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The Cambridge History of Western Music Theory
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    Sullivan, Michael B. 2014. ON HORACE'S PYRAMIDS (C. 3.30.1–2). The Cambridge Classical Journal, Vol. 60, p. 100.


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    Pritchard, Matthew 2012. ‘The moral background of the work of art’: ‘character’ in German musical aesthetics, 1780–1850. Eighteenth Century Music, Vol. 9, Issue. 01, p. 63.


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    The Cambridge History of Western Music Theory
    • Online ISBN: 9781139053471
    • Book DOI: https://doi.org/10.1017/CHOL9780521623711
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Book description

The Cambridge History of Western Music Theory is the first comprehensive history of Western music theory to be published in the English language. A collaborative project by leading music theorists and historians, the volume traces the rich panorama of music-theoretical thought from the Ancient Greeks to the present day. Recognizing the variety and complexity of music theory as an historical subject, the volume has been organized within a flexible framework. Some chapters are defined chronologically within a restricted historical domain, whilst others are defined conceptually and span longer historical periods. Together the thirty-one chapters present a synthetic overview of the fascinating and complex subject that is historical music theory. Richly enhanced with illustrations, graphics, examples and cross-citations as well as being thoroughly indexed and supplemented by comprehensive bibliographies of the most important primary and secondary literature, this book will be an invaluable resource for students and scholars alike.

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Page 1 of 2


  • PART I - DISCIPLINING MUSIC THEORY
  • View abstract
    Summary
    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. An elegant architecture of music theory is only to be found much later in Aristides Quintilianus's three-volume On Music. The task of both harmonic theory and the theory of musical affect involves the construction of taxonomies. Natural acoustics and notions of musical rhetoric combine to give the empirical evidence for the genealogy of music, and the mechanistic reconstruction of its common origins with language and dance. Just prior to the turn of the nineteenth century, Johann Nicolaus Forkel gives the following schema of musical studies in his Allgemeine Geschichte der Musik. Forkel's schema anticipates a final general remapping of music theory which occurs at the opening of the nineteenth century. The music theory of the past two centuries can be seen to be caught between the two paradigms of historicization and psychologism.
  • 2 - Musica practica: music theory as pedagogy
    pp 46-77
  • https://doi.org/10.1017/CHOL9780521623711.004
  • View abstract
    Summary
    One of the most consequential developments in the long history of music theory has been its gradual integration with the discipline of musica practica. A discipline that until at least the eighteenth century was considered largely distinct from the rarefied concerns of classical musica theorica. A putative division between practice and theory in music may be implicit in the distinction widely invoked by medieval authors between musicus and cantor. Whatever tension there may be in the Carolingian sources between practice and pedagogy, there is little dispute as to the major milestone of medieval pedagogical theory. The writings of the eleventh-century Italian monk Guido, active for most of his life in the cathedral of Arezzo. The earliest musical curriculum of the medieval universities drew heavily upon Boethius and his program of the seven liberal arts, in which music was included as quadrivial sciences.
  • 3 - Epistemologies of music theory
    pp 78-106
  • https://doi.org/10.1017/CHOL9780521623711.005
  • View abstract
    Summary
    Most music-theoretical writing betrays few of Schenker's epistemological qualms. Allen Forte's The Structure of Atonal Music characterized the contemporary scientific writing on which Forte modeled both his literary and his theoretical approach. For the historical interpretation of music theory, premised on its epistemological underpinnings, Dahlhaus distinguishes three basic traditions of theory. Empiricism requires a framework of epistemological regulation, which is frequently been lacking or at best tenuous in the theoretical noman's-land between musical art and nature. In Rameau's theory of music, there is a tension between induction and deduction, between the demands of veridical description and of theoretical adequacy. Schenker retained a belief in musical laws which are the exact analogue of the natural laws of classical science. The incorporation within generative theory of tonal music of this spatial model, based on the principal consonances of canonist theory, might be regarded as the final stage in the story of theorizing music between art and nature.
  • PART II - SPECULATIVE TRADITIONS
  • View abstract
    Summary
    The tradition represented by Greek works on music and harmonics assumed a prominence in the West. It acquired a sense of the esoteric and foreign, a duality of character as it retains in the modern conception of ancient Greek music theory. The corpus of ancient Greek music theory comprises three basic traditions: the Pythagorean tradition, a related scientific tradition of harmonics, and an Aristoxenian tradition. The Pythagoreans were particularly interested in the paradigmatic and mimetic characteristics of music, which they saw as underlying its power in human life. The Harmonicists are primarily known through Aristoxenus's negative assessment of them in his Harmonic Elements, at the beginning of which he defines the study of harmonics as pertaining to the theory of scales and tonoi. The most systematic discussion of ostensibly musical phenomena is found in the fragmentary Harmonic Elements of Aristoxenus and later treatises based on its principles.
  • 5 - The transmission of ancient music theory into the Middle Ages
    pp 136-167
  • https://doi.org/10.1017/CHOL9780521623711.007
  • View abstract
    Summary
    Since the transmission of ancient thought into Middle ages was both limited and enriched by the intellectual and spiritual contexts. The history of musica in the early Middle Ages cannot be separated from the history of education, of philosophy, and of learning in general. This chapter addresses the initial interaction between musica and cantus, and the intellectual and artistic synthesis that represents the beginnings of 'music theory'. It focuses the intellectual and artistic forces that shaped musical thought during the first millennium of the Common Era. Martianus transformed the Roman rhetorical tradition of the arts as evidence of humane erudition into a tradition in which the arts were intellectual disciplines that enabled the human mind to rise to the level of divine intellect. Alcuin grounded Carolingian intellectual and spiritual formation in both the Roman rhetorical tradition and the Platonic tradition of the early Middle Ages, and gave musica an important place in the program.
  • 6 - Medieval canonics
    pp 168-192
  • https://doi.org/10.1017/CHOL9780521623711.008
  • View abstract
    Summary
    Ancient Greek music theory developed canonics, describing ditones, trihemitones, tones, semitones, and dieses in a variety of sizes, organized into diatonic, chromatic, and enharmonic tetrachords. The profusion of monochord divisions in medieval music theory of course indicates the medievals' great interest in tuning. The comparison of measured string lengths was the only means they had for representing the tunings of intervals accurately. The tuning that took hold in the medieval West and is the basis of the vast majority of medieval monochord divisions; it has come to be called 'Pythagorean' tuning. Although the overwhelming majority of medieval monochord divisions were diatonic, a significant fraction of them, thirteen of the 143 monochord divisions that Meyer presents, include chromatic and enharmonic tunings. The terms diatonic, chromatic, and enharmonic reappear in the Lucidarium of the theorist, composer, and choirmaster Marchetto of Padua, not as varieties of tetrachords but of semitones.
  • 7 - Tuning and temperament
    pp 193-222
  • https://doi.org/10.1017/CHOL9780521623711.009
  • View abstract
    Summary
    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. Tuning and temperament theory was especially developed by eighteenth-century German authors. The time-honored monochord remained in use as the basic tool of tuning and temperament theory. Glarean's description of Pythagorean tuning will serve to explain both the use of the monochord at that time and the Pythagorean system. Despite its high theoretical prestige in the sixteenth century, just intonation was already known to be inappropriate as a tuning system for keyboards. Gioseffo Zarlino did work out a meantone temperament in his Dimostrationi armoniche. The calculation of tempered intervals was first performed towards the end of the sixteenth century by the Dutch mathematician and engineer Simon Stevin for the calculation of equal temperament. In the calculation of temperaments, logarithms serve especially well in the geometrical division of intervals, where they replace root extraction by division.
  • 8 - The role of harmonics in the scientific revolution
    pp 223-245
  • https://doi.org/10.1017/CHOL9780521623711.010
  • View abstract
    Summary
    This chapter emphasizes 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. It describes the key ancient and medieval sources on harmonic doctrine, of which the most important by far was Boethius's Fundamentals of Music. In the last quarter of the century, however, a coherent system of 'occult philosophy' began to be articulated in European courtly circles in which musical harmony figured prominently. Franchino Gaffurio's Theorica musice, which together with Francesco Giorgi's De harmonia mundi and Agrippa's De occulta philosphia served as Fludd's main source of musical doctrine. While Kepler construed his planetary laws in terms of harmonics, Newton situated his inverse square law of universal gravitation within the broader framework of a new mathematical physics. 'Human harmonies' focuses on how physicians such as Thomas Willis and William Cheyne used musical models to conceptualize the hidden workings of the body.
  • 9 - From acoustics to Tonpsychologie
    pp 246-271
  • https://doi.org/10.1017/CHOL9780521623711.011
  • View abstract
    Summary
    The rise of Tonpsychologie as a scientific discipline in the nineteenth century was a key moment in the history of music theory. Helmholtz, the empiricist, advanced physical and physiological acoustics; Stumpf, the mentalist, established a psychological frame of reference, Tonpsychologie. Research on five key acoustical phenomena, sympathetic resonance, complex tones, the harmonic series, beats, and combination tones, provided a base of axiomatic knowledge for nineteenth-century researchers. This chapter considers the work of some scientists in the early nineteenth century in the areas of physiology and experimental methods that, together with the earlier acoustical advances, would provide the foundation for Helmholtz's influential synthesis at mid-century. Stumpf was interested in the mental aspects of perception and in group differences, which, in his music research, translated into investigations of musical apperception, issues of musicality, and music of other cultures. Stumpf's early work on consonance and dissonance was limited to the perceptual fusion or non-fusion of dyadic tonal combinations.
  • 10 - Music theory and mathematics
    pp 272-304
  • https://doi.org/10.1017/CHOL9780521623711.012
  • View abstract
    Summary
    This chapter explores the association of music theory and mathematics from several perspectives: numerical models, geometric imagery, combinatorics, set theory and group theory, and transformational theory. Explaining musical intervals through ratios and combinations of ratios became the defining feature of the Pythagorean tradition of inquiry in music theory and acoustical science. The rich implications of Pythagorean and Platonic philosophy and mathematics, ratios and magnitudes and their geometric representation, governed the science of music from the Middle Ages to the Renaissance. Combinatorial processes were incorporated into music theory almost immediately upon their appearance in formal mathematical discourse by Mersenne. Babbitt documented the mathematical foundations of the system of twelve pitch classes using the vehicles of set theory and finite group theory. An outpouring of music-theoretical writings is inspired by Lewin's pioneering work in transformation theory, by authors such as Robert Morris, Richard Cohn, Brian Hyer, John Clough, and Henry Klumpenhouwer.
  • PART III - REGULATIVE TRADITIONS
  • View abstract
    Summary
    The musical developments of ninth century, which were part of the broader cultural movement known as the Carolingian 'Renaissance' or renovatio, are fundamental to the entire subsequent history of Western music. In this period, the set of melodic categories, the eight 'modes' or tones', used by the church to classify and organize the melodies of plainchant became linked to the structure of the newly established scale system. The basic theoretical concepts and structures which are applied in analytical discussions of mode from the later ninth century seem required for any technical analysis of melodies in structural term. The treatises, Musica enchiriadisand Scolica enchiriadis are widely known for containing the earliest extant descriptions of actual procedures for singing organum. Starting about the year 1000, theorists, combining elements selected from the disparate approaches of the Carolingians, produced new theoretical syntheses that incorporated, further developments in pedagogy and systematizing theory in the eleventh and later centuries.
  • 12 - Renaissance modal theory: theoretical, compositional, and editorial perspectives
    pp 364-406
  • https://doi.org/10.1017/CHOL9780521623711.014
  • View abstract
    Summary
    Sixteenth-century writers conflated Latin and Italian terms in ways that fundamentally altered the meaning of earlier modal theory while retaining its existing nomenclature. From a modern perspective, changes in modal thought are reflected in sixteenth-century theoretical writing, musical composition, and editorial practice. Didactic treatises of a different sort were aimed at composers and performers of polyphony. At the same time that Giovanni Del Lago published his treatise, one can see a general trend among music printers toward ordering publications of vocal polyphony in partbooks by 'tonal types'. Glarean's system now covered the possibilities framed by the diatonic system with twelve modes comprising six modal pairs representing the modes of classical antiquity. Zarlino draws on three strands of argument: the discourse of traditional modal theory, the specifically Venetian strand of modal theory, and the musica practica tradition. Much of the controversy that has surrounded interpretations of modal theory of the Renaissance has been generated for the analysis of Renaissance polyphony.
  • 13 - Tonal organization in seventeenth-century music theory
    pp 407-455
  • https://doi.org/10.1017/CHOL9780521623711.015
  • View abstract
    Summary
    Seventeenth-century theory comprises a rich mixture of myth, scientific research, rules for composition, and basic musical training. This chapter focuses on seventeenth-century theories of tonal organization that emanate from these various constituents. The conception of tonal space during the seventeenth century is founded on an inherited gamut that comprises litterae, background letters, and voces, hexachordally organized syllables. Solmization according to the system of hexachords remained little changed throughout the century. The eight tonalities that arose as accompaniments or substitutes for the eight psalm tones are known as 'psalm tone tonalities' or 'church keys' by modern scholars. the seventeenth century, transpositions were performed not only on compositions, but also on tonalities themselves; thus the church keys could be transposed to suit differing vocal ranges. As taught by Gasparini, the skill of making quick and easy transpositions on sight required, not only the mental insertion of key signatures, but also the substitution of a different clef in front of the notes.
  • 14 - Dualist tonal space and transformation in nineteenth-century musical thought
    pp 456-476
  • https://doi.org/10.1017/CHOL9780521623711.016
  • View abstract
    Summary
    Nineteenth-century music theory in German-speaking countries divides reasonably into two main traditions: thorough-bass styles of music theory and harmonic dualism. This chapter examines the theoretical approaches developed by Hauptmann, Oettingen, and Riemann, with a particular emphasis on the issues of chord structure and chord relations or transformations. It explores associated topographies of chords, and topographies whose dimensions are articulated by transformations. The chapter provides a sympathetic account of harmonic dualism as a structural premise and as a historical development. Contemporary music-theoretical debate about triadic structure is framed by a common acceptance, or better, the naturalization, of some variety of harmonic monism. Riemann establishes two classes of chord relationships or transformations. Riemann's interest in these transformations appears within the context of his topographical conception of tonality, which in turn arises from Oettingen's topographical conception of pitch relations. Dissonance in Riemann's view arises from the disruption of the unity of klang structure and klang meaning by foreign elements.
  • B - Compositional Theory
  • View abstract
    Summary
    A companion treatise, 'Cum notum sit omnibus cantoribus', paired with 'Quilibet affectans' in several manuscript sources, specifically invoke singers and their actions in its more extended treatment of contrapunctus. The multi-faceted, fluctuating domain of polyphonic theory in the Middle Ages concentrate on three defining phases in its history, phases distinguished in the treatises by the terms organum, discantus, and contrapunctus. The focus on issues of duration and notation as essential to discant and basic to generic distinctions within the general sphere of organum gave rise to a distinct dividing line between musica mensurabilis and musica plana. Contrapunctus teaching retains many features of the older discant teaching, but differs significantly in being conceived as strictly note-against-note in texture. The earliest dated treatise in which contrapunctus teaching is plainly evident is the Compendium de discantu mensurabili from 1336. The practices described in the treatises shaped the basic sensibilities of young musicians who subsequently create their own polyphony to be preserved in notation.
  • 16 - Counterpoint pedagogy in the Renaissance
    pp 503-533
  • https://doi.org/10.1017/CHOL9780521623711.018
  • View abstract
    Summary
    This chapter examines some of the compositional techniques of counterpoint pedagogy by reviewing some treatises written between the mid-fifteenth and mid-seventeenth centuries. The major authors whose treatises are the basis of our survey fall into four large groups. The first generation of Renaissance theorists includes Ugolino of Orvieto, Johannes Tinctoris, Bartolomeo Ramis de Pareia, and Franchino Gaffurio. Most fifteenth-century theorists presented six to eight fundamental voiceleading rules to regulate contrapunctus simplex. Mode is generally defined in terms of melodic features: ambitus, final, reciting or psalm tone, and characteristic species. Throughout the Renaissance, theorists normally maintained Tinctoris's distinction between note-against-note counterpoint and florid counterpoint. Contraponto fugato can be a means of giving form to music based upon a cantus firmus (CF). The constraints of double counterpoint, like those of contraponto fugato, are quite severe, and sometimes licenses were permitted. The techniques that were taught using a CF soggetto freely invent imitative duos in mixed values.
  • 17 - Performance theory
    pp 534-553
  • https://doi.org/10.1017/CHOL9780521623711.019
  • View abstract
    Summary
    This chapter provides several contrasting and examples of traditions in performance theory. Writers in ancient Greece had already distinguished the practice of music from its theory, the one dealing with performance, composition, and education, and the other with science, technique, and critical intellect. The changes in the music theory are evident in the writings of Marin Mersenne, the French Minim friar whose complex body of musical writings lies between the works of Zarlino and Rameau. The ever-increasing freedom in performance manifest in thorough-bass realization was perhaps even more pronounced in the approaches employed in the interpretation of solo parts, all in the interests of enhanced expression. This involved several facets: the embellishment of musical lines by the application of numerous ornamental devices, and expanded use of elaborative diminution techniques in melodies. In the twentieth century, many composers included a creative, contributory role for performers into their music, either through use of aleatoric or chance procedures, or through opportunity for improvisation.
  • 18 - Steps to Parnassus: contrapuntal theory in 1725 precursors and successors
    pp 554-602
  • https://doi.org/10.1017/CHOL9780521623711.020
  • View abstract
    Summary
    For 250 years, the Gradus ad Parnassum of Johann Joseph Fux has been a tabula by-no-means rasa on which theorists and pedagogues have written. The remarkable process of accretion and rewriting began within seventeen years of its initial publication, with its first translation, ironically into Fux's own language, German, in 1742. The newness of Fux's method has three stated aspects. First, it is occupied largely with practical music, and only very slightly with speculative music. Second, it does not rely on model compositions. Third, designed for easy mastery by beginners, it is based on the elementary reading pedagogy of the day. Fux avails himself of the German triadic tradition, but he does not surrender entirely to the theory. Nowhere, for instance, does he speak of the triad as embodying unity. Yet this lies at the very heart of seventeenth-century triadic theory, with its strong trinitarian parallels.
  • 19 - Twelve-tone theory
    pp 603-627
  • https://doi.org/10.1017/CHOL9780521623711.021
  • View abstract
    Summary
    The twelve-tone idea has a pivotal role in the development of music theory as a professional discipline, especially in the United States during the post-World-War-II period. There are two approaches available to scholars surveying the history of twelve-tone music and theory. An early statement of the twelve-tone idea found in a short monograph published in 1920 by the composer Josef Matthias Hauer. Hauer's aesthetic dualism casts off the material aspect of music wherever possible. Gnostic criticism of musical materialism forms the foundation for Hauer's arguments in favor of the twelve-tone idea. In comparing the dodecaphony of Hauer, Eimert, and Schoenberg, certain contrasts and similarities arise. Hill's essay had an important impact on Ernst Krenek's thinking about twelve-tone composition. Perle focuses his approach on each tone and its immediate neighbors; the row establishes functional relationships for each pc that the composer may employ freely without regard to the literal serial ordering of the pcs in the twelve available transformations.
  • C - Time
  • View abstract
    Summary
    This chapter indicates the important conceptual changes of this rhythmic notational evolution of Western art music, and its broader theoretical underpinnings and implications. It covers the contributions of John of Garland, Franco of Cologne, Jehan des Murs, Marchetto of Padua, and Johannes Tinctoris. In Garland's system, the length of the individual note can only be gathered from the mode itself, while Franco inverts this relation by making the mode dependent upon and determined by the individual notes or figurae that have incontrovertible durational values. In des Murs's time, diminution was used only in the tenors when these had slower note-values than the other parts. The chapter also looks at other measuring devices used in the Middle Ages, specifically, the Roman system of weights and measures. By the late fourteenth and early fifteenth centuries, a system of rhythmic proportions was introduced to allow for the notation of such breve and semibreve equivalency.
  • 21 - Theories of musical rhythm in the eighteenth and nineteenth centuries
    pp 657-694
  • https://doi.org/10.1017/CHOL9780521623711.023
  • View abstract
    Summary
    Rhythmic theories, like many other domains of music theory, are largely formulated in relation to a distinct compositional practice. Prior to the seventeenth century, rhythm in Western music was organized according to the mensural system. In this period, the mensural system gradually evolved into the modern system of note values and meters. At least two basic issues regularly prompted debate: the number of primary divisions in a measure, and the nature of compound meters. As a general rule, accent was linked directly to meter; the idea of nonmetrical accentuation arose now and then but did not become an important component of rhythmic theory until the nineteenth century. The wide variety of terms for accentuation used by Baroque theorists clearly reveal the conceptual difficulties attendant on metrical accent. Johann Mattheson's extensive list of twenty-six durational patterns, which he calls sound-feet in analogy to the feet of poetic meters, represents the most complete extant theory of musical rhythmopoeia.
  • 22 - Rhythm in twentieth-century theory
    pp 695-725
  • https://doi.org/10.1017/CHOL9780521623711.024
  • View abstract
    Summary
    This chapter focuses on musical and intellectual developments which shaped twentieth-century rhythmic theory. In the twentieth century a number of theorists have regarded motion and movement as the essential substrate of musical rhythm and form. Kurth accounts for rhythmic gestures from small to large in terms of a nested set of waves or wave-like motions. The theorist who most directly engaged Kurth's ideas of motion and the wave-metaphor to describe such motion, however, was Viktor Zuckerkandl. For Wallace Berry, musical structure involves 'the punctuated shaping of time and 'space' into lines of growth, decline, and stasis hierarchically ordered'. Schenker's comments on rhythm and motion at the most abstract levels of structure are somewhat contradictory. Cooper and Meyer examine rhythms on lower architectonic levels, that is, the ways in which each of the five basic groups can fit into various meters.

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