Two assumptions, common to all parties, lie at the heart of the dispute over the status of harmonic knowledge, and the possibility of supplanting it with a better foundation. The first assumption is that some sort of theory is necessary for the student’s foundation, whether technical, social, or otherwise: students need a theory upon which to build their thought. Second, whatever form this theory may take, its relation to practice is fixed: theory explains practice. If theory is necessary at all, in any form, it is to give students a reasoned basis for their own practice, or someone else’s. And yet, this presumed complementarity of theory and practice, and the debates addressing which practice to teach and by which method, ignore the radical possibility that music theory may reject these notions of “method,” “practice,” and “proper foundation” completely.
Rather than asking which theory is the best foundation for which practice, let me ask a different set of questions: why does elementary music theory, as we expect it to be taught, account for common-practice harmony and promote it through a strict disciplinary regimen, rather than encouraging students to imagine their own harmonic practices? What internal challenges to the authority of practice does this account omit or rewrite in its own history? What moments of “impractical” musical rationality—moments that redefine practice by exposing its contradictory logic—does it repress? What would a history of these moments look like, and how would it relate to the familiar history? By answering these questions, this dissertation serves as a tool for those who believe in the power of reason to trump the authority of practice: of the music student to reject the teacher’s expertise; of the composer to rewrite a musical tradition without paying the proper respects; of music historians to use their naïve reason to upset the balance of musical facts. Such a history celebrates the misidentification that puts any practice at odds with itself whenever musicians, even ignorant musicians, think and speak for themselves.
Such misidentification, in fact, complicates the Enlightenment theoretical tradition vilified by disciplinary progressives. The consistency of the harmonic tradition they malign is chimeric, and their intervention merely substitutes one irrational musical practice for another. Let us suppose, against their assumption of good and bad foundations and practices, the equality of musical reason that renders all other foundations superfluous, and that reconfigures any practice. The harmonic demonstrations of Euler, Riepel, and Rameau exemplify this impractical rationality: their treatises contain an intellectual adventure that the experts of the conservatory and university would rather forget.
This dissertation addresses two urgent problems of academia’s own common practice. The first is the intellectual bankruptcy of an elementary theory curriculum designed to teach its students the “language of the masters.” Aldwell and Schachter make this objective clear in the introduction to their popular textbook:
There are no shortcuts in learning music theory—especially in the development of writing skills. If twenty-first-century students wonder why they need to master such skills—why they need to take the time to learn a musical language spoken by composers of the past—they can be reminded that they are learning to form the musical equivalents of simple sentences and paragraphs. The purpose is not to learn to write “like” Mozart or Brahms, but to understand the language the great composers spoke with such matchless eloquence, the language that embodies some of the greatest achievements of the human spirit. {5}We need to dispense with the humility that compels us to explain the masterworks of the past, and to measure our own musical accomplishments against these so-called pillars of human achievement. We do not need to learn an ossified practice to make sense of our own; moreover, we have better uses for our musical thought than using it to justify our taste, or—worse, and more often the case—to justify imposing our taste on someone else, or—worst of all—to justify imposing Schenker’s taste on ourselves. The elementary theory curriculum in its common form imposes and replicates this bland ideal of musical authority. Radical Enlightenment theory, on the other hand, teaches us to consider the music we already know, and to imagine how to fix it, to make it our own. The problem of the students’ education is not to find a good practice for them to work with—the practice they bring to class is all they need—but to enable them to redefine their own practice. The power to “understand” is, after all, the power to invent, to alter, and to compare. Teachers and students alike have nothing to learn from the great works of the past that they cannot teach themselves through their amateurish musical reason alone.
Though the second problem may cut across all the academic sub-disciplines of music, it particularly affects my work as a composer. It is the tendency to celebrate music’s sound at the expense of its image. Composer Tristan Murail is adament in his conviction that notation, at worst, deceives the composer with its symbolic permutations, and, at best, merely approximates true acoustic content:
Murail is embarrassed by notation’s notes, rhythms, and dynamics, and he is not alone. Given premiums on rehearsal time, most composers, regardless of aesthetic conviction, likewise treat the score as a means to an end, adopting a conservative notational ethic to minimize confusion. For them, notation, the awkward signifier of acoustic meaning, is best forgotten. I, however, have no such interest in making notation disappear—to the contrary: I want to expose how notation can work with sound, and sometimes against it, to structure musical thought and experience. In a recent composition, for example, I project a graphic score for the audience to read along with the performers, so that everyone can participate in the game of musical signs. I propose this dissertation in the spirit of that game. By exposing productive tensions between sound and notation, I want to help other musicians and composers reevaluate their own strategies of reading and writing.There is a conceptual error from the very beginning: the composer does not work with twelve notes, x rhythmic figures, x dynamic markings, all infinitely permutable—he works with sound and time.
The sound has been confused with its representations, and we work with these with symbols. Since these symbols are limited in number, we quickly come up against the wall...
Musical notation no longer exists as a given, nor as a point of departure; it only serves as the end point of a compositional process and to transcribe the results obtained for the observer (quite often in a necessarily approximate manner). {6}
With the maturation of music theory as an academic discipline in American universities over the past twenty-five years or so, there has been a virtual renaissance in the historiography of music theory among American music theorists, with a growing concern to understand the genealogy of our profession and the work we carry on. ... Recent research can also be seen as an effort to bring music theory within the broader field of cultural and intellectual history. {7}In summarizing the general accomplishments of this movement, Christensen mentions three types of historical work that are relevant to my own project on Baroque harmonic theory. The first takes the form of the “biographical monograph” or “survey”: this history of facts includes Christensen’s own book on Rameau, {8} as well as Joel Lester’s work on eighteenth-century compositional theory. {9} Second, there is the body of work emphasizing “cultural hermeneutics”—more precisely, work using a Foucauldian methodology to structure a history of institutions and epistemologies. Christensen cites Moreno’s work as the prime example, but books and articles by Rehding, Blasius, Chua, and Braunschweig also fit into this category. {10} Third and finally, standing more or less on its own, is Judd’s work on the history of musical examples. {11} As Christensen explains, “Judd shows how the incorporation of printed examples in a text often complicates—and even undermines—the theoretical arguments of the author by introducing aurality within a visual medium.” My dissertation works at the intersection of these three histories, to sketch a portrait of radical thought in the Baroque’s harmonic theory.
Whatever their differences, all three historical methodologies assume a certain disorder in the history of music theory; the historian takes on the job of finding order in the chaos. Through the accumulation of contextual material, the historians of facts try to expose the logic behind the Baroque harmonist’s contradictory examples, faulty explanations, and empirical inconsistencies. This is how Christensen justifies his work on Rameau:
What makes Rameau’s theory such a fascinating and rewarding subject for investigation, I believe, is the rich dialectical interplay it manifests between musical and cultural forces, between the “internal” problems of musical practice and pedagogy that he addressed, and the “external” ideas and language indigenous to the French Enlightenment by which he solved them. To reveal this dialectic, the historian must move back and forth in a kind of counterpoint between Rameau’s texts and his social-cultural contexts. {12}In Christensen’s work, the facts of French intellectual history intervene to clarify “Rameau’s turgid and repetitious prose,” and to elucidate a “difficult and unwieldy body of literature that has frustrated redaction by even the most sympathetic of Rameau’s readers, both past and present.” {13} Foucauldian historians likewise write to restrain music theory’s unwieldy mess, but rather than building up a context around it, they imagine a subtext beneath it: that is, they posit an ideological consistency behind the veil of musical facts. Of course, to prove this consistency, the Foucauldian historian, like the historian of facts, must dig beyond the narrow boundaries of music theory, but the point of the digging is to unearth the profound regularities of musical discourse. In the preface to his book on absolute music, Chua describes his methodology in terms of Foucauldian archeology:
The question, for Foucault, is not “who makes history?” but how things are ordered. So in this book it is not so much who makes absolute music but what structures of knowledge need to be in place before absolute music can exist at all. This means that absolute music cannot be confined to the history of music as if it were purely musical, circling in its own autonomous sphere. What it claims to be is embedded in structures outside music(ology), and it is only by excavating these sites that the meaning of absolute music can be reconstructed. {14}Chua wants to reveal the currents of thought that flow underneath the surface of absolute music’s factuality. He clarifies musical facts by making them transparent—that is, contentless beyond their ideological meaning. Judd works on a smaller scale than Chua and the Foucauldians, and even Christensen and the historians of facts, by discovering ruptures between musical examples and the texts surrounding them: “Music disrupts the discourse, halts its progression, interrupts the rhythm of words.” {15} She make sense of this disorder not through the context of a broadly-defined intellectual history or the subtext of an archeology, but through the material history of the book, and the habits of musical print culture: “[I] began to think about the significance of music-theoretical treatises as material objects, as books which partake of a whole host of conventions and contexts that we overlook when we focus solely on the immaterial content of their abstract theorizing.” {16} In their histories of facts, institutions, and examples, then, scholars write three variations on the common theme of music theory’s disorder, and find three ways to resolve it.
Their order, however, comes at the price of excluding the most radical voices of Enlightenment theory. By default, the history of facts is a history of weighty names, a history that marginalizes the strange fantasies of the most independent theorists. Christensen’s work on Rameau is a case in point, and though Lester mentions the work of Euler and Riepel, it is only in passing: their facts are peripheral to the proper facts of Rameau, Fux, Kirnberger, and C. P. E. Bach. The silence is even more profound in the Foucauldian music histories that rewrite theoretical disorder as hidden social order. While Foucauldian scholarship makes a philosophical or political intervention possible, its overarching view of interdisciplinary regularities is too coarse to pinpoint the radical contributions of individual music theorists. The Euler of Blasius’ “Mapping the Terrain,” for example, stands hand-in-hand with Rameau, at the intersection of “four discrete systems of perspective,” “governed by shared epistemologies” that structure Baroque musical meaning. {17} Blasius’ method cannot explain the particular differences between Baroque music theorists, nor acknowledge the possibility of multiple Baroque epistemologies coexisting, nor allow any Baroque theorist to speak out against a dominant model of musical thought. Judd’s material history is often just as reductive as Foucauldian epistemological history, though in a different way: it subordinates the words of theorists to their material desire. Judd interprets Zarlino’s Le istitutioni harmonishe primarily as an expression of the author’s ambition:
I will argue that among Zarlino’s reasons for publishing the volume was an attempt to position himself for an appointment like the one at San Marco. Its date of publication neatly coincided with the advent of the Academia Veneziana but also, more significantly, with the declining health of Willaert and his extended absence from his duties at San Marco. {18}Insofar as the theorist speaks in Judd’s work, it is as one who wants, not as one who thinks. To organize the history of music theory, these historians each find a way to silence the disagreement of the past. But this is no surprise: the voices of reason always interfere with the orderly flow of history.
In other words—and this is obviously something that historians do not like to examine too closely—the clear division between reality and fiction makes a rational logic of history impossible as well as a science of history.
—Jacques Rancière {19}
How does one write the history of Baroque music theory’s counter-practice? Is it possible to help the radical voices of the musical Enlightenment speak? Following Rancière, we begin by rejecting the archeological method that reduces all dissent to the consistency of ideology:
I differ from Foucault insofar as his archaeology seems to me to follow a schema of historical necessity according to which, beyond a certain chasm, something is no longer thinkable, can no longer be formulated. ... Statements or forms of expression undoubtedly depend on historically constituted systems of possibilities that determine forms of visibility or criteria of evaluation, but this does not mean we jump from one system to another in such a way that the possibility of one system corresponds to the impossibility of the former system. {20}Different systems of possibility, then, may coexist in Baroque musical thought. The historian of theory does not need to unify them; their unification only silences marginal voices. This does not mean, however, that all historical possibilities coexist peacefully and independently. To the contrary, Rancière posits a dominant police, standing for “the way things are”:
The police is thus first an order of bodies that defines the allocation of ways of doing, ways of being, and ways of saying, and sees that those bodies are assigned by name to a particular place and task; it is an order of the visible and the sayable that sees that a particular activity is visible and another is not, that this speech is understood as discourse and another as noise. {21}I propose a practical order of music that functions analogously to the police. The practical order defines acceptable roles in a musical community (for example, the roles of theorist, student, and musicianship teacher); it creates spaces for acceptable relationships to develop (the classroom, the practice room, the recital hall); and it decides who may speak (the teacher) and who is condemned to silence (the student). This practical order also divides the legible from the illegible, through proper and improper uses of music notation, and, of course, audible music from inaudible noise and silence.
The practical order of the Baroque is “common practice”: a model of a musical community, and the harmonic theory used to justify this community’s impositions—its disenfranchisement of amateurs and eccentrics who need to learn to write “good harmony” as a prerequisite for musical thought. Paradoxically, the practical order is only possible if its radical alternative, an impractical order, is also possible: that these disenfranchised musicians may speak for themselves, substituting the true commonality of musical reason for the false commonality of practice. This alternative is analogous to Rancière politics, which reconfigures the police order’s distribution of the sensible by superimposing a distribution of its own:
Political activity is whatever shifts a body from the place assigned to it or changes a place’s destination. It makes visible what had no business being seen, and makes heard a discourse where once there was only place for noise; it makes understood as discourse what was once only heard as noise. {22}Music’s impractical order relates to the practical order just as politics relates to the police. It not only antagonizes common practice and practical theory, but does so by frustrating the roles and relationships that the practical order takes for granted, demonstrating their arbitrariness through the confrontation itself. Impractical theorists make themselves heard through their equal capacity for musical reason alone, a capacity that confounds the practical inequalities of, for example, amateur and expert. The mere demonstration of “the way music can be” transforms the dominant musical order, proving the contingency of common practice and the expediency of practical theory.
Music theory may distance itself from practice completely, by inventing a lofty music of the spheres or by emphasizing acoustic phenomena, but this is not what I mean by impracticality. Musical order is impractical, in my narrow technical definition, only if it literally “makes sense” of the practical order’s nonsense. That is, it must appropriate the practical order’s forms of representation and recontextualize them to expose their gaps, revealing meaning in noise or silence. In this respect, impractical theories must be distinguished from theories that simply resist the practical order without reconfiguring it. A theory that embraces parallel fifths and octaves, for example, is hardly impractical, because in the common practice, parallel fifths, though forbidden, are still visible and audible: the practical order must recognize them to reject them. (This is clear from Catel’s treatise, among others. {23}) Similarly, a power struggle does not change the practical order’s sensible structure: a student may refuse to practice, and a teacher may refuse to give an exam, but these disruptions do not reconfigure the audible or visible. The rationalization of music notation in Baroque theory, however, is extremely disruptive; rationalized notation literally creates a space on the page for chords that are senseless in practice. Euler’s mathematical theory makes sense of the visual and aural chaos of apparent tone clusters; Riepel’s permutations make sense of practically useless figuration; Rameau’s tabulation makes sense of chord inversions. The impractical theorists of the Baroque, through these exemplary demonstrations of musical reason, step beyond the implicit boundaries of common practice and practical theory, and, in doing so, redefine them.
It is important to distinguish the opposition of practical and impractical order to other critical rubrics currently in vogue. These musical orders do not draw a line between knowledge and lived experience: as Rancière says, “[T]he demonstration proper to politics is always both argument and opening up the world where argument can be received and have an impact—argument about the very existence of such a world.” {24} In this respect, a Rancièrean opposition is completely different from, say, the Jankélévitch-Abbatean opposition of drastic and gnostic, which supposes a performative excess inaccessible to abstract reason. Abbate sets live performance against “the tactile necropolis” of “recordings and scores and graphic musical examples.” {25} In this dissertation, on the other hand, I assume that the architecture of this necropolis—its distribution of words, sounds, and images—is necessary to make musical action possible at all. The politics of musical “liveness,” with its utopia of performing bodies that have forgotten how to read, write, speak, and rationalize, stands a world apart from the politics of musical representation that uses literacy, speech, and reason to highlight the contradictions and inequalities of practice.
This Rancièrean model also cuts across Carl Dahlhaus’ division of theory into speculative, regulative, and analytic branches. {26} Examples that are hard to categorize by Dahlhaus’ taxonomy may be easy to locate in the practical or impractical musical order. Kirnberger’s example of Froberger’s chromaticism is analytic, as it is an observation of practice; it is also regulative, presenting a rule for harmonic motion by example; and it is speculative, insofar as Froberger’s chord choice creates an acceptable correspondence between the visible and audible chords, in contrast with the unsightly enharmonic modulations of fully-diminished seventh chords. {27} The example slips between Dahlhaus’ terms, but falls squarely in music’s practical order, as expert practice that maintains an orderly relationship between sight and sound, implying an organic principle of harmonic motion—a principle the student must accept on faith. To take another example: when Rameau rewrites Zarlino’s two-part counterpoint exercise as his own, he, like Kirnberger, is engaged in all three theoretical activities as defined by Dahlhaus. His work is an analysis that borrows from the repertoire of practical theory, a speculation that conjures up a visible, inaudible fundamental bass as a harmonic abstraction, and a regulation that uses the abstraction to fill in Zarlino’s “missing parts.” {28} Rameau’s recomposition, however—unlike Kirnberger’s excerpt—exemplifies music’s impractical order: Rameau disregards Zarlino’s authority to generate new parts out of thin air, making sense of the practical order’s silence.
The impractical theorist’s demonstrations coordinate universal rules and particular examples. The rules are universal insofar as they appeal to the common musical reason of author and observer. They expose particular examples by filling in their missing representations: consider, again, Rameau’s extra voices for Zarlino’s counterpoint, Riepel’s unlikely figures, or Euler’s extravagent tone clusters. The rule reveals more than practice cares to reveal; its representation is excessive. If Baroque music theorists refined the rule-based demonstration, however, they also refined its opposite: the musical paradigm. This history of reasonable demonstrations must include that of musical reason’s fundamental antagonist.
Celebrating the paradigm, Giorgio Agamben describes it as “neither universal nor particular, neither general nor individual; it is a singularity which, showing itself as such, produces a new ontological context.” {29} A presumed “excess of meaning,” and equivalent lack of representation, defines the paradigmatic example. But paradigms cannot choose themselves: as Agamben admits later on, “the author” must “find and create the good paradigm.” Whereas the musical demonstration assumes and promotes the equal intelligence of teacher and student, the musical paradigm imposes an unequal knowledge: the teacher’s expertise, which is no more than the power to declare that an example is paradigmatic, set against the student’s ignorance, which is simply the powerlessness to identify the paradigm without the teacher’s help. The story of Baroque musial reason is also the story of this so-called expertise, as Johann Kirnberger and C. P. E. Bach extend the scope of paradigmatic examples to cover all harmonic knowledge. Historians of music theory, of course, recognize the Galant style’s emphasis on variation, improvisation, and organic development. {30} In particular, Karl Braunschweig demonstrates the importance of the paradigmatic binary oppositions of “essential/nonessential, norm/deviation, and necessity/freedom” in a number of later-eighteenth-century theoretical writings, including those by Kirnberger and Bach. {31} But none of these historians describes the unreasonable advantage that variations, improvisations, norms and exceptions give to the teacher of harmony, whose practical wisdom becomes a pedagogical wild card that can trump the student’s reason at any time.
All the activity of the disciplined individual must be punctuated and sustained by injunctions whose efficacy rests on brevity and clarity; the order does not need to be explained or formulated, it must trigger off the required behavior and that is enough.
—Michel Foucault {32}
Finally, the history of impractical musical theory must include the story of its necessary institutional failure, as the conservatory appears to reinforce the practical order through a model of expert knowledge. Cynthia Gessele’s work focuses on the codification and institutionalization of music theory in France in the latter half of the eighteenth century, up to the foundation of the Paris Conservatory. {33} She describes the abandonment of Rameauist “speculative theory” in favor of practical pedagogy: “The ‘science of music’ as the union of theory and practice was soon to be regarded as pointless abstraction and the division of the two approaches became an accepted and preferred methodology.” {34} The conservatory has no use for musical “abstraction”—that is, of any challenge to the practical order, which sustains its institutional authority. Perhaps, as Gessele writes, “The concept of ‘music as science’ was recast in the mold of ‘music as art’” {35}—but this redefinition is hardly an innocent epistemological shift. To the contrary, by making music inaccessible to reason, the conservatory can recast harmonic rationality in the mold of musical discipline. Discipline crafts optimal bodies, teaching them to be precise, obedient, and standardized; as Foucault explains, “The perpetual penality that traverses all points and supervises every instant in the disciplinary institutions compares, differentiates, hierarchizes, homogenizes, excludes. In short, it normalizes.” {36} Catel’s harmony textbook, the first adopted by the Conservatoire, outlines the disciplinary musical regimen par excellence, and serves as the model for our own musicianship curricula. Catel presumes obedience, rather than intelligence; he takes for granted the correctness of practice, invents a pedagogy by stringing together paradigmatic examples with a minimal appeal to reason, and shapes the student’s hands, eyes, and ears through exercise as orderly as it is thoughtless. We need only read Catel’s treatise against Fétis’ History of Harmony to understand the connection between the physical discipline of musicianship and the scholarly discipline of tonality. Ultimately they represent the same institutional practice of intellectual inequality—the inequality we celebrate whenever we celebrate musical practice, rather than our equal capacity to reinvent it.
In Leonhard Euler’s Attempt at a New Theory of Music (Tentamen novae theoriae musicae), {37} the famous mathematician devises a formula to assign an index of consonance to all chords in just intonation. {38} The treatise concludes with a remarkable table of gradated consonances, extending from the unison to unplayable tone clusters. This chapter begins with a technical account of Euler’s theory, highlighting its mathematical economy, distortions of conventional representation, and unplayability. I then analyze Euler’s argument aligning mathematical order with musical taste, and distancing both from contingent practice: “The more often we are aware that sounds have departed from the order which we decide should control them, the more we are displeased.” {39} I end with a revaluation of the widely-advertised “failure” of the Attempt, in its inability or refusal to adequately address the problem of harmonic progression, or as having “too much geometry for the musician and too much music for the geometer.” {40} Euler’s theory fails only if we assume that music theory exists to explain and justify practice. It succeeds as a demonstration of the theorist’s power to reject the false order of practice by creating a space for unfamiliar musical objects.
Euler’s theory is extreme in its rearrangement of music’s practical order. Baroque theorists tend to be more measured in their criticism of practical habits, more cautious in their impractical fantasies. Yet we may still find, scattered through their treatises, exemplary demonstrations of musical rationality. This chapter focuses on such demonstrations in the music theory of Joseph Riepel, whose exhaustive permutations of musical elements create a space for improbable harmonic figuration and melodic variation. {41} I analyze the incompatibility of two ideals of musical proportion in Riepel’s theory: those recommended by the master whose instruction directs the novice in the text’s dialog, and those established by the extravagant musical examples themselves. I compare Riepel’s rationalization of notation to Euler’s, noting that the same musical reason deduces entirely different impractical objects by formalizing different techniques of music writing.
Contemporary theorists celebrate Rameau as the father of modern music theory and the first theorist of music cognition. {42} But in their recognition of all that is familiar in Rameau’s work, they tend to neglect the strangeness of his examples—a strangeness that has little to do with the obvious complications of his prose or the repetitions of his subject matter. This chapter builds on Jairo Moreno’s analysis of examples from Rameau’s Treatise on Harmony, and their role in constructing the listener’s musical imagination. {43} The emphasis here, however, will be somewhat different, focusing more on the tabulation that makes all chord inversions visible and equal, in spite of a contrapuntal practice that emphasizes their unequal intervallic structure. I compare the tables of Rameau to those of Riepel and Euler, reflect on the incompatibility of musical tabulation with the linear order of modern music pedagogy, and suggest an ideal of “good taste” that deforms regularity to exceed both theory and practice. {44} Finally, I close the chapter—and Part I—with an analysis of the Euler-Rameau controversy. {45} The theorists’ debate over the validity of octave equivalence highlights Baroque reason’s profound challenge to any stable, normative musical order.
There is no progression, smooth or sudden, from an era of impractical harmonic theory to an era of practical harmonic theory. To posit such a progression is to ignore that music theory may only reject the practical order by example, through the appropriation of practical notation for unplayable, inaudible, or impracticible ends. The freedom to construct such demonstrations exists as long as the concept of “practice” exists; it is kept in check, however, by pedagogical strategies that bind theory to practice, minimizing theory’s disturbances of the practical order. Part II focuses on the harmonic paradigms of Kirnberger and C. P. E. Bach: examples that work against the assumption of universal musical reason by supposing, instead, the inequality of intelligence between musical experts, who are well-versed in practice, and practically ignorant amateurs.
Johann Kirnberger’s Art of Strict Musical Composition vacillates between tabular demonstrations of elementary harmonic reason and the advanced chromatic examples of the gallant style. {46} Whether celebrated as models of expert knowledge or condemned as exceptions to harmonic norms, Kirnberger’s examples counteract musical reason by imagining a harmonic essence that confuses or exceeds representation. First, I look at the specific example of enharmonic modulation with diminished-seventh chords, which Kirnberger criticizes for obscuring the listener’s impression of the fundamental bass—in other words, for making use of harmonic functionality that violates reasonable notation. {47} After that, I distinguish the rational tables of Euler, Riepel and Rameau from the list of models as embodied in Kirnberger’s chorale harmonizations, taking care to juxtapose the tables’ excess of visibility from the models’ excess of knowability. {48} It is this invisible knowability, this secret harmonic potential beyond explicit rules, that makes model composition possible and the subordination of the students’ intelligence necessary: Kirnberger forces his readers to take his practical expertise for granted, by disclosing no rational alternative.
In Kirnberger’s theories, despite the appearance of the paradigmatic example, there is still a space for the inventions of musical rationality. Reason still shapes the fundamental structures of music, and does so impractically, through a tabulation familiar to us from the work of Euler, Riepel, and Rameau. In C. P. E. Bach’s Essay on the True Art of Playing Keyboard Instruments, however, the paradigm invades the space reserved for music fundamentals. {49} Bach makes this possible by reinventing his audience, transforming them from rational novices—the inexperienced who possess an innate musical intelligence—to irrational experts—those practiced in the art of accompaniment, who nonetheless require the instruction of one even more experienced than they:
The most notable feature of this book is the attention given to artistic accompaniment ... . The observations are not speculative but rest on experience and wisdom. With no desire to boast, it may be said that this experience can hardly be rivaled, for it has grown out of many years of association with good taste in a musical environment which could not be improved. {50}Under the guise of the expert example, the paradigm replaces the reasoned principle at every step of instruction. The expert’s knowledge becomes an infinity of exceptional cases conforming to practice and rendering impractical musical reason inoperable. A detailed analysis of the chapter on thoroughbass shows that one may linearize these exceptional cases, but the consequent order is a disciplinary order. {51} Bach expects his readers merely to defer to his expert knowledge, not to question the authority of his practice with their own intelligence.
It remains only to institutionalize this discipline that disguises itself as musical rationality while frustrating it at every step; to rewrite the gap between lesser and greater experts as the gap of practice between teacher and student; to erase the free play of impractical theory with endless practical examples, excerpted from the good history of music. The institution will be known as the conservatory musicianship program; the scholarly discipline will be called tonality.
“In publishing his own system the author is far from depreciating those which differ from his doctrine. He has undertaken this work to simplify as much as possible the elements of harmony, and reduce them to their true origin, by showing that all discords are generated by concords.” {52} Charles-Simon Catel’s prefatory statement to his Treatise on Harmony echoes similar declarations by Rameau and Euler. In spite of this rhetorical affinity, however, Catel’s musical science has little to do with that of his predecessors. The unifying principle that makes his treatise “simple” is not the power of the overtone series to generate all tonal harmonies; though the author concocts a feeble demonstration of this “natural” relationship, it has no impact on a method animated instead by the nature of discipline—that is, the principle of exercise. The Treatise is a barrage of examples. Musical terminology interrupts the examples and constitutes their thin knowledge by proximity alone. The knowledge of terminology and examples is necessarily obscure for the novice and obvious for the expert. The practice that justified the selection of exceptional examples in C. P. E. Bach’s work, as a greater expert taught a lesser expert, now not only sets up the inequality of teacher and student, but also describes the only way that a student can surmount this inequality: through the rigorous exercise that is familiar to all students of modern musicianship programs. Thus the author inscribes the inequality of intelligence between teacher and student, and the discipline that is the student’s only option, at the heart of musicianship methodology.
1. See, among several examples in New York City, the requirements for an undergraduate music degree at Columbia, which include two years of (diatonic and chromatic) harmony and two years of ear-training; and New York University’s requirements, which are similar.
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2. Susan McClary: Feminist Endings: Music, Gender, and Sexuality (Minneapolis, MN: University of Minnesota Press, 1991), 4–8.
She is not alone. Suzanne Cusick likewise rejects “the essentializing and the dismembering strategies” of tonal analysis and harmonic discourse, instead privileging “less-valued, ‘sensual’ features like texture and timbre”:
3. Victor Kofi Agawu, Representing African Music (New York: Routledge, 2003), 8.
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5. Edward Aldwell and Carl Schachter, Harmony and Voice Leading (Third Edition) (Belmont, CA: Schirmer, 2003), xiii.
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6. Tristan Murail, “Spectra and Pixies,” in Contemporary Music Review, 1/1 (1984), 158–160.
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7. Thomas Christensen, “The History of Music Theory.”
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8. Thomas Christensen, Rameau and Musical Thought in the Enlightenment (Cambridge: Cambridge University Press, 1993).
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9. Joel Lester, Compositional Theory in the Eighteenth Century (Cambridge, MA: Harvard University Press, 1992).
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11. Cristel Collins Judd, Reading Renaissance Music Theory: Hearing with the Eyes (Cambridge: Cambridge University Press, 2000).
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12. Thomas Christensen, Rameau and Musical Thought in the Enlightenment, 4.
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13. Ibid., 2.
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14. Chua, Absolute Music and the Construction of Meaning, xii.
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15. Judd, Reading Renaissance Music Theory: Hearing with the Eyes, 8.
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16. Ibid., 5.
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17. Blasius, “Mapping the Terrain,” 38.
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18. Judd, Reading Renaissance Music Theory: Hearing with the Eyes, 183–184.
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19. Jacques Rancière (trans. Gabriel Rockhill), The Politics of Aesthetics: The Distribution of the Sensible (New York: Continuum, 2004), 35.
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20. Ibid., 50.
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21. Rancière (trans. Julie Rose), Disagreement: Politics and Philosophy (Minnesota: University of Minnesota Press, 1999), 29.
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22. Ibid., 30.
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23. Charles Simon Catel (trans. Cowden Clarke), A Treatise on Harmony (London and New York: J. Alfred Novello, 1854), 8.
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24. Rancière, Disagreement, 56.
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25. Carolyn Abbate, “Music—Drastic or Gnostic?” in Critical Inquiry, 30 (Spring 2004), 510.
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26. Noted in Christensen, “Introduction,“ in The Cambridge History of Western Music Theory, 13–14.
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27. Johann Philipp Kirnberger (trans. David Beach and Jurgen Thym), The Art Of Strict Musical Composition (New Haven: Yale University Press, 1982), 149.
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28. Rameau, Treatise on Harmony, 69.
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29. Giogio Agamben, “What is a paradigm?”
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30. In Absolute Music and the Construction of Modernity, Chua relates C. P. E. Bach’s musical forms to the emotions of the late-eighteenth-century body: “The constant twists and turns of the ornaments and squiggles that ‘bring life’ to the nerve fibers and the mutations of rhythms are the complex agitation of the vital spirits.“ see also David Ferris’ discussion of the “free fantasy” chapter at the end of Bach’s Versuch: “C. P. E. Bach and the Art of Strange Modulation,” in Music Theory Spectrum, 22/1 (Spring, 2000), 60–88.
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31. Braunschweig, “Enlightenment Asperations of Progress in Eighteenth-Century German Theory,” 274.
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32. Michel Foucault (trans. Alan Sheridan), Discipline and Punish (New York: Vintage, 1995), 183.
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33. Cynthia M. Gessele, The Institutionalization of Music Theory in France: 1764–1802 (Princeton dissertation: 1989).
“Base d’harmonie: A Scene from Eighteenth-Century French Music Theory,” in Journal of the Royal Musical Association 119/1 (1994), 60–90.
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34. Gessele, The Institutionalization of Music Theory in France: 1764–1802, 60.
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35. Gessele, “Base d’harmonie,” 61.
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36. Foucault, Discipline and Punish, 166.
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38. For more on the mathematics behind Euler’s Tentamen, see the following online articles:
39. Smith, Leonhard Euler’s Tentamen novae theoriae musicae, 71.
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40. Nicholas Fuss, “
Eulogy of Leonhard Euler (read at the Imperial Academy of Sciences of Saint Petersburg 23 October 1783).”
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41. Joseph Riepel, Grundregeln zur Tonordnung insgemein (Frankfurt and Leipzig: 1755), 218–233 (for permutations of melodies that modulate to related keys) and 301–308 (for permutations of two- and three-value figures).
Joel Lester mentions Riepel and cites the permutations of figures in Compositional Theory in the Eighteenth Century, “Permutation,” 226–229.
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42. See David E. Cohen, “The ‘Gift of Nature’: musical ‘instinct’ and musical cognition in Rameau,” in Music Theory and Natural Order from the Renaissance to the Early Twentieth Century (Cambridge: Cambridge University Press, 2001).
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43. Moreno, “The Complicity of the Imagination: Representation, Subject, and System in Rameau” in Musical Representations, Subjects, and Objects, 85–127.
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44. Note, for example, the irregularities in Rameau’s harmonization of an ascending bass scale, which exacerbate parallel fifths:
45. [Rameau-Euler correspondence]
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46. Johann Philipp Kirnberger (trans. David Beach and Jurgen Thym), The Art of Strict Musical Composition (New Haven and London: Yale University Press, 1982).
The tables are more striking in the original edition: see Kirnberger, Die Kunst des reinen Satzes in der Musik (Berlin: H. A. Rottmann, 1776–1779), 33.
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47. Kirnberger (trans. Beach and Thym), 146–150.
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48. Ibid., 300–305.
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49. Carl Philipp Emanuel Bach (trans. William J. Mitchell), Essay on the True Art of Playing Keyboard Instruments (New York and London: W. W. Norton & Company, 1949).
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50. Ibid., 169.
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51. Ibid., 198–311.
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52. Charles-Simon Catel, A Treatise on Harmony (London: S. Chappell, ca. 1827), 1.
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53. Mary I. Arlin, Esquisse de l’histore de l’harmonie: An English-Language Translation of the François-Joseph Fétis History of Harmony (Stuyvesant, NY: Pendragon Press, 1994), 157
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54. Brian Hyer, “Before Rameau and After,” in Music Analysis, 15/1 (1996), 75–100.
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