bring on a philosopher (or musician), in favour of an illustrative technique’.  But that position had been reached by a tortuous route; the primacy of notation had been instilled in him, in all of us, and he had become a brilliant practitioner; in Western musical culture reading was a prerequisite of making music, and Cardew was one of the finest ‘readers’ of his generation. 
Early Interpretations of Treatise
The performance practice of Treatise was developed empirically, and Cardew’s initial experiments were carried out with composers and instrumentalists from the field of contemporary music – highly trained music readers whom he quaintly described as ‘square musicians’: among others were Frederic Rzewski, Mauricio Kagel, Sylvano Bussotti, Roger Smalley, John White, David Bedford, Kurt Schwertsik, Peter Greenham and myself. Our attitude to notation might have been described as casually, or rather unostentatiously, reverential; after all, it was through notation that the superiority of Western music had been unequivocally established, and we carried that heavy burden on our shoulders as we strove, dutifully, to give musical expression to Treatise. Moreover we recognized the Western artistic conventions which seemed to inform the formal characteristics of Treatise; to those of us familiar with late-romantic music we could identify the gradual build-up of symphonic proportions, extending over two of my eight sections (pages 127-164) which culminates in a monumental climax of Brucknerian grandeur. This features black circles, increasing in frequency and magnitude until one of them, the largest covers almost half a page, completely obliterating the central line which had gamely held its position until that final cataclysmic moment.
In Western culture the musical work is hypostatized as an entity in itself. Music is non-representational, abstract; we analyse its inner structure and formal relations. Preparation for Treatise was therefore dominated in the early realisations by a search for rules, and the necessity to hold by them. The rules were implicit and their discovery and application would reveal at least some of the secrets of Treatise. Rather than a creative reading of the score, it became an exercise in scholarship, trying to match the fastidiousness of the score with a method of reading which was as ingenious as it was meticulous. But the tools we were using were often inappropriate, inadequate for the symbolization of the new modes of expression which Cardew sought to elicit from interpreters. Our performances carried a surfeit of historical and stylistic sedimentation through which we sold Treatise (or its composer) short. We were unable to shed a proclivity for the clichés of contemporary music and, in some cases, of jazz, our fingers and the shapes in our hands programmed by the obligatory repetition of time-honoured figurations. In particular, we were the precocious children of the avant-garde; we were familiar with the most recent works of Cage, so that when Cardew suggested grouping symbol together and reading them in relation to ‘time-line’ – through which various parameters of the sound could be derived – we knew that he had Cage’s Variations in mind. Christian Wolff’s scores, too, were for us an invaluable source of interpretative ideas. In our creative imagination the notational systems and performing practices, the representational apparatus’ of the avant-garde were influential as well as delimiting factors.
An unfortunate consequence of this was that we tended to interpret Treatise as a succession of events (despite the fact that Cardew had criticized the predominance of ‘event’ parameters in the two earlier experimental works: Autumn 60 and Octet ’61): a mechanical one-thing-after-another mode of procedure antithetical to the seamless flow which characterizes numerous sequences of pages in Treatise: In the Handbook Cardew forewarns against this mode of interpretation, positing two basic sets of parameters: even parameters and happening parameters; and he considered it to be of primary concern for the interpreter to identify and distinguish between these parameters: ‘Events: something short, compact, homogeneous that we experience as complete (though we may only experience a part of it) and as one thing. Happening: something that continues, the end is not legible in the beginning.’  By circumscribing symbols, by our concern for beginnings and endings, we forced our chosen signs into the ‘event’ category.
If it is true that Treatise generated considerable interest and commitment on the part of those who chose to involve themselves in it, it can also be said that some performers felt frustrated and skeptical; in Buffalo Cardew’s experiences with Treatise were not the happiest, probably because his own attitude towards it was shifting into an ambivalence which the performers sensed, and which probably undermined their confidence in their own contribution. For the two American performances he demanded an ever-increasing number of rehearsals and whereas on the one hand he would make precise demands from them, on the other he was unclear, perhaps unsure, as to what he wanted. If he wanted to create an ‘authoritative’ first version, this was not the right way to go about it. It seems to me that one has to live with Treatise for some time, just as the AMM lived with AMM music over the years, nurturing and refining it. Here, Cardew’s ‘city analogy’ is a good one, for all its limitations, because it exemplifies the depth and extent of commitment which musical interpretation demands:
Entering the city for the first time you view it at a particular time of day and year, under particular weather and light conditions. You see its surface and can form only theoretical ideas of how this surface was moulded. As you stay there over the years you see the light change in a million ways, you see the insides of houses – and having seen the inside of a house the outside will never look the same again. You get to know the inhabitants, maybe you marry one of them, eventually you are an inhabitant – a native yourself. You have become part of the city. If the city is attacked, you go to defend it; if it is under siege, you feel hunger – you are the city. When you play music, you are the music. 
Cardew’s documentation of early performances of Treatise, 1964-7, affords many insights not only into his own attitude to the work, but also into the idiosyncratic attitudes and anomalies of behaviour of those who were involved as interpreters: Rzewski’s interpretation of the middle line exclusively; John White’s precedent for ‘perverse readings’ by reading ascending lines as descending intervals; the composer’s own interpretation of the five-line system as a chord which is transformed according to rules connected with angles created in the course of the stave’s growth and development. More importantly, there were certain collective solutions arrived at in those early performances which were handed down and became part of a ‘tradition’ in subsequent realisations of Treatise. The frequent appearance of numbers, for example, has tended to be interpreted as note/chord repetition; that is, each player repeats his/her chose note ‘x’ number of times, resulting in the repetition, ‘x’ times, of a random chord. The numbers enjoy a degree of separateness, normally occurring in breaks in the score:
The numbers are included at the pauses for the reason that: any act or facet of the conception or composition of the score may have relevance for an interpretation. […] It is the fact that there were 34 blank spaces before the first sign put in an appearance. 
This is an interesting, if perplexing, note because it is one of the few references, in the Handbook or elsewhere, to the compositional method which Cardew employed in Treatise and suggests that his statistics for the appearances of individual signs were subject to a random procedure. Whatever ‘method’ was employed here Cardew treated it on at least one occasion in cavalier fashion; in the Buffalo performance in December 1966, according to the Handbook, ‘the number 34 at the beginning was reduced to 17 and the performance began with 17 pianissimo chords each lasting 17 seconds’.  No explanation is given. Perhaps 34 pianissimo chords was considered excessive by the musicians; perhaps there was a revolt; to save the concert Cardew had to compromise and the relation of 17 to 34 was close enough for him not to lose face.
Keith Rowe is not the only interpreter who regards the first 5 millimetres of Treatise – in which the number 34 appears – as possibly the most important detail in the whole work: a hurdle which has to negotiated right at the outset before access to the work is obtained, and it is tempting to see this conundrum as a deliberate ploy on Cardew’s part to discourage the faint-hearted. For Rowe it reflects Cardew’s attitude to performance, or rather to pre-performance (as he recalls it in those early AMM days): the thoughts calm and focused, the mind relaxed, alert, open. 34 – a significantly large number (the largest) in the context of Treatise – it creates a sense of gravitas right from the beginning, reminding Rowe of the poem which was used in a poster advertising a Tiger’s Mind performance on the last day of 1967:
I lay my harp on the curved table,
Sitting there idly, filled only with emotions.
Why should I trouble to play?
A breeze will come and sweep the strings. 
And which is echoed both in Lou Gare’s ‘poem’, an example of notated Scratch Music which is printed in Cardew’s anthology, Scratch Music:
I lay down my saxophone on the curved table,
Why should I trouble to play,
It is such hard work, and there
Aren’t any breezes about today.
And by Hermann Hesse:
[…] the whole world might be no more than a breath of wind playing over the surface, a ripple of waves over unknown depths. 
For musicians involved in both reading and improvising, it is instructive to contrast playing Treatise with improvising; in improvisation the stimulus to play and continue playing is generated from within, in response to the music as it unfolds, and the music develops organically; in Treatise the listener is intensely aware of a third force, an authority which impinges upon the music-making obliging the performer to stop playing where he might prefer to continue, or to go off on a new tack where he might prefer to remain where he is, or suddenly to introduce a contrasting instrumental technique at a juncture where it feels inappropriate. Eddie Prévost illustrates this ‘third force’ in more personal terms; for that reason, perhaps, his words produce a stronger, more lasting resonance. Whereas the investigative mode and dialogue are the dominant features of improvised music (at least, we should add, in Prévost’s preferred practice), with Treatise
[...] tracking the score, allowing its presence, history and associations to permeate the music, inevitably means that in an intellectual and an emotional way I am still engaging with Cornelius. It is a tangible way in which I can continue to invite him to enter my musical Life. 
With Treatise the characteristic flow of much improvised music is rarely allowed to establish itself, or rather, when the score flows, as Treatise often does, then the music is encouraged to flow, but only as long as the score allows. And even in those pages where the feeling of movement and flow is strong, small disruptive signs will occur to throw the music temporarily off balance – which was most likely the composer’s intention. Thus for the listener there can be a disorientating feeling of arbitrariness, of insecurity or, more positively, or unexpectedness; the influence of the score appears now benign, now malevolent.
By offering accessibility as well as extreme complexity Cardew’s magnum opus demonstrates its inherently democratic nature. No performer is turned away; through Treatise everyone can make music – from the tentative beginner to the awe-inspiring David Tudor – bringing a musical utopia tantalizingly within reach.  For whatever its illustrious status in the field of composition, Treatise does not belong to that category of arcane ‘modern’ scores. One does not pore over the score in order to intuit Cardew’s ‘meaning’; it means what the performer, or would-be performer ‘sees’. As Eddie Prévost remarked, ‘an interpreter of Treatise is drawn to the work because there is something within its weft and warp which fascinates’. 
Treatise is a long, complex story which needs to be sifted. Some of its pages might appear excessively challenging and the interpreter may feel intimidated, overwhelmed – as if Cardew had created a kind of Frankenstein’s monster. Worse, a feeling of frustration and failure can accompany a post-mortem of a performance. My own long relationship with Treatise evokes a feeling of inadequacy: a failure to do the work justice. Others share this feeling: the composer/performer Richard Barrett writes of ‘exquisite frustration’ accompanying his efforts to interpret Treatise, while composer Brian Dennis confessed to being ‘thoroughly inhibited’ from attempting any realization at all. And in Buffalo too, even the performing elite, whose expertise was hired on a regular basis by individual composers, could no longer understand, let along contribute to the kind of music-making that works such as Treatise demanded. The musicians were bemused; they were being asked to do things, to make decisions, which had never been within their remit; for even with Cage’s scores they were told what to do. Indeed, as we have seen, after Treatise, perhaps disillusioned by the results of his collaborations with professional musicians, Cardew distanced himself even further. But if Treatise was the culmination of his career as an avant-garde composer, it also carried within it the seeds of destruction of his relationship to the avant-garde.
20 Treatise Handbook, p.x. (CCR).
21 Tempo Magazine, ‘Notation – Interpretation, etc.’ p. 23, note 8. (CCR).
22 ‘Notation – Interpretation’, etc.’ p. 24, note 8. (CCR).
23 Ibid, (CCR).
24 Ibid, p. 27, note 22. (CCR).
25 Merrill B. Hintikka and Jaakko Hintikka, Investigating Wittgenstein (Oxford: Basil Blackwell, 1986), p. 238.
26 ‘It was all lies’ was Kurt Schwertsik’s cri-de-couer, echoing Cardew, in a conversation we had in an Indian restaurant sometime in the early nineties.
27 David Pears, Wittgenstein (Fontana/Collins, 1971), p. 113.
28 Treatise Handbook, p. xii. (CCR).
29 ‘Many of the remarks of the Tractatus have a proverbial quality that calls to mind the mystical writers of old China. Indeed a remark by one of these, Lieh Tzu – “is it likely that long short, loud soft, can entirely represent the true scheme of things” – applies well to Wittgenstein’s return to philosophy’. From a talk prepared in Englad for a forthcoming US tour. Jrnl. 12 September 1967.
30 Treatise Handbook, p.iv. (CCR).
31 In the following section I am indebted to Sophie Hampshire for the many pertinent and illuminating remarks she makes in her thesis ‘Language, Representation and Rules: a study of Wittgenstein’s theories of language and their relevance to visual art and music’. Undergraduate Thesis for the London Institute (1991).
32 William Blake: The Marriage of Heaven and Hell (Oxford University Press, 1975), Plate 23.
33 Regarding ‘rules’, the Italian composer/performer Andrea Rocca used them to construct the broad edifice of a piece based on page 92 of Treatise. However, he felt free, and without compunction, to jettison them at a later stage of the creative process when elements were introduced which were quite independent of the score – what he described as ‘inflorescenses of the main plant’. From Brief Notes on Infant Love Song. Andrea Rocca, July 1994.
34 Wittgenstein also makes use of triangles as examples in the Philosophical Investigations (Oxford: Basil Blackwell, 1991), p. 200.
35 ‘Notation – Interpretation, etc.’ p. 25, note 11. (CCR).
36 Ibid., p. 26, note 16. (CCR).
37 ‘And is there not also the case where we play and – make up the rules as we go along? And there is even one where we alter them – as we go along’. Philosophical Investigations Part I, 83.
38 ‘Notation – Interpretation, etc.’ p. 31, note 32. (CCR).
39 Ibid., p. 23, note 7. (CCR).
40 According to Stella Cardew this was the basis of his objections to her own suggestions; he would not tolerate the indeterminate blurs and smudges which appealed to her more painterly imagination. Interestingly, her most striking contribution to the pages o Treatise, specifically page 190, which is reproduced above, was not censored, precisely because it dramatically enhances the more ‘autobiographical’ nature of the later stages of the work. Moreover, they had nothing to do with the aesthetic consideration; Stella’s graphic gestures were made in anger and frustration; they erupted out of domestic strife.
41 Treatise Handbook, p. vii. (CCR).
42 Wittgenstein talking about chess: ‘Let us say that the meaning of a piece is its role in the game.’ Philosophical Investigations, Part 1, 563.
43 From a letter to JT, 2 June 1994.
44 For a performance at Morley College in 1969 the artist Tim Mitchell created a wooden relief structure based on one page of Treatise. During the performance, by Cardew’s Morley College students, the sounds of Mitchell’s sawing and drilling were incidental, ‘chance’, by-products of his interpretation. Thus, in this version the ‘music’ was consigned, arbitrarily, to a secondary, accompanying role.
45 ‘Notation – Interpretation, etc.’ p.22, note 4. (CCR).
46 Treatise Handbook, p.xvii. (CCR).
47 1966 was a momentous year, the first since Cardew became a student at the Royal Academy that produced not a single composition. In 1967 a single work: The Tiger’s Mind, which comprises solely a written text. 1968 saw another purely text piece, Schooltime Special, and Schooltime Compositions, a note-book of ideas including some references to traditional musical notation; and in April Paragraph 1 of The Great Learning, which does include a relatively conventionally-notated section for organ solo.
48 Treatise Handbook, p.iii. (CCR).
49 Ibid. p.xvii. (CCR).
50 Ibid, p.iv. (CCR).
51 Ibid, p.xii (CCR).
52 Attributed to Po Chü-I (772-846). Included in A Treasury of Asian Literature, ed. by John D. Yohannan (Meridan, Penguin Books, 1994).
53 Hermann Hesse, The Glass Bean Game (Harmondsworth, Middx: Penguin Books, 1972), p. 487.
54 Letter from EP to JT, 2 June 1994.
55 Without a utopian core perhaps no meaningful artistic endeavor can advance?
56 See note 54.