Cornelius Cardew's Camouflage and Bun No. 2

Cornelius Cardew's Bun No. 2 (1964) provides a unique opportunity to reconcile the composer's indeterminate graphic score Treatise (1963–7) with a more determinately scored orchestral work which uses orthodox staff notation. It represents an amalgamation of Cardew's approach to two notational systems that, owing to their concurrence of use in his oeuvre, can inform our understanding of how graphic scores can be used in determinate compositional processes and vice versa. This article explores why Cardew decided to embark upon this experiment, using contextual information relating to Autumn '60 (1960) and the influence of other composers, such as Morton Feldman (1926–1987). This is situated in Cardew's notion of 'camouflage', a socio‐musical construct relating to the situation and presentation of his widely varied compositional output in the changing musical environment of the late 1950s and early 1960s. The analysis itself covers a small portion of Bun No. 2, drawing extensively upon Cardew's Treatise Handbook (1971), identifying and extrapolating tendencies of musical‐graphical translation and focussing on the use of major and minor triads and their deformation using geometric concepts of 'perfection' and 'imperfection'. Finally, the article considers the implications of this work both for Cardew and for the aesthetics and wider study of graphic score readings, briefly offering a reflection upon the concept of isomorphism in Ludwig Wittgenstein's picture theory (building upon Cline 2020) in relation to the rhetorical notion of ekphrasis (Bruhn 2000) as a means of explaining the uneasy position that this piece occupied for Cardew, read through the lens of camouflage.

14th Feb 65

[A]sked what all those squiggles in Treatise mean, I might reasonably answer: a) that it is very complicated to explain, and explanations are of dubious value, and b) that in any case it is secret.

—Cornelius Cardew, Treatise Handbook, p. vii

Introduction

On the back cover of Cornelius Cardew's Treatise Handbook ([11]) – a text in which he describes the process of writing Treatise ([9]–7) and its early performances – the composer states that his eleven‐minute orchestra piece Bun No. 2 (1964) 'is based on pp. 45–51 (middle) of Treatise. In a way it represents an analysis of that passage'. No further information is given as to how this 'analysis' is carried out, but the use of 'analysis' rather than 'interpretation' (or some similar term) is of note, implying the identification or codification of formal or structural processes. This enigmatic process receives cursory mention in the recent scholarship on Cardew. Tony Harris mentions that both Bun No. 2 and Volo Solo (1965) are 'composed realisations' of Treatise ([19], p. 45). Similarly, Virginia Anderson, writing specifically on performer choice in Treatise, couples these two pieces together, describing them as 'written realizations of sections of Treatise' ([2], p. 297). David Cline's 'Treatise and the Tractatus' ([14]), perhaps the most relevant companion to this present study, centres on a robust and impressive analysis of Volo Solo, foregrounded by commentary on the influence of Ludwig Wittgenstein on Cardew's Treatise. For my purposes, the important quality of Volo Solo is that it retains a higher level of indeterminacy, in David Clarke's sense of 'compositions in which the order of events or the determination of content (or both) is rendered critically unfinalized by the creator' (Clarke [12], p. 170). This indeterminacy is registered with the absence of any sort of metre, and the fact that the piece is scored for 'any solo instrument'.

Whilst both pieces derive their source material from Treatise, the more traditionally notated example is Bun No. 2, and this could be said to have a lower level of indeterminacy. The significance of this is that a more determinate, notated and descriptive score, unlike that of Volo Solo, can be scrutinised in the fullest possible terms of its process of graphical‐musical translation. Cardew's biographer and former collaborator John Tilbury contributes the most to this discussion, identifying some brief interpretations of the graphical process, but he stops short of providing a comprehensive analysis of any full passage of this 'mutation' of Treatise (see Tilbury [30], pp. 256–8). The idiosyncrasies of Cardew's approach to notation and (in)determinacy with respect to these Treatise‐derived works (and indeed, the rest of his work of the 1960s) resonate with his notion of 'camouflage' (Cardew [10], p. 4), which will form a central part of the rationale of this article. This term, discussed in more detail in the following section, describes a system of 'protections' afforded to works through both notation and the balance between 'future‐oriented' and 'hereditary' characteristics – perhaps referring to two high‐profile strands of art music in this period: modernism (or avant‐gardism) and experimentalism.

In order to contextualise the analytical implications of Bun No. 2, it is important to consider the research already carried out in analysing graphic scores by other composers in this same period. Brian Ingliss proposed an analytical quasi‐treatise in 2015, modelling his work from Anderson's performative approach to graphic scores and making the salient point that 'graphic scores form a vital and actually bigger part of our musical culture than is usually acknowledged, providing [...] a largely untapped phenomenon for music analysis' (Ingliss [21], p. 11). Martin Iddon and Philip Thomas's mammoth volume dedicated to John Cage's Concert for Piano and Orchestra (1958; Iddon and Thomas [20]) is a testament to this cultural significance.[2] Clarke ([12]) offers reflections on a small section of Cage's Solo for Piano (1957), drawing upon and critiquing Jean‐Jacques Nattiez's ([24]) semiotic approach to poetics and aesthetics to demonstrate the issues surrounding the analysis of indeterminate music, deeming graphic scores to exhibit 'radical ambiguity [which] render[s] the work ambiguous at a fundamentally ontological level' (Clarke [12], p. 177). Beyond Cage, Cline's monograph explores methods of analysis of Morton Feldman's graph music (Cline [13]), and Tristan McKay's recent study proposes analyses of graphic 'open form' works, such as those by Earle Brown and Will Redman (amongst others; McKay [22]). As can be seen, this scholarship has focused mainly on highly indeterminate works which dispense partially or entirely with the rhetoric and function of Western five‐line staff notation in favour of graphic notation. This article aims to provide a novel approach to analysis with relation to both types of notations and their implications for Cardew's concept of camouflage.

A highly significant feature of this analysis, derived from the Handbook, is the role played by major and minor triads, whose control and deformation relate to the graphics of Treatise. The use of this harmonic device has both a functional and a social dimension. Functionally, the recognisable identity of the major and minor triads allows for a clear use of 'perfection' and 'imperfection' that Cardew sets up in his compositional logic in the Handbook, 'perfect' being an unaltered triad and 'imperfect' one that is deformed or altered (see the entry from July 1963, p. iv; this will be elaborated upon in due course). Socially, the use of these triads in Bun No. 2 can be seen as emblematic of a wider shift in Cardew's compositional philosophy, one that is related specifically to the influence of Cage and the New York School, and a turn away from the European fraternity of avant‐gardism that came to dominate the 1950s. Writing on György Ligeti's Fanfares and Horn Trio, Eric Drott makes the notable point that 'there is not a single exclusionary logic that explains the prohibition of triadic harmony during the ascendancy of atonal and serial music in the 1950s, but that there are a number of logics, which must be explored in their own particularity' (Drott [16], p. 286). Indeed, one might argue that the same can be said of the inclusion of triadic harmony in the following period. This seems particularly relevant when noting Tilbury's remarks on the New York School:

The fact that [they] had not banned certain chords and progressions from their work impressed me. True, [...] they too had created artificial systems, but these did not seem to 'police' the music in the way that European serialism did (Tilbury [29], p. 16).

I will argue that the coalescence of the functional and the social nature of the triad, and its treatment relating to tendencies outlined in the Handbook, can be seen as manifestations of Cardew's notion of camouflage, which creates the idiosyncratic approach to handling musical materials seen in Bun No. 2. Whilst triads provide a significant impetus for the analysis, an examination of musical texture and instrumental groupings will be important in consolidating this argument, namely through demonstrating the variety of ways in which Cardew analyses the Treatise pages as a means of constructing a camouflage. First, it is important to establish the context of Bun No. 2, noting the extent to which other works may bear upon the analysis.

Background to Bun No. 2 and the Notion of Camouflage

Bun No. 2 dates from a period of Cardew's life, culminating in the completion of Treatise in 1967, during which he was exposed to a wide variety of musical philosophies. From 1967, he took an increasingly political and social approach to music. Harris and Cline argue that one of the defining events of this period was the 'American Invasion' of Darmstadt in 1958 (where Cage lectured), leaving Cardew with 'Cage Shock' and fostering close relationships with the New York School (Morton Feldman, Earle Brown, and David Tudor), alongside his ongoing professional relationship with Karlheinz Stockhausen (see Harris [19], pp. 30–2 and Cline [14], p. 121). Harris further comments that the impact of these American musicians upon Cardew 'cannot be overstated' and that this also had a significant impact on Stockhausen (Harris [19], p. 30). This impact could be demonstrated in the sense of a stylistic hybridity that characterises Cardew's works of the early 1960s, in piano pieces such as Three Winter Potatoes (1961–5; Ex. 1a), which feels like a homage to Stockhausen's ultra‐modernist Klavierstücke of the mid‐1950s (Ex. 1b), and Memories of You (1964; Ex. 2), a distinctly Cageian conceptual work in which the score 'gives the location of a sound relative to a grand piano', rather than any instruction on how to play the instrument (Cardew [10], p. 30). Michael Nyman claims this piece 'sums up [the] new approach to the piano' in experimental music (Nyman [25], p. 21). This aesthetic duality, bearing influences of both Stockhausen and Cage (or more generally experimentalism and avant‐gardism), may be seen as being at the heart of Bun No. 2, with Cardew commenting in 1962 (with reference to Feldman's graph music), 'It is perfectly conceivable that a composer should be engaged in two widely divergent lines of investigation' (Cardew [[17]] [7], p. 46). Indeed, Cline has recently come to a similar conclusion with respect to Octet '61 for Jasper Johns ([17]), describing the work as 'a musical hybrid that combines freedoms inspired by American Experimentalism with architecture redolent of the post‐war European avant‐garde' (Cline [15], p. 294).

These contrasting approaches can be reconciled when considering Cardew's writing in the preface to Four Works ([10]),[3] in which he states:

[T]he pieces also need camouflage to protect them from hostile forces in the early days of their life. One kind of protection is provided by the novelty and uniqueness of the notations [...] but a more positive kind of camouflage is needed; something to persuade the watchful custodians of our musical garden that these tender young emergent plants bear more resemblance to flowers or vegetables than to weeds. So as seeds, besides containing a growth mechanism oriented towards the future, they also bear hereditary characteristics linking them with the past. [...] 'Solo with Accompaniment' and 'Memories of You' are more aggressive, tougher simpler in conception and consequently stand in less need of such camouflage. (1966, p. 4; emphasis added)

Here, Cardew demonstrates that the notion of style is one of symbiosis. The idea of camouflage suggests that there is a need to protect what Cardew viewed as the avant‐garde from those in positions of traditional musical power (perhaps read here as figures such as Pierre Boulez and Stockhausen). The need for camouflage itself could be traced back to Cage's activities in Darmstadt, which Cline claims 'destroyed the apparent collegiality of the leading Darmstadt composers by nurturing and exposing differences of ideology and approach, resulting in "open warfare"' (Cline [14], p. 121). Memories of You, a totally graphic, experimental work, is less in need of camouflage not only because of the novel notations, but also because it does not engage with traditional musical elements; there is no (apparent) pitch, no harmony, no rhythm.

Similarly, Cardew explains that in his mixed ensemble piece Material (1964), 'the rhythmic pulsation and development of the rubato idea provide a similar handhold' (Cardew [10], p. 4). The stance is clear that new musical expressions must, in some way, be stylistically hereditary to create a meaningful coherence for the 'watchful custodians' that listen to them, and thus forge an acceptance. In this way, it is unsurprising that Material is an arrangement of Cardew's Third Orchestral Piece (1960) and that Three Winter Potatoes contains elements from Material and Octet '61 for Jasper Johns (see Tilbury [30], p. 130): the material must cautiously establish itself. It is this heredity and camouflage that is so fascinating in Bun No. 2, which can be seen as an example of reconciling Cardew's experimentalism with more modernist output, in the form of the transcription of an indeterminate graphic score into a mostly determinate score. A useful comparison might be made between the overarching concept of Bun No. 2 and Feldman's Structures for Orchestra (1960–2). In the preface to the score, Feldman summarises his general notational practice before explaining the purpose of the piece specifically:

In various works of mine, such as The Swallows of Salangan [1960], all the pitches are given but the performer chooses [their] own duration (slow) for each sound. The effect is very much like a series of reverberations from a common sound source. What I did in Structures for Orchestra (1960–1962) was to 'fix' (precisely notate) what might occur if the work utilized indeterminate elements. (Feldman [17])

Here we see a similar desire to explore the spectrum between determinate and indeterminate musical practices, linking ideas of 'reading', or perhaps even 'performing', the polyvalent experimental score (indeed, this performative idea of composition resonates with Feldman's creative philosophy).[4] This is important in that Structures for Orchestra remains Feldman's only published work of the 1960s which utilises conventional notation. Nonetheless, it relies fundamentally on a conception of indeterminacy – a sounding or imagining of it. The singular nature of Structures for Orchestra and Bun No. 2 perhaps speak to this uneasy partnership between two notational philosophies. One wonders about the impact of this work on Cardew with respect to his close relationship with Feldman, having also performed his works. Indeed, Cardew was familiar with the score of Structures, commenting in 1963 that the work is written in a 'perfectly straightforward manner' (Cardew [9], p. 443).

Cardew's Autumn '60 is a notable work in this context, for in the preface to the published score Cardew demonstrates a possible reading of Figs K–M (complete with a rationale). However, it is clear that this is suggestive: as Cardew notes, 'it is not possible for a conductor to distribute parts for Autumn '60 amongst orchestral musicians and then get up on the rostrum and conduct the piece' (Cardew [10], p. 3). Ironically, this was precisely what Mauricio Kagel demanded of Cardew:

For performances [of Autumn '60] directed by Mauricio Kagel, I have had to write out a score, and since then I have added parts to his collection as they were required by him for performances with different instruments. This runs even more counter to the original idea, and I have noticed in these performances that the players have regained as often as not their usual attitude to contemporary music, i.e. 'we play it, but don't blame us for what it sounds like' which is exactly the attitude which these pieces try to circumvent. But the stock of the parts will be useful when, eventually, the work is attempted with an orchestra of reasonable size. (Cardew [1962] [8], p. 53)

It seems no coincidence that Bun No. 2 would be the next time Cardew would attempt such an exercise, especially considering that the work was commissioned by Kagel and scored for orchestra. As will be demonstrated, ideas of musical development in Bun No. 2 (e.g. repetition, variation, harmony) are controlled by the graphics of Treatise. In this way, the graphic source is expressed in a detailed and orthodox notational syntax which may (superficially) resemble those of the European and American avant‐garde. To an extent, this could be more generally characterised as a dichotomy between modernism and experimentalism as proponents of determinate or indeterminate approaches to notation, described by Cline as espousing 'architecture' and 'freedom' respectively (Cline [15], p. 294). This dichotomy is further elucidated through statements from Milton Babbitt and Nyman. Described by Zachary Bernstein ([4]) as 'a paragon of high modernism', Babbitt's polemical article 'Who Cares If You Listen' (1958) explores the issues surrounding 'serious, advanced contemporary music', which one may read through his own practice as that of total serialism and notational complexity. Babbitt makes the distinction that

each such 'atomic' [musical] event is located in a five–dimensional musical space determined by pitch‐class, register, dynamic, duration, and timbre. These five components not only together define the single event, but, in the course of a work, the successive values of each component create an individually coherent structure, frequently in parallel with the corresponding structure created by each of the other components [...]. It is this high degree of 'determinacy' that most strikingly differentiates such music from, for example, a popular song. (Babbitt [1958] [3], p. 237)[5]

In contrast, Nyman outlines the principles of experimentalism with regard to notation as follows:

A score may no longer 'represent' sounds by means of the specialized symbols we call musical notation, symbols which are read by the performer who does [their] best to 'reproduce' as accurately as possible the sounds the composer initially 'heard' and then stored [...]. Experimental composers are by and large not concerned with prescribing a defined time‐object whose materials, structuring and relationships are calculated and arranged in advance, but are more excited by the prospect of outlining a situation in which sounds may occur, a process of generating action (sounding or otherwise), a field delineated by certain compositional 'rules'. (Nyman [25], pp. 3–4)

This outlines the general characteristic of a highly determinate approach to notation, advocated by the European and American avant‐garde (Boulez, Stockhausen, Elliott Carter et al.), and a more indeterminate approach espoused by the experimentalists (Cage, Feldman, Christian Wolff et al.). In Bun No. 2 the graphics of Treatise are codified in terms of 'hereditary' musical systems: they are camouflaged. Moreover, Cardew also states that 'their best guarantee for survival would be a completely self‐contained, closed logical system for each piece' (Cardew [10], p. 4). It could be that Bun No. 2 represents this by virtue of being a mostly determinate score in staff notation. One might argue that, unlike Autumn '60 and Feldman's Structures (both of which have a comparatively high level of musical detail across various parameters), Cardew performs a kind of 'double reading' in Bun No. 2: firstly, of Treatise, to establish how a logical system of performance may be constructed (Nyman's 'compositional "rules"'), and secondly, to map this reading onto the orthodoxy of metrical staff notation (Babbitt's '"atomic" event' in 'five‐dimensional musical space'). It will be shown in the final section of the article that the oscillation between these two aesthetic positions creates the fundamental originality and interest of Bun No. 2, but also that it is this bricolage that proved difficult to reconcile in personal and political terms for Cardew, explaining the singularity and novelty of the piece and its process and perhaps rationalising Cardew's future artistic trajectory.

Structure

Bun No. 2 comprises two section types: 'RICHTIG' (correct) and 'FALSCH' (false). The preface to the score states that the piece should, if possible, be performed twice (non‐consecutively). In the first performance, only the parts marked RICHTIG should be played. In the second, all material is played. The RICHTIG and FALSCH sections are deployed alternately, as seen in Table 1. Significantly, Cardew states that 'with the exception of the passages marked FALSCH (2) and FALSCH (3) the piece is based on pp. 45–51 (middle) of Treatise'. It seems that pages 45–51 were amongst the first that Cardew committed to fair copy versions, completed in the summer of 1963 (see Cardew [11], p. i), and therefore may have been the most appropriate for this kind of experiment. In the context of camouflage, the general (although not total) equation of RICHTIG with Treatise, the graphical material, rings true: the 'analysis' of Treatise is the 'correct' material. The reason for the inclusion of FALSCH (1) in this process could be to hide further the discrepancy between the sections and allow the piece to camouflage better by merging the two types of material.

1 Table Basic structure of Bun No. 2

Section	Bars	No. of bars
FALSCH (1)	1–9	9
RICHTIG (1)	10–46	37
FALSCH (2)	47–63	17
RICHTIG (2)	64–77	14
FALSCH (3)	78–91	14
RICHTIG (3)	92–124	33

A similar approach to flexibility of form can be observed in Three Winter Potatoes. The second piece of the set is, in Cardew's words, 'cyclic', meaning that 'any barline may be used as the starting point, and the end may be joined to the beginning' (again showing strong echoes of Stockhausen's Klavierstücke). Indeed, Three Winter Potatoes, as a title, may be a link to this aesthetic situation of camouflage through the continued use of vegetal language; its camouflage achieved through its mobile form.

Whilst Bun No. 2 is much more structurally determinate, it nonetheless manifests the mobility of form that was prevalent in much contemporary music of the period (Boulez, Stockhausen, Cage et al.). Indeed, one could argue that, through utilising this device in Bun No. 2 and separating material types (dependent on process), Cardew is applying camouflage on a macro level through structure, as well as on a micro level by the derivation of musical materials through graphics. In other words, Cardew's depiction of his own graphic score is achieved via a referential cultural context of modernist contemporary music. This is notable when considering Andrea Phillips's assessment of Treatise:

With no instructions whatsoever for the performer, Treatise already opened up the concept of 'indeterminacy' but was still harboured within the high modernist language of the avant‐garde, despite and through its coincidence with [the improvisation group] AMM, its score a language of potentially arcane symbols and refined motivations. Treatise is mainly opaque to anyone without an explicit relationship with the development of scoring from Boulez, Ligeti, Nono, et al. (Phillips [26], p. 43)

This contrasts somewhat with Cline's assessment that Treatise was the 'pinnacle in [Cardew's] own output and arguably within the experimental music wing of music composed in the 1960s' (Cline [15], p. 294), instead still aligning it within the intellectual tradition of the high modernist avant‐garde. The larger debate around this issue is worthy of its own separate study, but for the purposes of this article it raises a question about the relationship between the 'hereditary' and 'futuristic' aspects of camouflage, considering that Bun No. 2 was written during the same compositional period as Treatise. In a sense, it may further help to provide an explanation as to why Cardew carried out the experiment in the first place, which can be further explored in testimony from the Handbook.

Analytical Approaches Drawn from the Treatise Handbook

It is important to understand not only musical context but also Cardew's graphical philosophy by examining parts of the Treatise Handbook. Most important for this study will be passages written around [9]–4, during which time Bun No. 2 was composed. These excerpts allow for an application of particular systems when analysing the score that will best represent Cardew's compositional logic, which can then be extrapolated into further considerations of Treatise (and perhaps other graphic scores).

In an entry to the Handbook dated July 1963, Cardew stresses the control of the musical score and the construction of logics: 'The score must govern the music. It must have authority, and not merely be an arbitrary jumping‐off point for improvisation, with no internal consistency' ([11], p. iv; emphasis in original). These 'internal consistencies' in Treatise are surely important in a process of translation across different notational systems, from indeterminate to determinate. Whilst not going so far as to criticise improvisation (indeed, this was a huge part of Cardew's socio‐musical philosophy), it nonetheless hints at the analytical approach that could be applied to Treatise. This approach can be seen in the following entry, written in the same month:

[July 63]

Just as the perfect geometrical forms are subjected in the score to destruction and distortion, corresponding perfect forms can be sought in sound (octaves and simultaneous attacks are two leads that spring to mind) and these destroyed or distorted. (Eg [sic] a circle with an opening might be read as an open fifth with major and minor thirds trilling). (Cardew [11], p. iv)

This clearly shows the beginnings of a basic approach to how the symbols of Treatise may be represented in a more determinate manner: through the concept of geometry as well as distortion being linked to similar ideas in music – for example, 'perfection' as an aligned musical gesture of an octave (i.e. the same pitch class) or simultaneous attack (i.e. the same rhythm), with 'distortion' representing bimodal triads which are unstable through rapidly alternating thirds (trilled). Indeed, the idea of the triad continues in a later passage from 1963 in which Cardew links the degree of distortion to the manipulation of a triad:

Oct 63

(What makes this live is the distortion of the 'any' chord. The way in which it has been derived from the triad. 'Any chord' is nothing particular, but if it bears the marks of a distortion then it has that character. This makes work on Treatise alive – the various interfering forces distorting and changing everything. The way the elements act on each other – it is like chemical processes: Acid bites, circles roll and drag, and bend the stave‐lines of 'musical space'.) (Cardew [11], p. v)

As will be seen, triads feature heavily in Bun No. 2, and thus it is possible to understand the harmony as a result of 'distorted' graphical processes, or the relation of perfection to imperfection, in geometric terms.

In December 1963 Cardew recorded at length his attempts to apply musical parameters to 'enclosed spaces' and thus categorise them:

Dec 63

A practical attempt. Take the enclosed spaces and divide them into the following categories: triangles, circles, circle derivatives (not very many), squares, square derivatives (horizontal and vertical rectangles), irregular enclosures. Musical categories can be matched up with these: triads, trills, irregular tremolos, periodicities, deviating periodicities, clusters that disintegrate in the direction of whatever shape is closest. Dynamics for all shapes can be determined thus: horizontal dimension gives the degree of loudness; vertical dimension gives the degree of dynamic contrast (this works well with most figures especially circles, because the lower the dynamic the lower the contrast. Vertical rectangles will present problems, as they demand low dynamics with high degree of contrast.) (Cardew [11], p. vi)

The specific approach that Cardew shows here further stresses the analytical implications of graphical scores to be realised using more determinate staff notation. It shows an interpretation that enhances internal logics and makes these 'enclosed spaces' into symbols that have functional properties. 'Distortion' here is eschewed in favour of 'derivatives', similarly linking properties of geometric shapes together but adapting the semantics to perhaps imply more self‐similarity across the family of shapes in their symbolic musical function. A visualisation of this geometric‐dynamic relationship can be seen in Fig. 1.

It is important to highlight that this is Cardew's interpretation of his own graphic score, published four years after its completion. As a handbook, it is presented to offer possibilities rather than curtail them to a singular reading, but they must maintain the logics highlighted in the July 1963 entry. This interpretation is a codified one that becomes an analysis when it is fixed in determinate staff notation, as seen in Bun No. 2:

[Dec 63]

(To a person who thinks the piece is a code to which a key is missing, what I am doing will look like providing a key. Actually, I am simply interpreting. The piece is an abstract work of design, to which meanings have to be attached such that the design holds good.) (Cardew [11], p. vi)

Two mentions of Bun No. 2 appear in the Handbook, dating from September and November of 1964. The first is a quote from the Austrian philosopher Robert Musil's modernist novel The Man without Qualities (1930), taken from the first book, entitled A Sort of Introduction. There is a semantic and conceptual link here: Bun No. 2 is an introduction to the graphical transformations derived from Treatise, which is in itself an introduction to the possibilities of improvisation through graphic scores on a never‐before‐seen scale:

19th Sept 64

Bun for Orchestra: '... for all those who give up halfway, the fainthearted, the soft, those who comfort their souls with flummery about the soul and who feed it – because the intellect allegedly gives it stones instead of bread – on religious, philosophic and fictitious emotions, which are like buns soaked in milk.' (Musil)

The bun is a stone soaked in milk. (Cardew [11], p. vii; emphasis in original)

This image is at once poetic and revealing. Cardew aligns himself with the analytical and scientific mind portrayed in Musil's novel (centred on a mathematician), but he is also making an aesthetic statement on the process in the work: the non‐absorptive qualities of stone are situated in the 'milk'. One interpretation could be that the analytical processes that Cardew applies to his graphical translations are situated within more intuitive compositional methods; Bun takes on both characteristics. This reading could be consolidated by considering the formal structure of Bun No. 2, which exclusively contains musical sections marked as RICHTIG and FALSCH, with the former being linked to the analysis of Treatise (stone) and the latter being excluded from the first (of two) performances (milk), as discussed earlier.

The final consideration from the Handbook will examine Cardew's motivation to apply this process of graphical translation to Bun No. 2. Writing in November 1964, either as a retrospective of writing Bun No. 2 (which premiered in December) or perhaps as a summary of its near‐completion, Cardew states:

3rd Nov 64

Making [an] orchestra transcription of Treatise (for instance) is not undertaken for the sake of public recognition, but simply surrendering to the vulgar desire to hear what I imagine. (Cardew [11], p. vii; emphasis added)

It is interesting that Cardew had a specific interpretation in mind for these pages of Treatise, especially when one views the detailed and varied performance history of Treatise (pre‐publication) in the Handbook (Cardew [11], pp. ix–xiii). Indeed, this stands in stark contrast to Cardew's reluctance to produce realised parts for Autumn '60. Nonetheless, this is coherent with the strong analytical tendencies shown throughout the Handbook, which stress the 'authority' of the score and can perhaps further strengthen the poetic analogy discussed above. The 'vulgar desire' can surely be equated with Musil's milk of religion, philosophy and fictitious emotion. It doubly shows the analytical tendencies squared with the intuitive, or more personal, desire to fix a specific interpretation of an indeterminate graphic score.

Analysing Bun No. 2

A thorough examination of a continuous passage (bars 1–27), corresponding to pages 45 and 46 of Treatise in full, can demonstrate the analytical method. These pages contain a useful synthesis of Cardew's analysis as demonstrated in the Handbook, as well as extensions of these processes, which can help form a more detailed understanding of how Cardew's camouflage functions. To an extent, their relative simplicity (compared with the later pages) is ideal and economical for the exploration of the research questions posed in this article, allowing for extrapolation to other areas of Treatise. Moreover, page 46 contains a very clear orientation point for such a novel undertaking, giving both a point of departure and a point of arrival from which to structure the present analysis.

Owing to the covert nature of translation from Treatise to Bun No. 2 (Cardew gave no details of his process other than outlining which pages he used), it is necessary to approach this analysis in an unorthodox fashion. There are some symbols in the pages of Treatise that are more 'obvious' and easy to find than others. For example, on page 46 there is a use of staff notation outlining two tritones in bass clef (G–D♭–G). This allows one to locate this phrase in passages of the notated score, which then allows for its situation in the graphical space of Treatise, and thus of Bun No. 2. After all, Cardew highlighted that pages of Treatise are to be read left to right, and thus a linear progression of time can be assumed that would befit a determinate orchestral score, despite his insistence that 'space does not correspond to time' in a strictly proportional sense (Carew [11], p. iv).

Initial Orientation in the Graphical Space: RICHTIG (1)

To aid this analysis, I have divided the second half of page 46 of Treatise into four subsections, shown in Ex. 3b through letters and dotted‐line annotations (the full page is reproduced in Ex. 3a). There is no doubt that this graphic in Treatise (marked A in Ex. 3b) is representative of bar 10 of Bun No. 2, where the contrabassoon plays the specified notes in a solo which marks the beginning of RICHTIG (1) (Ex. 4). The rhythms are approximated spatially: a longer first note and shorter second two. The stem of the D♭, which stretches off the stave, aligns rhythmically with the piano cluster in a lower register than the contrabassoon, thus representing the high–low axis of pitch that a traditional stave implies. From this assertion, one can identify two key formal characteristics pertinent to this graphical analysis: (1) RICHTIG sections need not start at the left‐hand side of the Treatise pages, meaning they are not strictly aligned; and (2) RICHTIG sections may span multiple Treatise pages.

Bars 11–14 (B)

Now that there is an orientation point, one may work forwards (or backwards) in identifying musical features that correspond to graphical symbols. Take the section marked B in Ex. 3b. Two elements are featured: a complete circle (with a slightly flattened right side) and an inclined centre line. From the discussion of the Handbook we can begin to look for certain characteristics that represent the 'perfection' of the circle, and by using the pitch material immediately preceding in bar 10 in a standard 'up:high–down:low' presentation (i.e. the conventional stave), we can equate the incline with a rise in pitch. These two elements are represented in the music of bars 11–15. Looking at the upper woodwinds and brass (Ex. 5), one can observe brief sectional homophony with co‐ordinated attacks. This is one of the ways in which Cardew suggested that circles may be represented: 'simultaneous attacks' to reflect the perfection of the shape. Moreover, the durations of the upper woodwinds attack and the brass attacks are identical, offset by a quaver, showing that the circle is not necessarily represented as a tutti orchestral gesture, but that it is being represented independently within both sections through simultaneous attacks (Ex. 5). Perhaps the flattening of the circle could represent this sectional independence through the slight imperfection of the shape.

The latter brass music alludes to another characteristic highlighted in the Handbook: dynamic level and contrast determined by the height and width of the shape, as demonstrated in Fig. 1. In this case, a circle has equal height and width. Judging by the physical size of the image relative to other materials on the page, it is a large space. As such, the music will have substantial levels of dynamics with a high level of dynamic contrast. This can be seen in Ex. 5 through both the combination of f woodwinds and p brass, and then particularly by the subsequent fp swells in the brass.

Here the brass harmony is related to the idea of perfection and imperfection. Throughout this piece major and minor triads dominate harmonic fields, and thus distortion of these triads can act as a modifier that can be related to a graphical symbol. Within this graphical analytical framework, it is helpful to read the brass music in bar 12 as constituting two minor triads. The second attack, in bar 13, changes the spacings of the B♭ minor chord (implying consistency or harmonic stability) but, crucially, alters the E minor triad by a semitone, resulting in the two differing triads.

Following Cardew's logic of reading from left to right, the alteration from G to A♭ could be representative of the imperfection in the lower right part of the circle, especially considering it is the lowest pitch that was altered. As such, the distortion of the E minor triad is reflected in the distortion of the circle. As has already been established, the woodwinds and brass represent the same shape but only within their individual sections, so that certain levels of sectional independence are retained. Whilst the brass express the symbol in a multitude of ways, the woodwinds do not strictly follow suit; to do so would surely result in banality through plain repetition. Rather, this approach, in which the symbol can govern any number of parameters, allows the composer to create effective orchestral textures, allowing balance as well as idiomatic writing (as seen in the fp brass swells).

The rising centre line in section B, which Cardew ([11], p. ix) describes as the 'lifeline', is represented in a more orthodox way. It is first important to note that the idea of the lifeline – the thick central line that runs throughout nearly all of Treatise – is not to represent a single continuous variable, although it has been previously performed as such, representing a 'continuous sound' (ibid.). Rather, Cardew states that it is 'imagined as the life‐line of the reader, [their] centre, around which all manner of activity takes place' (ibid., p. x). Indeed, in her discussion of the philosophy of music in Cardew and Wittgenstein, Magda Polo Pujadas describes the lifeline as the 'horizon of logic' or a 'point of reference' ([27], p. 1431). In essence, it represents some sort of focus that can determine musical material. It can come in and out of focus, judged on its distortion or deviation from its omnipresence. The inclined lifeline in section B is arguably represented in the violins and violas in bar 11, where we find an eight‐part rising glissando, much like the treatment of 'ruled surfaces' in Iannis Xenakis's Metastasis (1954). The harmony in this passage is similarly triadic, with a final attack on a diminished E minor triad (Ex. 5). Indeed, the background nature of the lifeline could be represented through the p dynamic and the use of mutes, contrasting with the f woodwinds and brass, which represents the circle that circumscribes the lifeline. Thus, the interaction of graphical images, as well as the images themselves, can inform textures and orchestral balance.

Bars 15–20 (C)

Section C introduces many more graphical elements, including dots, lines, triangles and a treble clef (Ex. 6). There is a continuation of the material from section B, with the horn notes in bar 15 representing the end of the circle material through not only a reduced sectional texture, but also the prolongation of the B♭/F dyad, becoming isolated in the texture (see Ex. 7). This would identify the horns in bar 15 with the thinner line emanating from the lifeline (labelled C1), which can be verified by observing the preceding attacks in the woodwinds and strings that overlap with the dyad. A harmonic analysis demonstrates that the situation of the dots from the central line determine not register but the degree of distortion in the harmony.

The concern is not necessarily with maintaining the interval of a fourth (or interval class 5 [ic5]), but with the degree of divergence from the original harmony. The initial dyad (shown in Ex. 8) could be thought of as the graphic line. The two dyads in chord ii thus represent the dot above that is nearest this line. The movement away from the line is represented through a distortion in the addition of a transposition of ic1. Similarly, chord iii represents a dot further away from the line than in ii, and this is represented through modification of intervals to ic3, themselves offset by ic2 but still kept as a pair of dyads. Similarity can also be implied through the maintenance of the original pitches (B♭ and F) as the inner voices in chord iii, creating ic5 from chord i. It could also be argued that the expansion of register in bars 15–18 is representative of the diverging lines in C1, further implying the use of general registral mapping through graphics (Ex. 9).

Cardew theorises the distinction between 'events' and 'happenings' in relation to dots and dashes in an early entry in the Handbook.

26th May 63

The dot‐dash relationship of events and happenings. Events: something short, compact, homogenous that we experience as complete (though we may only experience a part of it in fact) and so as one thing. Happenings: something that continues, the end is not legible in the beginning. Two sets of parameters: events parameters and happening parameters. (Cardew [11], p. iii)

It could be extrapolated that the dots that proliferate this section are events, while the group of events, a domain, is the happening. When considering bar 15, this makes sense: the dots are represented as short, compact, homogeneous attacks in a sparse texture (Ex. 10). This completeness is alluded to with the termination of the horn note in line with the woodwind and string chords.

The graphic seen in the middle of section C, here marked C2, is constructed of two parts: an angular line emanating from a dot and a triangle that hangs from the ascending part of the line, as seen in Fig. 2.

The line acts as a musical contour (using an 'up = high/down = low' orientation) for the violins in bars 15–16, whose entry is highlighted through the use of pizzicato, heightening the short 'dot' characteristic, whilst the triangle applies its perfect geometric properties to the orchestral texture, resulting in homophony in the immediately preceding music of bar 17 (Ex. 13).[6] At once, there is both a registral modulator and a textural modulator derived from a single graphic entity. The additional notes in the trumpets, tenor trombone, bass clarinet and cor anglais could be representative of the falling line in the latter part of the C2 graphic, which acts as an imitation of the violin writing in bar 16.

The upper part of the graphic in section C, marked C3 (Ex. 11), shows similar registral mapping, with the treble clef hinting at where the line may be represented in pitch space. This shape is suggested in the flute, oboe and clarinet parts from bars 17–18, where there is a co‐ordinated jump upwards (reflecting the triangle modulator) to extreme registers for each instrument. The figure on the right of C3, a kind of 'constellation' image (Exs 11 and 12), unseats the triangle and results in four 'fall‐offs' at semiquaver intervals, represented by grace notes – one for each line of the graphic, thus reflecting the left‐to‐right reading of Treatise. These constellation figures occur throughout pages 46–51 of Treatise, and this reading could be expanded to subsequent grace note passages. Whilst the bass clarinet plays the same gesture, this can be considered an intuitive response (rather than a specific translation dictated by the score) owing to the insertion of a treble clef within the graphic combined with the fact that the bass clarinet does not form part of the initial attack – that is to say, it was not part of the preceding line in the graphic. Furthermore, its p dynamic does not match up with the f dynamic of the upper woodwinds; rather, it acts as an echo of the gesture that relates to a specific desire in orchestration or timbral balance.

The final part of section C can be identified through the same glissando gesture representing the lifeline's incline, which is played by the double bass in a high register (Ex. 13). The imitative pizzicato glissandi gestures in the second double bass and violin could allude to the 'imperfect' or 'distorted' rectangle shape (Cardew called rectangles 'square derivatives' [1971, p. vi]) in which the lifeline is situated. The subsequent tutti pause clearly marks the absence of the lifeline whilst also marking the end of a musical section. However, there is another function to the absence of the lifeline, shown at the start of section D.

Bars 21–27 (D)

The lifeline is absent through the opening of section D (Ex. 14), which is characterised by the most static harmony in the entire piece, seen in bars 21–26 (Ex. 15). The somewhat jarring shift in harmony, texture and instrumentation collectively marks this as a new musical section, as does the new metronome mark. If one interprets the lifeline as a stream of consciousness or thought, then its absence would imply a shift or departure from that thought process – a parenthetical expression. It may also be read as a prolongation of an idea, as if one is stuck, suggested graphically through the contained space of the square derivatives. This static harmony can be observed in the electric organ, which holds a single chord (B♭ and F triads, linking back to the dyads at the beginning of section C at bar 15) for the entire section. The other material, in the woodwinds, is constructed around the number three, creating small motifs that repeat in polyrhythm at either a p or pp dynamic. Indeed, the number three is depicted on page 45 of Treatise, and Cardew has spoken about how numbers link to repetition and pauses (see Cardew [11], p. x). This highlights the potential for a parenthetical, or non‐linear, interpretation of the section (cutting across Treatise pages) when considering Cline's view of the lifeline in Treatise, which 'encourage[s] the interpreter to read pages in the given sequence as loose narrative structures, or "arguments", in Cardew's terminology' (Cline [14], p. 139). As such, the absence of this line might imply that this is a break in the logic, or sequence, of the piece.

The musical effect is quasi‐minimalistic, strongly contrasting with the preceding music. The contrabassoon, which initiated the beginning of section A (and the whole RICHTIG (1) section), is disruptive, introducing a non‐harmonic pitch: E. Following this addition, groups of three begin to change into fours and the harmony diverges from the static B♭/F chord, after which the section abruptly ends, signified by a return to the previous tempo and the reintroduction of a more diverse harmonic and motivic soundscape. Thus, the lifeline is returned and the music continues as if from bar 20, especially in terms of the use of drum roll and pizzicato strings in bars 19–20 and 27 and their absence in bars 21–26 (see Ex. 16). Having now reached the end of Treatise page 46, the analysis will now move backwards to connect to the initial starting point of bar 10.

Bars 1–9, FALSCH (1)

As mentioned earlier, despite the exclusion of FALSCH sections from the first performance of Bun No. 2, FALSCH (1) is specified as using Treatise material and thus can be included in the current analysis. The structure of FALSCH (1) is provided in Table 2.

2 Table Structure of FALSCH (1) in Bun No. 2

Section	FALSCH (1)
Treatise page no.	45	46
Bar no.	1	2	3	4	5	6	7	8	9

The immediate difference when observing page 45 of Treatise is the appearance of five stave‐like graphics of differing widths and varied position on the page (Ex. 17). As in RICHTIG (1), the use of a stave with a clef gave a specific indication of where the musical action may take place. It could be argued that in FALSCH (1) the presence of stave lines themselves, combined with the relative positioning of those lines, creates a registral plan for the page. This is shown in Ex. 18 through the analysis of sustained pitches (i.e. lasting two beats or longer), which matches up with the positioning of the staves on page 45 of Treatise.

If one were to begin at the left‐hand side of the page, a pitch‐time reading could be applied to make sense of the opening material. The static brass material represents the upper stave lines, whilst the high double bass writing matches the shape of the descending bold line. The addition of a dotted line in the double basses (to indicate voice leading) further matches with the graphic (Ex. 19). The numbers in Treatise are not clear in this passage. One could read the numbers of page 45 as pauses, but this does not make for a consistent reading. It could be argued that, if treated literally in a notated score, this would allow for too obvious a tracing of the process, which might affect the camouflage of the piece. The proliferation of pauses within this piece, however, could be a general gesture of the interruption of the numbers in Treatise, applied to the entirety of Bun No. 2.

One particularly interesting feature of this passage is the association of musical symmetry to symmetrical graphics, of which there are only two on page 45 of Treatise. The right‐hand rectangle, as will be shown later, acts as a dynamic modifier with no position on a stave line. The other is the box with bold lines, marked F1 in Ex. 17. Reading from left to right, this box exists as part of the stave graphic. The use of bold lines, which signifies the lifeline, implies an important gesture, heralded by two dots which match the f percussion attack in bar 3, implying an initiating gesture ('short, compact' as a graphic dot). The stave lines mark out specific, registrally fixed pitches, seen in bar 3 in the tenor trombone, piano and double basses. As the music moves into this 'perfect', emboldened symmetrical square on page 45, all of these instruments play arpeggios of the four pitches, further reflecting the boundary of the pitch that the stave implies. These arpeggios are notable for their construction, which compound the geometric perfection. Taking the double basses, one can observe that the second player has the first's material in retrograde (or vice versa), which implies the creation of a symmetry. This is the first instance of the double basses playing in rhythmic unison and sharing all the notes of the phrase. Whilst not as clear, the musical contours of the tenor trombone and piano are mirror images of one another (Ex. 20).

A particularly difficult passage to interpret is the far‐right‐hand side of page 45 of Treatise (Ex. 21), here represented in bars 5–7 (Ex. 22). The use of graphics which resemble tremolo markings on a stave are represented as flutter‐tongue in the brass. The situation of this graphic next to a rectangle creates a dynamic modifier. Taking Cardew's logic of dynamic contrast in geometric shapes (Fig. 1) we can see that, the narrow width and tall height indicate a soft dynamic level with a high level of contrast: pp to mp, supported by the use of mutes. There is an awkwardness inherent in this interpretation, and Cardew acknowledges the difficulty of realising these kinds of shapes: 'Vertical rectangles will present problems, as they demand low dynamics with high degree of contrast' ([11], p. vi). One could assume that contrast is proportional to the starting dynamic, or perhaps that a high degree of contrast can be achieved over a short space of time, as opposed to a longer crescendo, which would create a more gradual contrast.

The distortion of the lifeline, marked F2 in Ex. 21, performs a function in bar 7 similar to when it was absent in bars 21–26 through the creation of periodicity and static harmony. The distorted shape of the lifeline, now in a tremolo style, is reflected not only in the musical contouring of this passage, with each repeated quaver gesture generally ascending, but also in the staccatissimo articulation (Ex. 22). Indeed, when one considers what a tremolo is – a repetition of attack – this could be seen as a drawn‐out reflection of that gesture, which has disrupted the flow of the music. The number three may behave as a metric modifier, creating triplets which are heard clearly against quavers, thus making this 3:2 polyrhythm clear through repetition. Both pitch and rhythm are controlled by symbols that take a creative interpretation to translation, and ones that are not explicitly stated in the Handbook. This shows the rich possibilities of combining logical systems with intuition.

The final example to examine, which links neatly to bar 10 and the beginning of RICHTIG (1), is the beginning of page 46 of Treatise, reproduced with annotations in Ex. 23 and represented in Bun No. 2 by bars 8–9 in Ex. 24. Here dots and lines are characterised into two gestures. The dots provide the rhythm, approximated spatially with respect to the graphic, which is accented by the percussion and piano; these two instruments play f accented staccato semiquavers. The lines are represented by instruments that can effectively sustain at a low dynamic, here woodwinds. The woodwind entries are aligned with the piano until the graphic regularity is interrupted by a dot that is disconnected from its line (marked d).

At this point, the percussion assumes the role of the piano, whilst the piano joins the woodwinds in playing a held sonority (played f to allow for the decay over the pause). Pitch orientation is also maintained in this passage, with the lower dots representing lower pitches and the upper ones representing higher pitches. The final piano chord in this passage may represent the linear incline before the '1' of the graphic, especially if one understands the tutti rest of bar 10 as a 'pause' (which is a suggested implication of numbers in Treatise, as discussed earlier). The contrabassoon entry in bar 10 signals that RICHTIG (1) has begun, and thus ends FALSCH (1).

This section has demonstrated how Cardew used the symbols and spatial layouts of two Treatise pages to create the more determinate, orthodoxly notated music of the first 27 bars of Bun No. 2. Cardew's analysis, outlined in the Handbook, makes clear how he applied his principles of camouflage to Bun No. 2. The dual aspects of being oriented 'towards the future' but still exhibiting a 'hereditary link to the past' are manifested in the graphical control of musical parameters expressed in staff notation (in a sense creating a fixed interpretation of a graphic score, working across the two systems), as well as the use of some structural indeterminacy (and obfuscation, when considering the inclusion of a FALSCH section with Treatise material) within a harmonic framework privileging the major and minor triads. Indeed, the admitted awkwardness of some of my interpretations speaks to the deeply enigmatic approach that Cardew's own analysis took (the Handbook is relatively brief and sometimes contradictory) and could further be seen as another layer of camouflage: problematising that relationship between the metaphorical 'stone' and 'milk' within the philosophy of Bun No. 2.

The Implications of Bun No. 2

Tilbury describes the works of the mid‐1960s as Cardew's 'swansong to the avant‐garde', which centred on the need for patronage, recognition and favours (2008, p. 277). This need is particularly salient considering that Cardew received no commission fee for Bun No. 2 (ibid., p. 182). It is in this image where the idea of camouflage can be understood socially, alongside the ways in which it is achieved musically through graphical translation. Being experimental whilst also appeasing the establishment proves a difficult balance to strike. Indeed, it might be that Bun No. 2 represents, to Cardew, a failure in this regard. Tilbury writes that Cardew refused to bow after a performance on 12 December 1964, owing to 'considerable embarrassment' (ibid., p. 258). Arguably, this was a turning point in Cardew's musical philosophy: graphic notation and traditional staff notation could not be reconciled, showing the limitations (or at least the inflexibility) of orthodox contemporary music notation. It is not surprising that there is no further example of such an experiment in graphical translation as Bun No. 2. Bun No. 1, completed in 1965 as part of an orchestration course taught by Goffredo Petrassi in Rome, did not have any of these graphical tendencies.

The irony of Bun No. 2 is that it was Cardew himself who was the 'hostile force' from which the camouflage, as mentioned in Four Works, was meant to provide protection (Cardew [10], p. 4). The translation of Treatise into a determinate, singular interpretation clearly proved musically and cognitively unsatisfactory to Cardew. Tilbury makes an interesting comment regarding the affective quality of Treatise: '[F]or 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' (Tilbury [31], p. 86).

One could perhaps posit that this ironic, perceived failure is a manifestation of this 'psychological drama', but from the composer's perspective. The fixed, mostly determinate aspects of Bun No. 2, paradoxically, do not allow any performative relation to the drawn symbols in Treatise through their deconstruction and analysis – a symptom of Cardew's 'vulgar desire' (Cardew [11], p. vii). Indeed, the lack of reconciliation between graphic score and determinate score could add credence to Cline's summation of the changing viewpoint of experimentalists in the 1960s, where they began 'questioning the authority of graphic scores as specifications of actions or sounds, and using them instead as they saw fit', further suggesting that 'this attitude is reflected in Cardew's evolving stance towards his Treatise, with later entries in the Treatise Handbook portraying the intended use of his score in increasingly flexible terms' (Cline [13], p. 326). Beginning in the late 1960s Cardew's philosophy became more absolute and radical, relating to political issues (his conversion to Maoism), shifting to a more social view of music (centred on improvisation and participation) and denying the authorial supremacy of the 'artwork'. Arguably, these movements would mean that Cardew's music was less in need of camouflage owing to its clear function, utility and intended audience – see, for example, Song of the Communist Youth Union of Britain (1979).[7]

In an aesthetic sense, I would like to build upon Cline's linkage of Cardew's Treatise and Wittgenstein's picture theory (a concept developed in his Tractatus Logico‐Philosophicus [1921]). Arguably, Bun No. 2 aims to achieve a 'sharpened' relationship between 'picture' and 'pictured' using an isomorphic relationship between graphic and music. Cline summarises Erik Stenius's viewpoint of the isomorph:

[P]icture and situation correspond when they are isomorphic, and this transpires when there is a general rule that establishes a one‐to‐one correspondence between possible configurations of elements in the picture and possible configurations of the objects associated with them by pictorial relationship. A rule of this type can exist only if two conditions are met: there must be a one‐to‐one correspondence between objects in the world and the elements in the picture; and there must be a one‐to‐one correspondence between possible arrangements of the objects in question and possible arrangements of picture elements. (Cline [14], p. 127)

The theorising in the Handbook demonstrates a clear affinity to this viewpoint, with Bun No. 2 being a trial of these concepts. There is a great similarity between the notion of picture theory as applied here and the rhetorical device of ekphrasis (description), but they differ subtly in their intended goals. Siglind Bruhn defines musical ekphrasis as 'the representation in one medium of a text created in another medium' (Bruhn [5], p. 8) and explains how the construction of musical meaning (i.e. the interaction of musical and non‐musical sign systems) can be achieved through the use of two categories: depiction and reference:

I wish to argue that what and how music communicates about any extra‐musical stimulus does indeed fall into the two categories that can be seen as analogous with those pertinent in the context of painting and poetry: depiction and reference. I use depiction by musical means as encompassing not only instances of mimicry [...] but also sensual impressions of hues, shapes and spatiality. Correspondingly, reference by musical means [...] will be understood as relying on cultural and historical conventions. (Bruhn [5], p. 10; emphasis in original)

Depiction relates to the immediately spatial and visual aspects of the graphics, and reference can be understood as relying upon those notions of 'perfection' and 'imperfection' in the geometry of Treatise (which seemed to lead to the use of the triad as harmonic device). If we read Bun No. 2 as similar to the Kagel‐led performances of Autumn '60 (in its nature as a 'realised' indeterminate score), then the aesthetic issue of picture theory is in the instability of realising the indeterminacy. We see this in the preface to Autumn '60, where Cardew shows that in the first beat of his example, 'Cello 2 has decided to not only ignore ↓ but to contradict it' (see Ex. 25). This suggests that Cardew factors in the agency of the performer(s) in the realisation of the indeterminate score, and one wonders whether the trickier, somewhat contradictory or non‐linear passages of Bun No. 2 shown above (like the end of FALSCH (1)) are emblematic of this act of symbolic transgression. This resonates with Clarke's view of the analysis of indeterminate scores, where he states that '[t]he analyst here must think like a performer, in terms that are somatic and dynamic' (Clarke [12], p. 188). Such a reading would therefore make any attempts at a graphical‐musical isomorphism inherently difficult, but would not impede the work from being an act of ekphrasis, such that the majority of readings (as demonstrated in my analysis) 'hold good' and manifest themselves not only in the depictive (formal) and referential aspects, but also in the curious case of camouflage (another confounding level which informs Cardew's analysis of Treatise).[8] Ekphrasis allows for a suggestive analytical reading of Bun No. 2 that takes into account a wider range of contextual information but stops short of representing the 'truth' of the image by not only invoking instability and/or non‐linearity in performance (which is, paradoxically, inherent to texts produced in an indeterminate language) but also by deliberately obscuring it for the social notion of camouflage. This reading adds further weight to the reasons Cardew deemed the work a manifestation of 'vulgar desire', which may allude to the perceived imperfections of such attempts at notational reconciliation.

Indeed, the notion of the isomorphism between graphics and music is described by Iddon and Thomas as being in its nascency in the late 1950s and early 1960s. They explain Stockhausen's 'Musik und Graphik' lectures at Darmstadt in 1959 as being a possible outlet for this (and indeed, these must have been impactful for Cardew, whose own February Piece I [1959] was featured in the lectures) and surmise that the isomorphic relationship between sound and sign was a 'relatively recent historical phenomenon' (Iddon and Thomas [20], p. 414). Hence, one might suggest that the infancy of the concept in contemporary music may contribute to this troubled reconciliation in Bun No. 2. The concept of the isomorph would subsequently find a more comfortable bedfellow in music and technology: one thinks of Xenakis's UPIC system from 1977, a tablet computer designed to represent any graphic depiction to sound (see Xenakis [34]), and the significant scholarly inquiries behind the notion of 'sonification' in sound and music studies (see Worrall [33], pp. 312–13 and Scaletti [28], pp. 371–2).

***

Bun No. 2 is a truly unique experiment within Cardew's output, charged with both analytical and aesthetic energy. Arguably, the implications of camouflage are particularly manifested in Bun No. 2, contributing to the momentum in establishing Cardew's new musical direction, which centred more on improvisation and the social aspects of music. Cardew included the following addendum to the introduction of the Handbook in 1970, written two years after the original introductory text: 'Not that I consider Treatise "improvisatory" any more than I did while writing it. But it does seem (using hindsight) to have pointed in the direction of improvisation' ([11], p. i). The unsatisfactory nature of Bun No. 2, the failure of its camouflage, must have been significant in reaching this retrospective view. The notion of fixing an interpretation in earlier works such as Autumn '60 was at least acknowledged in terms of its pragmatism. However, there is a crucial difference in the two works: the nature of their notation. The extra layer of reading necessary to make a logical system for Treatise (as stated in the Handbook), which derived large portions of its harmony from the recently liberated concept of the triad, perhaps meant that things became almost too fixed and inflexible. In this sense, Cardew's statement in the preface that the work is an 'analysis' of pages 45–51 of Treatise should inform its reception, remembering Kofi Agawu's influential notion of analysis as performance ([1], p. 273). Perhaps this is a rare example of analysis as performance as composition (linking back to Feldman's comments on the performative aspect of composition).

Therefore, the analysis carried out in this article is a hearing or performance which uses Cardew's Handbook as a stimulus – similar to how one might approach the performance of Treatise itself. The evidence gathered and method used, I believe, makes this a valid interpretation, but by no means does it claim to be an authoritative reading of the Treatise pages. Rather, it hopes to show how one could approach the analysis of graphic scores more generally, incorporating logics of geometry and spatial design which find parallels in musical material, as well as unpicking the multifarious aspects of these scores in their specific contexts. In the same way that Ingliss describes the analysis of graphic scores as 'a niche, within a niche, within a niche' ([21], p. 11), one might argue that this article shows a 'proof of a proof of a concept'.

The concept of camouflage is a useful one for truly understanding this experiment. The 'hereditary' aspect of the system explains the use of musical categorisation (triads, (im)perfection, repetition, structure, etc.) which, in their simplistic conception, held the best chance of enacting pictorial equivalencies and thus representing the graphics of Treatise. Tilbury comments on Bun No. 2 that 'the music is straining at the notational leash, urged on by its fascination with Treatise, to which it is in thrall; Cardew had reached a stage where traditional notation was too restrictive to the impulse of his thought' ([30], p. 257). Perhaps this explains the somewhat doomed use of camouflage in this piece: the notation barely conceals its graphical source, bolstered by unusual and idiosyncratic approaches to harmony and orchestration. This is telling when one considers Cardew's earlier comments on notation and interpretation: 'As a composer you have both aspects in your hand, but when you come to open your hand you find only one thing and it is not divisible' ([6], p. 21).

The relegation to graphical notation would 'expose' the piece, meaning no camouflage is needed, but it would not be acceptable to the establishment that commissioned it (remember Kagel's insistence upon parts for Autumn '60). One can also see a commercial aspect at play when considering that Cardew's publisher objected to the use of piccolo trumpet since it limited the possibility of future performances (Tilbury [30], p. 182). Camouflage, as a concept, is a symptom of Cardew's 'widely divergent lines of investigation' (Cardew [1962] [7], p. 46) situated in his personal experiences and oscillation between the modernist and experimental schools of thinking, manifested particularly in terms of musical notation and (in)determinacy; Bun No. 2 is a prime example of this.

NOTE ON THE CONTRIBUTOR

Thomas Metcalf is a researcher working in the field of comparative arts and contemporary music. He completed his DPhil at Oxford University in 2021 and has since held a Junior Teaching Fellowship at the Ashmolean Museum, alongside teaching at various colleges in Oxford. For 2022–3, Thomas is the Junior Anniversary Fellow at the Institute for Advanced Studies in the Humanities at the University of Edinburgh, pursuing his interdisciplinary project Photography and/as Music. His research also has been published in Tempo, Leonardo and Principles of Music Composing. Outside of musicology, Thomas is an active composer, with recent commissions from the National Youth Choirs of Great Britain, Red Note Ensemble and the Lonelinoise Collective. His works have been performed across the UK and internationally, with 2023 seeing releases on NMC Recordings and Métier. More information can be found at www.thomasmkmetcalf.com.

1 I am grateful to the Development Fund administered by the Society for Music Analysis, which afforded the reproduction of copyrighted materials. 2 See in particular Chs 5, 'Interpreting the Concert for Piano and Orchestra', and 6, 'Interpreting the Solo for Piano'. 3 This is an eclectic collection of differently scored pieces consisting of Autumn '60, Materials, Solo with Accompaniment and Memories of You. 4 When discussing Projection II (1951), Feldman commented, 'My desire here was not to "compose", but to project sounds into time, free from a compositional rhetoric that had no place here. In order not to involve the performer (i.e., myself) in memory (relationships), and because the sounds no longer had an inherent symbolic shape, I allowed for indeterminacies in regard to pitch' (Feldman [1962] [18], pp. 5–6). 5 It is notable that Babbitt's reference to aspects of indeterminacy in popular song is reflected through Cardew's subsequent forays into that medium, when considering his politically charged popular songs such as 'Not Afraid' and 'Spirit of Cable Street'. See the compilation album Consciously (2006) for a selection of these works. 6 See Cardew ([11], p. vi) for a thorough description of how triangle shapes might be translated. In this case, however, owing to the harmony and situation of the graphic, it seems that the triangle functions as an element of 'perfection' rather than a modulator of triadic harmony, which isn't pronounced in this passage. See also Cline ([14], pp. 132–4). 7 For a more in‐depth discussion of the style of Cardew's later music (and repudiation of his earlier works), see Harris ([19], pp. 116–19). 8 The idea of isomorphic relationships within an ekphrastic framework is the central idea behind my notion of graphical ekphrasis, which aims to privilege spatial references in so‐called transmedial processes. See Metcalf ([22], pp. 45–71). Agawu, Kofi, 2004 : ' How We Got Out of Analysis, and How to Get Back In Again ', Music Analysis, 23 / ii–iii, pp. 267 – 86. Anderson, Virginia, 2006 : '" Well, It's a Vertebrate ...": Performer Choice in Cardew's Treatise ', Journal of Musicological Research, 25 / iii–iv, pp. 291 – 317. Babbitt, Milton, [1958] 1966 : ' Who Cares If You Listen? ', in Gilbert Chase (ed.), The American Composer Speaks: a Historical Anthology 1770–1965 (Baton Rouge : Louisiana University Press), pp. 235 – 44. Bernstein, Zachary, 2021 : ' Milton Babbitt ', Oxford Bibliographies, January 12, https://www.oxfordbibliographies.com/view/document/obo‐9780199757824/obo‐9780199757824‐0283.xml, accessed 15 September 2022. Bruhn, Siglind, 2000 : Musical Ekphrasis (Hillside : Pendragon Press). Cardew, Cornelius, 1961 : ' Notation – Interpretation, Etc.', Tempo, 58 (Summer), pp. 21 – 33. Cardew, Cornelius, [1962] 2006a : ' The American School of John Cage' [Cardew's notes for a radio programme broadcast by WDR on 27 December 1962] in Edwin Prévost (ed.), Cornelius Cardew: a Reader (Harlow : Copula), pp. 39 – 48. Cardew, Cornelius, [1962] 2006b : ' Autumn '60 – a Lecture Given to the Heretics Society ', in Edwin Prévost (ed.), Cornelius Cardew: a Reader (Harlow : Copula), pp. 49 – 54. 9 Cardew, Cornelius, 1963 : ' Contemporary Music ', in Gerhart von Westerman, trans. Cornelius Cardew, Concert Guide: a Handbook for Music Lovers (London : Sphere Books), pp. 422 – 44. Cardew, Cornelius, 1966 : Four Works (London : Universal Edition). Cardew, Cornelius, 1971 : Treatise Handbook (London : Edition Peters). Clarke, David, 2016 : ' Musical Indeterminacy and Its Implications for Music Analysis ', International Journal of the Dutch‐Flemish Society for Music Theory, 3 / xi, pp. 170 – 96. Cline, David, 2016 : The Graph Music of Morton Feldman (Cambridge : Cambridge University Press). Cline, David, 2020 : ' Treatise and the Tractatus ', Journal of the Royal Musical Association, 145 / i, pp. 119 – 66. Cline, David, 2022 : ' Architecture and Freedom in Cornelius Cardew's "Octet '61 "', Music Analysis, 41 / ii, pp. 293 – 331. Drott, Eric, 2003 : ' The Role of Triadic Harmony in Ligeti's Recent Music ', Music Analysis, 22 / iii, pp. 283 – 314. Feldman, Morton, 1962 : Structures for Orchestra (New York : Peters). Feldman, Morton, [1962] 2000 : ' Liner Notes ', in Bernard Friedman (ed.), Give My Regards to Eighth Street: Collected Writings of Morton Feldman (Cambridge : Exact Change), pp. 3 – 7. Harris, Tony, 2016 : The Legacy of Cornelius Cardew (London : Routledge). Iddon, Martin and Thomas, Philip, 2020 : John Cage's Concert for Piano and Orchestra (Oxford and New York : Oxford University Press). Ingliss, Brian, 2015 : Towards an Analytical Framework for Graphic Scores, and a Proposed Typology (London : Middlesex University Research Repository). McKay, Tristan, 2021 : A Semiotic Approach to Open Notations (Cambridge : Cambridge University Press). Metcalf, Thomas, 2021: 'Labyrinths, Liminality, and Ekphrasis: the Graphical Impetus in the Music of Kenneth Hesketh ', Tempo, 75/ccxcv, pp. 45 – 71. Nattiez, Jean‐Jacques, 1990 : Music and Discourse: Toward a Semiology of Music, trans. Carolyn Abbate (Princeton : Princeton University Press). Nyman, Michael, 1999 : Experimental Music: Cage and Beyond, 2nd edn (Cambridge : Cambridge University Press). Phillips, Andrea, 2010 : ' The Revolution Will (Not) Be Improvised ', in Kate McFarlane, Rob Stone and Grant Watson (eds), Play for Today (London : The Drawing Room and Antwerp: M HKA), pp. 38 – 45. Pujadas, Magda Polo, 2018 : ' Philosophy of Music: Wittgenstein and Cardew ', Revista portuguesa de filosofia, 74 / iv, pp. 1425 – 36. Scaletti, Carla, 2019 : ' Sonification ≠ Music ', in Roger T. Dean and Alex McLean (eds), The Oxford Handbook to Algorithmic Music (Oxford and New York : Oxford University Press), pp. 363 – 86. Tilbury, John, 1981 : ' The Experimental Years: a View from the Left ', Contact: A Journal of Contemporary Music, 22 (Summer), pp. 16 – 21. Tilbury, John, 2008 : Cornelius Cardew (1936–1981): a Life Unfinished (Essex : Copula). Tilbury, John, 2010 : ' The Time Is Now, The Place Is Everywhere ', in Kate McFarlane, Rob Stone and Grant Watson (eds), Play for Today (London : The Drawing Room and Antwerp: M HKA), pp. 86 – 91. Wittgenstein, Ludwig, [1921] 2021 : Tractatus Logico‐Philosophicus (London : Anthem Press). Worrall, David, 2011 : ' An Introduction to Data Sonification ', in Roger T. Dean (ed.), The Oxford Handbook of Computer Music (Oxford and New York : Oxford University Press), pp. 312 – 33. Xenakis, Iannis, 1978 : ' Mycenae Alpha ', Perspectives of New Music, 25 / i, pp. 12 – 15.

By THOMAS METCALF

Reported by Author

Thomas Metcalf is a researcher working in the field of comparative arts and contemporary music. He completed his DPhil at Oxford University in 2021 and has since held a Junior Teaching Fellowship at the Ashmolean Museum, alongside teaching at various colleges in Oxford. For 2022–3, Thomas is the Junior Anniversary Fellow at the Institute for Advanced Studies in the Humanities at the University of Edinburgh, pursuing his interdisciplinary project 'Photography and/as Music'. His research also has been published in Tempo, Leonardo and Principles of Music Composing. Outside of musicology, Thomas is an active composer, with recent commissions from the National Youth Choirs of Great Britain, Red Note Ensemble and the Lonelinoise Collective. His works have been performed across the UK and internationally, with 2023 seeing releases on NMC Recordings and Métier. More information can be found at www.thomasmkmetcalf.com.