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Marx's 'Lehre' and the science of education: towards the recuperation of music pedagogy.

'I am trying to psychologise the instruction of mankind.'

Johann Pestalozzi(1)

This study explores A. B. Marx's composition treatise, Die Lehre von der musikalischen Komposition, in the light of various pedagogical theories of the early nineteenth century.(2) The Lehre's educational background tends to be overlooked today, since Marx's reputation rests on his taxonomy of musical form, in particular his codification of sonata form.(3) The fate of the Lehre is emblematic of the reification of much music theory of the past. Although the work of figures such as Johann Mattheson, Joseph Riepel and Heinrich Koch was often presented in the shape of a teaching method, this pedagogical aspect, evinced in the choice and sequencing of course material, is generally interpreted as mere scaffolding from which the music-theoretical content can be safely scooped out. By contrast, the critical disputes of Marx's day indicate that this theoretical content was thought to inhere partly in its very layout. Gottfried Fink, the conservative editor of the Allgemeine musikalische Zeitung (henceforth AmZ) and Marx's chief opponent, attacked the Lehre for being a confused mixture (Zusammenmischung) of elements which in themselves were hardly new and which would have been better taught separately.(4) On the margins of this debate, the preface to Matthaus Zeheter and Max Winkler's long-forgotten Harmonielehre of 1847 disarmingly disclaims any originality for its material.(5) The novelty of the book lies instead in its organization:

This volume brings nothing new, no views or principles which have not been heard and appreciated before. Rather with regard to their material, the authors have closely followed the course of older and better teaching manuals . . . With regard to format, however, the authors believe that they can organize the material in a better order than found in other course books.(6)

Zeheter and Winkler conclude their preface by wishing the student a rewarding 'journey'.(7) By invoking the standard trope of learning as a voyage of discovery (of which Goethe's Bildungsroman, Wilhelm Meister, is the nineteenth-century paradigm), the authors also reactivate the original Greek meaning of theoria as 'travel'.(8) In its representation of musical knowledge as a process unfolding through time rather than as a structure - as 'performative' rather than 'declarative' - music pedagogy is thus both very ancient and rather modish. In England, a move towards a more practical definition of knowledge lies behind a series of reforms embodied in the new National Curriculum for primary and secondary music education.(9) According to Keith Swanwick, one of the curriculum's chief architects, its reforms are shaped by the realization that 'knowing music is much more than processing factual information'.(10) Music, though a non-verbal medium, is a valid mode of cognition in itself. 'Musical knowledge' - the title of one of Swanwick's many books(11) - is a matter of 'knowing how', not just 'knowing that '; it is an activity which is implicated in the manipulation of a musical instrument, in the handling of compositional materials, and even in the auditive appraisal of musical sounds. This practical conception of musical knowledge is strikingly anticipated by Marx:

Neither abstract knowledge, nor mere technical training, constitute, or even can prepare, the education of an artist; both are the very opposite of art.(12)

The School of [Musical] Composition is a school of art, and therefore intended not merely to impart knowledge, but to lead to productive activity. The student, therefore, must by no means be contented with knowing and understanding the different doctrines of the School, but he must be able to produce works of art with ease and certainty.(13)

Marx's ideas are not only concordant with the modern orthodoxy; in some ways, they could even be said to be more advanced. The Lehre was taught to undergraduates at Berlin University. By contrast, the National Curriculum's ethos has yet to percolate into tertiary education, although books such as Nicholas Cook's recent Analysis through Composition point the way forward.(14) As we will see below, although Marx's treatise was aimed at adults, it applied reforms originally achieved in the field of child-centred learning. This, in short, is possibly the most important fact about Die Lehre von der musikalischen Komposition, and it will be the focus for this study. By adapting child-orientated methods to the teaching of young adults, Marx crosses two distinct domains. The domain of child education (literally 'pedagogy') receives the lion's share of theoretical attention because it coincides with the time when human beings undergo their most profound physical and cognitive development - which is why so many of the concerns of education theorists are shared by psychologists. Conversely, to the extent that adult education normally takes place after these developments have slowed down (the 'hardening of the arteries', in Swanwick's felicitous phrase),(15) it is more amenable to study from sociological and cultural perspectives. The contents of study at university are generally more abstract and 'informational', and it is accordingly harder to reconcile them with a dynamic or creative model of musical knowledge. Yet Marx's Lehre achieved precisely that, and in so doing revealed crosscurrents between fields that have since become institutionalized as separate disciplines, such as psychology and aesthetics. Renewed examination of Marx's pedagogy will teach us that music theory is far more entangled in processes of learning and narratives of teaching than is commonly supposed. The present study attempts to recuperate Marx's ideas into the modern discourse about disciplinary rapprochement. I will begin by reconstructing Marx's model of education theory according to modern parameters. I identify two opposite tendencies in his thought, which I call the 'child-orientated' and the 'adult-orientated'. The main body of my study explores each of these strands in turn.

THE MODEL

In this section, I outline a model of education theory which can be mapped on to Marx's practice. Such an exercise begs two key questions concerning, respectively, the nature of 'theory' and its relationship to the past. In the first regard, the claims of education to being theoretical or even scientific in a truly coherent and predictive sense are often disputed. Moreover, although the field exerts a growing influence at all levels of schooling in modern society, there is a strong case for rejecting its relevance to teaching on a practical level: that is, its prescriptive efficacy.(16) In the second regard, Marx's writings draw from an educational culture which, though coherent in itself, is very different from our own. Even if a commonality could be established between Marx's thought and modern theory, it is not clear whether it would be attributable to real historical influence or, as seems more likely, to the independent rediscovery of a set of common-sense truisms. Although it is premature to extract a cross-historical model of education theory on a prescriptive level, it is nonetheless possible to stake out shared concerns on the more modest level of description. My own description utilizes a typology of 'educational codes' borrowed from a classic essay by the sociologist Basil Bernstein.(17)

According to Bernstein, formal educational knowledge is realized through the 'message systems' of curriculum and pedagogy: 'Curriculum defines what counts as valid knowledge, pedagogy defines what counts as a valid transmission of knowledge'.(18) Curriculum and pedagogy can be described in terms of their contents - the knowledge that is deemed worthy of learning, and the specific context of teaching. Nevertheless, Bernstein is more interested in the relationship between these contents: the degree of separation between the subjects of the curriculum; and the degree of control exercised by the teacher over the selection, organization and pacing of the knowledge transmitted. He calls the former 'classification'; the latter is termed 'framing'. Strong separation between subjects yields a 'collection-code curriculum' (a feature of the specialization practised in English secondary schools). When boundaries are weak, an 'integrated-code curriculum' results (typical of infant-school teaching).(19) Similarly, strong framing tends towards 'instruction', whereas weak framing teaches through 'encounter', a process which foregrounds the personal dimension and the student's freedom of choice.(20)

Bernstein's ideas have been influential in the writings of music educationists such as Charles Plummeridge and Keith Swanwick.(21) On the whole, high value has been set on weak classification (integrationist curricula) and weak framing (encounter-based teaching). In the first instance, theorists argue that skills such as performing, composing and listening, rather than representing separate disciplines, are all facets of a single, though broadly defined, 'musical intelligence'. In the second instance, 'encounter' recognizes that not all aspects of music are amenable to instruction or evaluation. For example, a musical composition should display a degree of individuality, and if all its elements can be predicted, then the teacher has failed in his or her task. Whereas the mechanical aspects of skill acquisition (learning scales, compositional formulas, etc.) are better served by instruction, the aesthetic dimensions of music teaching are more suited to 'encounter'.(22) Marx's curriculum and pedagogy mix education codes in interesting ways.

The Lehre's curriculum is in some respects extremely closed, since it is governed by a powerful ideology. The treatise springs from the intellectual milieu of Wilhelm von Humboldt, Hegel, and Friedrich Schleiermacher (the latter two lectured with Marx at Berlin University). On a political level, Marx operates within the context of Prussian nationalism, which viewed education, accessible to all and regulated from above, as an adjunct to state-building. On a musical level, Marx seeks to inculcate the values of formal coherence associated with the masterworks of the Austro-German tradition, chiefly those of Beethoven? These values are beholden to the ideology of organicism, partaking of its teleological determinism (expressed either as the growth of an organism or the progress of Geist), as well as its aesthetic idealism (the art work is unified by an overriding Idee which sublates conventional rules).

In other respects, however, such as in its definition of musical knowledge as compositional activity rather than dry facts, Marx's curriculum is open. Although nominally a composition treatise, the Lehre employs the teaching of form as a means of fostering musical understanding. This combination of strong and weak classification is also found in Marx's pedagogical method. From one perspective, the Lehre is framed exceptionally strongly according to a sharply defined developmental progression. Yet the book combines its progression with a large element of encounter in that it attends to the wholeness of musical experience at each stage. Whereas previous pedagogical course books typically proceed from the simple to the complex, Marx's method unfolds not through the acquisition of an increasing harmonic vocabulary but by the internalization of whole musical utterances.(24) Marx's Formenlehre progresses from simple forms, the Satz and Gang, to ever more complex structures: period forms, the members of the Liedform family, such as the minuet and trio, the family of rondo forms and, finally, sonata form. Marx rejected the artificial separation of musical parameters (harmony, melody, rhythm and structure) because it reflected neither how composers worked nor how listeners engaged with music. Consequently, each staging post of the Lehre is marked by a fully comprehensible musical form. In short, the thrust of the Lehre is integrationist, although such integration is achieved via pedagogy which is framed along a prescribed pathway. By fusing together the teaching of Harmonielehre, Formenlehre and Kontrapunkt, Marx anticipates our modern conception of musical knowledge as essentially dynamic and integrated. Yet he overtakes us in one crucial area: Bernstein had noted in 1971 the difficulty of institutionalizing 'forms of the integrated code . . . above the level of the infant school child'.(25) How does Marx achieve the same end in the context of higher education?

The Lehre's greatest significance lies in reconciling two essentially distinct traditions of music pedagogy. These two traditions pull in opposite directions, and I call them, respectively, the 'child-orientated' and the 'adult-orientated'. The most radical developments in late eighteenth- and early nineteenth-century education theory were achieved through the observation of children, and gave rise to what became known as the 'kindgemasser', or child-orientated, model.(26) The figure of the child was the emblem of Nature in that it exemplified a 'natural' course of behaviour and development free from cultural interference. Furthermore, the 'kindgemasser' model was then projected as a template on to older age-groups, and employed to regulate education according to these 'natural' principles. Pedagogues such as Johann Heinrich Pestalozzi (1746-1827), Hans Georg Nageli (1773-1856), Johann Bernhard Logier (1777-1846) and Friedrich Adolf Diesterweg (1790-1866), all of whom are discussed below, were concerned primarily with practical training, since Art was deemed to be ultimately unteachable. Marx was the first theorist to take up the challenge and demonstrate that child-orientated techniques could indeed be directed towards aesthetic ends. His Formenlehre is adult-orientated because it has its eye on compositional mastery. In particular, as Scott Burnham has shown, Marx's system is directed towards the example of Beethoven, the 'Master' par excellence. I will argue that Marx's pedagogical thought interweaves the child- and adult-orientated tendencies in a similar, but not identical, way to that in which modern theorists talk of 'naturalization' alternating with 'enculturation'.(27) Marx's system can be schematized as a quadratic model [ILLUSTRATION FOR FIGURE 1 OMITTED], and I will consider each of its four aspects in a separate 'mini-chapter'.

Fig. 1 indicates that the curriculum and pedagogy of the Lehre are both subject to principles of naturalization (child-orientated) and enculturation (adult-orientated). In Part I of this study (naturalization), I will show, first, how Marx seeks to ground formal categories such as Gang and Satz in students' inborn faculties of perception; and second, how the sequencing of Marx's pedagogical method shadows students' natural cognitive development. In Part II (enculturation), I explore, thirdly, how the Lehre inculcates knowledge as internalized mental models; and fourthly, how Marx's teaching utilizes standard 'plots' of the time.

Before embarking on this pedagogical journey, it is worth considering how much credence to give Marx's attempts to ground his theories in psychological processes. Marx likes to cite the founding fathers of a discipline which became known as psychology in the twentieth century - figures such as Johann Friedrich Herbart (1776-1841) and Friedrich Eduard Beneke (1778-1854). These philosophers developed the 'psychologizing' tendencies of Kant's theory, focusing on the mind's dependence on 'hard-wired' faculties of perception. Whereas the Lehre is usually presented as an outgrowth of German Idealism - the tradition of Fichte, Schelling and Hegel - Marx's openness to the ideas of the early psychologists suggests that he falls within a more empirical school? The problem is that any empirical perspective on Marx's theories is bound to lead to invidious comparisons with the infinitely more scientific methodologies of modern psychology. A modern educational theorist will ground models of cognitive development, acquisition of skills and information processing on experimental data? Since this protocol was not available to Marx, it is difficult to avoid portraying his system as comparatively primitive. This is not a line that I wish to take. In the wake of Thomas Kuhn's epoch-making writings of the 1960s, historians of science have adopted a far more sympathetic view of scientific systems of the past.(30) I will argue that Marx's paradigm works well in its own terms. An effective singing manual or composition treatise is empirical to the extent that it is based on the teacher's personal experience in the classroom. Observations on what students can actually do, and how their skills develop, are tested upon generations of children; they are enshrined in the organization of each teacher's method as well as the kind of material used. That Marx thought deeply about what we would nowadays call the 'psychological reality' of his method is attested by its publication history. It is clear from the prefaces to the Lehre's later editions that Marx's revisions were motivated largely by his continuing experience as a teacher. Since it is uncharacteristic of this ebullient writer ever to admit to making mistakes, Marx presents these revisions not as corrections but as improved realizations of an ideal. Thus, on the one hand, the 1841 preface (2nd edn.) states that 'continuous examination, varied experience and the agreement of a lot of evidence' has served only to vindicate the author's educational theories. 'Nevertheless', says Marx, 'I did not permit myself to rest; I was compelled to strive towards my educational ideal with ever greater energy.'(31) The revisions embrace order of presentation as well as content. For example, Marx points out that a section on harmonic figuration has been shifted so as to come after a section on chorales, whereas it had originally fallen earlier. Similarly, Marx streamlines the course by relegating the more arcane material to an appendix. The 1852 preface (4th edn.) is most explicit, as befits an edition with such extensive revisions:

I derived great assistance from my connection with the Berlin Academy of Music (established a year ago by Messrs Kullak, Stein and myself), as it afforded me an opportunity of testing my system and method of teaching on a number of young persons . . . in a course of lessons in which I was artistically and technically more free than in my academic lectures. If my system and method have come out of this trial unchanged in any essential point, it must be ascribed . . . only to the fact that the new experiment has confirmed my former convictions.(32)

In the preface to his final edition of 1863, Marx explains that he has 'recast half the book, so as to leave no new observation and experience unused'.(33) A comparative study of the evolution of the Lehre is of course well beyond the scope of this study. Nevertheless, I shall occasionally dip into the respective editions to demonstrate that they were responsive to the realities of teaching.

NATURALIZATION: MAPPING FROM THE CHILD TO THE MAN

Marx's Lehre invokes Nature from its first page: the object of a compositional course is to 'elevate the natural capabilities of the student'.(34) Marx understands the 'natural' in three senses. First, a 'natural' system of instruction must reflect the nature of musical experience; this is its phenomenological sense. Second, it must accord with the nature of a pupil's mental faculties and normal rate of development; this is its cognitive sense. A compositional course must be natural in a third, pedagogical, way: it should be predicated on psychological principles of learning. All three aspects of the natural - cognitive, phenomenological, pedagogical - were grounded in early nineteenth century representations of children. Then as now, the figure of the pre-school child was used in arguments over the innateness, priority or universality of various skills and faculties. For Marx, musical talent is natural because we can all sing: 'As the psychologist already takes for granted, most people are endowed with their own, joyous, faculty for singing; and this gift has already blossomed in most well-constituted children'.(35) Accordingly, Marx argues from this premiss that melody is 'the first and fundamental element of all music', and that, consequently, a natural compositional method should be predicated on melody.(36) Marx even uses song (in particular, the mother's lullaby) to naturalize the pedagogical method: 'the mother's simple song, in which the child may join, is the most natural and often the most effective medium of instruction'.(37)

The natural creativity of children's singing functions as both anchor and benchmark in Marx's system of thought. It informs Marx's attitude to the nature of musical understanding, while shaping his highly graduated model of musical development. Musical meaning for Marx was 'performative', rather than 'declarative': since the highest form of understanding is composition, musical knowledge can only emerge from 'productive activity'.(38) Since, from the standpoint of composition, melody, rhythm, harmony and form are inseparable, Marx is dismissive of the intellectual abstractions of academic music theory, which tended to reify and compartmentalize these parameters. The holism of Marx's theory is qualified by his interest in the order of (musical) language acquisition. According to Marx, pitch is acquired before rhythm ('the development of rhythmic perception succeeds that of pitch'), with harmony and form coming later.(39) Marx attempts to project the pattern of development of musical knowledge in children on to acoustic and historical domains. He detects the same pattern in the generation of the octave, triad and dominant seventh from the fundamental, as well as the evolution of musical style from plainchant (unisons), through organum (fifths) and polyphony (thirds and sixths) to modern-day tonality.(40) Questionable as they are, these homologies actually make sense as part of Marx's heuristic system, whereby unfamiliar or abstract ideas are always taught in connection with facts which are concrete and known. As we shall see, Marx's pedagogy proceeds along twin tracks: syntagmatically, it develops in a linear, step-by-step, progression; paradigmatically, it moves from concrete to abstract. In the first regard, the advantage of a well-planned formal method is that no exercise 'presents greater difficulties than any previous one, for each is derived from and based upon those which precede it; and although it may appear more complicated, and require closer application, the student finds himself on every point prepared'.(41) In the second regard, bad schools and primers 'teach the signs before they have explained the things which those signs represent'.(42) Marx appropriated a slogan from the Berlin educationist Diesterweg as the epitaph for his Lehre: 'Proceed from impressions to concepts, from the particular to the general, from the concrete to the abstract, not the reverse. This principle serves the entire task of teaching, as well as upbringing.'(43) Marx's life's work was founded on this pedagogical ideal. As we have seen above, the prefaces to the six editions of the Lehre testify to his continuing endeavour to harmonize his theories with educational realities, that is, with what students can actually do in practice. Paradoxically, it is the tensions between Marx's own theory and practice - between what he claims and what he does - which motivate his revisions.

A case in point is Marx's difficulty in settling on a clear definition of his main musical categories, the Satz and Gang. Marx's first edition describes the Satz and Gang as 'musical structures [Tongebilden]'. A Satz is 'a simple, self-sufficient, well-formed structure' (Ex. 1).(44) A Gang is 'a structure which eschews such formal closure' (Ex. 2).(45)

[Musical Text Omitted]

[Musical Text Omitted]

Later in this edition, in his discussion of 'Gangbildung' and 'Satzbildung', Marx speaks of these prototypes not as structures but as principles, respectively of dynamic development and formal definition.(46) The first edition of the Lehre is never clear about the distinction between structure and principle, and this ambiguity increases in subsequent editions. For example, the section in the sixth edition on 'The Formation of the Gang' (Gangbildung), in which Marx teaches the student to chain motifs together as sequences, locates the Gang's essence as much in the implications of the motivic material as in the student's activity of composition.(47) Marx now differentiates Gang and Satz not as two Tongebilden but in terms of opposing forces: the 'tendency of the motifs towards indefinite continuation' colliding with the drive towards 'formal definition'.(48) The most striking testimony to Marx's involvement with this problem is the sixfold expansion of the 'Gangbildung' section between 1837 and 1863: the section occupies a single page in the first edition, and six in the last? Marx devotes his expansion to illustrating the manifold ways in which a motif can be developed. Arguing that creativity consists not in the talent of fashioning interesting ideas, but rather in the ability to manipulate basic material, he hits on an arresting analogy: 'A piece of gold that I find is only worth its value in money to me; but a skill which I have acquired may be a source of constant profit'.(50)

The small, yet crucial, step from a formal to a cognitive interpretation of the Gang, a step which Marx was so loath to take, was actually accomplished in Riemann's 1887 version of the sixth edition. Riemann portrays the Gang's dynamic drive as the property of raw, pre-compositional material, to be tamed and structured by a schematizing mental act. The latter is termed a 'formal impulse [gestaltende Wille], whether it be fully-conscious or half-instinctive',(51) while the Gang represents 'not a closed form, but just a creative dynamic, a preparatory stage of composition which attains true form only through external definition'.(52) Readers conversant with the theories of Leonard Meyer will grasp the modernity of Riemann's cognitive turn. Meyer's work attends to the way that compositional decisions deflect implicative patterns in melodies, and to how the frustration or fulfilment of these patterns is processed by listeners? At the end of his reworking of Chapter 1, Riemann illustrates the argument with a quintessentially Meyerian device. After presenting the theme from the finale of Mozart's Piano Sonata in C minor, Riemann concocts a hypothetical version Mozart might have written had he allowed the implicative patterns of the Gang to run their course (Ex. 3). We see, for instance, that in Riemann's version the skip from b [flat] to a [flat] in bar 2 generates another leap of a seventh, e [flat]'-d", in bar 4 (a third, e[flat]'-g', in Mozart's original).

[Musical Text Omitted]

While it could be said that Riemann merely extrapolated ideas that were already immanent within Marx's system, it is equally possible that Marx was prevented from fully psychologizing his formal principles by his fidelity to Diesterweg's maxim. If teaching was to proceed from the concrete to the abstract, then it was reasonable for Marx to anchor the Gang in the 'real world' of compositional activity as opposed to the theoretical realm of pattern cognition. As an expression of creativity in action, the Gang reflects Marx's practical, even behaviourist, conception of musical 'nature'. One reason, therefore, why common-sense truisms of good pedagogy cannot apply universally is that interpretations of the 'natural', including Diesterweg's categories of the 'concrete' and the 'particular', can diverge diametrically. This relativity of the 'natural' is epitomized in Marx's and Riemann's opposing teaching styles: that is, in the rhetorical ploys which structure their 'lessons'. Diesterweg's maxim counsels an 'inductive' approach to pedagogy, by which the teacher begins with concrete examples and only afterwards abstracts theories out of them. And yet Marx seems to teach 'deductively', proceeding from intellectual reasoning to example. This is how Marx introduces the student to the concept of rhythm.

Chapter 1 presents a scale of undifferentiated crotchets with no bar-lines (Ex. 4). Marx wants to endow the scale with more variety, and he wonders what the best way to group the notes might be. He reasons that the simplest division is by two, and so arranges them as in Ex. 5. He then worries that this line of reasoning is only obvious to

[Musical Text Omitted]

[Musical Text Omitted]

the understanding. In order to make us feel the justness of this division, he recommends that we perform the music accenting the first beat of each bar. Riemann's edition of the Lehre reverses this strategy. Instead of reasoning from first principles, and then illustrating them with rhythmic notation, Riemann begins with a shapely rising - falling arch contour (Ex. 6), and then interprets its rhythmic implications (Ex. 7). He

[Musical Text Omitted]

'feels' that the 'comer notes' of the melody, its first and last notes, as well as the melodic crux, are marked for consciousness and therefore imply strong metrical placement. This, in turn, suggests bar-lines and grouping.

It would be wrong to conclude from this comparison that Marx's method is less 'natural' than Riemann's. Given that Marx's lesson moves from the familiar (binary ratios; divisions by two) to the unfamiliar (the concept of metre), it could be said to be just as 'inductive' as Riemann's, but on a different level. Furthermore, the underlying sophistication of Marx's teaching will emerge in the second main part of this study (see pp. 512 ff., below), which uncovers the Lehre's adaptation of Herbart's psychologically-orientated pedagogical system.

The lesson to be drawn from this brief conspectus of the Lehre's editions is that talk of a musical 'nature', or of a 'naturalizing' teaching method, has no meaning outside a historical context. To fill in the background to Marx's naturalizing programme, the rest of this section considers both his theoretical categories and pedagogical method as an imaginative response to the challenging ideas emanating from the Pestalozzi circle in Switzerland. In the first part, I will trace Marx's ideas about the nature of musical experience to Johann Pestalozzi's theory of perception (Anschauung). I will argue that Marx's Lehre develops the concept of 'Anschauung' in two important directions. First, it extends an originally cognitive category into the field of aesthetics. Second, it translates a process rooted in spatial, static, geometric principles into temporal, dynamic, physiological terms. In the second part, I will show how the organization of the Lehre enshrines a theory of musical development which can be traced to pedagogues such as Nageli, Logier and Diesterweg.

1 Perception

At the heart of Marx's method is the belief that education can shape modes of perception. Although we are equipped by nature with certain predispositions, such as 'a tendency to perceive difference and order', Marx is clear that listening to music is something we learn how to do.(54) This constructivist approach, which holds that the mind's perceptual categories are built up, rather than inherited, departs radically from Kant's transcendental model, and follows in the train of post-Kantian philosophers such as Herbart and Beneke. Without renouncing philosophy's empirical grounding, they nevertheless rejected talk of a priori faculties. For example, the principles of Euclidean geometry, taken by Kant to be universal and foundational to visual perception, were held by Herbart to be contingent phenomena internalized through experience? More important to Marx than philosophy was the specific example of the Swiss pedagogue Johann Pestalozzi. Pestalozzi's 'A B C of Anschauung', a kind of alphabet of geometric forms designed to train the child to see more accurately, was the visual analogue of Marx's Lehre. We will see how Marx applied lessons about the psychology of vision to that of listening. In so doing, he seems to conform to a historical pattern whereby psychologically-orientated music theorists tend to borrow ideas originating in the visual realm?

Johann Pestalozzi was the most significant educational reformer of the modern age. His current neglect is due, paradoxically, to the fact that so many of his ideas are taken for granted in schools today. Strongly influenced by his compatriot Rousseau's Emile, ou De l'education (1762), Pestalozzi pioneered what is nowadays called 'child-centred learning'. According to this approach, children are treated as people with their own special needs and abilities rather than as miniature adults. Pestalozzi's first-hand experience as a schoolteacher endowed him with a sensitivity to what children could reasonably be expected to understand at various levels of their development. He accordingly devised curricula and teaching methods appropriate to each stage of the education process, from primary school through to university. Whereas primary education in the Swiss villages was based on mechanical rote-learning, Pestalozzi instituted a method which encouraged children to cultivate their powers of observation and judgement. Emphasis was placed on concrete or immediate experience rather than on words or abstractions. A child's interaction with his or her physical environment through 'self-activity' (Selbstatigkeit) is supported by, and in turn reinforces, developing powers of observation and reflection (Anschauung). 'Anschauung', Pestalozzi's key concept, is difficult to translate, since he uses it in a way which conflates a range of seemingly diverse activities: the direct intuition of objects (i.e., sense-impressions); the mental act by which these impressions are obtained - observation; contemplation of this knowledge; finally, even contemplation of ideas in the mind, namely, introspection.(57) In fact, 'Anschauung' is a dynamic principle traversing each of these activities: 'the gradual process by which sensuous impressions become clear conceptions'.(58) Crucially, Pestalozzi showed that this process could be controlled by instruction: children's skills of observation could be improved by teaching them to draw. Pestalozzi's 'A B C of Anschauung', very much the mechanical arm of his whole philosophy, reduced the art of drawing - and the art of seeing - to their first principles; that is to say, lines, angles and curves. His Method presented these three 'primary forms' in a diagram (Fig. 2).(59) He describes his technique in action in his later work How Gertrude Teaches her Children:

As soon as the child draws the horizontal line, with which the A B C of Anschauung begins, readily and correctly, we try to find him, out of the whole chaos of objects seen and shown, figures whose outline is only the application of the familiar horizontal line . . . Then we go on to the vertical line, then to the right angle, and so on. As the child, by easy application of these forms, becomes stronger, we gradually vary the figures . . . While in this way the children bring every drawing to perfection, before they proceed farther, a consciousness of the result of perfected power is developed in them.(60) Pestalozzi extended the principle of 'Anschauung' from vision to sound: 'Simply bringing sounds to the ear and rousing a consciousness of the impression made through the hearing is as much sense-impression for the child as putting objects before his eye'.(61) Nevertheless, Pestalozzi explored sound only in relation to language acquisition. It was left to more technically knowledgeable disciples to import his method into music. In his Vorlesungen uber Musik, the composer and publisher Hans Georg Nageli proposed prime forms based on the properties of fundamental numbers - what he termed a 'Grundzahlgesetz'.(62) Nageli believed that all artistic activity is driven by the interaction between qualities of the numbers 3 and 4, or 'Dreyzahl' and 'Vierzahl'. He associated 'Thirdness' with the dynamic and creative drive of 'becoming'; 'Fourthness' with static or formal qualities of 'existence'. The kinetic impulse, typified by the intensity curve of a melodic line, interacts with the impulse for symmetry, such as four-bar phrasing: 'Just as "Thirdness" unfolds throughout the rhythmic course of individual progressions, "Fourthness" regulates these progressions into units within a metrical structure, thereby fashioning a balance of proportions'.(63) According to Nageli, 'Fourthness' dominates all well-crafted compositions.

The link with Marx is striking. For Marx, music arises from the interaction of principles of motion (Bewegung) and stability (Ruhe), embodied by his prime forms of Gang and Satz.(64) As we have seen, Marx is clearest on this matter in his sixth edition. Arguing that Gang-like progressions (here, rising or falling sequences), since they contain no internal compulsion for closure, could in theory continue for ever, he states that 'the progressions must receive formal definition from without'.(65) Unlike Nageli, Marx was not interested in the transcendental qualities of numbers as such, but only in their implications for musical structure. When he speaks of the contrast of 'Zweizahl' and 'Dreizahl', it is to point out that phrases which seem to fall in three parts can often be understood as deviations from or expansions of a symmetrical two- or four-part framework.(66) Nevertheless, Marx can be said to complete the project which Nageli began: the translation of Pestalozzi's 'A B C of Anschauung' from vision to sound. He admits as much in a footnote to his Die alte Musiklehre, which praises the Vorlesungen for its ideas while also criticizing Nageli for failing to work them out in a systematic way.(67) Marx's main debt to Nageli was the idea of a dynamic model for music. 'Motion', according to Nageli, 'is the fundamental element of music', and the perception of notes in motion constitutes our earliest musical experience.(68) Nageli sought, albeit unsuccessfully, to project this model on to rhythmic as well as melodic relationships. Notes, he argued, are subject to 'extensive' oppositions of short and long rhythms, as well as 'intensive' oppositions of high and low pitch? As we have seen, the metaphor of motion allowed Marx to accomplish a project which Nageli only adumbrated: to integrate the various musical parameters of pitch, rhythm, harmony and form into whole utterances, and to mediate the pupil's journey from simple melodies to full-scale sonatas. The dynamic model had a further use for Marx: it allowed him to explore analogies between musical processes and processes in other domains, that is, the body and the mind. In pursuit of this analogy, Marx was repeatedly drawn to the writings of the psychologist and pedagogue Friedrich Eduard Beneke.

Beneke's works are cited approvingly in Marx's Die alte Musiklehre and are the major influence behind the psychological musings in his later writings, especially Die Musik des neunzehnten Fahrhunderts und ihre Pflege. Beneke's historical importance rests on his being the first philosopher to recognize the physiological dimension of experience as an input to mental operations. He conceived of the mental life as compounded of dynamic impulses [Triebe] that are activated by external stimuli.(70) The resulting affinity, or 'Sympathie', between inner thoughts or feelings, and bodily motion and expression, was even reflected in the rise and fall of speech-tone or melodic contour. It was this aspect of Beneke's thought that Marx found most suggestive. In Die alte Musiklehre he quotes the following passage from Beneke's Erziehungs - und Unterrichtlehre:

Given that the contents of consciousness are striving, at every moment of our life, to cancel out each other's dynamic impulse in a general equilibrium, mental activity (concepts, desires, feelings etc.) takes root both within (in so far as it awakens other concepts, desires, feelings etc.) and without, where it gives rise to external transformations (in facial expression, gesture, the movement of our limbs or of tones, etc.).(71) Just as we straighten our posture and stretch up our arms when confronted with elevated thoughts, so, Marx observes, 'our speech-tone rises, fills and grows stronger'. Conversely, 'depressive thoughts make our eyes, gestures, speaking voice and melodic contour sink'.(72) For Marx, music is just another channel for expression, akin to smiling or frowning. He conflates these physiological and aesthetic modalities in the name of a homeostatic 'unity of powers', by which 'the whole sensuous man' submits to 'a universal law of nature'.(73) Marx, like Beneke, is obscure about the precise manner in which inner and outer impressions are mediated, claiming that 'the same mood is communicated to the various organs of the body and the various outlets of spiritual activity'.(74) Instead, Marx speaks of 'the sound which enters my ear from without, and the outburst of my own excited mind in words and tones' as 'twins, or rather, identical processes occurring in different spheres of existence'? At best, Marx explains this synchrony through the metaphor of sympathetic vibration: 'What is this sound? It is the elastic vibration of a body . . . Exactly the same process takes place within myself. My mind or spiritual existence is excited and moved by pain, joy, or anger; my nerves tremble, the muscles of my body contract'.(76)

Given the state of knowledge of the time, it would be unfair to criticize Marx's (and Beneke's) speculations for being empirically unfounded or naive. In actual fact, his notion of a motion/emotion contour has become central to modern performance theory, though it was independently rediscovered by Manfred Clynes with his research into 'sentic' curves.(77) The first edition of Marx's Lehre expressly links the idea of melodic contour with affective curves:

Ascending progressions arouse a sense of rising, elevation and intensification, falling progressions, conversely, a sense of relaxation, depression, and resolution; neither progression keeps exclusively to one contour, but partakes of both sides in alternation, oscillating between the two.(78)

It is striking to see how Marx's idea of the curve, or 'Schwebung', takes hold over the subsequent editions of the Lehre. The second edition illustrates the above description with a notated curve (Ex. 8):

[Musical Text Omitted]

The final edition overhauls the entire first chapter, replacing the scale - Marx's original model of a simple musical utterance - with a rising and falling melodic arch.(79) As with his reformulation of the Gang, Riemann's 'arch' can be interpreted as a clarification of a Marxian ambiguity, in this case between pitch and register. Thus, although the starting-point of Marx's system is an octave scale, this scale is described in terms of a departure from and a return to a state of rest: that is, an opposition between the tonics an octave apart and the scale-steps in between (tonic versus scale). Marx is not concerned that the closing tonic of the scale is an octave higher than the opening: it nevertheless represents a 'return'. With Riemann's arch, by contrast, the pitch and register of the return are congruent. Nevertheless, for both Marx and Riemann the tonic/scale opposition is an analogue of 'an opposition operative for the entire art of composition: stability (Ruhe) and motion (Bewegung)'.(80) The virtue of the Ruhe/Bewegung opposition is that it permits the theorist to homogenize all musical parameters into a single principle. Hence the scale or arch becomes the paradigm for analogous oppositions of harmony (I-V-I), tonality (tonic, modulation, resolution) and form (beginning-middle-end). On a deeper level still, Marx learnt from Beneke that the arch conflates categories from different domains of experience: the melodic, the affective and the physiological. The pan-dimensional arch thus represents the limits of Marx's development of Pestalozzi's theory of 'Anschauung'.

2 Development

Aside from his 'A B C of Anschauung', Pestalozzi's second major contribution to pedagogy was to concentrate teachers' minds on the rate of the acquisition of knowledge in children. The realm of music education held its own special problems for the Pestalozzian method. First, what counts as musical 'knowledge' ranges across a variety of domains: playing an instrument, understanding music notation, knowledge of theory, and application of theory either in strict exercises or free composition. It is by no means clear that these various activities can be successively arranged in ascending order of difficulty, or associated with specific age-groups. Second, the psychologizing tendencies of the Pestalozzian school proved very difficult to square with the artistic and cultural aspects of music. The Pestalozzian teacher was predisposed towards the performance side of musical knowledge, ostensibly practical, physical and natural, and was generally suspicious of the more abstract kind of knowledge enshrined in complex musical structures or scores. As a result, the early methods are directed towards technical exercises with no pretence to artistic quality. The student is led to focus on musical parameters in isolation (typically rhythm first, then pitch) to encourage purity of 'Anschauung'. In the context of this tradition, it will become apparent that Marx's Lehre resolves both these difficulties. It is the first course book to extend Pestalozzi's principles to the teaching of composition. It achieves this, paradoxically, by reversing the Pestalozzian penchant for atomistic/parametric layout of material. Marx naturalizes composition by discovering artistry and wholeness in the simplest of musical elements.

The first direct application of Pestalozzi's principles to music was in the form of a singing-course book. Nageli and the composer Michael Pfeiffer published their Gesangbildungslehre nach Pestalozzischen Grundsatzen in Zurich in 1810. Their singing-course is Pestalozzian in its systematic progression from the concrete to the abstract, the general to the particular, the simple to the complex, from clear understanding of single parameters (rhythm, pitch etc.) to their combination as wholes. Pfeiffer and Nageli's work is extraordinarily systematic. Its 48 chapters are grouped in two broad parts ('General' and 'Specialized'), which are split, respectively, into five and four divisions. Part I begins with basic rhythms (Division 1), proceeds to pitch and dynamics (Divisions 2-3), and only combines these parameters into integral melodies in Division 4. It is most characteristic of this Pestalozzian method that standard staff notation is introduced at a late stage, in Division 5. Prior to that, Pfeiffer and Nageli avail themselves of Rousseau's movable Do notation (the basis of what became the French Cheve method), by which the notes of the scale are indicated by arabic numerals. Part II introduces words and texts, but still confines the students to one-part singing. Nageli provides examples of duets and trios in an appendix. Most striking is the omission of real music from the course materials; the authors deliberately restrict themselves to mechanical exercises.(81) Nageli explains in his appendix that Art, as an expression of taste rather than technique, cannot be taught: it is a province of cultivation (Befruchtung) rather than education (Beschulung). While the acquisition of skill is foundational for art, it is confusing or even harmful for the child to be introduced to art works at too early a stage of development. In a radical move, Nageli argues that 'teaching and learning actual art works is not a means to complete artistic understanding [Kunstanschauung], but rather splits Nature damagingly into separate functions of "knowing" and "doing"'.(82) The subsequent history of the Pestalozzian method is in many ways a search to reconcile art works with 'Kunstanschauung'. One way of doing this was to mitigate the emphasis on mechanical system in favour of richer content. For example, the nineteenth-century pedagogue Bernhard Christian Natorp introduced real melodies at the outset of his Anleitung zur Unterweisung im Singen, as opposed to artificial exercises.(83)

The hostile critical reception of Nageli and Pfeiffer's Gesangbildungslehre pointed to the difficulty of accommodating the richness and complexity of art works within a programme of linear, sequential learning.(84) When, for example, does technique stop and art begin? In his later work, the Vorlesungen of 1826, Nageli talks of an opposition between 'developing' (entwickelnd) or 'evolving' (evolutiv) methods, and 'positive' (positiv), 'manifest' (offenbar) ones.(85) Singing-courses are 'entwickelnd' on account of their natural development of music from breathing, speaking and intoning. The subject is his own instrument, and the development of the instrument (the voice) is organically linked with that of the acquisition of musical knowledge. By contrast, course books based on piano playing are 'offenbar', because the entire compass of registral and harmonic possibilities is laid out, 'manifest', across the keyboard. The act of playing implicates the student, if only unwittingly, within the vertical realm of musical harmony from the outset of his or her development. Students are not introduced to the musical parameters incrementally; they plunge in. There is also the fact that the piano is external to the student, unlike the voice. Having set up his polarity between 'entwickelnd' and 'offenbar' models, Nageli concedes that, in practice, pedagogy makes use of aspects of both. Nevertheless, he gives priority to 'entwickelnd', in the form of vocal training, which he considers foundational for music education.

The counter-proof to Nageli's theory, and one to which he may have been reacting, was the phenomenal success of the so-called Logier Method, the 'offenbar' system par excellence. Johann Logier, a German pedagogue who settled in London, was famous throughout Europe for producing child composers in a matter of weeks. He did this by merging the teaching of harmony and piano. A celebrated report by Louis Spohr, acting as independent observer, vouches for Logier's efficacy:

Another advantage of Mr. Logier's system is, that he instructs his pupils in the principles of harmony along with the first practical lessons on the piano-forte. How this is done I know not: it is a secret which, for the payment of 100 guineas, he communicates to those teachers who choose to adopt his plan. The result of Logier's system, as evinced by the progress of his pupils, is most astonishing. Children of from 7 to 10 years of age, who have been learning no longer than four months, solve the most difficult musical problems.(86)

Logier produced results and was certainly no quack. But his method of instruction - essentially a simplification of the Generalbass tradition - was too oral in nature to be transmitted through textbooks. The Logier phenomenon is a reminder that successful teaching, in the final analysis, is due to a good teacher rather than to a good theory. Marx's objection to a teacher whom he otherwise praised as 'talented' and 'methodical' was that Logier's method produced a merely mechanical facility, just 'as a watchmaker learns to put together the different parts of a clock'. Instead, the art of composition should 'grow in a living form out of the mind of the student'.(87) The achievement of Marx Lehre was to reconcile 'entwickelnd' and 'offenbar' principles of instruction; to synthesize methods originally associated, respectively, with singing and piano tuition; to accommodate the practice of composition into a tradition predicated on musical performance.

Through Adolph Diesterweg's Wegweiser, A. B. Marx formally enters the Pestalozzian curriculum.(88) While Marx's Die alte Musiklehre refers to the Wegweiser's second edition of 1838, Diesterweg's fourth edition of 1850 returns the compliment by citing Marx's Lehre itself. The Wegweiser covers most subjects under the German sun, from geology to astronomy. A chapter on singing teaching offers a comprehensive list of singing-courses, including Pfeiffer and Nageli's Gesangbildungslehre and Marx's own Die Kunst des Gesanges of 1826.(89) The 1850 edition appends an Anhang, which incorporates Marx's Lehre into a comprehensive study plan (Bildungsplan). This eight-stage Bildungsplan stretches the whole gamut from vocal and instrumental teaching to composition and general education. At the eighth and final stage, the student plays or sings the masterworks of the literature, studies old scores, composes freely, and reads academic tracts such as Nageli's Vorlesungen or articles from the Berlinische musikalische Zeitung. Composition begins at the fourth stage of the plan, after song, piano, notation and simple exercises, and at the point where the child is just starting to play piano sonatas by Haydn and Mozart. Diesterweg explains that composition comes at this late stage 'for the same reason that, in language teaching, the higher structures of grammar and style are constructed over a foundation of practical competence'.(90)

Marx's Lehre finds its place in the Pestalozzian education ladder as part of Diesterweg's Bildungsplan. On a deeper level, however, the Lehre may be said actually to incorporate this tradition, recapitulating each stage of the Bildungsplan sublimated on a higher level. To conclude this part of my study, I will present two arguments: first, that the organization of the Lehre outlines and rehearses the progression from song through piano to composition; and second, that this progression enshrines a theory of development in the terms Marx had available to him. Nowadays, cognitive psychologists would express the same insights in more technical language. Rather than rejecting Marx's model as primitive, we should seek to understand it within the framework of his own historical paradigm.

As we have seen, one of the basic tenets of Marx's holistic approach to teaching is that melody, harmony, rhythm and form are to be presented not in separate compartments but in combination as integral musical utterances at all stages of his treatise. This is not to say, however, that the weighting of these parameters does not change; in fact, the Lehre as a whole unfolds a genuine progression. The first book of Vol. 1 deals with 'Elementary Composition' for one to four voices; the second book moves on to 'Accompaniment of Given Melodies' (including chorales and folksongs). This broad drift from melodic to textural consideration continues into Vol. 2, most of which (books 4-5) is devoted to counterpoint (book 3, though nominally dedicated to 'The Periodic Forms', is actually dominated by discussion of accompanimental matters). Vol. 3, 'The Study of Applied Composition', finally introduces the student to forms proper, such as the etude, the character-variation, the five rondo forms and the sonata. To be sure, the Lehre had engaged with formal principles from its very start, as witness the periods and Liedform examples in Book 1. But in these earlier stages of his Lehre, Marx throws his spotlight on melody and harmony, or on the interaction of several voices in contrapuntal and figurational textures. The architectonic dimension, as a chief focus of interest, emerges only in Vol. 3.

Overall, the trajectory of Marx's Lehre runs from line through texture to form. A striking feature is that this progression recurs at lower levels, too. Marx's overview to Vol. 1 echoes the course of the entire treatise: we begin with unaccompanied melody and 'as we proceed, we learn to accompany every note of a melody with a separate chord', arriving at last at simple forms of folksong, chorale and prelude.(91) Similarly, these simple homophonic forms can reappear at the start of Vol. 2 because they are melody-orientated, and thus representative of 'line', the first stage of the line-texture - form trajectory. In accordance with this model, Vol. 2 proceeds from homophonic song forms or dances to a discussion of polyphonic textures, ending with identifiable contrapuntal forms such as fugue and canon. Marx's Lehre unfolds rather like a spiral; in his words, the various artistic forms 're-appear in a more independent character'.(92) This cyclical, recursive aspect, which some writers have likened to the Hegelian dialectic or the hermeneutic circle, has masked the arguably more significant route which the trajectory takes: the sequence of line-texture-form. What is the importance of this model? The line-texture-form sequence internalizes the Pestalozzian course of music pedagogy, from singing to piano-playing to composition. Just as the lyrical stage is represented in the sections of the Lehre devoted to melody, the pianistic stage informs Marx's teachings on accompanimental figuration, harmony and counterpoint. As Nageli argued, this pianistic stage is 'positiv' and 'offenbar' because the student is put literally in touch, via the keyboard, with the whole world of harmony.(93) The third stage, that of creative compositional activity, eluded Pestalozzian thinkers before Marx. Marx's achievement was to take this developmental progression to the final, symbolic stage. We see therefore that Marx's Lehre crowns this tradition in three ways. First, it achieves a culmination, as Diesterweg's Bildungsplan indicates. Second, it synthesizes the developmental (entwickelnd) aspects of the singing-courses with the integrated (offenbar) nature of piano teaching. Finally, the very organization of the Lehre rehearses and recapitulates the course of music education from the aural/oral stage of early childhood to the abstraction of maturity. This third aspect raises some important questions: why it should echo previous developmental stages, and why these stages are associated with modes or media of music-making. To answer these questions, we can look to more recent perspectives on developmental psychology.

Modern psychologists, after Jean Piaget, consider the development of the child's intelligence in terms of a progression from 'figurative' to 'operative' knowledge.(94) Keith Swanwick summarizes this approach as it applies to music education.(95) Figurative knowledge, or 'thinking with the body', functions in a sensorimotor level in terms of perceiving and imitating sounds or actions. Operative knowledge, or 'conceptual intelligence', evolves by internally representing sounds and actions as mental schemas, recognizing relationships between them, and transforming them into a system or signs, such as language. An example of the sensorimotor stage is when a child 'strums with his thumb across the open strings' of his teacher's guitar, or when he sings 'snatches of songs he knows' to a given accompaniment.(96) The operative knowledge required for musical mastery develops in the context of formal musical education. It is evinced in activities such as discussing and reflecting upon performance away from one's instrument, analysis of music enshrined in scores, and composing through the manipulation of musical symbols. Though the child's earliest musical experiences are often through singing, and composing is usually left until the final stage of schooling, the activities of singing and composing do not correlate with the development from figurative to operative knowledge. As Lyle Davidson has shown, 'song singing' skills can themselves develop across the entire range of a musical career, right up to an operative level of mastery.(97) Conversely, Swanwick argues that the creativity we associate with composition is manifest in children's 'imaginative play' with musical materials.(98) In short, although the successive stages of musical development suggest various domains of activity (singing, performance, composing), they actually unfold through each of them: they are not domain-specific. It is on this point that early nineteenth- and late twentieth-century approaches to musical development chiefly differ. Notwithstanding the crudeness of their theoretical tools, Nageli, Diesterweg and Marx were pioneers on a project we think of as being modern: their problematic is essentially continuous with ours. However, the terms in which they articulated their solutions were historical ones, and we must make allowance for them. It was natural for these writers to identify each stage of musical development with a field of activity: song for the figurative; composition for the operational. The middle stage, that of piano playing, performs the same mediating role as Piaget's 'concrete operational' stage. Learning harmony or composition at the piano is often easier than away from the instrument (the 'formal operational' stage).(99) At the piano, the student's manipulation of notes depends on externalized tone production and contact with the keyboard. Knowledge here is 'concrete' rather than 'formal' so long as the student is pushing keys instead of symbols. Marx's Universal-Lexicon proposes a progression according to specific age ranges: free singing (3-5 years); singing instruction (7-14 years); piano instruction (starting not later than 14 years); composition (after piano).(100)

We can turn now to our second question: why Marx's Lehre internalizes the song - piano-composition sequence into its layout as a pattern of line-texture-form. By recapitulating these earlier stages of development on the more abstract level of compositional theory. Marx is breaching the domain-specificity we noted above. On the one hand, song is associated with the initial stage of development; on the other, this category is mapped on to the final stage, that of composition. Viewed from a negative standpoint, Marx is guilty of conflating child-orientated (pedagogical) and adult-orientated (andragogical) teaching methods.(101) But, more positively, Marx's strategy would receive sympathy from modern developmental psychologists such as Howard Gardner, who believe that a hallmark of adult artists is that they keep alive, or rediscover, the creativity inherent in early childhood. According to Gardner, 'important dimensions of adult creativity have their roots in the childhood of the creator'.(102) Similarly, study of children's singing, drawing and story-telling indicates that they 'are very close to the wellsprings of creativity and that they share some similarities with gifted adults in both the processes and products of artistry'.(103) Historically, Georg Sowa emphasized the importance of child-orientated (kindgemasser) teaching methods for early nineteenth-century institutional reform at all levels of German music education.(104) In particular, he drew attention to the writings of the theologian and music pedagogue Karl Gottlob Horstig (1763-1835). Horstig, observing his own children at play, noticed a continuity between performance and improvisation: 'My little four- and six-year-old children sang and whistled whatever occurred to them. To be sure, at first only familiar melodies, but with so many additions, changes, decorations and transpositions that it was often difficult to make out the original.'(105) Horstig's ideas inspired a host of plans and manifestos for music curricula, instituting a more integrated and creative basis for music education. In the wake of this reform movement, Marx himself submitted an education plan in 1832, in the form of a handwritten letter to the Preussische Staatsministerium des Geistlichen.(106) Marx's plan is notable for its systematic layout and its greater emphasis on music theory. Like previous reformers, Marx is anxious to create a bridge from Kindergarten through Volksburgerschule and Gymnasien up to university. It is not fanciful to see in this preoccupation with a graduated regime a projection from the 'entwickelnd' or 'kindgemasser' progression of singing courses. On a theoretical level, Marx's subsequent Die Lehre von der musikalischen Komposition projects the same child-orientated model on to the teaching of advanced composition. The Lehre rediscovers and recuperates the creativity of children's song-singing. In conclusion, the process which motivates this 'kindgemasser' method might be termed 'mapping from the child to the man'. It is now time to explore the opposite tendency in Marx's thought, which maps from the man to the child.

ENCULTURATION: MAPPING FROM THE MAN TO THE CHILD

We have seen a strong tendency in Marx to ground theory in the mind's natural faculties: inborn predispositions and their course of development. The behaviour of children seemed to embody these principles at their purest, before the onset of cultural and social influence. We turn now from the natural to the normative side of education theory, a province of values and interests whose truth-content is adjudicated by political rather than scientific considerations. This will mean looking at many of the same ideas from the opposite point of view, directed not towards origins but goals. Education, in the form of 'Erziehung', took as its highest goals the formation of sound judgement, good character and the responsible participation of the individual in society. Song, in particular the lullaby, was held up not only as a cognitive model of teaching (in Marx's words, 'the most effective medium of instruction')(107) but also as a paradigm of social and even nationalistic interaction: 'With song the mother lulls her babe to sleep... Why has not the Art of ages taught us to join the nursery lullabies to a series of national songs?'(108) For Pestalozzi, the basis of 'Volkerziehung' was 'Singerziehung', on account of its 'powerful capacity to forge social relationships', and as an 'expression of communal thought and feeling'.(109) One reason for Marx's championship of the German oratorio revival was his awareness of the political implications of choral singing.(110) It would be wrong to conclude from this that the special blend of pedagogy and politics called 'Erziehung' was not susceptible to theorizing. On the contrary, for writers such as Nageli, pedagogy and politics were the only true disciplines: 'To all intents and purposes, there are only two core sciences; all the others are subsidiary sciences. The two core sciences are: pedagogy and politics.'(111) In this section, we will see how the normative side of education, associated with the stages of adulthood or mastery, are inculcated through Marx's system. As before, the section divides into two parts. In the first part, I will outline Marx's ideas on the aesthetic side of musical experience, and relate them to Johann Herbart's theory of internalization by which concepts and values are transformed into mental models. In the second part, I will turn to the influence on the Lehre of Herbart's theory of pedagogical emplotment, that is, the narrative structures which guide the student's journey.

3 Internalization

Many of the Lehre's intellectual underpinnings are presented in Marx's Die alte Musiklehre of 1841. Although Die alte Musiklehre was published as a polemical Gegenschrift against Siegfried Wilhelm Dehn's reactionary Theoretisch-praktische harmonielehre of 1840,(112) the work is in many ways a retrospective prolegomenon to the Lehre, coming out four years after the first edition of Vol. 1. Much of the book is a critique of theories that propose a natural grounding of music in sensory stimulation. In general, Marx is hostile towards any idea of unmediated perception in music. To understand music in acoustic terms, as a mere play of consonance and dissonance, is to neglect its spiritual (geistig) content. It relegates musical judgement to the pleasure principle, the favouring of pleasant sonorities (Wohlklang) against the ugly (Ubelklang).(113) If music really were governed by the search for stimulating sensations, then the modern orchestra would have been given over to meretricious sound effects (Kling und Klang).(114) Furthermore, Marx reminds us that counterpoint, the most prestigious of musical idioms, lacks obvious charm or variety, is unpleasurable to uneducated listeners, and neglected by weaker composers because of its difficulty.(115) In reality, notes and chords cannot be categorized in themselves, according to their acoustic quality, but only in terms of their relationship to other notes and chords: that is, their activity or context.(116) The main impediment to a science of music is the fact that musical objects are always functions of artistic processes, and are not given in the natural world.

A superficial reading of Die alte Musiklehre might suggest that Marx's position was in line with the anti-psychological prejudice of the mainstream Idealists. To be sure, on one level, the work operates as an argument for the inherently cultural character of musical knowledge, with a critique of naively naturalizing theories. On a higher level, however, the book functions as defence of the author's Lehre as a mechanism for effecting musical enculturation. To this end, Marx cites the writings of Johann Herbart, the philosopher, psychologist, and author of perhaps the most influential pedagogical tract of the whole nineteenth century - the Allgemeine Padagogik.(117) Marx's relationship with Herbart was curiously ambivalent: he quarrelled with the philosopher's old-fashioned conception of the musical object but warmly endorsed his pedagogical theories. Marx cites a passage from Herbart's Encyclopadie der Philosophie, which discusses the cognition of poetry and the plastic arts.(118) According to Herbart, cognition in these domains relies on the learning of concepts and images through experience, and their internalization as mental models (Vorbildungen). For example, we would not be in a position to understand paintings without experience of human faces or gestures. Marx argues that musical learning is altogether different. Whereas an appreciation of painting or poetry requires only an experience of life, the precondition of musical understanding is experience of music. We can only make sense of a musical impression (such as the beginning of a work) in the full context of the work's unfolding: 'the relationship of this beginning to the developing artwork is so remote and obscure, that to understand it presupposes a high level of education'.(119) Marx differentiates the objects of musical education from those of poetic or artistic education on three counts. First, as we have seen, musical objects are defined to a greater degree by their structural context. Second, the plastic and literary arts deal, respectively, with spatial and temporal schemata (Gestaltung), whereas music mixes both together.(120) Third, musical effects are much more transient or fleeting. Marx's argument nevertheless leaves the main burden of Herbart's theory untouched, his point being that the kind of experience necessary to internalize the 'Vorbildungen' for musical understanding is afforded by a specifically musical education, rather than the university of life.

The ambivalence of Marx's relationship to Herbart was part of a wider distrust of any theory which was not grounded in musical practice. For example, the problem of Marx's debt to an even greater figure, Hegel, is nicely encapsulated in a footnote to page 12, which cites Hegel's own apology for his limited technical knowledge of music. Again and again, Marx emphasizes that only a Kompositionslehre can teach us to hear, not a Kunstphilosophie.(121) It is often the case that the forays of philosophers into music are less suggestive to the music theorist than those philosophers' core ideas.(122) Thus Marx, while purporting to admire Herbart's theory as a whole, rejects his somewhat outdated conception of music, which seemed to be rooted in thorough-bass. Herbart's relevance to Marx rests on the broader level of method. This method, which informs both the learning process and the teaching regime, is a kind of associationist psychology.

Associationist psychology seeks to explain all of mental life in terms of a few laws of association. According to Gary Hatfield, 'typical associationist explanations emulated the explanatory structure of the new physics: mechanisms or processes were analyzed into elemental components (corpuscles or atoms in the physical case, simple or atomic sensations in the mental) and the laws governing their interaction'.(123) For Herbart, presentations (Vorstellungen) are the elements of mental life, and the various combinations and interactions give rise to the manifold contents of consciousness. Interactions produce derived presentations. Once these presentations are created, they are no longer dependent upon the sensuous impressions which originated them. These impressions have been internalized within consciousness as representations. Representations are in turn capable of development by the processes of comparison, abstraction, and generalization into concepts. Concepts occupy the highest levels of thought. Though the formation of concepts through the internalization of impressions is a psychological process, it is not a 'natural' one. On the one hand, the source of the child's presentations is not innate categories but experience; on the other, they can only develop through education, which moulds experience into knowledge. This process has, as it were, a 'hard' and a 'soft' form. Herbart's 'hard' theory is cast in the language of mechanics: it treats each presentation as a force, and expresses the interaction of these forces mathematically. This side of his work need not detain us here. Herbart's 'soft' theory is educational, dealing with the ethical side of character development. It is equally concerned with 'associationist' complexes of relations; but this is expressed in aesthetic terms, and, as will emerge, it is epitomized by music.

Herbart's first published work was entitled Pestalozzis Idee eines A B C der Anschauung (1802), and its second edition (1804) included a supplementary essay, 'The Aesthetic Revelation of the World as the Chief Work of Education'.(124) This essay deals with the formation of character, proposing that morality is the highest aim of humanity. Herbart explores the paradox that moral law, though binding, must nevertheless be freely chosen and, though universal, has no logical foundations. In a passage which seems a close paraphrase of a section from Kant's Critique of Judgement, Herbart argues that the only realm which deals with necessary, yet non-provable, relationships is aesthetics: 'The characteristic of this necessity [aesthetics] is that it speaks in purely absolute judgments entirely without proof'.(125) Moral judgements are formally coherent or incoherent with each other as in an aesthetic work. To be educated, ultimately, means to make an aesthetic response which is either favourable or unfavourable. Significantly, Herbart's paradigm for this process is music:

Among the arts, music in this respect affords a striking example. It can definitely and collectively enumerate its relations of harmony, and just as definitely show their correct use. If, however, the teacher of thorough bass were asked for proofs, he would only laugh, or pity the deaf ear which had not already perceived them.(136)

For Marx, the foundational stage of an associationist music course is mimetic: the teacher plays a note at the piano and the child hears it, identifies it, and sings it back ('With children, even in the first year of life, the impulse to imitate what they have heard [tone and pitch] is active').(127) Marx is most explicit on the transition from the aural/oral stage to the compositional stage in his Die Musik des neunzehnten Jahrhunderts und ihre Pflege.(128) He grades this transition in six steps: first, the seven notes of the octave are played on the piano by the teacher and named; second, the whole scale is played; third, the teacher plays each note of the scale and the student sings back each note in turn; fourth, the process is reversed - now the student sings each note, and the teacher plays it; fifth, the student sings the whole scale unaided; and sixth, the scale is now divided into motifs of two or three notes. At this point Marx refers the student to the opening chapter of his Lehre, concerning the generation of melodic forms out of motivic building-blocks: 'From this it may be inferred that new motives may be derived from simple ones by one or the other of these proceedings'.(129)

The Lehre rehearses the same associative principles at a more abstract level. In Herbartian terms, the aural/oral 'presentations' have been internalized as 'representations'. One interesting feature of the six stages of the singing-course is the turn, in the last step, from what might be called a 'divisive', 'top-down' viewpoint to one which is 'combinational', or 'bottom-up'. Initially, the focus is on the whole scale, as a unit to be sung back. The focus changes to a generative one, building up from the scale's constituent motifs. The Lehre's opening chapter is organized on the same lines.(130) It falls in two sections. Marx's Erster Abschnitt (pp. 17-25) deals with the scale as a model of a well-formed musical phrase, or Satz. Marx illustrates this with a paradigmatic example of a scale which starts and finishes on a metrically strong tonic (shown in Ex. 1). The Erster Abschnitt thereby unfolds, with cumulative logic, from basic principles to a fully worked out phrase which instantiates them. For good measure, Marx completes the rising scale with a falling one, producing a balanced antecedent-consequent structure (Ex. 9). Having reached this goal, the Lehre reverses direction and returns to first principles. The Zweiter Abschnitt (pp. 25-33) works its way through the same material, but now from the standpoint of small-scale, motivic, units rather than large-scale Gestalts. Turning back to his summary example, the Satz (see Ex. 1), Marx isolates what he takes to be its smallest well-formed structure: a three-note unit in crotchets (Ex. 10). Marx then shows how this motif can be transformed and multiplied, generating new ideas (Ex. 11).

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Through 'Gangbildung', the open-ended structure of the Erster Abschnitt (the Gang shown in Ex. 2) is reformulated, from the bottom up, as the sequential repetition of a motif (Ex. 12). By an analogous process of 'Satzbildung', Marx concatenates his motifs into a variant of the antecedent-consequent, rising and falling scale which had been reached at the end of the first Abschnitt (Ex. 13; compare with Ex. 9). This period

[Musical Text Omitted]

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structure can be regarded equally as a unit which is subdivided, and as a chain of motivic segments. Nowadays, we would say that the cognition of a musical phrase is both 'concept-driven' in a top-down fashion, and 'data-driven' from the bottom up.(131) A competent listener is adept at switching between the two standpoints. The same principle underlies Marx's comment in the fourth edition of his Lehre regarding the 'Fate' motif from Beethoven's Fifth Symphony: 'It is not the motive for its own sake, but both that and the manner in which it is developed, which constitutes the value of any artistic production based upon it'.(132) We are reminded of Marx's remark, in Die alte Musiklehre, that beginnings of pieces can only be comprehended in relation to the unfolding whole. Chapter 1 of the Lehre trains the listener in the facility to switch between local and global viewpoints. Having internalized the two viewpoints, he or she is now equipped to understand the culminating music example synoptically.

Herbart's term for such switching is 'mental respiration'. Just as modem theorists speak of cognition as a switching between data- and concept-driven processes, 'mental respiration' entailed for Herbart an alternation of 'Concentration' (Vertiefung) and 'Reflection' (Besinnung):

Vertiefung and Besinnung, as forming the act of mental respiration, ought always to alternate with each other. Vertiefung takes place when presentations are successively brought into consciousness in sufficient strength and purity, as far as possible without obstructions. Besinnung is the collecting and binding together of these presentations. The more perfectly and purely these operations are performed, the greater will be the success of instruction.(133)

In so far as Pestalozzi's 'Anschauung' intermingled the intuitive and regulative sides of perception, Herbart's 'mental respiration' separates and refines these activities, arranging them as the arsis and thesis of a cognitive rhythm. A further advance over Pestalozzi's thought is Herbart's clearer understanding of the teacher's role in the development of mind. As the above quotation suggests, mental respiration will not happen of itself; it requires the active intervention of instruction. Psychology is placed in the hands of pedagogy, which, like political government, 'is cognisant of something which may be called compulsion; it is indeed never harsh, but often very strict'.(134) This is the point where the naturalizing, or 'kindgemasser', side of teaching yields to its cultural, or adult-orientated, obligations: 'everything must proceed from this single thought, namely, that the teacher must represent the future man in the boy. Consequently, the aims which the pupil will as an adult place before himself in the future must be the present care of the teacher; he must prepare beforehand an inward facility for attaining them.'(135)

4 Emplotment

Herbart occupies a doubly ambiguous position in the history of pedagogy. Neglected in his own lifetime and forgotten today, he has only a tenuous relationship with the spectacularly influential Herbartian movement launched after his death by two of his disciples, Tuiskon Ziller and Wilhelm Rein.(136) Ziller's Grundlegung zur Lehre vom erziehenden Unterricht of 1865 drew the world's attention to a teaching method which Herbart had first developed in his Encyclopadie der Philosophie of 1831 and which became known as 'The Five Formal Steps of Education'. The Steps originally numbered four: 'Clarity', 'Association', 'System' and 'Method'.(137) The first step, 'Clarity', was subdivided by Ziller into 'Analysis' and 'Synthesis', and I maintain this division since it accurately reflects two distinct elements in Herbart's original category.

The 'Five Formal Steps' provides the teacher with a clear regime through which to lead the student; in particular, it provides the 'Vertiefung/Besinnung' cognitive rhythm with a mechanical arm. The teacher begins (Herbart's 'Clarity') by reviewing the student's current state of knowledge as clearly as possible. By focusing on a single object as clearly as possible, the student is practising 'Vertiefung' - concentration. The analytical step of 'Clarity' involves the picking out of distinctive features; the second, synthetic, step leads the student to recognize these same features when a new object is brought into view. It is a central tenet of Herbart's pedagogy that students learn new facts by assimilating them to what they already know; Herbart calls the reception of new knowledge via old 'Apperception'. According to an early commentator, Catherine Dodd, 'Apperception may be generally defined as the power of understanding new ideas by means of related old ideas already in the mind'.(138) On the basis of the new facts uncovered in the second step, the teacher's third step, 'Association', is 'to discuss them with the children, and to compare and contrast them with known facts in order to lead the pupils to form the general truth for themselves'.(139) In other words, the comparison of objects with shared qualities leads the children to form abstract categories. This step thus involves the exercise of 'Besinnung'. The fourth step ('System') reviews the progress so far, generalizes conclusions from the lesson, and arranges these conclusions in a systematic order. With the fifth and final step ('Method'), the teacher leads the students to the practical application of what they have learnt. This can take the form of utilizing a grammatical construction, solving a mathematical problem, or even drawing a picture. According to Henry Felkin, 'it is this continuous application of newly acquired knowledge to previously existent groups of ideas, and the power which grows from it of passing through these groups at will, which constitutes what Herbart terms an interconnected circle of thought'.(140)

We know from Marx's Die alte Musiklehre that he was familiar with Herbart's Encyclopadie (which he frequently cites). Although the introduction of the Lehre never invokes Herbart by name, it nonetheless adopts his method. Step one, 'Clarity' (conflating 'Analysis' and 'Synthesis), is described as follows: 'first, the construction and meaning of every artistic form is clearly explained'.(141) We can see this in action in Marx's opening chapter. He begins by discussing the principles of pitch formation. In very general terms, he states that pitches can be arranged in rising or falling, mixed or repeating patterns.(142) He then instantiates a specific scale.(143) He does the same for rhythm, first dividing rhythmic patterns into equal and unequal, and then illustrating the point with a normative 2/4 metrical pattern.(144) His procedure here, therefore, is to focus the students' minds on what they already know (general principles of pitch and rhythm - 'Analysis'), and then to introduce something new (a concrete example of a scale or rhythmic pattern - 'Synthesis'). The next step, 'Association', is described in the introduction in these terms: 'In examining a new form, we first inquire into its relation to previous forms, and then consider its character as a stepping-stone to further progress'.(145) Accordingly, Chapter 1 then brings together all the previous requirements in a summary example, listing and interrelating four principles of pitch and rhythm.(146) Marx's example is another rising octave scale (as Ex. 1, above), illustrating the principles of tonal closure (starting and ending on the tonic) as well as strong metrical grounding (the first and final tonic are both strong beats). Interestingly, Marx points out that these two principles are normally in conflict with one another; for example a scale of regular crotchets in duple metre will either begin or end on a strong beat, but not both. To regularize the scale, the a' and b' must be reduced to quavers and tucked into the penultimate bar, so that the scale can end on a strong minim c". When a modern student of music analysis has learnt to handle issues of parametric noncongruence, he or she has reached the stage of Marx/Herbart's 'Association'. Further 'Association' follows when Marx juxtaposes, for the first time, his three fundamental forms, the Periode, the Satz and the Gang.(147) Interestingly, the first edition divides these forms more schematically than Marx's second edition, which considers them in more discursive fashion.(148) The schematism of the first edition can be seen in Plate I, which indicates steps 3 to 5: 'Association, 'System' and 'Method'. In the words of the introduction, the fourth step ('System') 'provides a number of facilitating maxims, intended to guide the student'.(149) These take the form, in the body of the chapter, of a Ruckblick, or overview: namely, a list often points all nicely arranged (see Pl. I).(150) The fifth step, that of application, spills over into the Zweiter Abschnitt, which begins with the words: 'after these preliminary observations, the student's own activity begins, becoming gradually freer'.(151) This second section puts principles into practice.

'Apperception', the learning of new ideas via existing frames of reference, guides students at all stages of their journey through the Lehre. Marx's method, cumulative yet circular, takes on the appearance of a spiral: in musical terms, a process of developing variation. The overture or exposition of this process is described in the Lehre's introduction, where Marx derives the principles of modulation from chord progressions and melodic contours.(152) According to Marx's narrative, the opposition in a melody between tonic (the boundary notes) and scale (departure and return) is expressed at a higher level in terms of the harmonic polarity of tonic and dominant chords. At the highest level, the same opposition appears when we modulate from the tonic to another key.(153) It is important to stress that Marx is not making any claims about the evolution of tonality here. His story merely seeks to explain to the student the concept of modulation on the basis of what he or she already knows: melody. Marx emphasizes the importance of sequentiality in learning: 'The student who . . . slips over the simpler or more familiar opening stages . . . in order to arrive sooner at subjects which appear to him more interesting, novel or striking, will never come into full possession of his art'.(154) When Marx refers to 'the development of one form out of another, none of which can be obtained and understood without the preceding ones', he is talking as a teacher.(155)

Later on, the Lehre represents the analogy between the three levels of tonal shape (melody, harmonic progression, form) in a couple of diagrams [ILLUSTRATION FOR FIGURE 3 OMITTED]. The common denominator linking these levels is an alternation of stability (Ruhe) and motion (Bewegung). The point of this homology, however, is not to reduce all music to a substratum of stability and motion: that would reveal very little. It is, rather, to open up an avenue of learning. In modern parlance, although Marx's diagrams verticalize the formal levels paradigmatically, they unfold syntagmatically. It is vital that the student have first-hand experience of journeying along a pathway, and the journey metaphor is very special for Marx:

We proceed in small steps, from one form to another. It is the privilege of the Master, who has already worked through and internalized every development, not to have to pass through the whole chain of derivations again. In practice, however, we follow him on the same path; we have set out on the same road, are only a lot further behind; his goal is merely more distant and personal, while ours is of the most general nature. This is why it is imperative that we justify every step we take and keep closely to the matter at hand, while the artist can stride lightly over ground already familiar to him towards his goal, hardly conscious of the connections and silent crossings.(156)

As Scott Burnham has convincingly argued, the model for Marx's conception of the 'Master' was Beethoven.(157) Beethoven's compositional mastery epitomizes the 'adultorientated' trajectory of the educational process. Indeed, Marx's monograph characterizes Beethoven's journey of self-discovery as a 'Laufbahn'. Nevertheless, there is a deeper sense, overlooked by Burnham, in which Beethoven's 'heroism' synthesizes the child-orientated and adult-orientated perspectives. Marx's programmatic interpretations of the Third and Fifth Symphonies portray them as heroic journeys. Marx calls the representation of joy in the triumphal finales a 'kindliche Spiel'.(158) In the more technical domain of thematic process, Marx, perhaps echoing Schiller's theory of the 'play-drive', talks of childlike playfulness as the vital counter-weight to the disciplined pursuit of unity. Rejecting the principle that every element of an art work should necessarily follow the 'idea of the whole', Marx states that

This absolute necessity, whereby every detail signifies, is possible in no art-work, because it would run against the fundamental character of art, that sense of blissful playfulness, which Beethoven gladly bestowed to so many works, just as he remains, throughout both good times and bitter sorrows, ever the man of childlike but hard-won happiness.(159)

'Spielseligkeit', the aesthetic side of child-orientated pedagogy, is thus revealed as a central component of perhaps the most influential musical style of the nineteenth century: Beethoven's heroic style.(160) This 'blissful playfulness' also informs contemporary representations of the composer, which often remarked on Beethoven's 'childlike' qualities.(161) In the music academy, the Janus-faced figure of the child-man composer, compounded in equal measure of artlessness and mastery, could function simultaneously as the ground and apex, paragon and totem, of the whole Marxian educational adventure.

WHAT MARX CAN TEACH US TODAY

We have seen that Marx structures his theory of education around a quadratic mode, by which Curriculum and Pedagogy (vertical axis) are subject to processes of Naturalization and Enculturation (horizontal axis). This model permits Marx to bridge traditions of teaching that had previously occupied opposite extremes of the educational spectrum: kindergarten and university. A modern theorist unsympathetic to Marx's enterprise could easily attack his apparent conflation of categories. Instead, I would like to close by suggesting that Marx's sins of conflation - ostensibly a Romantic trademark - are actually forward-looking.

'In order to accomplish any form of integration', says Bernstein, 'there must be some relational idea, a supra-content concept, which focuses upon general principles at a high level of abstraction'.(162) Furthermore, 'if the relationships between sociology and biology are to be opened, then the relational idea . . . might be the issue of order and change examined through the concepts of genetic and cultural codes'.(163) Marx integrates child- and adult-orientated traditions by rethinking the idea of motion (borrowed from Nageli and Beneke) at a level deep enough to encompass 'natural' and 'cultural' types of progression. Metaphors of motion are all-pervasive in Marx's writings, applying equally to formal categories (the Gang), aesthetic categories (the experience of Beethoven's teleological processes), musical narratives (the hero's journey in a Beethoven sonata-form narrative), the educational regime (the student's progress through the treatise), biological development (the growth of the student's mind), and even the course of music history (from plainchant to Beethoven). Aside from motion, the other 'relational idea' in Marx's system is the concept of 'wholeness'. In Burnham's words, 'the student must be treated as a whole being; works must be treated as wholes; and the elements of musical language must not be artificially separated'.(164) The ideas of motion and wholeness allow Marx to conflate categories which would nowadays be subject to different genres of discourse. For Marx, they represent points on a sliding scale between symbolic and technical engagements with experience, between figurative and systemic representations of theory. The ideas permit Marx's pedagogy to flow from what Bernstein terms a 'deep structure'.(165)

These relational ideas are not identical with the compositional Idee which Burnham and others have detected in Beethoven's structures.(166) Rather, they comprise organizational principles at the heart of the theorist's own creative endeavour - what I have elsewhere called 'regulatory images'.(167) Beethoven, as a dominant cultural figure of Marx's time, was both a source and screen for the development of such images. Paradoxically, it is the very waning of the Beethoven hegemony, together with the dissolution of the myth of the absolute and self-contained musical work, which permits modern pedagogy to recuperate the integrated code of the early nineteenth century. Bernstein states that 'a movement away from collection to integrated codes symbolizes that there is a crisis in society's basic classifications and frames'.(168) The crises in Marx's time and in our own neatly mirror each other: Marx was writing against a background of political turmoil, yet enjoyed the benefit of a stable musical canon; since the Second Word War, we have benefited from a stable political scenario, yet our curriculum has been thrown open to multi-cultural and experimental perspectives.(169) In other words, the Beethoven 'image' functions as a binding agent for Marx in much the same way as our cultural pluralism is accommodated by a catch-all definition of 'musical knowledge': both are ideological in their own way.

We cannot go back to Marx, of course. But Marxian pedagogy, as a demonstration of the interdependence of music theory, aesthetics and psychology, is a salutary reminder that disciplinary boundaries are always historically contingent. The moral of the Lehre is thus twofold, relating to the categorization of modern discourse about music, as well as the way we write its histories. First, much of the hostility between 'cultural' and 'scientific' approaches to music theory can be avoided. Examples of such boundary building are rife. On the side of cultural critique, Dahlhaus has articulated the typical concern that the search for psychologizing grounds usually serves some ideological purpose, as when a particular theoretical system or musical style is being defended.(170) On the scientific side, Eric Clarke has criticized 'a tendency to confuse cultural norms (such as the norms of formal design) which are established by convention, with perceptual norms which are the consequence of the characteristics and limitation of perceptual systems'.(171) My second point is that a successful history of music theory, music pedagogy or music psychology will only be written when their interdependence is recognized. In Dahlhaus's survey of nineteenth-century music theory, pedagogy features only as an extrinsic, and primarily negative, factor.(172) Conversely, it is curious that even the most extensive histories of music education ignore music theory.(173) Finally, Hermann Ebbinghaus's remark that psychology has a 'brief history' but a 'long past' has been forgotten by modern writers:(174) music psychology's pre-history shades all too uncomfortably into aesthetics. To be sure, in the formation of a discipline, processes of institutionalization proceed in tandem with acts of demarcation. Thus Hermann Helmholtz, the 'grandfather' of music psychology, ended an 1857 lecture on the physiology of harmony by relegating the question of aesthetic expression beyond the scope of his field: 'But I have reached the confines of physical science and must close'.(175) Now that music psychology has been delimited as an autonomous field of study, many of these confines can be lifted, and we can reclaim some of the continuities operative in the early nineteenth century. Music pedagogy, a practice on the interface between mind and society, suddenly becomes very timely.

1 Johann Heinrich Pestalozzi, How Gertrude Teaches her Children, trans. Lucy E. Holland, London, 1938, p. 199.

2 A. B. Marx, Die Lehre von der musikalitchen Komposition, Leipzig, 1837-63. The treatise went through six full or partial editions in Marx's lifetime alone. The complex publication history is given in MGG, viii, cols. 1734-8:

i: 1837, 1841, 1846, 1852, 1858, 1863, 1868, 1875, 1887, 1903;

ii: 1838, 1842, 1847, 1856, 1864, 1873, 1890;

iii: 1845, 1848, 1857, 1868, 1879; iv: 1847, 1851, 1860, 1871.

A further complexity is that the sixth edition of Vol. 1 (the last before Marx's death) exists in two versions: Marx's original and Hugo Riemann's radically reworked edition of 1887. I shall refer to both versions, since Riemann's interpretation sheds light on many of Marx's ideas. For the most commonly available English translation (based on the 4th edn.), see The School of Musical Composition, trans. August Heinrich Wehrhan, London, 1852.

3 The best study of Marx from a pedagogical viewpoint is still Kurt-Erich Eicke's Der Streit zwischen Adolph Bernhard Marx und Gottfried Wilhelm Fink um die Kompositionslehre ('Kolner Beitrage zur Musikforschung', xlii), Cologne, 1966. See also idem, 'Das Problem des Historismus im Streit zwischen Marx und Fink', Die Ausbreitung des Historisrnus iiber die Musik, ed. Walter Wiora, Regensburg, 1969, pp. 221-32. For a study which focuses on Marx's formal theory, see Lotte Thaler, Organische Form in der Musiktheorie des 19. und beginnenden 20. Jahrhunderts, Munich, 1984. Of recent studies in English, the most comprehensive is Scott Burnham, Aesthetics, Theory and History in the Works of Adolph Bernhard Marx (unpublished dissertation), Brandeis University, 1988. See also idem, 'The Role of Sonata Form in A. B. Marx's Theory of Form', Journal of Music Theory, xxxiii (1989), 247-71; and 'Criticism, Faith and the Idee: A. B. Marx's Early Reception of Beethoven', 19th Century Music, xiii (1989-90), 183-92.

4 See Gottfried Wilhelm Fink, 'Der neumusikalische Lehrjammer oder Beleuchtung der Schrift: Die alte Musiklehre im Streit mir unserer Zeit', Leipzig 1842, p. 2: 'Zusammenmischung alles dessen, was sonst eben so gut und noch besser, aber, wie es sich gebuhrt, in einzelnen Disziplinen gelehrt worden war'.

5 Matthaus Zeheter & Max Winkler, Vollstandige theoretisch-praktisch Generalbass und Harmonielehre fur junge Musiker, ii (Wurdlingen, 1847).

6 Ibid., pp. ii-iii: 'Auch dieser zweite Theil bringt nichts Neues, nicht Ansichten und Grundsatze, die noch nie gehort und gewurdigt worden waren. Vielmelar sind die Verfasser bezuglich des Materiellen strenge dem Gange der alteren und besseren Lehrbficher dieser Art gefolgt . . . Im Bezuge auf das Formelle glaubten jedoch die Verfasser besser zu thun, wenn sie die Kunstmittel in einer andera Ordnung gaben, als man sie in andera Lehrbuchern findet.' All translations are mine unless otherwise indicated.

7 Ibid., p. iii: 'Und so moge denn auch dieser Theil seine Fahrt beginnen, von den Verfassern mit dem Wunsche begleitet, dass er eine eben so gute und vielseitige Aufnahme finden mfge, wie sein Vorganger'.

8 See Eugene Walter, Placeways: a Theory of the Human Environment, Chapel Hill, 1970, p. 18: 'Originally, theoria meant seeing the sights, seeing for yourself, and getting a world-view. The first theorists were "tourists" - the wise men who traveled to inspect the obvious world. Solon, the Greek sage whose political reforms around 590 B.C. renewed the city of Athens, is the first "theorist" in Western history.'

9 Music in the National Curriculum (England), London: Department of Education and Science, 1992. The curriculum directs teaching according to two Attainment Targets: AT1 ('Performing and Composing') and AT2 ('Listening and Appraising'). The latter fosters students' ability to listen to and appraise music, including knowledge of music history and their own diverse musical heritage, as well as a variety of other musical traditions.

10 Keith Swanwick, Music Education and the National Curriculum, London, 1992, p. 13. The book crisply describes the problems of reconciling an educational theory with political exigencies. In particular, Swanwick voices his disquiet about the false symmetry of the two Attainment Targets, which were imposed upon an originally ternary model of 'Performing-Composing-Appraising'. Moreover, AT2 had initially been drafted as 'Knowledge and Understanding', reflecting an undue slant towards a factual, historical approach. This was reformulated as 'Listening and Appraising' following a fax sent by Swanwick to the then Secretary of State for Education, Kenneth Clarke (Swanwick's booklet ends with a dramatic account of this intervention; see pp. 25-31).

11 Keith Swanwick, Musical Knowledge: Intuition, Analysis, and Music Education, London, 1994. See also idem, Music, Mind, and Education, London, 1988.

12 Marx, The School of Musical Composition, p. xvi.

13 Ibid., p. 9.

14 Nicholas Cook, Analysis through Composition, Oxford, 1996. Cook's course (designed mainly for first-year undergraduates) attempts to mediate the teaching of Schenkerian concepts such as prolongation, diminution and voiceleading via the practice of composition and arrangement in the Classical style. For my review, see Music & Letters, lxxviii (1997), 599-600.

15 Swanwick, Music, Mind, and Education, p. 85.

16 See Colin Griffin, Curriculum Theory in Adult and Lifelong Education, London, 1983, p. 41: 'Generations of teachers in training have failed to see the point or the relevance of much of the theoretical element in their courses: its concerns have seemed to them far too removed from the problems of classroom practice'.

17 Basil Bernstein, 'On the Classification and Framing of Knowledge', Knowledge and Control: New Directions for the Sociology of Education, ed. Michael Young, London, 1971, pp. 47-69.

18 Ibid., p. 47.

19 Bernstein understands 'integration' not in the trivial sense of overlap between subjects but as 'the subordination of previously insulated subjects or courses to some relational idea, which blurs the boundaries between the subjects' (ibid., p. 53).

20 Framing also varies according to educational maturity. Thus framing is normally tight in the early years, but 'with increases in the educational life, there is a progressive weakening of the frame for both teacher and taught. Only the few who have shown the signs of successful socialization have access to these relaxed frames' (ibid., p. 57).

21 See Charles Plummeridge, Music Education in Theory and Practice, London, 1991; Swanwick, Music, Mind, and Education, esp. pp. 120-38.

22 Historically, 'encounter' is also characteristic of a breakdown of the old certainties about curriculum content; that is, the scope of the canon, even the nature of the musical object. See Swanwick, Music, Mind, and Education, pp. 127-34.

23 For the close links between the inception of Marx's formal theories and Beethoven reception, see Scott Burnham, Beethoven Hero, Princeton, 1995. See also my review-article 'Convergences: Criticism, Analysis and Beethoven Reception', Music Analysis, xvi (1997), pp. 369-91.

24 See, for example, Johann Logier, System der Musik-Wissenschaft und der praktischen Composition, Berlin, 1827. Logier's treatise is interesting for its hybrid or transitional nature. On the one hand, its chapter plan follows the conservative, eighteenth-century progression, starting with the basics of harmony and counterpoint (fundamental basses, modulation, suspensions and passing notes, secondary and chromatic harmony) and considering rhythm, metre and phrase structure only in its final chapters. On the other hand, Logier's deliberate simplification of theoretical categories, for example in repeated use of a C major scale as a vehicle for explaining tonality, profoundly influenced Marx's method.

25 Bernstein, 'On the Classification and Framing of Knowledge', p. 59.

26 See Georg Sowa, Anfange institutioneller Musikerziehung in Deutschland (1800-1843), Regensburg, 1973, p. 55.

27 See Rosamund Shuter-Dyson & Clive Gabriel, The Psychology of Musical Ability, London, 1981. The authors explore processes of 'naturalization' and 'enculturation' in chapters devoted to, respectively, 'The Development of Musical Ability' (pp. 97-170) and 'The Determinants of Musical Ability' (pp. 171-237). The former focuses on the universal and cross-cultural aspects of children's aptitude, from birth to adolescence. The latter is directed more towards differences: the effects of home and social environment; the impact of specific practice and music lessons. This division does not fit strictly with a 'nature/culture' or 'innate/learnt' distinction. For example, the authors include within their 'determinants of musical ability' the influence of genetic inheritance. For an alternative scheme, see John Sloboda, The Musical Mind: the Cognitive Psychology of Music, Oxford, 1990, pp. 194-238. Sloboda divides his chapter 'Musical Learning and Development' into two sections. The first section, on 'enculturation', deals with commonalities: 'a shared set of primitive capacities which are present at birth . . . a shared set of experiences which the culture provides . . . roughly similar ages at which the various achievements occur' (pp. 195-6). The second section, on 'training', concentrates 'on specific experiences which are not shared by all members of a culture' (p. 196). Increasing accomplishment follows on from particular types of instruction (loc. cit.).

28 Even Marx's best critics have found it difficult to reconcile the idealist and empirical strands of his thought. Eicke regards Marx's Hegelianism as a scaffolding for his pedagogical method. He points out that, with his interest in the scientific foundations of teaching, Marx distances himself from Hegel's notion of music as an art of 'subjektiven Innerlichkeit' ('Das Problem des Historismus', p. 227). But the empirical/idealist distinction is difficult to sustain. Eicke, confusingly, also correlates the dispute between the old theory (epitomized by the reactionary Fink) and the new (Marx) with a turn from Kantian Naturwissenschaft to Hegelian Geisteswissenschaft - with a shift from static to dynamic models of thought. Taken as a teacher, Marx is 'sinnliche' (empirical); as a theorist, he is 'geistig' (idealist).

As we shall see, one way out of this crude empirical/idealist distinction is the tertium quid of the so-called Neo-Kantian philosophers. Figures such as Herbart and Beneke, whom Marx studied, developed Kant's theory of psychologically-grounded categories of thought into a developmental model capable of showing how categories change in response to experience. Lotte Thaler also views Marx dualistically, but she fills the empirical slot of the formula with Goethe, rather than Pestalozzi. Marx, according to Thaler, filters Goethe's organic model of the metamorphosis of plants through Hegel's 'Stufengang der Befreiung'; that is, the progression of 'artistic reason' towards intellectual freedom (Organische Form in der Musiktheorie, p. 75). Nevertheless, Hegel fits Thaler's model much better than Goethe. In Marxian terms, the summit of artistic reason, when the composer is free to range over the entire gamut of artistic possibilities, is reached at the end of the Formenlehre with the fantasia. But Goethe's metamorphosis, as Thaler herself concedes, has no comparable end-point. Thus her Goethean interpretation is ultimately just figurative window-dressing for a narrowly idealistic conception of Marx's Lehre, and one with severe problems. For example, it ascribes to the succession of musical forms a teleology or inevitability which it clearly does not have.

29 See, for example, Keith Swanwick & June Tillman's spiral model of musical development presented in 'The Sequence of Musical Development', British Journal of Music Education, iii (1986), 305-39. This model is based on a survey of 745 compositions from 48 children between the ages of three and eleven.

30 See Thomas S. Kuhn, The Structure of Scientific Revolutions, Chicago, 1962. For a penetrating discussion of 'presentist' versus 'historicist' viewpoints, including a helpful survey of the secondary literature, see Thomas Christensen, 'Music Theory and its Histories', Music Theory and the Exploration of the Past, ed. Christopher Hatch & David W. Bernstein, Chicago, 1993, pp. 9-39.

31 Marx, Die Lehre, i (2nd edn., 1841), p. vi: 'Konnten auch die Lehrsatze, die dem Ganzen zum Grunde liegende Kunstanschauung und das Wesentliche der Methode keine Aenderung erleben, ich vielmehr durch fortgesetzte Prufung, vielfaltigere Erfahrung und die Beistimmung so vieler Sachkundigen nur noch fester von ihrer Wahrheit uberzeugt werden: so liess es mich doch nicht ruhen; ich war gedrungen, meinem Lehrideal immer energischer zuzustreben'.

32 Marx, The School of Musical Composition, p. 14.

33 Marx, Die Lehre, i (6th edn., 1863), p. vii: 'Freudig habe ich das halbe Buch umgestaltet, um keine neue Anschauung und Erfahrung unbenutzt zu lassen'.

34 Marx, The School of Musical Composition, p. 1.

35 See A. B. Marx, Die alte Musiklehre im Streit mit unserer Zeit, Leipzig, 1841, p. 29: 'Hier konnten sie nun begreifen, - was der Psychologe schon vor voraussetzen wird, - dass die lustvolle Gabe eignen Gesanges in den meisten Menschen angelegt ist, in den meisten wohlorganisirten Kindern schon in frischer Blutte sich entfaltet'.

36 Ibid., p. 31: 'Und zwar ist . . . die Form der Melodie die erste aller musikalischen Gestalten, die sich der Mensch aneignet; viel spater erst gelangt er zur Auffassung und noch spater zum eignen Versuch der Harmonie'.

37 See A. B. Marx, Universal-Lexicon der Tonkunst, Leipzig, 1835-8, trans. A. H. Wehrhan as The Universal School of Music, London, 1853, p. 322. The Lexicon is not a course so much as a reference work.

38 Expressed as 'das Konnen' or 'die That': Marx, Die Lehre, i (2nd edn., 1841), 9.

39 See A. B. Marx, Die Musik des neunzehnten Fahrhunderts und ihre Pflege: Methode der Musik (1855), trans. C. Macfarren as The Music of the Nineteenth Century and its Culture: System of Musical Education, London, 1855, p. 184.

40 Marx, Die alte Musiklehre, pp. 96-101.

41 Marx, The School of Musical Composition, p. 6.

42 Marx, The Universal School of Music, p. 344.

43 Cited in Marx, Die alte Musiklehre, p. 55: 'Gehe vom Anschaulichen aus und schreite von da zum Begrifflichen fort, vom Einzelnen zum Allgemeinen, vom Konkreten zum Abstrakten, nicht umgekehrt. Dieser Grundsatz gilt auf dem ganzen Gebiete des Unterrichts, wie der Erziehung.'

44 Marx, Die Lehre, i (1st edn., 1837), 24: 'Ein in sich genugendes, bestimmt abgeschlossenes einfaches Tongebilde, das also nicht Periode ist, nicht aus Vorder- und Nachsatz besteht, nennen wir Satz'.

45 Loc. cit.: 'Ein Tongebilde, das eines solchen Anschlusses entbehrt nennen wir Gang'.

46 Ibid., pp. 28-33.

47 Marx, Die Lehre, i (6th edn., 1863), 35-41.

48 Ibid., p. 41: 'dem Triebe des Motivs, sich in das Unbestimmte hin fortzusetzen, tritt die bestimmende Form entgegen'.

49 Compare Marx, Die Lehre, i (lst edn., 1837), 28-9, and i (6th edn., 1863), 35-41. By contrast, the length of the analogous section on Satzbildung remains stable at four pages across the six editions: i (lst edn, 1837), 29-33; i (6th edn., 1863), 41-5.

50 Marx, Die Lehre, i (6th edn., 1863), 41: 'Ein Goldstuck, das ich finde, hat nur eben seinem Geldwerth fur mich; eine Geschicklichkeit, die ich mir erworben, kann fortwahrend Frucht bringen'.

51 Marx, Die Lehre, i (9th edn., 1887, ed. Hugo Riemann), 44: 'Wir konnen daraus die Lehre ziehen, dass der gestaltende Wille, den - gleichviel ob vollbewusst oder halb instinktiv - hohere Gesichtspunkte leiten, die strenge Form des Ganges beliebig durchbrechen kann; der Gang wird gleichwohl seine Bedeutung als nachstliegendes Mittel der Fortfuhrung behalten'.

52 Ibid., p. 39: 'Der Gang ist deshalb keine geschlossene Form, sondern nur ein Formen, Bilden, eine vorbereitende Thatigkeit, die erst dutch anderweite Bestimmungen zu wirklicher Form fuhren kann'.

53 See Leonard B. Meyer, Explaining Music, Chicago, 1973, pp. 115-30.

54 Marx, Die Lehre, i (lst edn., 1837), 21: 'Unser Gefuhl drangt uns, zu unterscheiden, zu ordnen'.

55 See Gary Hatfield, The Natural and the Normative: Theories of Spatial Perception from Kant to Helmholtz, London, 1990, pp. 117-28.

56 As in Helmholtz's initial work on optics, and the influence of the Gestalt school on the work of Meyer, as well as on Lerdahl and Jackendoff. Even today, connectionist or neural-net models of music perception adapt techniques originally developed for vision.

57 For Kant's interpretation of 'Anschauung' as 'intuition', especially in relation to the geometry of space, see Immanuel Kant's Critique of Pure Reason, trans. Norman Kemp Smith, London, 1986, p. 578: 'The shape of a cone we can form for ourselves in intuition, unassisted by any experience'. This differs fundamentally from Pestalozzi's belief that the principles of perception are learnt. For Kant's theory of the categorical nature of spatial intuition, see ibid., pp. 65-74, esp. p. 68: 'Space is a necessary a priori representation, which underlies all outer intuitions . . . It must therefore be regarded as the condition of the possibility of appearances, and not as a determination dependent upon them'; and pp. 68-9: 'The apodeictic certainty of all geometrical propositions, and the possibility of their a priori construction, is grounded in this a priori necessity of space. Were this representation of space a concept acquired a posteriori, and derived from outer experience in general, [it would] share in the contingent character of perception . . . what is derived from experience has only comparative universality.'

58 Pestalozzi, How Gertrude Teaches her Children, p. 201. For a good overview, see Kate Silber, Pestalozzi: the Man and his Work, London, 1976. According to Silber, the term 'Anschauung"may mean sense-impression, observation, contemplation, perception, apperception, or intuition' (p. 138). Silber traces Pestalozzi's theory of perception to Leibnitz.

59 Johann Pestalozzi, The Method, a Report by Pestalozzi, included in How Gertrude Teaches her Children, pp. 199-211. In his A B C der Anschauung, Zurich, 1803, Pestalozzi includes a more complex chart illustrating the interaction of horizontal, vertical and diagonal lines (p. 84).

60 Pestalozzi, How Gertrude Teaches her Children, p. 123. Pestalozzi includes a report on his method by a friend, who vividly describes his personal experience of learning the 'A B B': 'Now everything that I saw suddenly stood between lines that defined its outline. In my representations I had never separated the outlines from the object. Now, in my imagination, they freed themselves from it, and fell into measurable forms, from which every deviation was sharply distinct for me. But as at first I saw only objects, now I saw only lines' (p. 68).

61 Ibid., p. 147.

62 Hans Georg Nageli, Vorlesungen uber Musik, Stuttgart, 1826.

63 Ibid. p. 42: 'So wie die Dreyzahl durch die rhythmischen Bewegungen der einzelnen Tonreihen sich hindurch spielt, so bildet die Vierzahl diese Tonreihen zu rhythmischen Gliedern aus, und gestaltet so eine Eurythmie der Theile'.

64 Marx, Die Lehre, i (lst edn, 1837), 19.

65 Marx, Die Lehre, i (6th edn., 1863), 41: '[Der Grand zu einem Abschlusse] muss von aussen kommen . . . Dem Triebe des Motivs, sich in das Unbestimmte hin fortzusetzen, tritt die bestimmende Form entgegen.'

66 Marx, Die Lehre, i (lst edn., 1837), 33.

67 Marx, Die alte Musiklehre, p. 57.

68 Nageli, Vorlesungen uber Musik, p. 38: 'Worin besteht nun hier unsere einfachste Wahrnehmung, was nehmen wir am Tithe wahr? - Bewegung - was an einer Reihe von Tonen? - mehrfache Bewegung - was weiter an geregelten Tonreihen? - deren Verbindung zu einem Kunstwerke durch vervielfachte Bewegung. Bewegung ist also das Grundelement der Tonkunst.'

69 Loc. cit.

70 See James F. Brennan, History and Systems of Psychology, Englewood Cliffs, NJ, & London, 1994, pp. 129-30.

71 Marx, Die alte Musiklehre, p. 43: 'Jede innere Erregung (des Vorstellens, Begehrens, Fuhlens u.s.w.) pflanzt sich vermoge dessen (des Bestrebens aller psychologischen Gebilde, in jedem Augenblick unsers Lebens die in ihnen beweglich gegebnen Elemente gegeneinander auszugleichen bis zu volliger Gleichgestimmtheit, - s. dessen Psychologie, S. 36) theils im Innern weiter fort (indem sie andre Vorstellungen, Begehrungen, Gefuhle u.s.w. weckt), theils nach Aussen hin: wo dann gewisse aussere Veranderungen (in Mienen, Geberden und andern Gliederbewegungen, Tonen u.s.w.) hervortreten.'

72 Loc. cit.: 'So erhebt sich bei erhebenden Vorstellungen der Blick, die Gestalt richter sich auf, die Arme breiten sich nach oben; zugleich erhebt, fullt und kraftigt sich aber auch der Sprachton, und zugleich erhebt sich die Melodie; wahrend bei niederschlagenden Vorstellungen das Auge und die Geberde und mit ihnen die Stimme des Redenden und die Richtung der Melodie sinkt'.

73 Marx, The Music of the Nineteenth Century, p. 21.

74 Marx, Die alte Musiklehre, p. 43: 'Wiederum beruht der Eindruck der Musik zum Theil auf den gleichartigen Wirkungen und Vorstellungen, die ein und dieselbe Stimmung auf die verschiednen Organe des Korpers und in die verschiednen Richtungen geistiger Thatigkeit ubertragt'.

75 Marx, The Music of the Nineteenth Century, p. 20.

76 Loc. cit.

77 See Patrick Shove & Bruno Repp, 'Musical Motion and Performance: Theoretical and Empirical Perspectives', The Practice of Performance: Studies in Musical Interpretation, ed. John Rink, Cambridge, 1995, pp. 55-83.

78 Marx, Die Lehre, i (lst edn., 1837), 18: 'Wir bemerken, dass steigende Tonfolgen uns das Gefuhl der Steigerung, Erhebung, Spannung erwecken, fallende das entgegengesetzte der Abspannung, Herabstimmung, der Ruckkehr in Ruhe, schweifende aber keine von beiden Emphindungen festhalten, sondern unentschieden an beiden Theil haben, zwischen beiden schweben'.

79 Marx, Die Lehre, i (9th edn., 1887, ed. Riemann), p. 22.

80 Marx, Die Lehre, i (2nd edn., 1841), 23: 'Hierin haben wir einen durch die ganze Tonkunst wirksam hindurchgehenden Gegensatz, - Ruhe und Bewegung'.

81 In his Der Streit zwischen Adolph Bernhard Marx und Gottfried Wilhelm Fink, Eicke distinguishes two types of musical unit in this course: the 'Baustein' (static) and the 'Keimzelle' (dynamic) (p. 66). According to Eicke, composition for Nageli and Pfeiffer entails the combination of a single note, their 'Baustein', in rhythmic, melodic and dynamic configurations. He terms this system 'abstract-synthetic' (loc. cit.).

82 Nageli & Pfeiffer, Gesangbildungslehre, p. 226: 'Das Lehren und Lernen an den Kunstwerken selbst ist nicht Bethatigung der Kunstanschauung in ihrer Einheit, sondern ein storendes Spalten der Natur in die Funktionen des Wissens und Konnens'.

83 For a discussion of Natorp's song treatises, see Max Schipke, Der Deutsche Schulgesang, von Adam Hiller bis ZU den Fallkschen Allgemeinen Bextimmungen, 1775-1875. Ein Beitrag zur Geschichte der Gesangpadagogik, Berlin, 1913, pp. 136-7.

84 Schipke cites two main reviews (ibid., p. 108): according to a contemporary critic in the AmZ, 'This work is useless for teaching purposes' (AmZ, 1811, p. 28); a second review by Friedrich Dittes (1874) is equally hostile: 'Kann man noch von einer "Naturgemassheit des Verfahrens" reden, wenn Nageli so starr an dem Getrennthalten der Elemente und dem synthetischen Gange festhalt, dass das Kind erst am Ende vines mehrhahrigen Elementarkursus zum Liede kommt, wahrend die Natur den Sinnen nichts als Erscheinungskomplexe darbietet?'

85 Nageli, Vorlesungen, pp. 243-4. See also his Umriss der Erziehungsaufgabe, Zurich, 1832, p. 15.

86 Spohr's account is quoted in Richard Hunter, A Short Account of the Progress of J. B. Logier's System of Musical Education in Berlin and its Subsequent Introduction by Order of the Prussian Government into the Public Seminaries for its General Promulgation through the Prussian States, London, 1824, pp. 37-40. See 'Musikalische Notizen gesammelt von Louis Spohr wahrend seines Aufenthalts in London vom Ende Februars bis ende Juny 1820', in AmZ (1820), 521-30, esp. p. 527.

87 Marx, The School of Musical Composition, p. xv.

88 See Adolph Diesterweg, Wegweiser zur Bildung fur deutliche Lehrer, 4th edn., Essen, 1850. Diesterweg (1790-1866) was Pestalozzi's first major exponent in Germany. Though working initially in Frankfurt, he opened a seminary in Berlin in 1832.

89 Ibid., pp. 559-671 (see also Marx's late work, the Vollstandig Chorschule, Leipzig, 1860).

90 Ibid., p. 654: 'Warum die Kompositionslehre jetzt erst eintritt? Aus demselben Grunde, wesshalb man beim Sprachunterricht das Gebaude der Grammatik und Stylistik erst auf tuchtiger, praktischer Grundlage errichtet.'

91 Marx, The School of Musical Composition, p. 4.

92 Ibid., p.5

93 In this respect, Dahlhaus's complaint that Marx's theory is too piano-orientated is correct, but for the wrong reasons. See his 'Formenlehre und Gattungstheorie bei A. B. Marx', Heinrich Sievers zum 70. Geburtstag, ed. Richard Jakoby & Gunter Katzenberger, Tutzing, 1978, pp. 29-35, esp. p. 34: 'Marx's historical-philosophical model is founded on a concept of form which is in turn abstract and architectonic. Its abstraction reveals itself in the semblance that piano music is the same as "music pure and simple" [Musik schlechthin]. And the architectonic concept of form impels Marx to exclude vocal forms from the "authentic" Formenlehre, since choral fugues and motets cannot be meaningfully comprehended according to the concepts of periods.' Dahlhaus detects the 'outline of a second Formenlehr' beneath the surface of Marx's method, one predicated on vocal forms (ibid., p. 35). The latter conceives of form not as a static 'disposition of parts', but as a process whereby an Idee becomes manifest. Again, Dahlhaus is right for the wrong reason: the subcutaneous 'outline' is vocal because it is 'evolutiv'; that is, it is indebted to the organization of singing-courses.

94 See Howard Gardner, Developmental Psychology, Boston, 1982, pp. 408-18.

95 Swanwick, Music, Mind, and Education, pp. 48-9.

96 Ibid, p. 52.

97 Lyle Davidson, 'Songsinging by Young and Old: a Developmental Approach to Music', Musical Perceptions, ed. Rita Aiello, Oxford, 1994, pp. 99-130.

98 Swanwick, Music, Mind, and Education, pp. 45-6.

99 See ibid., pp. 48-9.

100 Marx, Universal-Lexicon, pp. 330-37. Marx warns that composition, attempted too early, becomes 'a mere childish play', a 'cold and unfruitful mechanism'. 'This is the greatest fault of a system of instruction according to which pianoforte-playing and composition are taught simultaneously, and which, with various modifications, is practised by a considerable number of teachers' (ibid., p. 337).

101 See David Jones, Adult Education and Cultural Development, London, 1988. The concept of 'Andragogy' as a discipline distinct from 'Pedagogy' was developed in the work of Malcolm S. Knowles. According to Jones, 'Knowles appears to define adulthood, not so much in terms of chronological age, but in terms of individuals accepting responsibility for the direction of their own lives. He sees the role of the adult educator as dependent upon an acceptance that adults are self-directed' (pp. 156-7).

102 Howard Gardner, Creating Minds: an Anatomy of Creativity, New York, 1993, p. 30.

103 Ibid., p. 94.

104 Sowa, Anfange institutioneller Musikerziehung in Deutschland (1800-1843).

105 Ibid., p. 38: 'Meine kleinen vier- und sechsjahrigen Knaben singen und pfeifen, was ihnen einfallt. Freylisch zunachst immer nur bekannte Melodien, aber mit so vielen Zusatzen, Abanderungen, Verzierungen und Versetzungen, dass man oft das Original nur mir Muhe erkennt'. See Karl Gottlob Horstig, 'Lasst den Musikus doch selbst spreehen!', AmZ (1801), 645-8, esp. p. 648.106 Ibid., p. 74.

107 See n. 37, above.

108 Pestalozzi, How Gertrude Teaches her Children, p. 204.

109 Sowa, Anfange institutioneller Musikerziehung, p. 34.

110 See Glenn Stanley, 'Bach's Erbe: the Chorale in the German Oratorio of the Early Nineteenth Century', 19th Century Music, xi (1987-8), 121-49, at pp. 126-32.

111 Nageli, Vorlesungen, p. 236: 'Es gibt eigentlich, praktisch genommen und praktisch gesprochen, nut zwey Real-Wissenschaften; alle andere sind Hulfswissenschaften. Die zwey Real-Wissenschaften sind: Padagogik und Politik'.

112 Siegfried Wilhelm Dehn, Theoretisch-praktische Harmonielehre, Berlin, 1840.

113 Marx, Die alte Musiklehre, p. 70.

114 Ibid., p. 69.

115 Ibid., pp. 68-9.

116 Ibid., p. 83.

117 See Johann Friedrich Herbart, Allgemeine Padagogik, Gottingen, 1806, trans. Henry & Emmie Felkin as The Science of Education: its General Principles Deduced from its Aim, London, 1897. The best recent book on Herbart's pedagogy in English is Harold B. Dunkel, Herbart and Herbartianism: an Educational Ghost Story, Chicago, 1970. See also Catherine Isabel Dodd, Introduction to the Herbartian Principles of Teaching, London, 1898; Henry M. Felkin, An Introduction to Herbart's Science and Practice of Education, London, 1901; Frank Herbert Hayward, The Critics of Herbartianism, London, 1903. For literature in German, see especially Adolf Rude et al., Herbart und die Herbartianer, Langensalza, 1910; Johann N. Schmidt, Herbart-Bibliographie 1842-1963, Weinheim, 1964.

118 Marx, Die alle Musiklehre, p. 10.

119 Loc. cit.: 'So ist doch der Zusammenhang dieser Anfange mit dem gewordenen Kunstwerk einen hohern Grad von Kunstbildung voraussetzt'.

120 Ibid., p. 11.

121 Ibid., pp. 11-12.

122 See Music and Aesthetics in the Eighteenth and Early-Nineteenth Centuries, ed. Peter le Huray & James Day (abridged edn.), Cambridge, 1988, pp. 306-8. The editors cite two works by Herbart dealing specifically with music, his Psychologische Betrachtungen uber die Lehre des Tons (1811) and Psychologische Untersuchungen (1839): 'Herbart felt that since harmonic relationships were based on mathematical principles, music's effect on us might be definable in terms of the way those principles operate' (p. 452).

123 Hatfield, The Natural and the Normative, p. 6.

124 Included in Herbart's The Science of Education, pp. 57-77. Herbart's chief debt to Pestalozzi is revealed in his Standpunkt der Beurtheilung der Pestalozzischen Unterrichtsmethode, Gottingen, 1804. Herbart met Pestalozzi while working as a tutor at Interlaken in Switzerland from 1797 to 1800. In 1809, he founded a pedagogic seminary at Konigsberg, designed to train teachers in the Pestalozzian method. Herbart's reforms aroused the liveliest interest in Prussia, and received the warm support of the Prussian Minister of Education, Wilhelm von Humboldt.

125 Ibid., p. 54. Compare with Immanuel Kant, The Critique of Judgement, trans. James Greed Meredith, Oxford, 1989, p. 159: 'We have a faculty of judgement which is merely aesthetic - a faculty of judging of forms without the aid of concepts, and of finding, in the mere estimate of them, a delight that we at the same time make into a rule for everyone, without this judgement being founded on an interest, or yet producing one. On the other hand we have also a faculty of intellectual judgement for the mere forms of practical maxims... a faculty of determining an a priori delight, which we make into a law for everyone, without our judgement being founded on any interest, though here it produces one. The pleasure or displeasure in the former judgement is called that of taste; the latter is called that of the moral feeling' (from Chap. 42: 'The Intellectual Interest in the Beautiful').

126 Herbart, The Science of Education, p. 65. In a footnote, Herbart adds that 'we can transfer to the relationships of will an approval or disapproval like those existing for the relationships of notes' (loc. cit.).

127 Marx, The Music of the Nineteenth Century, p. 186.

128 Ibid., p. 188.

129 Loc. cit.

130 The following discussion will refer to Marx's first edition.

131 See David W. Green, Cognitive Science: an Introduction, Oxford, 1996, p. 295: 'The most obvious distinction is probably between data-driven and conceptually-driven operations. Data-driven processes involve bottom-up analysis of perceptual features. Thus, for example, deciding how many vowels there are in the word WHITE is a data-driven process, and reading versus hearing a word will require different data-driven operations. In contrast, conceptually-driven processes are much more top-down and involve the extraction of meaning. Knowing that white is the opposite of black would be an example.'

132 Marx, Die Lehre, i (4th edn, 1852), 28.

133 Herbart, The Science of Education, p. 126.

134 Ibid., p. 103.

135 Ibid., p. 109.

136 For a colourful account of Hiller and Rein's activities, see Dunkel, Herbart and Herbartianism, pp. 209-39.

137 Dunkel describes Herbart's 'Steps' ibid., pp. 165-71.

138 See Dodd, Introduction to the Herbartian Principles of Teaching, p. 127.

139 Herbart, The Science of Education, p. 131.

140 See Felkin, An Introduction to Herbart's Science and Practice of Education, p. 117.

141 Marx, The School of Musical Composition, p. 12.

142 Marx, Die Lehre, i (1st edn., 1837), 17: 'Wir beginnen mir dem Einfachsten, namlich mir einer einzigen Tonreihe . . . [Die Tone der Tonfolge] konnen einander so folgen, dass wir von tiefern Tonen zu hohern, oder von hohern zu tiefern, oder auch hin und her gehen'.

143 Ibid., pp. 18-20.

144 Ibid., pp. 21-3.

145 Marx, The School of Musical Composition, p. 12.

146 Marx, Die Lehre, i (1st edn., 1837), 23.

147 Ibid., p. 24.

148 Marx, Die Lehre, i (2nd edn., 1841), 28.

149 Marx, The School of Musical Composition, p. 12.

150 Marx, Die Lehre, i (1st edn., 1837), 24-5.

151 Ibid., p. 25: 'Nach diesen vorausgegangenen Betrachtungen hebt nun die eigne, allmahlig freier werdende Thatigkeit des Jungers an'.

152 Marx, The School of Musical Composition, pp. 4-6.

153 Ibid., p. 4.

154 Ibid., p. 10.

155 Loc. cit.

156 Marx, Die Lehre, i (6th edn., 1863), 32. There are some subtle changes from the first edition (p. 26), indicated in parentheses. Italicized text indicates interpolation. 'Wir uns in kleinen [engen] Schritten von einem Gebilde zum andera bewegen [werden]. Aber jenes [dies] ist [eben] das Beruf [Geschaft] des Meisters, der alle [unsere] Entwicklungen schon in seinem Innern durchgearbeitet und sich zu eigen gemacht [hat], [der] also nicht mehr nothig hat, die ganze Kette [Kette der Gebilde] nochmals zu durchlaufen. Gleichwohl bewegen wir uns mit ihm in der That auf demselben Pfade; wir haben denselben Weg schon jetzt betreten, sind nut viel weiter zuruck; seine Ziele [seine Ideen] sind nur entlegenere, ihm allein (oder Wenigern) gesetzte [angehorige], wahrend unsere die allgemeinsten sind. Daher eben konnen und mussen wir uns noch von jedem Schritt Rechenschaft geben und stets genau an das Vorhandene anschliessen, wahrend der Kunstler leicht [und weit] uber die ihm schon bekannten Punkte zu seinem Ziele hinwegschreitet [fortschreitet] und sich der Anknupfungen und des stillschweigend Uebergangenen kaum [nicht einmal durchaus] bewusst ist.'

157 See Burnham, Beethoven Hero.

158 See A. B. Marx, Ludwig van Beethoven: Leben und Schaffen, 2nd edn., Berlin, 1863, p. 276.

159 Ibid., pp. 276-7: 'Diese absolute Nothwendigkeit, diese durch alles Einzelne gehende Bedeutsamkeit in keinem Kunstwerke vorhanden ist, weil sie sogar dem Grundkarakter der Kunst, jener Spielseligkeit zuwider sein wurde, der Beethoven vor Vielen sich gern uberlasst, wie er denn durch alle hohen Stunden und bittern Leiden hindurch stets der kindliche, nur gar zu gem frohe Mensch geblieben ist'. Marx's notion of 'play' is also indebted to Schiller's theory of the 'play-drive', the aesthetic condition through which the 'sense-drive' is reconciled with the 'formal-drive'. See Friedrich Schiller, On the Aesthetic Education of Man, ed. Elizabeth Wilkinson, Oxford, 1967, esp. p. 77.

160 'Spielseligkeit' also forms the first stage in Marx's triadic model of music history, which is conceived as a process of increasing maturation and individuation (Marx, The Music of the Nineteenth Century, pp. 36-44). Here, Marx characterizes the entire contrapuntal tradition before Bach as 'a mere play with material objects . . . without regard to their deeper spiritual contents and meaning' (ibid., p. 36). He views the second stage, that of Bach, Haydn and Mozart, as a 'revelation of inner life' (ibid., p. 39). Beethoven's music, with its 'truthful delineation of character' (ibid., p. 44) fulfils this process. Strikingly, Marx unfolds this model using a metaphor of a child's cognitive development borrowed from Nageli: 'The suckling babe at first distinguishes only light from darkness; he then observes the forms that move around him . . . So the first dawn of mental consciousness only conveys to us an indefinite impression of the general condition of our inner life: we, then, gradually become aware of the different kinds and degrees of emotion that fill our heart with joy and pain' (loc. cit.). Marx's Beethoven monograph makes clear the extent to which 'Spielseligkeit', albeit a foundational stage of music history, is recuperated in the third stage in its 'heroic' form.

161 The journalist Friedrich Wahner, for instance, 'spoke of Beethoven's "childlike naivete" and likened him to "an amiable boy"': see Maynard Solomon, Beethoven, London, 1978, p. 258.

162 Bernstein, 'On the Classification and Framing of Knowledge', p. 60.

163 Loc. cit.

164 Burnham, Beethoven Hero, p. 70.

165 Bernstein, 'On the Classification and Framing of Knowledge', loc. cit.: 'With integrated codes, the pedagogy is likely to proceed from the deep structure to the surface structure'.

166 See especially Burnham, 'Criticism, Faith and the Idee'.

167 See my 'Creativity, Life and Music: Three Books about Beethoven', Music Analysis, xv (1996), 343-66, at pp. 354-7. I borrow the term 'regulatory images' from the work of the creativity theorist Howard Gruber on Darwin's sketches. See his Darwin on Man: a Psychological Study of Scientific Creativity, London, 1974.

168 Bernstein, 'On the Classification and Framing of Knowledge', p. 67.

169 For an accessible introduction to these issues from an ethnomusicological viewpoint, see Jonathan P. J. Stock, 'Concepts of World Music and their Integration within Western Secondary Music Education', Teaching Music, ed. Gary Spruce, London, 1996, pp. 152-67.

170 See Cad Dahlhaus, 'Die Musiktheorie im 18. und 19. Jahrhundert. Erster Teil: Grundzuge einer Systematik', Geschichte der Musiktheorie, x, ed. Frieder Zaminer, Darmstadt, 1984. Dahlhaus seems to associate 'psychology' purely with the Gestalt school, and states that the latter has little to do with the tradition of thematic development: 'The art of motivic working, of thematic contrast and of developing variation, which Brahms took over from Beethoven and Schoenberg from Brahms, cannot be grasped in Gestalt terms' (ibid., p. 93).

171 See Eric Clarke, 'Mind the Gap: Formal Structures and Psychological Processes in Music', Contemporary Music Review, iii (1989), 1-13, at p. 11.

172 See Dahlhaus, 'Die Musiktheorie im 18. und 19. Jahrhundert', especially pp. 116-30. Dahlhaus reifies the theoretical and practical dimensions of pedagogy as an opposition, rather than recognizing that theory inheres in practice on a performative level. This false opposition leads Dahlhaus into conceptual paradox. For example, he complains that texts such as Charles-Simon Catel's Traite de l'harmonie (1802), which endeavoured to teach musical fundamentals by simplifying course materials, in reality manage to achieve the worst of both worlds: they are empty theoretically and irrelevant to current compositional practice. Similarly, he argues that the Lehre elides its conceptual premisses with its terminological categories, so that the theory appears to be self-grounding. As a result, the student can discover the justification for what he or she learns only at the end of the course, when the circle of Marx's thought is complete. Of course, Dahlhaus's argument founders on his narrow definition of 'theory', which he understands purely in music-theoretical terms. He ignores the possibility that pedagogical practice can embody a 'theory' of an educational type.

173 For a particularly broad survey, from ancient Greece to the present day, see Bernarr Rainbow, Music in Educational Thought & Practice, Aberystwyth, 1989. Rainbow cites Marx solely in the context of German institutional reform, that is, as the holder of the first Chair of Music at Berlin University. For surveys focusing on the German tradition, see Hermann Kretzschmar, Musikalische Zeitfragen, Leipzig, 1903; Georg Schunemann, Geschichte des Schulgesang Unterrichts, Berlin, 1913; Gerhard Braun, Die Schulmusikerziehung in Preussen von den Falkschen Bestimmungen bis zur Kestenberg-Reform, Kassel, 1957; Sigrid Abel-Struth, 'Materialien zur Entwicklung der Musikpadagogik als Wissenschaft', Musikpadagogik, Forschung und Lehre, i, ed. Sigrid Abel-Struth, Mainz, 1970; Helmuth Hopf, Walter Heise & Siegmund Helms, Lexicon der Musikpadagogik, Regensburg, 1984.

174 Hermann Ebbinghaus, Abriss der Psychologie, Leipzig, 1908, p. 1.

175 Hermann Helmholtz, 'The Physiological Causes of Harmony in Music', in idem, Selected Writings, ed. Russell Kahl, Middletown, Connecticut, 1971, pp. 75-108.
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