the cambridge history of western music theory.pdf

How does one go about putting together a history of Western music theory? Onthe evidence of The Cambridge History of Music Theory, billed as `the firstcomprehensive history of theory to be published in the English language',today one does it with soul searching and a measure of self-consciousness. Inhis introduction, Thomas Christensen reminds us of Carl Dahlhaus's admoni-tion that theory ìs a subject that notoriously resists its own history', not leastbecause its `subject matter has shifted so dramatically over time' (p. 1).1

Publications universally acknowledged as belonging to the discipline thereforemay seem to have little to do with one another. As an example, Christensencites three treatises ± by Thomas Campion, ReneÂ Descartes and Robert Fludd± written and published contemporaneously in the early seventeenth century,which he characterises respectively as à practical guide for the novice com-poser', à classic text of musical canonics' (defining and measuring intervals)and a neo-Platonic `paean to the harmonic cosmos' (p. 1).

There are precedents for such a history, above all Hugo Riemann'sGeschichteder Musiktheorie, published in 1898.2 But Riemann's history begins rather late(with the ninth century), and by current standards presents an inordinatelypersonal and biased view of its topic, designed to give the impression thatWestern musical thought evolved inexorably toward, and found its culminationin, the author's own work. In addition, a fifteen-volume history of theory inGermany edited by Frieder Zaminer is now underway, with individual volumesdevoted to particular periods, genres, geographical areas, specialised topics andcritical assessments of the discipline.3 Conceived on a scale altogether differentfrom Christensen's, it awaits completion. There are also a number of specialisedstudies in the discipline, many in English. Christensen's volume, however, likeRiemann's (though without its prejudices) presumes to encompass Westernmusic theory's entire history within a single cover.

Given the present degree of specialisation in the field no single person couldwrite a consistently authoritative account of this history. And since, over time,individual expertise has been increasingly channelled into circumscribed areas,Christensen has wisely decided to assign individual chapters to thirty-onespecialists (twenty-six of whom teach in the United States or Canada, four inGreat Britain and one in The Netherlands). The result is an extraordinarilyrich and varied collection of more than a thousand pages: by any standard it is amilestone in English-language musicology.

Who should review such a book? Aside from the fact that most of the usualEnglish-language suspects participated in writing the volume, there is the

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inescapable difficulty that no one could do justice to the full range of itscontents. I make no claim for the range of knowledge required to commentauthoritatively on much of what is contained here. In general, I will refrainfrom judging entries as individual scholarly accomplishments, but focus ratheron how, and how well, they contribute to the overall project. My comments areintended to give a sense of the volume as a whole: what it does and does notcontain and what types of choice have been made. Finally, I will also commenton the historiographic aspects of the project.

Organisation and Contents

Christensen's long introduction, after a consideration of the etymology of theterm `theory', offers an encapsulated account of the historical vagaries of itsconceptions and reconceptions in relation to music. Christensen also notes therecent, somewhat surprising, establishment of the history of music theory as acentral topic of scholarly interest, and acknowledges the influence of Dahlhaus(who probably had more to do with raising interest in the field than anyone else)on his own thinking: in particular, he observes that the history of theory cannotbe adequately presented in simple chronological order but must be viewed interms of a number of different, and often conceptually quite separate,`traditions'. This is reflected not only in the four unequal divisions that groupthe volume's contents but also in their titles: `Disciplining Music Theory',`Speculative Traditions', `Regulative Traditions' and `Descriptive Traditions'.Each division is chronologically ordered, reflecting Christensen's wish (despiteDahlhaus) to provide an overall historical survey: but this strategy also ensuresthat within the chronology there is a pronounced synthetic component.

Part I: `Disciplining Music Theory'

The first, shortest section comprises three `metahistorical' considerations ofthe various ways `theory' has been conceived and the often hidden presupposi-tions on which theorists have depended when trying to control ± or, inChristensen's word, `discipline' ± this unstable field. Leslie Blasius's `Mappingthe terrain' examines the ways theorists have defined theory and orders theresult in three chronological periods: antiquity to 1700 (`architectures andharmonizations'), 1700 to 1900 (`taxonomies and mechanics') and 1900 to thepresent (`histories and psychologies'). This underscores the field's stubbornresistance to neat categorisation, and highlights the diversity of theory'smanifestations and the variable extent of its claims and ambitions. Robert W.Wason's `Musica practica: music theory as pedagogy', which also provides ahistorical summary, begins with the Middle Ages and limits its focus topractical theory and pedagogy. This covers a wide range of theorists who

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emphasised practice and instruction, from Zarlino to Nadia Boulanger andHindemith, and defines a major sphere of music theory. Like Blasius, NicholasCook's Èpistemologies of music theory' distinguishes three chronologicallydistinct `traditions' (drawing, again, on Dahlhaus): a speculative traditionextending to the end of the Renaissance, focused on àbstract intervallic andscalar structures'; a more practical one in the seventeenth and eighteenthcenturies, concerned with `codification and classification'; and an empirical andinterpretative one from the late eighteenth century to the present, directedespecially toward individual compositions. Cook also notes that tensionsbetween àrt and nature' promoted vacillations between empirical observationand speculative system building. Taking Rameau as the central figure `whoestablished the discursive space within which [subsequent] music theory hasoperated' (p. 91), he traces a `constant epistemological transition from the outerworld to the inner: from natural science and on to phenomenology' (p. 99), thatissues today in a `performative' turn concerned more with convincing us oftruths and less with imparting them.

Part II: `Speculative Traditions'

The seven essays in this section deal with the attempts in the earlier stages ofwestern music theory to understand music as a reflection of a larger cosmicorder. These are usually based upon the Pythagorean and Platonic belief that theessential features of reality are tied to numerical relationships that are harmonicin nature, an assumption which fuelled attempts to derive the pitch gamut fromrational principles, and, more recently, to formulate mathematical models forpitch relationships found in particular compositions. Thomas J. Mathiesen's`Greek music theory' differentiates two approaches in Pythagorean thought: anàbstract and idealized' one associated with the Harmonicists, and a moresystematic one attuned to òstensibly musical phenomena' associated with theAristoxenians. Calvin M. Bower's `The transmission of ancient music theoryinto the Middle Ages' charts the influence of these on two correspondingmedieval traditions: musica, which linked music with science and the liberal arts;and cantus, which applied musica's a priori concepts to chant. The latter's shiftfrom quantification to practice and function helped to resolve the troublesometensions that existed between inherited tradition and contemporary practice,paving the way for the establishment of music theory in the modern sense. JanHerlinger's `Medieval canonics' examines the practice of deriving fixed pitchgamuts through measurement of string ratios on a monochord, which havingbeen transmitted from ancient Greece through Boethius, proliferated after 1000and continued into the Renaissance. Later refinements in string-lengthmeasurement are detailed in Rudolf Rasch's `Tuning and temperament' throughthe use of mathematical root extraction in the fifteenth and sixteenth centuries,

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logarithmic measurement in the seventeenth, and frequency measurement after1800. The last, which eventually replaced string division entirely, alsostrengthened links between theory and practice.

Penelope Gouk's `The role of harmonics in the scientific revolution'examines transformations in tuning brought about by the growth of scientificthinking during the seventeenth and eighteenth centuries. She focuses onseveral seventeenth-century philosophical and scientific figures, includingRobert Fludd, tied to the occult tradition associated with harmonics, JohannesKepler, still convinced of music's connections with the cosmos, and ±surprisingly ± Isaac Newton, who, though lacking musical training, did notrefrain from theoretical musical speculation. The mechanistic character ofNewtonian thought, however, compromised the intellectual centrality ofmusic, and by 1750 diminished its status markedly by bringing about its almostcomplete separation from scientific inquiry. Thereafter, the traditional con-cerns of speculative harmonics were fragmented into new disciplines such asacoustics and rational mechanics. Burdette Green's and David Butler's `Fromacoustics to Tonpsychologie' deals with a subsequent symptom of that process:nineteenth-century scientific investigations into the psychology of tone, whichsimultaneously reformulated questions formerly addressed by speculativeharmonics and prefigured new ones related to music perception. Green andButler distinguish two major approaches: the first, associated with Helmholtz,examines matters of harmony, acoustics and perception from a scientific andevidential perspective, stressing `natural law' and the physiology of the ear; thesecond, associated with Carl Stumpf, embraces a more `holistic' phenomeno-logical approach dependent upon perceptual judgements reported bymusically-aware subjects. The final article in this section, Catherine Nolan's`Music theory and mathematics', provides an overview of the Pythagoreanlegacy up to the present, and traces the evolution of mathematical contri-butions to Western music theory as manifested in the use of mathematicalmodels, geometric images, the circle of fifths, Tonnetze, combinatorics and set-theoretic and harmonic-transformational conceptions.

Part III: `Regulative Traditions'

This section is devoted to the practical, pedagogically-oriented aspects of musictheory which have become increasingly central. Predictably, this is the longestsection, and is divided into four subsections differentiated by concentration:`Mapping tonal spaces', `Compositional theory', `Time', and `Tonality'. Thefour essays in the first sub-section are concerned with attempts to codifycompositionally significant pitch configurations, as opposed to the moreabstract speculations found in the previous section. David E. Cohen's `Notes,scales, and modes in the earlier Middle Ages' discusses early conceptualisations



of `discrete pitch, pitch space and pitch-intervallic scalar systems' (p. 307).Originating in Greek theory, this development underwent a significantevolution from the ninth to the eleventh centuries when Carolingian concernsfor standardisation promoted efforts to fix specific pitches and intervallicdistances and thus provided a more accurate delineation of the eight modes.Cristle Collins Judd's `Renaissance modal theory: theoretical, compositional,and editorial perspectives' picks up this thread in the sixteenth century at apoint when modal theory had become especially complex and confused. Shepresents a `local study' centred on mid-sixteenth-century Venice, seenprimarily through a single composer-theorist, Zarlino. This allows her toprovide a surprisingly full picture of the many issues associated with modality'scontinuing links to chant theory and performance. Rejecting the idea thatmodality represents an all-encompassing `pre-tonal' system, Judd argues ratherthat a multi-faceted and ambiguous situation held sway in modal thought andpractice until well into the seventeenth century. Gregory Barnett's `Tonalorganization in seventeenth-century music theory' treats another puzzlingperiod, during which modality was gradually and sporadically replaced bymajor-minor tonality. As he puts it: `at different times . . . and to differingdegrees, one set of theoretical concerns . . . replaced another, such that thepicture of tonal organization [and the] . . . language used to describe it changedalmost completely' (p. 408). Barnett covers fugal practices, competing eight-mode and twelve-mode theories, and the eventual emergence of the system oftwenty-four transposable major and minor keys, representable as a `musicalcircle', that persists to the present day. Jumping forward some two centuries,Henry Klumpenhouwer's `Dualist tonal space and transformation innineteenth-century musical thought' considers harmonic dualism. The dualistcontention that major and minor triads are equal, symmetrically-relatedmanifestations of a unitary harmonic source was developed by MoritzHauptmann, Arthur von Oettingen and Riemann, partly in response to theacoustical discoveries of Helmholtz. Klumpenhouwer summarises themysterious transformational types underlying Riemann's harmonic systemand notes the important influence of his thought on recent `neo-Riemannian'developments in the United States.

The next subsection, on compositional theory, turns from the abstract totheoretical matters concerned with the control of pitch relationships in specificcompositional practices. Sarah Fuller's `Organum ± discantus ± contrapunctus intheMiddle Ages' distinguishes three stages in early polyphony: (1) organum-in-symphoniae, beginning in the ninth century and limited to single-line, note-against-note elaborations of chant, mainly with perfect fifths and fourths inparallel motion; (2)musica mensurabilis, from the mid-thirteenth century, whichallowed for more differentiated durations in the added voice; and (3) contra-puntus, or simplex discantus, from the mid-fourteenth century, which reverted to



an exclusively consonant, note-against-note texture, but now with both perfectand imperfect intervals and taken as the foundation for a varied polyphonicsurface. Although Tinctoris, in his Liber de arte contrapuncti (1477), associatesthe last of these types with compositions written down by master composers,Fuller notes that in its earlier stages, this tradition was concerned more withperformance and `musical production' (adding parts to a given cantus) thanwith free polyphonic composition. Peter Schubert's `Counterpoint pedagogy inthe Renaissance' carries this line forward, arguing that, while contrapuntalwriting was increasingly codified during the later period, theory's primaryconcern was not so much with control of dissonance and voice leading as with arange of procedures grouped around the concept of suggetto, a melodic subjectexpressible variously as a brief single voice, a duo, or even an entire polyphoniccomposition. Schubert considers a number of practices, including contrapunctussimplex (Fuller's third stage), florid counterpoint, modal influences, imitation induos and pairs of duos, double counterpoint, and the rhetorical concept ofcomposition as an `assembling of fragments'. Albert Cohen's `Performancetheory' stresses western music's reliance on oral traditions and improvisation.As the only chapter devoted to performance practice, it opens with a briefsurvey of early manifestations in medieval organum and discant, whose texts hedescribes as 'little more than the codification of existing principles forextempore elaboration of chant' (p. 535), and closes with a word on moderndevelopments, such as the `positivistic' turn toward fully notated scores, use ofchance procedures, and the influence of technology. Cohen's main concern,however, is with the Baroque, reflected in his discussion of Marin Mersenne`scomments on performance, and in his treatment of thorough bass and themelodic-embellishment practices of the time.

The next essay is the first devoted to a single theorist. Ian Bent's `Steps toParnassus: contrapuntal theory in 1725 precursors and successors' examinesFux's abstraction of the rules of counterpoint reduced to their basic principlesand set out in a pedagogically-graduated sequence. While noting that this ideawas not unprecedented, Bent stresses that no previous theorist had gone aboutit in such a systematic manner. Since the practice of teaching counterpoint inFux's laboratory-like formulation proved enormously popular, his legacy isexamined in considerable detail, with a commentary on subsequent figuresseen as occupying either Fuxian or non-Fuxian camps. Finally, John Covach's`Twelve-tone theory' moves on some two hundred years and is less concernedwith twelve-tone practice (since, according to Covach, twelve-tone music failedto establish itself as a `marker' of modernism) than with what Covach calls `thetwelve-tone idea' as an area of theoretical speculation. He is especiallyinterested in this idea as an abstract, non-motivic conception of the chromaticaggregate as `background' from which `modal' chromatic material can bederived. This results in an alternative to the `canonic' Schoenbergian history,



one that foregrounds a theoretical line extending from the early work ofHerbert Eimert and Josef Matthias Hauer through Richard S. Hill and GeorgePerle to Milton Babbitt.

Part III's third subsection, `Time', consists of three essays on rhythmictheory, the first of which, Anna Maria Busse Berger's `The evolution ofrhythmic notation', guides us through the labyrinths of early rhythmic thoughtand notation. She details the initial, rudimentary notational system thatemerged in thirteenth-century Paris, linked to modal rhythmic measurementsand developed in response to western music's evolution from a largely oral to awritten tradition. Although this extremely restrictive approach soon under-went improvements, loosening its ties with specific rhythmic values, it wasonly fully dissolved in the ars nova of the early fourteenth century, whose lessconstrained system allowed freer combinations of duple and triple values. Afterdiscussing the introduction of proportional notation, Berger credits Tinctoris,writing in the fifteenth century, with bringing order to the profusion ofnotational signs used for rhythmic purposes. William E. Caplin's `Theories ofmusical rhythm in the eighteenth and nineteenth centuries' traces the trans-formation of Renaissance mensural practice into the modern rhythmic systemof accentuation, metres and durations, bringing about equality between dupleand triple divisions, clear distinctions between simple and compound metre,and eventually leading to theories of metrical accentuation. He then concen-trates on the eighteenth century, when theorists began thinking of phrasesrhythmically, as groups of measures, a tendency expanded during the followingcentury and culminating in Riemann. Subsequent approaches are detailed inJustin London's `Rhythm in twentieth-century theory', which subsumes anumber of more recent approaches under four overarching categories: theoriesof musical time and motion influenced by scientific ideas; Schenkerianapproaches to rhythm; architectonic or hierarchical theories influenced bylinguistics and gestalt psychology; and post-tonal rhythmic theories.

The final subdivision, `Tonality', fills in the `common-practice' gap betweenthe seventeenth century and harmonic dualism left hanging in the firstsubsection. Brian Hyer's essay, also titled `Tonality', is a general introductionthat tracks the term's origins, its associated rhetoric (tonality as `God-given',`natural', etc.), its emergence during the seventeenth century, and its eventualformulation as a `monotonal' subordination of all events to a single tonic. Hyeralso examines various nineteenth-century developments that underminedtraditional tonality, eventually leading to the Schoenbergian notions of sus-pended, floating and multiple tonality. Joel Lester's `Rameau and eighteenth-century harmonic theory', the second essay on a single theorist, focuses on hiswork in relation to predecessors and followers. Lester notes that, despiteRameau's originality, his great strength as a theorist was to unite manypreviously independent theoretical concerns, including thorough bass, funda-



mental generation, chord inversion, cadential practice and major and minor keysystems. Integrating these with his own conception of fundamental bassprogression, Rameau achieved an explanation of melodic and harmonic motionof unprecedented precision. Lester also details Rameau's enormous influenceon subsequent harmonic developments, including scale-degree and functionaltheory, and fundamental bass theory itself. David W. Bernstein's `Nineteenth-century harmonic theory: the Austro-German legacy' takes up the threeschools that grew out of these lines of influence, all centred ± despite theirFrench origin ± in Germanic countries. Beginning with scale-degree theory, hedetails Georg Josef Vogler's and Gottfried Weber's conception of tonality as acommunity of chords erected on all diatonic scale degrees, a position leading tothe use of Roman numerals and (in Weber) to the first Tonnetz, or abstractchart of chords ordered by relational proximity. Subsequently Simon Sechterand Karl Mayburger extended Rameau's theory of fundamental bassprogression to include more chromatic relationships, and Riemann developeda chord-based theory of tonal harmony dependent upon three basic `functions':tonic, dominant and subdominant, the latter two symmetrically positioned atthe upper and lower fifth from the first. Bernstein closes with Georg Capellen'sand Schoenberg's end-of-century attempts to replace Riemann's dualism withmonistic harmonic systems capable of generating a wider range of harmonicpossibilities. In his `Heinrich Schenker', William Drabkin notes thatSchenker's mature theory, with which he is commonly equated, was precededby a sizeable body of less systematic work that is itself of considerable interest,and preferred by many. The mature theory is itself summarised withexplanations of critical Schenkerian concepts, often with discussion of theirorigins in the earlier work. Schenker's historical and intellectual background isalso examined, as is his posthumous reception (especially in the United States),along with various more recent extensions of his work.

Part IV: `Descriptive Traditions'

The somewhat confusing title of the book's final section is a catch-all fordisparate, mainly twentieth-century approaches grouped in two subsections:`Models of music analysis' and `Music psychology'. Patrick McCreless's`Music and rhetoric', after briefly surveying rhetoric's origins in antiquity andrevival in the Renaissance, focuses on its extension in the baroque concept ofmusica poetica. Three pivotal figures are discussed ± Joachim Burmeister,Johannes Lippius and Christoph Bernhard ± with tabular listings given formusical figures used by the first and last. McCreless notes Bernhard'scentrality in this tradition, as the first theorist to associate figures with specificstyles and to suggest that the apparent licenses of seconda practica were in factgrounded on prima practica conventions. Although the waning of rhetoric was



already evident in the writings of Johann Mattheson in the early eighteenthcentury, and its fate sealed by the ascendancy of text-independent àbsolutemusic', its importance as the first systematic framework for work-specificmusical analysis was considerable; and it has recently enjoyed something of arevival. Scott Burnham's `Form' addresses the `sprawling' growth of formalanalysis that, since the later eighteenth century, flourished in response to musictheory's newly developed `work concept'. Initially restricted to shorter formalunits, its subsequent extensions during the nineteenth century responded tothe growth of organicist conceptions of musical structure. Burnham, takingsonata form as his example, traces the turn from a primarily harmonic concep-tion of form to a thematic and rhythmic one. Tovey's and Schenker's`challenges' to this tradition, the former focusing on more particularisedstylistic matters, the latter viewing form as a mere surface manifestation, arenoted, as are recent attempts to return to the eighteenth-century idea of form asa principally tonal phenomenon. Jonathan Dunsby's `Thematic and motivicanalysis' closes the subsection with consideration of various post-nineteenthcentury frameworks for analysing music's thematic dimension: developingvariation (Schoenberg), concealed patterns (Rudolf ReÂ ti), functionalrelationships (Hans Keller), prolongational structures (Schenker), set theory(Allen Forte) and semiotics (Nicolas Ruwet).

The opening essay of `Music psychology', Lee Rothfarb's Ènergetics',examines the pervasive idea that music communicates motion, a conviction thathas a long pedigree ± from antiquity to medieval pitch theory, baroquerhetorical conceptions, tonal harmonic theory and nineteenth-century formaldynamics. Rothgeb's main concern, however, is the establishment in the earlytwentieth-century of a well-defined ènergist' analytical tradition (the term wascoined by the historian of music aesthetics, Rudolf SchaÈ fke), based on theassumption that music communicates underlying `forces'. This plays anessential role in the thought of August Halm, Schenker, and especially, ErnstKurth; and it is also evident in Arnold Schering's musical hermeneutics andHans Mersmann's phenomenology, as well as in more recent developmentsassociated with theorists such as Wallace Berry and Leonard Meyer. In thebook's final essay, `The psychology of music', Robert Gjerdingen points outthat, whereas questions pertaining to music's relation to the human mind aredeeply embedded in the western tradition, the psychology of music as a distinctfield has had a relatively brief history. After noting anticipations in FrancisBacon and John Locke, Gjerdingen turns to two contrasting late nineteenth-century Germanic developments associated with Wilhelm Wundt and Stumpf:empirically-oriented Tonpsychologie and conceptually-oriented Musik-psychologie. Additional sections address American `functionalism' (CarlSeashore), behaviourism and recent work in cognitive psychology.



Commentary

It would be easy to find fault with some of Christensen's choices. There arechronological gaps in the sections (to cite just one instance, there is no essay onthe early history of work-oriented analysis), one could question the location ofparticular essays (why is the article on `performance theory' located in`Compositional theory'; and why are articles on dualist tonal space andnineteenth-century harmonic theory placed in different sections?), and perhapsthere is an overemphasis on post-renaissance German theory (at the expense of,say, French or Italian theory). Some will find that too much space is allocatedto tuning theory (though, curiously, twentieth-century microtonal tuning iscompletely ignored), and others may question the value of the two principalmetatheoretical ruminations in the `disciplining' section; still others will regretthe absence of an article on the close yet intricate connections that have linkedmusic analysis and music theory. The fact that `Compositional theory' containsno synoptic treatment of its twentieth-century manifestations, a matter ofconsiderable theoretical interest, is disappointing. (One must make do withCovach's rather special treatment of twelve-tone and serial thought, along withLondon's sparse comments on twentieth-century rhythm.)

From my experience, I know that an editor must make difficult decisions;and this is surely exaggerated when the historical-geographical scope is as greatas it is here. As a whole I find the book both remarkably well thought out andimpressively realised. If one accepts it for what it is, the book succeedsadmirably; and I doubt that it will be soon surpassed. But I must say that itsaim is decidedly restricted. Although any one-volume survey covering such avast chronological spread is bound to be confined, what is notable here ±particularly in view of current intellectual tendencies ± is that music theory islargely limited to its more technical dimensions, and that its application iscircumscribed by western art music as traditionally defined.

Since it is highly unlikely that anyone other than a reviewer will read thebook straight through, its primary use will probably be as an aid to researchand as a source of information on specific topics. (It is too long and covers toomuch ground to be useful as a textbook.) But for anyone, student or profes-sional, who wants to explore the history of a particular theoretical orcompositional idea, it will be a welcome companion. Using titles, index,cross-references and the extensive bibliographies included at the end of eachentry, readers will be able to discover a wealth of information on countlesstopics, along with ample suggestions for further study.

However, not all chapters fulfil their function equally well. A generalcomplaint expressed by many contributors is that the topics and historicalperiods they cover are too complex and diverse to allow for an accurate picturein the space provided. In her chapter on medieval polyphony, for example,



Fuller notes that, while Riemann could view its history in terms of an evercloser approximation of universally valid laws, the modern writer, aided ± or isit burdened? ± by the wealth of subsequent scholarship, is confronted with aradically different and much less manageable picture:

[T]o read even a handful of theorists from the ninth through the fifteenthcenturies is to become aware that goals vary, that those who write on proceduresfor organum, discant, or contrapunctus are largely concerned with quite

elementary training in the production of many-voiced music, and that theconventions they relay cannot be held universally valid for their time but relateto particular practices in delimited cultural strata and geographical locales . . . .The practices described in the extant treatises doubtless shaped the basic

sensibilities of young musicians . . . but the sphere of these practices had to dochiefly with oral polyphony and (to varying degrees) theoretical principle andonly partially overlapped the sphere of written composition. (p. 499)

Similarly, Schubert, referring to his treatment of contrapuntal pedagogy in theRenaissance, remarks: `For each theorist included here, there is another whoseideas make equally valuable contributions to the picture as a whole, whether inbasic concepts, terminology, or examples. No single theorist tells us everythingwe want to know, and there is little consensus among them' (p. 528).

The most successful articles, I find, face up to this problem, limiting theirscope so as to allow for a more orderly presentation. Fuller's and Schubert'schapters are exemplary, as are, among many others, Berger and Caplin onrhythmic theory, those by Mathiesen, Bower, Herlinger and Rasch on theearlier phases of the speculative tradition (though here this judgement may beinfluenced by my own deficiencies in this area), and Bernstein's thoughtful andefficient presentation of nineteenth-century Austro-German harmonic theory.The three chapters by Bent, Lester and Drabkin devoted to single figures ±Fux, Rameau, and Schenker ± have an obvious advantage in this regard, and allare first-rate. As part of his consideration on Schenker, for example, Drabkin isable to include and comment upon the complete first four graphic levels ofSchenker's monumental analysis of the first movement of Mozart's G minorSymphony, K. 550, along with the Urlinie-Tafel for the first 132 bars; and heprovides Schenker's middleground graphs for several other pieces. Bent'ssweeping chapter on Fux, with its wide-ranging treatment of both predecessorsand followers, is one of the gems of the collection.

On the other hand, Wason, assigned the daunting task of surveying theentire pedagogical tradition, must deal with so many different theorists, withsuch diverse aims (Guido of Arezzo, Zarlino, Rameau, Koch, Riemann,Schoenberg and Schenker are some of the more prominent included), as topreclude doing them justice, and his article leaves the reader with anunfocussed idea of the topic as a whole. One also wonders why this chapter,so different from its two companions, appears in the `disciplining' section. An



analogous problem arises with Covach's treatment of twelve-tone theory, asubject that would seem, on the face of it, to be concerned with a much morecircumscribed area. His decision to provide an alternative perspective forceshim to treat too cursorily a number of theorists who will be little known to mostreaders. Schoenberg, whom most will think of first and foremost in connectionwith the topic, receives relatively short shrift, with much of the segmentbearing his name devoted to his pupil Erwin Stein. (Covach allots Babbittmore space than anyone else.) Given its emphasis, this entry would be moreappropriately located within the `tonal mapping' section than in `compositionaltheory'. Similarly, London's reduction of the complexities of twentieth-century rhythmic theory to four categories that have overtly fluid boundaries(as he himself seems to recognise) and that cover a confusing breadth ofpossibilities hinders adequate presentation. Albert Cohen's chapter, the onlyone concerned with the theory of performance practice, is regrettably thin.

One might also raise questions about the extensive overlapping amongentries. My general impression, however, is that this is an advantage. The factthat critical figures like Zarlino and Riemann, for example, who have no entryof their own (or for that matter Rameau and Schenker, who do), appearprominently in several different entries, often at considerable length, providesa valuable multiple perspective on their work. Problems of repetition are oftenneatly negotiated (Mathiesen, in his article on Greek theory, focuses on theorigins of a number of concepts that helped shape the birth and development ofmusic theory in the West, while Bower concentrates on their transmission inthe work of prominent theorists during the Middle Ages). Similarly, the firsttwo sections of Rasch's article, devoted to later Pythagorean and just-intonational tunings involving monochord division, overlap with Herlinger'sentry on harmonics but concentrate on two sixteenth-century theorists(Glarean and Salinas) who are absent from Herlinger's account.

Most of the essays are consistently `presentational': they seek to offeressential information rather than argue for some special interpretation of theirtopic. Readers will find the essays dealing with areas in which they haveparticular expertise relatively non-controversial; they give up-to-date data butdo not unnecessarily grind axes. There are exceptions. Nolan's article onmathematical applications in music theory, which provides a very effectivesurvey of some of the ways mathematical thought and numerical conceptuali-sation have contributed to the discipline, also argues repeatedly for theusefulness, even essentialness, of that methodology's `generalizing power'.Dunsby's `Thematic and motive analysis' is exceptional for a different reason.It provides very little basic information about the analytical approaches hesurveys, evidently assuming the reader will be fully acquainted with them.Shunning exposition, Dunsby offers a series of fearfully dialectical meditationson the advantages, disadvantages and assumptions associated with each. In his



treatment of `semiotic' approaches, for example, almost half his space is givento a discussion of the general semiotic conception of signs as `arbitrary' innature, having both `synchronic' and `diachronic' implications, and beingeither `paradigmatic' or `syntagmatic' in function. When Dunsby finally turnsto musical applications, he opens with the following, not atypical paragraph:

It is a hallmark of such studies that comparisons, that is, music-analyticalstatements about similarity and difference, are explicit, so that for example theapproximations and excesses of informal critical language as well as the

positivism of `pure' (one might even say, non-Schenkerian) formal theory areequally shunned, the one because of the semiotic ideal of precision, the otherbecause of the ideal of consistency. The `explicit' entails not only the metaphors

and metalanguages themselves of technical musical description and explanation,but also their epistemological status: it entails the attempt at a continuousawareness of what kind of knowledge they are and from what kind of knowledgethey are derived; in the semiotic `tripartitional' analysis of any signifying

process knowledge is regarded as being inevitably some combination of thepoietic, the esthesic, and the `neutral'. It is an incidental result of thisinterrogatory character of music semiotics that any particular inquiry can

necessitate the process of relatively large amounts of information. (p. 921)

This will not be of much use to most readers, I suspect (though some alreadyconversant with the topic may find it stimulating). Dunsby subsequentlyreprints and comments on a brief melodic analysis by Ruwet, but offersnothing concrete about the form it has been given or the properties it contains,or how it differs from a non-semiotic analysis.

A Word on Historiography

The final section of Brian Hyer's `Tonality', entitled `Historiography', is alsoexceptional. His aim, unlike Nolan's or Dunsby's, is essentially critical innature. What he says is interesting because it is unlike anything else in thevolume and because it appears to call into question the very assumptions uponwhich the book was conceived, including the previous sections of his ownessay. It provides a useful source for considering certain historiographic issuescentral to the entire collection.

The first paragraph of this essay, quoted in its entirety below, is directed atan aspect of Hyer's topic, but its ramifications, as will become evident, go farbeyond it:

The diachronic account of tonal music given in the preceding section is mostoften related in terms of musical evolution as continuous progress, a masternarrative in which the historical course of tonal music is directed toward its ownend, depicted either as a completion or (as is more common) a tragic demise. In

either case, the telos of these stories reflects (perhaps ironically) the strongforward momentum toward a cadential goal so often thought to be an essential



attribute of tonal music. While these histories are sometimes recounted astechnological allegories in which tonality collapses, breaks down, or wears outfrom overuse, it is more common to imagine them as genetic narratives, organicprocesses of growth and decay, birth and death. (p. 745)

This may seem unobjectionable yet it is already overstated. Few today woulddescribe the development of tonality in terms of `completion' and `tragicdemise'. But Hyer ventures onto considerably thinner ice when, subsequently,he attempts to flesh out this argument and draw conclusions about the sorts ofassumptions we make in charting the history of tonality. He begins byquestioning tonality as a topic: `[C]omposers, music historians, and musictheorists have tended to exaggerate the importance of tonality as a theoreticalconstruct. The entire historical account in the previous subsection [his ownbrief survey of the history of tonal `practice'] could be rewritten withoutreference to the idea' (p. 746). He then offers three reasons why one mightreject an evolutionary view of tonality and, more broadly, `the application ofevolution to cultural phenomenon in general' (p. 745): it makes us ignore thefact that composers are human agents with particular historical intentions; itobscures the complexities of historical process by identifying a dominant`mainstream'; and it privileges later practices over earlier ones.

It is not clear to me why any of these conclusions need follow, sinceèvolution', tonal or otherwise, does not have to be conceptually tied to`progress' or to a dominant mainstream, nor need it be unaffected by humanagency. Hyer, moreover, gives little indication of how he, or anyone else, mightactually rewrite his previous account without using the concepts of `tonality'and èvolution', however they might be defined. His statement that `the historyof tonality is better understood in terms of specific harmonic practices ratherthan immutable laws' is no help, since there is no reason why one cannot createan evolutionary narrative based on practices rather than laws. Indeed, thatwould be consistent with the way most, if not all, theorists and historians nowthink about tonality. (Does anyone believe today that there are ìmmutable'musical `laws'?) Hyer's objection to the organic, biological narrative is there-fore based on a misconception: that organicism, instead of being a more-or-lessuseful metaphor, obligates one to join evolutionary processes with scientificnotions of `necessity'. Surely we know now that the organicist metaphor, whiledrawn from the natural sciences, takes on a very different, non-scientificmeaning when applied to music.

Despite Hyer's claim, no one believes that tonality `no longer exists'. All onehas to do is open one's ears to what is going on in the musical world to realisehow absurd such a position would be. (Even traditional, `common-practice'tonality continues to be taught in many classrooms.) The point should be that,while tonality still exists, it exists in a context that has radically altered themeaning of tonality as a musical and social phenomenon. Tonality is now part



(even if, assuming a much broader definition than Hyer's, it is the dominantpart) of an enormously expanded set of possibilities ± a situation that, forexample, makes us newly conscious of how difficult it is to draw a sharp linebetween what is and what is not tonal.

There is a certain validity in Hyer's objection (in the paragraph quotedabove) to the kind of evolutionary narrative that has sometimes been associatedwith tonality's history in the past: as ineluctable progress toward an idealisedgoal that, once attained, gives way to a process of gradual (and regrettable)decline. What is problematic is his objection to the theoretical concepts oftonality and evolution themselves. When he complains, for example, thattonality is àn ideological as well as a theoretical concept' (p. 747), the incon-gruity of his position within the context of this book becomes conspicuous: alltheoretical concepts, including those used throughout this survey, have anideological dimension. Constructs like `tonality' or èvolution' are not given`neutrally' as pre-existing features of the world, but are imposed upon it to giveit shape and meaning.

One indication of tonality's unreliability, Hyer remarks, is the fact that ideasabout tonality have been àppropriated for both conservative and radicalaesthetic agendas'; but that charge could be levelled equally against almost anytheoretical idea found in this book. Even something as basic as the distinctionbetween consonance and dissonance, for example, though still virtuallyuniversally accepted (even in this post-Schoenbergian age) has been con-sistently reinterpreted to accommodate changing musical circumstances; and ithas also been used on numerous occasions to bolster both `conservative' and`radical' musical causes. This does not make it any less useful, or even essential,for writing a history of western music or its theory. All of Christensen'sauthors use such constructions, whether self-defined, borrowed from others, orlifted from one of the book's theoretical `traditions'. They are indispensable tothe entire project.

Yet Hyer holds up a different ideal: a `disinterested view of the historicalpast' (p. 749), even à neutral account of music history' (p. 750). If this meansavoiding musical constructs such as tonality, however, there simply is no suchthing (or to the extent that there is, it is of little interest or use to anyone). Theeditor and authors, for example, have had to make countless choices: what toinclude and exclude, what to emphasise, which categories to use in organisingtheir material, and so forth. Whether their concern is with the history oftonality, the evolution of medieval contrapuntal thought, transformations intuning, or differences in the way rhythm is organised, their evolutionarynarratives are in that sense ìdeological'. They make their descriptionsmeaningful by placing them in conceptual structures that are, by definition,`loaded'. One is at liberty to reject one of more of these structures, but to rejectone is inevitably to assert another.



My intention is not to argue for historical relativism. Issues of music theoryand its history stem from a real, external musical world, independent of thescholars who write about them, and they can be rationally debated (otherwise,why is music worth arguing about?) But in order to discuss these issues,interpersonally and meaningfully, we make assumptions and formulate con-ceptual frameworks with which to think and write. What is disconcerting aboutHyer's position, then, is that he dismisses an interpretation with which hedisagrees as ideologically tainted while maintaining that his own is ideo-logically innocent, absolving him from any need to debate. One can perhapsrecognise the source of this position in the evident inconsistencies of his ownargument, as when he states that the historical narratives of tonality fail `toaccount for the continuous use' of tonal resources in twentieth-century music,but then in the very same sentence refers to a `renewal of tonal resources', ortwo sentences later to the `re-emergence of tonal idioms within the post-modern avant garde' (p. 750). Similarly, immediately after acknowledgingjazz's òngoing experiments with atonal idioms', he baldly states that in jazz`[tonality] has never loosened its grip on the musical imagination' (p. 746).

These reflections on the historiographic nature of Christensen's Historysuggest that there may be a critical omission in his table of contents: a `meta-theoretical' chapter examining the concept of theory from a more fundamentalperspective than the editor in his introduction or the authors of the `disciplin-ing' section provide. Such an essay would undertake a truly fundamentalexamination of `music theory', not simply in terms of how it has been conceivedwithin a particular group of western `traditions', but directed rather to how itcould be conceived ± or perhaps even should be conceived.4 Such an essay mighthave examined recent developments in musicology that have raised questionsabout the entire theoretical discipline as traditionally constituted, and couldpoint out that the word `theory' has been (and in general continues to be) used inour discipline in a much more restricted sense than in other humanistic fields inwhich it has come to represent a virtually unlimited set of interdisciplinaryconcerns intended not only to investigate but also to interrogate basic assump-tions. This would bring out questions that are largely ignored here: what sort ofthinking is theoretical thinking; for whom is theory written; for what purpose isit written; what do different genres and cultures of music tell us about inheritedtheoretical assumptions; how do differences in ethnic, gender and sexualidentity impinge upon theory; to what extent do theoretical pronouncementsmerely bolster entrenched positions; and what might a truly alternative theorylook like? It could also address an additional question that, though clearlyrelevant (and pressing), has also been skirted: to what extent have more recentcompositional developments ± àvant-garde', èxperimental', `postmodern',`crossover', `world-music', etc. ± served to transform our conceptions of theory,indeed our very sense of what music is and what is worth saying about it?



Admittedly, such a chapter would seem out of place in this traditionallyconceived survey, both disturbing and distorting; and I understand why it wasnot included. But I also wonder whether we have not reached a stage in ourdiscipline where we can no longer afford to exclude such questions ± questionsthat, assuming a more catholic perspective, are of as much `theoretical' concernas any touched on in this volume.

Conclusion

Cambridge University Press should be commended for producing thisextraordinary book. Its size and weight alone provoke wonder. In addition toa generous quantity of musical examples, there are numerous graphicillustrations taken from treatises discussed within its pages. Many of theseare not only conceptually helpful but of considerable visual interest, evenbeauty. (One of the more pleasing aspects of music theory's evolution is that somuch of it has been realised with the aid of striking visual presentations ± oftunings of the monochords, relations between music and cosmic ratios, musicalcircles, formal charts, and prolongational reductions, to name only a few).There are also many tables containing information to help readers find theirway through what might seem to be impenetrable thickets of information.Another welcome feature is the use of boxes to separate tangential but relatedmaterial from the main body of the text. Many of these cover an odd butpleasingly disparate group of topics, including the history of early musicprinting (Judd), the influence of Roman measurements on rhythmic concepts(Berger), chromatic and enharmonic divisions (Herlinger, quoting ChristianMeyer), notational methods suggested for twelve-tone notation (Covach), andTovey's analysis of the first movement of Beethoven's Op. 10 No. 1(Burnham).

In closing, and to underscore some of the aesthetic-historiographic issuesraised, I quote an especially revealing passage from Bower's essay. Although itrefers to the Pythagorian myth of the divination of harmonic ratios from theweights of a blacksmith's hammers, it states an important truth applicable tomany of the theories covered by this volume and provides one reason why it issuch a valuable publication:

The roots of this myth so fundamental to the history of Western musicalthought are buried within ancient values and archetypes that can never be fullyfathomed. The empirical data offered in the myth is wholly specious. . . .However, the myths and dreams of a civilization are judged not by their

empirical truth or falsity, but by the expression of intellectual and spiritualcomplexes they reveal within a culture. (p. 143)



NOTES

1. Though these are Christensen's own words, their reference is to Dahlhaus's `Washeisst ``Geschichte der Musiktheorie''?', in Ideen zu einer Geschichte derMusiktheorie, ed. Frieder Zaminer, Geschichte der Musiktheorie 1 (Darmstadt:Wissenschaftliche Buchgesellschaft, 1985), p. 28.

2. Hugo Riemann, Geschichte der Musiktheorie im IX.-XIX. Jahrhundert (Leipzig:M. Hesse, 1898).

3. Geschichte der Musiktheorie, ed. Frieder Zaminer (Darmstadt: WissenschaftlicheBuchgesellschaft, 1984± ).

4. The first edition of the New Grove Dictionary of Music and Musicians (London:Macmillan, 1980) revealed a similar lack: as was noted by at least one reviewer, itcontained no general entry on `music'. (This lapse was remedied in the revised2001 edition by an unusually wide-ranging article by Bruno Nettl.)



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