The obituary notices following Poe's death in 1849 struggled to make sense of what fellow-authors felt was the central contradiction of his life: that he was one of the country's preeminent literary “geniuses” yet he had lived a life of misery and privation. Overwhelmingly, Poe's contemporaries were forced to conclude that his peculiar personality was responsible for his lack of professional success. Many, like fellow-author Nathaniel Parker Willis, felt that Poe's particular habits and talents as a writer foreclosed the possibility of material reward: “Mr Poe wrote with fastidious difficulty, and in a style too much above the popular level to be well paid.” George R. Graham agreed: “[T]he very organization of a mind such as that of Poe - the very tension and tone of his exquisitely strung nerves . . . utterly unfitted him for the rude jostlings and fierce competitorship of trade.”

Among the notable eighteenth-century expositions of Newton's achievements were Henry Pemberton's A View of Sir Isaac Newton's Philosophy (1728), Willem Jacob 's Gravesande's Mathematical Elements of Natural Philosophy confirm'd by experiments: or, an introduction to Sir Isaac Newton's Philosophy (6th edn, 1747), and Colin Maclaurin's posthumous An Account of Sir Isaac Newton's Philosophical Discoveries (1748). To the modern eye, there is something puzzling about these titles. We note the terms “philosophy,” “natural philosophy,” and “philosophical,”and we wonder what they mean in this setting. Take Maclaurin's Account, the best of the genre, and written by one of the leading Newtonians of the day. Newton made great scientific discoveries, and we can learn what most of them are from reading An Account, but what philosophical discoveries did he make? Maclaurin describes Newton's work in mechanics, rational and celestial, and in physics, theoretical and experimental (though not optics). But Newton the philosopher? To answer these questions requires a preliminary disentanglement of the disciplinary classifications that clustered around the business of “philosophy” in the seventeenth and eighteenth centuries.

Sphinx or hoax? Aside from the poète maudit, the satanic dandy revered by Baudelaire, and the alleged dope-ridden neurotic gratifying public tastes with the morbid paraphernalia of his Gothic tales, Poe was also a born humorist equally inspired by parody and self-mockery. In an anti-romantic vein so common among the popular humorists of his time, he enjoyed applying his acumen to deride the outpourings of emotions too often surging from mediocre fiction and poetry. Through a mysterious alchemy, humor was at least for him a short-lived euphoric response apt to exorcise the fiendish visions harassing his mind. This Janus figure seemed to view the world in two opposite directions, yet sometimes provided a dual perspective to reconcile extremes paradoxically. In his Anthologie de l'Humour Noir, André Breton held that the contradiction between the acclaimed poet of “The Raven”and the wretched drunkard, was itself humorous since it implied an open conflict involving logical lucidity at odds with the vapors of liquor. Plagued with his physical insufficiencies and mental strains, Poe was able, however, to overcome his sense of alienation and filter the agonizing material he stumbled over in his private life and literary career, thus intermittently giving himself narcissistic comfort through an economy of expenditure in feeling, as Freud later defined the process.

The presumption of a notated musical “score” as the subject for realization by the performer – and the object of analysis by the theorist – has become a foundation of Western musical aesthetics, one whose ontology underlies much of the theory described in the present volume. It is clear, however, that a great deal of music has been based not upon written scores, but rather upon oral transmission and traditions of improvisation. This is most evident, of course, in popular and non-Western repertories. But it is also true of much Western “art” music, particularly during medieval times, when a precise notation had yet to develop. Even after such a notation gradually did evolve, though, a large degree of improvisational freedom continued to be practiced in many different repertories and styles. The result is that the distinction between composer and performer in such music is blurred, if not non-existent. In essence, the musical “work” is the performance.

Improvisational performances are rarely arbitrary. Most genres of music having extempore elements commonly presume guidelines of syntax and style that constrain performers. These guidelines – sometimes explicitly formulated, sometimes informally so – become “theories” that can be understood as historical counterparts to the more formalized prescriptive rules that guide the composition of written scores. Still, the distinction is not always a clear one, and many treatises, particularly in the early modern period, blur the guidelines between written, improvised, and “realized” musics. The resultant theories are often as complex and intricate as are the musical structures for which they purport to account.

NEWTON’S ALCHEMICAL MANUSCRIPTS

It may seem suprising to present Isaac Newton, the founder of modern mathematical natural science, as a serious student of alchemy. He himself must have felt this anomaly, since at all stages of his life he was concerned to hide his occult interests from the public. Until very recently his large collection of alchemical manuscripts was hardly looked at, much less systematically sorted or studied, in contrast to his better-understood manuscripts dealing with mechanics or the theory of matter. Yet Newton dedicated at least as much time to alchemical and theological studies as to his mathematical and physical ones.

The process of dating his manuscripts has shown that Newton worked on alchemy at all periods of his productive life, in parallel with his scientific work. This evidence proves that his occult studies were not the aberrations of senility. Newton would hardly have devoted so much time to such “absurdities” if he had not been convinced that some deeper knowledge lay hidden, which he eventually believed that he had at least in part discovered.

Newton attempted to make a synthesis of his occult-alchemical and exact-scientific research. For him a means of attaining this goal was the study of the so-called “prisca sapientia,” a tradition of ancient wisdom. Newton considered that the original wisdom of the ancients, which had been gradually lost through the ages, was most fully retained in the writings of the Hermetic tradition. He saw himself as endeavoring to explain, by means of experimental science, this “sapientia,” which had grown unintelligible.

Scholarly editions of Poe’s writings

When James A. Harrison completed his seventeen-volume edition of Poe's works in 1902, he may not have realized that, a century later, his work would remain the single most complete edition of Poe. Thomas Ollive Mabbott, who imagined a thoroughly annotated, scholarly edition of Poe's works through much of his life, never fully brought the project to completion. Mabbott edited Politan, Poe's unfinished drama, as his doctoral dissertation at Columbia University in 1923, and he was preparing an edition of the poems and tales at the time of his death in 1968, which appeared posthumously in three volumes. Ostensibly continuing Mabbott’s editorial work, Burton R. Pollin has edited several more volumes of Poe texts, which contain much valuable annotation, but whose overall quality is uneven. The two Library of America editions offer good collections of Poe’s imaginative and critical writings. Due to their accessibility and general overall quality, The Cambridge Companion to Poe cites these two volumes primarily. Readers, however, should consult the Mabbott and Pollin editions for their detailed annotations. Though John Ostrom has edited Poe’s letters, a thorough edition of Poe’s correspondence remains a desideratum of Poe scholarship. For letters to Poe, readers should consult the last volume of Harrison’s edition.

Rhetoric is the original metalanguage of discourse in the West. From the fifth century BCE until around 1800 it served the educated classes as the most prestigious and influential means of conceptualizing and organizing language, and articulating how it can best be effective, persuasive, and elegant. Given that rhetoric shares with music the structured unfolding of sound in time, aspects of performance and delivery, and even a rudimentary notion of the “work” (the oration in rhetoric, the composition in music), it was natural and even inevitable that analogies would be drawn between the two. Analogies between rhetoric and music were common even in antiquity: Quintilian, for example, pointed to the expressivity of music as a model for the orator. In later times it was rhetoric that more frequently served as a model for musicians. Although musico-rhetorical analogies occurred sporadically in the music theory of the medieval period, they began to play a more extensive role only in the sixteenth century, when musicians appropriated rhetoric, by then a central element in the humanistic education of the time, as a model for the teaching of musical composition. It was the theorists of a uniquely German musico-rhetorical tradition who imported the apparatus of rhetoric directly into music theory, in effect making it a metalanguage for music as well as for language by interpreting it as a model for musical composition. What distinguished this German effort in the long history of the interaction between rhetoric and music was precisely that it went beyond the mere drawing of analogies to a thoroughgoing attribution of specific musical substance to rhetorical terms and concepts.

We have seen in the previous chapter how Riemann attempted to consolidate various trends in nineteenth-century rhythmic theory, synthesizing rhythm, meter, agogics, and phrase structure within his overarching theory of harmonic functionality. As was perhaps inevitable with such a comprehensive project, various tensions and problems remained in Riemann’s mature theory. Many early twentieth-century theorists such as August Halm, Ernst Kurth, and Hans Mersmann were critical of Riemann’s accentual theory, and so in part the history of rhythmic theory, at least at the beginning of the century, can be characterized as “a reaction to Riemann.” In addition, there were other musical and intellectual developments which shaped twentieth-century rhythmic theory, among which can be mentioned:

1. There were new ideas of motion and time, from physics, philosophy, and psychology, that led a number of theorists to place musical energetics and motion at the center of their approach to rhythm.

2. Schenker’s theory of tonality and tonal dynamics influenced a number of approaches to rhythm and the temporal unfolding of musical events, especially amongst North American theorists in the second half of the century.

3. Developments in linguistics and gestalt psychology influenced “architectonic” approaches to rhythm, engendering structuralist theories that emphasize the hierarchical aspects of rhythm and form.

4. Radical changes in musical style, especially the rise of atonality and serialism, demanded new conceptions of rhythm and meter. This led to various prescriptive theories of rhythm that were often developed (and commented upon) by the composers themselves.

This chapter will selectively review the work of theorists and musicians from each of these four areas.

Newton's achievements in celestial mechanics tend in popular accounts to be underestimated in some respects, exaggerated in others. This chapter seeks to correct a number of misconceptions arising from inattention to the detailed history.

KEPLER’S FIRST TWO LAWS, SO-CALLED, AND NEWTON

The claim that the planets move in elliptical orbits, with the radii vectores from Sun to planet sweeping out equal areas in equal times, first appeared in Kepler’s Astronomia Nova of 1609. Since the late eighteenth century the two parts of this claim have been referred to as Kepler’s first two planetary “laws,” understood as empirical laws. According to the popular account, Newton relied on these “laws” as thus established.

Writing to Halley on 20 June 1686, Newton stated: “Kepler knew ye Orb to be not circular but oval & guest it to be elliptical.” Whether Newton ever saw the Astronomia Nova is unknown.

The Astronomia Nova is an innovative work. It establishes important empirical results, such as the passage of the planet’s orbital plane through the Sun’s center and the orbit’s oval shape. Was the orbit’s ellipticity also a straightforwardly empirical result, say by means of triangulations of Mars, as sometimes asserted? Kepler carried out many such triangulations, but they were subject to sizeable observational error, of which he was acutely aware.

This chapter aims to highlight the influential role that harmonics played in the “scientific revolution,” which historians of science see taking place in Western thinking between the sixteenth and early eighteenth centuries. Between the publication of Nicolaus Copernicus’s De revolutionibus in 1543 and Isaac Newton’s Principia mathematica in 1687, a profound transformation took place in understanding about the laws governing the universe and man’s place within it. Why harmonics should have been relevant to this process may require some explanation, especially since music itself is now classified among the arts rather than the sciences, and harmonics is no longer recognised as a viable scientific discipline.

In its narrowest sense, harmonics has been understood since the Greeks as the study of the mathematical relations (harmonia) underlying the structure of audible music. This branch of mathematics was also known as “canonics,” a term recalling Euclid’s Sectio canonis (fourth to third century BCE), in which the propositions of harmonics are demonstrated as mathematical theorems. Greek harmonic writings which focused on musical organization and structure characteristically fell into one of two categories, following respectively the “Pythagorean” and the “Aristoxenian” schools of thought. There was a traditional component of physical explanations for these mathematical relationships (e.g., the weights of Pythagoras’s hammers), but this was only put on a sound experimental footing in the seventeenth century, by which time the field had been redefined as acoustics.

Long after his major writings on harmony, counterpoint and analysis began to appear, Heinrich Schenker (1868–1935) remains one of the most important and influential theorists in the history of Western music. His achievements have often been compared to those of eminent thinkers of his age working in other fields, e.g., his Viennese compatriots Sigmund Freud in psychology and Albert Einstein in physics. His influence, modest (though not negligible) in his own lifetime, has grown steadily since the middle of the last century and shows no signs of abating. Already a paradigmatic figure in North American universities by the 1970s, he has since exerted a powerful influence in British and, more recently, European academic circles. Indeed, the interest shown in his life’s work is, in some respects, comparable to that of some of the twentieth century’s leading composers, and in this respect his reputation as a theorist is unequaled.

That which is called “Schenkerian theory” is a complex set of regulatory principles that were initially intended to explain the tonal music of the eighteenth and nineteenth centuries; it is at the same time a synthesis of many traditions, embracing Fuxian counterpoint, the thorough-bass teaching of Carl Philipp Emanuel Bach and late nineteenth-century harmonic theory. It is at once a sophisticated explanation of tonality, but also an analytical system of immense empirical power. Schenker’s ideas and work touch on, or have implications for, virtually every topic addressed in this volume.

This chapter includes a synopsis of Schenker’s life and works, an explanation of the rudiments of his theory, remarks on its historical background, and a survey of its reception both as a pedagogical tool and as a basis for further investigation of a wide range of music.

In Chapter 6 of The Manual of Harmonics (early second century CE), Nicomachus of Gerasa narrates the legendary story of Pythagoras passing by the blacksmith’s shop, during which in an epiphany of sonorous revelation, he discovered the correlation of sounding intervals and their numerical ratios. According to Nicomachus, Pythagoras perceived from the striking of the hammers on the anvils the consonant intervals of the octave, fifth, and fourth, and the dissonant interval of the whole tone separating the fifth and fourth. Experimenting in the smithy with various factors that might have influenced the interval differences he heard (force of the hammer blows, shape of the hammer, material being cast), he concluded that it was the relative weight of the hammers that engendered the differences in the sounding intervals, and he attempted to verify his conclusion by comparing the sounds of plucked strings of equal tension and lengths, proportionally weighted according to the ratios of the intervals.

Physical and logical incongruities or misrepresentations in Nicomachus’s narrative aside, the parable became a fixture of neo-Pythagorean discourse because of its metaphoric resonance: it encapsulated the essence of Pythagorean understanding of number as material or corporeal, and it venerated Pythagoras as the discoverer of the mathematical ratios underlying the science of harmonics. The parable also established a frame of reference in music-theoretical thought in the association between music and number, or more accurately, music theory and mathematical models, since it is not through number alone but through the more fundamental notions of universality and truth embedded in Pythagorean and Platonic mathematics and philosophy that one can best begin to apprehend the broad range of interrelationships between music theory and mathematics.

Special edition from the past

NEW YORK CITY, April 13, 1844 - In an unprecedented feat of human ingenuity and artistic audacity, Mr. Edgar Allan Poe of Fordham today reported a purely imaginary feat of science and technology as a fait accompli, creating a near-riot outside the offices of The New York Sun. The stir was caused by citizens who sought to purchase a special edition containing the fallacious report of a hot air balloon's crossing of the Atlantic. By making facts of physical philosophy the basis and central concern of an adventure tale, Mr. Poe has invented science fiction. The seriousness and high-mindedness of this fictional mode will soon undoubtedly allow it to take its place among the most highly esteemed and prestigious genres of literature.

Countless unsuspecting readers were duped by Poe’s report, which claimed the paper’s front page with the large-type headline, “Astounding News! By Express Via Norfolk! Signal Triumph!” The article described in minute and technically plausible detail the flying apparatus allegedly invented and flown by well-known aviator Mr. Monck Mason. In all instances the author of the report was careful to explain the principles of aeronautics, meteorology, navigation and mechanics upon which the unexpected phenomena observed by his protagonists relied.

Introduction: tonal systems without scales

Nineteenth-century music theory in German-speaking countries divides reasonably into two main traditions: thorough-bass styles of music theory and harmonic dualism. The approaches are usually thought of nowadays as scale-degree theory and functionalism, respectively; since the emphasis in the account here is on chord structure and chordal relations as expressions of such structure, the traditions are characterized so as to foreground these particular aspects in their approach.

Interestingly, by the last half of the nineteenth century, the two traditions had become connected to different geo-political formations in Central Europe, such that we may properly speak of thorough-bass theory as Viennese (or more generally, Austrian) and harmonic dualism as Prussian, in the sense that these approaches were developed or extended within the context and dynamic of relevant educational institutions and their corresponding research ethoi in those two areas. A third major tradition, the fundamental-bass theory emanating from the work of Rameau, was more international in scope and influence. In spite of obvious dissimilarities, it was considered by harmonic dualists (in particular, Riemann) to form an important early articulation of a number of theoretical concepts basic to their own approach, a judgment shared less positively by Heinrich Schenker, who saw Riemann’s approach to tonality as little more than warmed-over Rameau. This particular alignment of approaches seems based entirely on whether one held that the structure-forming relations within chords could withstand registral rearrangement (as both Riemann and Rameau did) or not (as asserted by thorough-bass theorists).

INTRODUCTION

Between 1715 and 1716 Gottfried Wilhelm Leibniz and Samuel Clarke were engaged in a theological and philosophical dispute mediated by Caroline, Princess of Wales. Ten letters were exchanged, five on each side, before the controversy was brought to an end by Leibniz's death in November 1716. During the controversy those involved agreed to publish the texts, which were edited in 1717 by Clarke, who also translated Leibniz's letters into English. His editio princeps is considered to be both fair and excellent, and contains Leibniz's original French on facing pages, as well as a useful selection of additional explanatory materials. This extraordinarily influential controversy is among the most famous and heavily studied philosophical disputative texts of all times, and, in the words of a recent interpreter, its intellectual intricacies are reserved only for the very learned or the foolhardy.

Despite the extent of interest and studies the correspondence has attracted, however, we still lack a comprehensive critical edition taking into account all the relevant texts, including Caroline’s and Clarke’s. Interestingly, eighteenth-century editions did not include the private correspondence between Caroline and Leibniz, which was first made available in the nineteenth century, notably by Onno Klopp in the most complete form. The private correspondence of the Princess ofWales was probably not available to Clarke and, even if it had been, publishing it at the time would have been highly inappropriate. That correspondence, however, provides interesting perspectives on the exchange between Leibniz and Clarke.

Why must Arthur Gordon Pym, the protagonist of Poe's only book-length fiction, be identified on the title page as someone who is of Nantucket? Nantucket is of no apparent interest to Pym and plays no memorable part in his narrative. Psyche-wise and plot-wise, it seems to be nothing more than what westering Americans in the mid-nineteenth century called a “jumping-off place,” a town where travelers assemble to make preparations for an upcoming journey. Why must Pym be identified as belonging to, or hailing from, this place? Other questions are implicated in that one. Why must a person be identified as the product of his or her influences? Why must an idea be identified as the precipitate of prior ideas? Why must an action be identified as the effect of prior actions? Why, more generally, must it be taken for granted that every element of one's existence is subject to genealogical criticism?