Edgar Allan Poe, poet, short story writer, and critic, was a controversial figure in the publishing world of antebellum America. His ability to spark controversy stemmed not only from an image concocted by his contemporary detractors but from the sharp tone and pointed content of the critical articles he wrote during his lifetime. He worked as an editor and contributor to magazines in several American publishing venues, including Richmond, New York, and Philadelphia. His continuing ambition was to found and edit his own magazine, an outlet that would have granted him financial security and artistic control in what he deemed an antagonistic literary marketplace. Poe's challenge to moralistic strictures against literature, his confrontations with the New England literary establishment, and his caustic and satirical critical style won him many enemies.

In the Preface to the first edition (1687) Newton informs the reader straight off that he intends the Principia to illustrate a new way of doing what we now call empirical science:

Surprisingly, however, the main body of the first edition contains only two further comments about methodology: (1) a cryptic remark at the end of the opening discussion of space and time, announcing that the purpose of the work is to explain “how to determine the true motions from their causes, effects, and apparent differences, and, conversely, how to determine from motions, whether true or apparent, their causes and effects”; and (2) a scholium buried at the end of Book 1, Section 11 in which Newton proposes that his distinctive approach will make it possible to argue more securely in natural philosophy.

When the newly reformed Baltimore professional football team chose to call itself the Ravens in 1996, Poe received a fin-de-siècle apotheosis as one of popular culture's favorite sons. The fact that football and Poe have nothing to do with each other only highlights the extent to which this nineteenth-century American author has remained not only present, but much appreciated in the minds of the general public throughout the world. Poe pops up almost everywhere: from a commemorative stamp issued by the US Post Office to a somewhat confused John Wayne listening to Robert Mitchum recite lines from Poe's poem “Eldorado” in the Hollywood western of the same name. Poe's face appears amidst the crowd on the cover of the Beatles' Sgt. Pepper's Lonely Hearts Club Band; the enigmatic “I am the Walrus” on Magical Mystery Tour includes the line “Man, you should have seen them kicking Edgar Allan Poe.” The Simpsons has made several allusions to Poe, including an admirable cartoon dramatization of “The Raven.” The Crow (1994) offers a triple-level tribute as Eric Draven (Brandon Lee) quotes “The Raven” after returning from the dead and entering a pawn shop in search of his murdered fiancée's ring. In the world of consumer goods, Raven Beer uses a publicity poster incorporating an irresistible pun: “I Know You're in the Pits. How about a Raven?”

The word “mode” is one of the most richly textured and problematic terms of Renaissance discourse about music. The difficulties associated with interpreting modal theory are hardly recent creations: sixteenth-century writers frequently framed their discussion of modal theory with assertions that they intended to clarity a difficult concept that earlier writers had not fully grasped. Thus Pietro Aaron claimed in 1525:

The central problem - a problem that Aaron appears to have been the first to articulate explicitly - hinges on the nature of the relationship to polyphony of a theory intimately tied to monophonic music in its origins. If anything, twentieth-century attempts to recover, explain, and in some cases extend, modal theory have become even more subject to contention than their sixteenth-century antecedents. Several facets of the tradition, history, and reception of the body of writings generally known as “modal theory” contribute to these difficulties. Discussions of mode appear in wide-ranging contexts that reflect antecedents in classical and ecclesiastical traditions as well as a complex, and at times contradictory, network of concepts associated with the term.

The word “aesthetic” and its cognates have clung to the name of Edgar Allan Poe. A handful of his more resonant statements about poetic art have found a place within histories of “aesthetic theory,” and he has formed a permanent posthumous association with the late-nineteenth century cultural movement or mode of sensibility known as “aestheticism.”On the strength of a scattering of suggestive lines from his critical prose, posterity has assured Poe an early, in some accounts freakishly early, position in the genealogy of the various doctrines grouped together under the label “Art for Art's sake.”

The word “aesthetic” was still working its way into the English language in Poe's lifetime. It had first come into use as a technical term in Germany in 1750, in the title of A. T. Baumgarten's treatise, Aesthetica, which attempted to set out a philosophically-grounded theory of taste; it later furnished Immanuel Kant with the basic concept for an inquiry into the philosophy of art in his Critique of Aesthetic Judgment (1790).

On 1 January 1875, William M. Cash, an Alexandria, Louisiana news carrier, had a special New Year's Day gift for the customers on his paper route: he presented each with The Bells, a handsome, eight-page pamphlet reprinting the well-known poem by Edgar Allan Poe. Louisiana newspaper subscribers were not the only people to receive copies of The Bells as presents during the 1870s. In Philadelphia, a china and glassware retailer issued a complimentary edition of the poem for its customers during Christmas time, 1872, and the week after Christmas, grocery boys in the employ of Philadelphia grocer, Mitchell and Fletcher, gave copies of The Bells to their customers as New Year's Day presents. Since bells had been a commonplace holiday motif for centuries, perhaps it should come as no surprise that copies of The Bells were being distributed to Philadelphia grocery shoppers or Louisiana newspaper subscribers. Anyone who believed what they read in the literary periodicals of the day, however, would hardly find Poe's writings suitable material to pass through the hands of impressionable young news carriers and grocery boys.

As a music-theoretical term, “tonality” was first used by Alexander Choron in 1810 to describe the arrangement of the dominant and subdominant above and below the tonic and thus to differentiate the harmonic organization of modern music (tonalité moderne) from that of earlier music (tonalité antique). One of the main conceptual categories in Western musical thought, tonality most often refers to the orientation of melodies and harmonies toward a referential (or tonic) pitch class. In the broadest possible sense, however, it refers to systematic arrangements of pitch phenomena and relations between them.

Usage

A number of musical and discursive factors have contributed to a veritable profusion of definitions for the term. To begin with, there has been considerable indecision about what musical domain the term covers: whether it applies to both Western and non-Western music, or whether, within Western musical traditions, the term can be restricted to the harmonic organization of music from the so-called common practice (1600–1910) or includes all music that evinces a basic difference between consonance and dissonance. There have also been some basic theoretical disagreements about whether its constituent musical elements are melodies or harmonies: however narrow the definition given to the term, the domain of tonal music is so enormous, diverse, and complex that one can choose almost any combination of musical phenomena and theoretical principles as the basis for discussion. In addition to these musical problems, enormous discursive difficulties have arisen from the conceptual languages used to describe tonal phenomena, theoretical vocabularies that vary dramatically according to the aesthetic and epistemological commitments of the writer.

In the course of a long life Isaac Newton made many enemies: Francis Linus (or Hall), Robert Hooke, John Flamsteed, Gottfried Wilhelm Leibniz, Johann I Bernoulli. Of these Leibniz was by far the greatest intellect and above all an outstanding mathematician and philosopher. Newton defeated them all and outlived them all except the last, twenty-five years his junior.

It was a sad chronology that brought two such inventive mathematicians as Newton and Leibniz to live in the same age; never were temperaments and intellectual characters more at odds. Almost the only feature that they had in common was Protestant piety, yet even in appealing to God the Creator they could not agree. In mathematics and its applications to celestial mechanics, and more particularly in the development of the calculus, though the methods promulgated by the two men were equivalent, they had been reached and were justified by wholly distinct arguments. Newton was by choice a geometer, Leibniz an algebraist; the difference does not of course imply that they could not tackle the same problems. J. E. Hofmann has written that Leibniz’s “first major [mathematical] discovery in Paris [in 1673] originated in thoughts strongly influenced by considerations of logic and philosophy – and as so often with Leibniz, was not fully established but came as the fruit of a particular insight observed in simple examples and generalised by a stroke of genius.”

During the mid-1970s, Robert Motherwell created a series of Abstract-Expressionist collages inspired by the works of Edgar Allan Poe as well as a lithograph entitled Poe's Abyss. These creative efforts indicate Motherwell's lifelong fascination with Poe's writings, which he first encountered in his youth and returned to as a young man after discovering Charles Baudelaire and Stephane Mallarmé, both of whom also received homage at Motherwell's hands. Being interviewed near the end of his life, Motherwell reiterated his devotion to Poe, naming him as a poet with whom he felt especially close.

“He keeps coming back, doesn't he?” the interviewer, aware of Motherwell's longstanding interest in Poe, observed. “What do you care especially for: the tales, the poetry?”

“Everything, really, the whole man,” Motherwell responded. “I think he was a one-man modernist, at a moment when America was moving in the opposite direction. His English is so alive, sophisticated.”

The tuning of musical instruments has kept music theorists busy since antiquity. It is a commonplace – although no less true for that – to say that each period in the history of music has had its own theory of tuning in order to meet its own musical needs. Likewise, the quantitative language used to calculate and represent these various tuning systems has changed. In the medieval and Renaissance periods, theories of tuning were usually formulated in terms of relative string lengths on a monochord, to be calculated by arithmetic methods.

From the end of the sixteenth century, until around 1800, string lengths remained in use by theorists, but their calculations were often refined by the use of mathematical tools such as root extraction. With root extraction, the various equal and unequal temperaments that dominated theory and practice from the sixteenth century onwards could be adequately described. Musically, this meant that intervals of any size could be divided into equal parts. (This was possible with arithmetic methods in exceptional cases only.) At some point in the seventeenth century, logarithmic measures of pitch were added to the common string-length values, by which a psychologically more realistic picture of the relations among pitches could be presented. Logarithms facilitated the description and calculation of virtually any tuning system conceivable.

Tuning and temperament theory was especially developed by eighteenth-century German authors. They used a variety a methods to describe a great number of tuning systems, both equal and unequal. From about 1800, string lengths were progressively replaced by frequency values to indicate pitches, making it possible to establish empirically the relations between theory and practice.

Isaac Newton deserves to be included in a series of companions to major philosophers even though he was not a philosopher in the sense in which Descartes, Locke, and Kant were philosophers. That is, Newton made no direct contributions to epistemology or metaphysics that would warrant his inclusion in the standard list of major philosophers of the seventeenth and eighteenth centuries - Descartes, Spinoza, Locke, Leibniz, Berkeley, Hume, and Kant - or even in a list of other significant philosophers of the era - Bacon, Hobbes, Arnauld, Malebranche, Wolff, and Reid. The contributions to knowledge that made Newton a dominant figure of the last millennium were to science, not to philosophy. By contrast, Galileo, the other legendary scientific figure of the era, not only published the most compelling critique of Aristotelian scholasticism in his Dialogues on the Two Chief World Systems, but in the process turned the issue of the epistemic authority of theology versus the epistemic authority of empirical science into a hallmark of modern times. Although Newton clearly sympathized with Galileo, he wrote virtually nothing critical of the Aristotelian tradition in philosophy, and the immense effort he devoted to theology was aimed not at challenging its epistemic authority, but largely at putting it on a firmer footing. Newton made no direct contributions to philosophy of a similar magnitude. Indeed, from his extant writings alone Newton has more claim to being a major theologian than a major philosopher.

How did Renaissance composers learn their craft? They could have learned much of their technique from treatises, especially from those portions devoted to counterpoint. Today, we often think of counterpoint as consisting primarily of rules of voice leading. Such rules, which are found in virtually every music treatise of the time, teach the student to regulate the melodic motions of lines in relation to the simultaneous intervals between them (e.g., conditions for approaching perfect consonances or for preparing and resolving dissonances). They were learned by young singers for the purpose of improvisation, and following them would have been as natural as speaking in grammatically correct sentences. Yet just as the art of oratory consists of more than correct grammar, so musical composition goes far beyond mere voice leading. Composers had to choose between many large-scale contrapuntal techniques involving texture, motivic and structural repetition, and variation. While there has been extensive study by scholars of the rules of voice leading in Renaissance music, less consideration has been given to these more advanced compositional techniques.

In this chapter, then, we will examine some of these compositional techniques by reviewing some two dozen treatises written between the mid-fifteenth and mid-seventeenth centuries. We will see that the real challenge for a Renaissance composer consisted not of employing “correct” contrapuntal voice leading but rather of elaborating primary musical material – sometimes called a soggetto – by varying it or combining it with some other melodic material. (As we will see, a soggetto need not be simply a melodic subject in equal or mixed rhythmic values; it could also be a duo, or, in the case of parody technique, even an entire polyphonic composition.)

Every musical culture possesses its own representation of what constitutes its music theory, a “map” of the domains of inquiry or precept and the relations between these domains, thus providing a degree of completeness and coherence to the discipline. The works of some theorists contain explicit and comprehensive mappings: this is particularly the case in music theory of the sixteenth and early seventeenth centuries. Yet there also are implicit mappings of music theory, which are to some degree recoverable by the historian. Often, the appearance of new theoretical constructs is symptomatic of an underlying remapping of the realm of theory. Particularly after the middle of the seventeenth century explicit mappings of theory come to have a metatheoretical and disciplinary function, often seeming to be attempts to stabilize a discourse perceived as being on the verge of fragmentation. For the purposes of this exposition, we will distinguish three broad historical cartographies, the first governing music theory through the sixteenth century, the second governing seventeenth- and eighteenth-century theory, and the last governing theory after the turn of the nineteenth century.

Architectures and harmonizations

The most basic representation of music theory is the schema, an attempt to analyze or systematize a body of knowledge through its division into idealized categories. As such, it is akin to classification, with the distinction that the latter pertains to autonomous data (harmonies, pieces, styles, etc.). A simple phenomenal schema of music might hypothetically distinguish the attributes of pitch and temporality, and indeed, theoretical schemas often do involve such binary discriminations.