Faust has been seen as the paradigmatic text of modernity almost since its conception. By 1836 Karl Gutzkow was claiming that Goethe was 'set by the gods as a boundary-stone to mark where the past ends and modernity begins', while for Matthew Arnold he was the great manifestation of the modern spirit. Innumerable critics have identified Goethe's most famous work as the beginning of this or that tradition. Whether or not one fully agrees with these characterizations, Faust is undeniably one of those rare works that capture some major turning point in our history. Composed over six decades, from 1773 to 1832, Faust comprehends far-reaching changes in philosophy, science, political and economic organization, industrialization and technology that might best be summarized as Europe's confrontation with the impact of secularization. Europe entered the eighteenth century with institutions and structures still defined in terms of a cosmos ordered by a divine principle; but increasingly the universe was felt to operate on its own and sometimes seemed entirely the product of natural processes.

Johann Wolfgang Goethe (1749-1832) was the first German writer of unquestioned European stature. And no other writer of his stature has his range and diversity. Author at the age of twenty-five of the first German international bestseller, Die Leiden des jungen Werther (The Sorrows of Young Werther), his impact on the literary scene at home and beyond Germany's borders was immense. Throughout his long productive life (he finished the second part of Faust only months before his death in 1832) he continued to surprise his contemporaries with the freshness and unexpected new departure of each work. He was a supreme lyric poet who also produced masterpieces in the genres of drama, prose fiction and verse epic. He was a serious natural scientist, an art critic and art historian as well as a painter, a chronicler of his own life and times, a theatre director and actor, a Privy Councillor and administrator. He conducted a vast international correspondence and was acquainted and had dealings with many of the prominent political players of the time. His collected works, the amount known about his life, the amount written about it and about his works are all huge. While this volume cannot begin to do justice to its subject, it aims to give the reader approaching Goethe for the first time some sense of the character of his work, some impression of his achievement, and some awareness of and orientation in the critical debates that have raged and still rage over aspects of his work and status.

For much of his adult life, Goethe had a dominant position in the Republic of Letters in Germany as well as abroad. No one who amounted to anything, whether it was Kleist or Heine, Scott or Byron, Musset or Saint-Beuve, Mazzini or Pushkin, could possibly bypass him and his work. Admirers and opponents alike would agree on one point: 'He disposes of the poetic world, like a conqueror of the real earth.' Confronted with his monumental stature and output, they took a position either in favour of Goethe or against him, sometimes even switching sides in the course of their careers. As a result, Goethe became a controversial figure both for poets and critics, for Germans as well as for Europeans. But what has been his enduring impact?

By the end of his life, Goethe felt less accepted by German than by European contemporaries, who between 1827 and 1831 not only sent him birthday gifts (medallions and books) from Paris, Moscow, and Scotland (Carlyle in 1831), but also published three reviews of his ‘Helena’ tragedy (Faust II, Act iii) in the same year (The Foreign Review, Edinburgh; Le Globe, Paris; The Moscow Messenger, 1828). Goethe was delighted, since this lively response seemed to confirm his venture to promote Weltliteratur (world literature) as a network of communication among intellectuals and peoples across national frontiers. For him Weltliteratur was neither the sum of all national literatures nor the ever increasing canon of world masterpieces, rather he conceived of it as a dynamic process of rapprochement among European nations – above all Britain, France and Germany – with the goal of breaking down the walls of national prejudices that hampered peaceful coexistence in the wake of the Napoleonic Wars.

Even aged sixteen Goethe strove for authority. He may not have achieved the sublime degree of autoritas he envisaged as a Leipzig fresher in 1765 - that of a German university professor. But among his peers he quickly acquired unparalleled poetic authority. After the publication of his first major innovative works, the Shakespearean patriotic drama Götz von Berlichingen (1773) and the Rousseauesque sentimental novel Die Leiden des jungen Werther (The Sorrows of Young Werther, 1774), Goethe was lionized. In his Pandaemonium Germanicum (c. 1775) Jakob Michael Reinhold Lenz portrayed Goethe atop the German Pantheon, surrounded by adoring critics whom he must shake off like flies. Johann Caspar Lavater's Physiognomische Fragmente (Physiognomical fragments, 1775-8) presented Goethe for page after page as a divine poetic genius. This poetic charisma remained undiminished as generations and literary paradigms passed. Twenty years on, in Über die asthetische Erziehung des Menschen (On the Aesthetic Education of Humanity, 1795), Friedrich Schiller painted Goethe's portrait as the model classical poet. Such admiration also stretched across literary ideologies. In 1798 the leading early German Romantic Friedrich Schlegel asserted that Goethe's classical novel Wilhelm Meisters Lehrjahre (Wilhelm Meister's Apprenticeship, 1795-6) represented one of the age's three fundamental tendencies).

When Goethe first drew up a schematic diagram for his planned autobiography in October 1809, he had just completed work on his novel Die Wahlverwandtschaften (Elective Affinities), whose formal elegance contrasts all the more glaringly with the moral and societal crisis depicted therein. In the years since the death of Schiller in 1805, Goethe had witnessed the dissolution of the Holy Roman Empire, the defeat of Prussia, and the reorganization of the political map of Europe by Napoleon. His mother had died in 1808, removing yet another link to his childhood and youth. Under these conditions he undertook the re-examination of his life and career as a writer from the vantage point of a sixty-year-old interested in imbuing individual stages of his life with historical significance.

It is in this context that the title Aus meinem Leben: Dichtung und Wahrheit (From my Life: Poetry and Truth, 1811–33) assumes its meaning: while not neglecting factual information (Wahrheit), Goethe is above all concerned with the refashioning and interpretation of his recollections (Dichtung). In the process, the specific events and individuals depicted in Goethe’s autobiographical writings become paradigmatic not only of important stages in the individual development of the poet, but also of significant moments in the social, cultural, religious and literary life of German-speaking Europe.

Goethe left a rich and heterogeneous body of work in the dramatic genre. Besides the five major dramas (Götz von Berlichingen, Egmont, Iphigenie auf Tauris, Torquato Tasso and Faust), various completed works survive of differing style, length and quality, as well as a large number of fragments and sketches. But even if we isolate the major dramas, we are again struck by their diversity. To be sure, while Faust (which is treated separately in this volume) is unique and incommensurable, Götz and Egmont are both historical plays written in prose, while Iphigenie and Tasso are both written in blank verse. A closer examination will show, however, that each work has its own unique features. For Goethe each dramatic work represented a fresh challenge to discover the appropriate vehicle for his immediate needs. In view of this diversity I shall not confine myself here to the small canon of major works, as some other critics have done, but shall try instead to do justice to the breadth of Goethe's remarkable body of work in this genre.

It is difficult to exaggerate the importance of rhythmic notation to the early history of Western art music. While the early chant repertories were by no means sung uniformly with even note values, our understanding of their rhythmic performance must remain speculative given the lack of any form of secure rhythmic notations. It was only in the thirteenth century that musicians in Paris first established a rudimentary notation to indicate rhythmic patterns using a system of six rhythmic “modes.” Over the next two centuries, as musical culture gradually evolved from one that was largely oral to one that was written, more precise rhythmic notations were developed to accommodate the increasingly complex polyphonic innovations of musicians. At the same time, though, it must not be overlooked that the development of increasingly precise rhythmic notations contributed to these innovations by allowing composers greater stylistic freedom. A good example can be seen in the emergence of the isorhythmic motet, which could not have come into existence without the development of new rhythmic notations. The principal innovation here was the “mensural” system by which ever more complex rhythmic relationships, allowing for duple or triple subdivisions of note values, could be expressed within the duration of a given unit of time. In the late fourteenth and early fifteenth centuries, rhythmic possibilities were further augmented through the use of a system of proportions. Eventually, however, a profusion of competing notational systems led to widespread confusion that the great theorist-reformer Tinctoris tried to eliminate in the late fifteenth century, although with only partial success.

Isaac Newton's Observations upon the Prophecies of Daniel, and the Apocalypse of St. John, prepared for the press from his manuscripts by his nephew Benjamin Smith, was published in two editions in London and Dublin in 1733. According to Richard S. Westfall, Newton's finest twentieth-century biographer, the author “had cleansed his Observations”and his heirs “could publish the manuscript without concern.” Yet one might be permitted to wonder whether either the actual or the intended reception of Newton's posthumous work was as uncontroversial as it has seemed to late twentienth-century eyes. The book was dedicated to Peter King, baron of Ockham, the lord chancellor, who had defended Newton's sometime disciple, William Whiston, during his trial for heresy in July 1713. Although Whiston later fell out with King, he nevertheless continued to maintain that King's youthful writings on the primitive Church supported the Arian position for which he had himself been condemned. King was also the dedicatee of other works of dubious theological orthodoxy, such as Daniel Mace's attempted revision of the New Testament.

The opposition between analytical and synthetic proof methods has an intriguing and complex role in the history of Western mathematics. In Antiquity analytical method (in brief, analysis) was conceived of as a method of discovery, or problem solving: it starts from what is sought as if it had already been achieved, and, working step by step backwards, it eventually arrives at what is known. This and similar rather vague definitions were aimed at describing in a general way a whole apparatus of geometric problem solving procedures developed by the Greeks. Synthesis goes the other way round: it starts from what is known and, working through the consequences, it arrives at what is sought. The axiomatic and deductive structure of Euclid's Elements was the model of the synthetic method of proof. Analysis (or resolutio) was often thought of as a method of discovery preliminary to the synthesis (or compositio), which, reversing the steps of the analytical procedure, achieves the true scientific demonstration. Analysis was thus the working tool of the geometer, but it was with synthesis that one could demonstrate things in an indisputable way. In the Middle Ages this pattern of definitions became bound up with the philosophical and logical tradition. A question which was often raised concerned the relationship between the mathematical proof methods and other accepted forms of deductive proof, typically those codified in Aristotle's Organon.

Western music, with its origins in liturgical chant, can be said to be inherently melodic: the word “theme” was in use in the seventeenth century, and “motif” (later, “motive’) became a common term in art, literature, and music criticism two centuries ago. In the nineteenth century the common English translation of the German word Motiv was “figure,” and the definition of this in 1906 (Parry, at a time when recognizable music theory might be said to have become clearly underway) was comprehensive and prescient:

This definition is almost as all-embracing as was to be Bent’s definition some seventy years later of “analysis” itself (see p. 913 below), and this indicates that “motive” has been a critical element of the whole modern music-analytical enterprise. The definition also captures, and anticipates, a central impetus in music theorizing as a language analogy. The subject of this chapter has been, then, overtly or implicitly universal in Western music-theoretical writings. Its treatment here will be constrained by the dual aims of concision and plenitude. The conceptual and compositional background will be restricted sharply to recent centuries, and the invocation of “theme” and “motive” will be examined in just three readily identifiable areas: developing variation, set theory, and the one which needs least detailed exposure but perhaps greater critique, semiotics.

The chronicle of musical thought in the Latin world from the beginning of the Common Era through the first millennium of European history presents a metamorphosis of various intellectual traditions into what we today call “music theory.” The adjectives “middle” and “dark” hardly apply to these ages when one is writing the history of musical thought, for these centuries witness the beginning – indeed the birth – of that Western discipline which attempts to reflect systematically about given musical phenomena and apply these reflections to the analysis and composition of musical repertoires. While one might speak of a tradition of musical thought during the early Middle Ages, the integrity of that tradition is achieved not by any continuous thread that runs through the whole, but by a number of overlapping strands that give strength to a broad tradition. Often these strands forming the very core of musical thought draw their character from traditions other than music, and the continuity of musical reflections must be viewed from proximate perspectives.

While the first millennium saw the birth of Christianity and the flourishing musical liturgy built principally around psalmody, in the first centuries of the new millennium the study of music theory as a technical discipline remained largely isolated from the fresh artistic tradition. The development of musical learning in the Latin West basically grew from the technical subject formulated by the ancient Greeks, namely musica (μoνσiκή) or harmonica (αρμoνiκα). (see also Chapter 4, pp. 109–35). Hence in the early sections of this chapter, music theory as a general discipline will be referred to as musica to distinguish it from “music,” which would imply the totality of musical experience, practical and theoretical, or from “music theory,” which would imply some relation between a repertoire and systematic reflections concerning music.

Otherwise known as the Age of Reason for the scientific undertakings and discoveries it witnessed, the seventeenth century is frequently seen as a period of uncertainty and confusion in the context of musical thought. From our own present perspective, musical thought of this period is overshadowed both by what precedes it and by what follows: the opposing poles of Renaissance modal theory and eighteenth-century harmonic tonality each seem more intelligible than that which we perceive as the transition between the two. Indeed, much of what we find in seventeenth-century theory appears to present a puzzling mix: ideas that accord strikingly well with the precepts of major-minor tonality appear to mingle freely with the teachings and terminology of modal theory. Added to this seeming paradox is the darkened mood of the theorists themselves, many of whom lament the confusion of their age.

And yet, seventeenth-century music treatises paint a clear, if richly detailed, picture of musical thought if we keep in mind that they address widely different purposes: to serve the church singer in a long-standing and relatively stable practice of liturgical chant; to train keyboardists and other chord-playing instrumentalists in the art of extemporizing harmonies over a bass; to educate the well-rounded musician in the established traditions of counterpoint and modal theory; to instruct the rational mind in the scientific bases of tuning systems; and finally, to enlighten the curious on more speculative and imaginative musical topics, such as Pythagoras’s fabled discovery of harmony in the sound of hammers at the forge, the Boethian harmonic strata, and the legendary origins of music itself.

This chapter will trace some of the major strands of a tradition of musical thought that reaches from the late eighteenth century to our own time: the analysis of large-scale tonal form. Whereas a fascination with formal analysis undertaken purely for its own sake is mostly a twentieth-century phenomenon, the emphasis on form has been a central preoccupation of music-theoretical writings ever since the “work concept” (consolidated around 1800) decisively shifted theoretical focus to whole works of music and thus to overall form. As notions of organic musical process became more prevalent, musical form became less self-evident, more in need of elucidation. Mainstream music criticism in the early nineteenth century was increasingly characterized by intuitive professions of aesthetic unity (the urge to demonstrate such unity analytically was only faintly in evidence at first); this trend was of a piece with a romanticized view of the creative artist as a second Creator, whose unifying spirit was thought to hover over the great variety that could now be brought together within the selfsame work. In short, form became more than a matter of conventional arrangement: it was the extensive manifestation and discernible logic of the creative imagination.

At the same time, the pedagogical context of music-theoretical writing broadened: the Satzlehre tradition became that of the Kompositionslehre, as theoretical treatises were now concerned with promoting the composition of entire pieces in the available forms. The analysis of musical forms began in this context as a pedagogical exercise in emulation, and the works of Haydn, Mozart, and Beethoven were increasingly held up as exemplary.

The basis of most musical instruction, thought, and activity in the Western world is a particular conceptualization of pitch. We understand musical pitches as distinct sonic entities (“discrete pitch”), specifiable by name, and we mentally represent them as a series of points occupying higher or lower, intervallically defined positions on an imaginary, quasi-spatial, vertically aligned two-dimensional continuum – or basic “pitch space.” (We may also conceive the positions as defined by absolute pitch, determined by vibrational frequencies; this modern concept will not be considered here.) The pitches, or as I shall usually call them, “notes,” constitute a system defined by various intervallic and other relationships and comprising a multitude of specific structures, including our familiar major, minor, and chromatic scales. These conceptualizations of discrete pitch, pitch space, and pitch-intervallic scalar system have their ultimate origins in the music theory of Greek antiquity. But the particular scale system we use is the result of a long historical evolution, in which the most crucial developments occurred in the ninth and eleventh centuries. Sections I and II of this chapter, respectively, will provide a fairly detailed examination of those developments, together with others to which they are closely connected, especially those concerning the early stages of pitch notation, solmization, and the theoretical systematization of the church modes. Section III, a brief postscriptum, will indicate some of the developments of the later Middle Ages and early Renaissance, to c. 1500.

Music theory, Carl Dahlhaus has warned us, is a subject that notoriously resists its own history. How, he challenges us, is it possible to write any meaningful history of a discipline whose subject matter has shifted so dramatically over time? Topics of musical pedagogy that we today take for granted as integral to music theory were not always so considered – rules for writing counterpoint or realizing a figured bass, for instance. Conversely, many of the traditional components that made up the quadrivial science of musica theorica are now considered peripheral subjects lying precariously close to occult and esoteric thought, or more benignly, perhaps, as part of some mathematical or acoustical subdiscipline. Nor are these contrasting allegiances mutually exclusive at any given historical period. Widely diverging conceptions of music theory can often be found jostling with one another in the same historical culture, within the oeuvre of the same writer, and occasionally even in the same publication.

As a pointed illustration of this diversity, we might consider three texts stemming from the same decade of the early seventeenth century: Thomas Campion’s A New Way of Making Fowre Parts in Counter-point by a Most Familiar, and Infallible Rule (London, c. 1618), René Descartes’s Musicae Compendium (c. 1618; printed Utrecht, 1650), and Robert Fludd’s Utriusque Cosmi, maioris scilicet et minoris metaphysica (Oppenheim, 1617–21). Each of these works has been classified as “music theoretical” (although ironically, none of them actually employs the title “music theory”). Yet it is certainly not the case that all three works represent similar kinds of theory.

INTRODUCTION

The first edition of Isaac Newton's Principia was published in 1687, followed by a second edition in 1713 and a third in 1726, the year before he died. The Principia is universally held to have been a major turning point in natural philosophy in the seventeenth century. That turning point is clearly reflected in the comparison of the title of Descartes's 1644 Principles of Philosophy with the title of Newton's Mathematical Principles of Natural Philosophy. Even though both men were noted mathematicians, Newton's book is distinguished from that of Descartes by virtue of being a mathematical description of nature. In the General Scholium of the second edition Newton sets out the difference quite clearly: “But hitherto I have not been able to discover the cause of those properties of gravity from phenomena, and I frame no hypotheses . . . And to us it is enough, that gravity does exist, and acts according to the [mathematical] laws which we have explained.” Although Newton was strongly influenced by the Cartesian mechanical philosophy during the first two decades of his scholarly work, he nevertheless expressed himself analytically from the very beginning of his work in 1664. By 1684, however, he had rejected Cartesian mechanical explanations for gravity, and in the Principia he emphasized the analytical expression of the inversesquare law for gravity. The final impetus for that rejection came from Newton's correspondence in 1679 with Robert Hooke, which led Newton to derive Kepler's area law as a geometrical measure of time to employ in analyzing orbital motion. That same correspondence has shown that Newton's later work is an extension, not a revision, of his earlier work.

The more complex a natural entity is, and the more interrelated its components are, the harder it often is for us to comprehend how it could have evolved from completely independent constituent elements. Human vision, for instance, is so immensely complex, with numerous specialized parts both in the eye itself and in the way that the brain processes visual signals, that it is difficult to imagine how each component evolved both separately and in interaction with its affiliates before the final, highly integrated developmental stage existed. The same is true of complex cultural systems that have evolved over long periods of time, among which is harmonic tonality. Virtually every aspect of harmonic tonality (tertian harmonies as primary compositional structures, contrapuntal voice leading connecting those harmonies, the bass as a harmonic foundation, notions of root generation, harmonic motion directed toward cadential goals, the interaction of diatonic scales and chromaticism, and the interaction of harmony and counterpoint with rhythm and meter) arose before tonal harmonic syntax existed. Even though those components interact quite intricately in tonal music, each arose within different musical contexts, and each was explained autonomously by teachings having long, independent theoretical traditions.

The individual who first recognized that all those components interacted to create a sense of tonality was the French theorist and composer Jean-Philippe Rameau (1683–1764). Although Rameau proposed some original ideas, a major part of his theorizing in the treatises he published between 1722 and 1761 consisted of reformulating and combining long-standing concepts into a single harmonic, directional perspective. Rameau is an instance of that relatively rare theorist who was a major composer as well. Because of this, as much as he pursued theoretical ideas for their own consistency, he generally remembered that the function of a theory of harmony was to explain music as he understood it compositionally. This chapter traces many of these concepts and their attendant pedagogical traditions as inherited by the early eighteenth century, and then considers Rameau’s brilliant accomplishment of consolidating them into a unified (if not completely stabilized) harmonic theory. Lastly, this chapter surveys the evolving legacy of this now-dominant heritage in the late eighteenth century and beyond.