Music Theory Online
The Online Journal of the Society for Music Theory
Volume 6, Number 1 January, 2000
Copyright � 2000 Society for Music Theory
 The last time I spoke at a meeting of our Society, there was trouble. That was in New York in 1995, where several colleagues and I responded to the challenge of the then so-called New Musicology. A vigorous discussion followed for a few weeks after the meeting, but as often happens with these things, interest soon waned and many went back to business as usual.
 But not all of us went back to business as usual. The challenge posed by the new musicology was to formalism. This challenge hit a raw nerve among theorists, for our field thrives not on unanchored observations but on aural and visual observations that, however heterogeneously motivated, are gathered into coherent form. Some left New York still unable to imagine life as post-formalists. For others, however, the intellectual force of the new musicological challenge to music theory was such that, even if they remained deeply skeptical, they were compelled to begin thinking about fresh ways of practicing music theory that would escape the limitations of formalism.
 Contemporary American music theory is best thought of as a constellation of practices. Indeed, music theory has always been a pluralistic discipline even though certain institutional representations of it have come to suggest that Schenker, sets, and a dose of the history of theory are the things that a well-trained theorist should command. But pluralism does not eschew hierarchies. The pluralist profile speaks to intellectual freedom and ensures that no matter what they are or how they are conceived, our ideas will find an audience of at least one. In practice, however, effective pedagogy demands that one approach or another predominate at a given historical moment. And what predominates in turn is determined not necessarily by intellectual cogency but by practical or pragmatic factors, including a given theory's "pedagogability."
 It was a wise move on the part of the Society of Music Theory to seek to involve theorists who operate outside the United States. Such a move may in principle lead to the rejuvenation of theory by bringing us into contact with other methodologies. It may also reassure us that we are not doing badly after all, that the capitalist machine has in fact made it possible for us to be the pacesetters. Those among us with imperial ambitions will find the prospect of internationalizing music theory welcome, an inevitable byproduct of broader processes of globalization. Those of us alert to the negative consequences of other peoples' imperial ambitions will look upon these developments with some trepidation.
 It is a matter for debate whether our guests represent radically different intellectual orientations, or whether the only difference between us and them is that they had to obtain visas in order to enter the U.S., or that they speak with accents. (Does anyone not speak with an accent?) But the topic of otherness is both complex and dangerous, and is perhaps best left to those who have appropriated the right to construct their own and--especially--others' subjectivities. Still, the stated intent of this plenary session, which is to expand the purview of music-theoretical thinking in the United States by incorporating international perspectives, seems to me to be entirely worthwhile.
 The four papers in this session are of course different from one another, although there are points of resonance among them. Jose Luis Martinez draws on Peircean semiotics to develop a comprehensive framework for the analysis of Indian art music. Danuta Mirka, departing from within the proto-semiotic field of structuralism, explores logical relations among the constituent parameters of texture in order to illuminate the sonoristic style of Polish composer Penderecki. Nicolas Meeus seeks an efficient way of explaining harmonic progression in European music of both the tonal and pretonal periods. And Willie Anku writes about rhythmic procedure in traditional African music using an analytical methodology influenced by notions of rhythmic sets and their compositional manipulation.
 Although American theory is not overwhelmingly preoccupied with these topics, it is by no means unsympathetic to the issues raised. Thanks, for example, to the contributions of people like Nattiez, Monelle, Lidov, Tarasti, Dunsby, and Hatten the semiotic gospel can be read in French- and English-speaking communities. And although fundamental questions remain as to what semiotics finally achieves (is it a way of framing what we know already, or can it release first-order musical insights?) the force of certain prominent demonstrations of semiotic rationale has been decisive in helping some American theorists to overcome the urge to resist semiotics. In this respect, the papers of Martinez and Mirka could play a role in heightening semiotic awareness.
 Similarly, the field of harmonic theory to which Dr. Meeus's paper belongs, is of course one of the backbones of American theory. In this, our largely Schenkerian age, non-Schenkerian approaches to harmony are encountered by students in courses that are historical--occasionally antiquarian--in orientation. And yet, the growing attempts to rehabilitate certain ideas of under the banner of neo-Riemannian theory serve as a salutary reminder that harmonic and even voice-leading life may well exist outside Schenker's intellectual purview. Finally, Anku's paper, although it deals with a repertoire that is largely unfamiliar to American theorists, invests in a quantitatively-oriented descriptive approach that is very familiar to theorists. By urging us to study African repertoires not as repositories of certain mystical essences but as structure, temporal projections of considered musical behaviors aiming to make an aesthetic impact, Anku performs a service with which theorists are deeply sympathetic.
 Obviously, then, the intellectual orientations of our visitors from abroad pose no serious threat to the profile of American music theory (on the surface, at least). This state of affairs must be comforting to some and worrying to others. It would be especially worrying to those who had hoped to use this occasion to court difference and now find themselves deprived of that opportunity.
 Let me turn now to the individual papers and comment on each briefly.
 Dr. Meeus is concerned with efficient and comprehensive ways of understanding chordal succession and tonal progression. Starting with the corrective remark that Rameau's basse fondamentale is not about chord inversion but about chord progression, Meeus reviews competing interpretations of relative strength in harmonic progression. Opposing the view that tonality is precompositional (that is, prior to any specific usage), he elaborates a concept of harmonic substitution, explaining progressions of a 2nd, for example, in terms of substitution. Then he takes a paradigmatic or well-formed tonal phrase I-IV-V-I and shows how it is made up of so-called "dominant progressions" (Rameau's term). He ends by applying this conception of phrase to a comparative statistical analysis of tonal and pre-tonal music. The results are perhaps not entirely surprising. Whereas the proportion of dominant progression to subdominant progression in tonal music is 75% to 25% (or 80-20), that in pre-tonal progression is roughly 50-50. And where tonal progressions, according to Meeus , can be fully construed on four roots only, pretonal musics need six or seven roots, sometimes more. And where tonal progressions are usually based on sequences of dominant progressions, pretonal musics have sequences of subdominant progressions. (Incidentally, there are strong resonances between this work and that of American theorist Allen Irvine McHose, whose Contrapuntal Harmonic Technique of the 18th Century of 1947 remains obscure).
 Dr. Meeus attempts to pack a great deal into a short paper, the result being that some points are not fully elaborated. It would be helpful to learn, for example, which repertories might be surveyed by one who wishes to test the applicability of his theory. In what sense is the recuperation of Rameau's basse fondamentale as a theory of chord progression a radical interpretation? How does this square with Schenker's verdict that with the Traite "the seeds of death already had penetrated into music theory and indirectly into composition" (Das Meisterwerk III, essay "Rameau or Beethoven")? Finally, in view of the recent growth of interest in sub-surface voice leading focused on adjacencies, how might one begin to reconcile explanations that take the periodic phrase as point of departure with those premised on arhythmic and abstract harmonic progression?
 Willie Anku's paper is a contribution to the theory of rhythm of African music. Rhythm is, of course, the hotly contested issue in writing about African music, and although there is a certain amount of hot air in such writing, there are genuine and fundamental disagreements among authors. Anku takes ensemble musics of Ghana, specifically Adowa and Bawa dance drumming, as the site for developing his theory. His aim, in part, is to explain as precisely as possible the ways in which the master drummer's ostensibly improvised patterns, which are also the most elaborate of the entire ensemble, are organized. But before he can get to the master drummer, he needs to explain how a typical drum ensemble works, how the individual rhythms are structured and coordinated. This in turn entails the development of an appropriate vocabulary for naming various procedures.
 One striking thing about Dr. Anku's paper is the extent to which it manages to integrate insider and outsider views, indeed to render the distinction between insider and outsider deeply problematic. He stresses the importance of "ethnically perceived norms of beat perception" in order to give priority, at the compositional level, to those who actually carry these musical traditions. (He might have added that the dance or choreographic supplement provides the strongest clue to metrical orientation in West African music.) On the other hand, he does not hold back from adopting apparently foreign' tools, tools from atonal theory that allow him to express certain structural properties concisely.
 Three issues that we might discuss are, first, the claim that the three types of set have specific extra-musical connotations in the culture: 12-set is associated with serious social and festive music, 16-set with recreational or light music, and the cross set with ritual worship. As far as I know, no one has previously made this correlation, even though other writers (such as Gerhard Kubik) have often emphasized the historical depth of so-called time lines. Second is the very conception of rhythmic sets in African music as well as the corollary tendency to understand progression in terms of circles as distinct from lines. Is this so different from European music based on cycles? Third, is the demonstration of a high level of compositional planning in the master drummer's part, planning based on the interpolation of sets, the use of successive sets, the shifting of set orientations, the introduction of bridges and waiting patterns, and so on. Is this planning structural? In other words, do different performances of a given dance use the same procedures?
 Several questions also come to mind about Dr. Anku's paper. One of them concerns the notion of time points. Is there any evidence from carriers of the tradition that they are aware of the significance of the number of attack points in a given set--say 7 in the standard pattern? In other words, is the morphology of the set a western invention? A second and related question is whether the additive conception of rhythm built into the matrixes of set structures 1 2 2 1 2 actually derives from indigenous conception.
 The cross-cultural approach developed by Dr. Anku holds the greatest promise for our understanding of African musical procedures. By now we should put away the aggressively nativist postures that seek to envelop African music in mysticism even while refusing technical investigation. It may well be that African music is more like European music than we have been willing to grant.
 With Dr. Martinez we move from Africa to India, and from the narrowly technical to a global framework for musical interpretation. Dr. Martinez is concerned with developing a comprehensive framework for the analysis of Indian art music. For this task, he has found some natural allies among the semioticians, for the latter's totalizing schemes and promise of complete control on all variables prove enticing to young people. An advocate for Peircean semiotics, Martinez begins by proposing an analytical model comprising three interrelated fields of inquiry dealing with intrinsic musical semiosis, musical reference and musical interpretation. He then uses an Indian raga malkauns composed by D. C. Vedi to explore each of the three fields of inquiry.
 This is a wide-ranging inquiry that cannot be adequately summarized here. Suffice it to say that Martinez' model provides a home for internalist analysis, externalist analysis (when music is construed as a set of symbols), and various aspects of musical interpretation, ranging from historical through the systematic. By its breath, Mr. Martinez's model is readily applicable to other repertoires. Indeed, readers of Jean-Jacques Nattiez will recognize similarities between his Molino-inspired tripartition and Martinez's model.
 A model that attempts to cover all the bases, to file away all the possible thoughts and utterances elicited by a musical work can leave you either impressed with the range of its explanatory power or unmoved by its relatively modest attention to purely musical relationships. Perhaps it is the idea of the "purely musical" that is under siege here. And yet, despite the range of information from various sources (systematic as well as--especially--historical), the performative dimension of note-by-note analysis, the semiosis of musical materiality, is given less prominence in this paper than some might wish. It would be interesting to inquire into the priorities enshrined in Dr. Martinez's model.
 Danuta Mirka's paper shows what can be gained from a narrower focus if not on the music at least on sound. The specifically technical focus is only a point of departure for her, however. For by the end of the paper, we have moved from essentialized modes of dimensional behavior through a field of combinatorial possibilities to larger questions of musical narration. The advantage of deliberately setting limits at the start of an investigation are thus made clear, rendering possible accusations of theoretical myopia thoroughly impotent.
 The repertoire that Dr. Mirka analyzes is Penderecki's so-called sonoristic style of the 1960s. If you approach this music armed with uninflected notions of pitch or pitch class, your life may well be made greatly complicated. But if proceed in terms of notions of sound masses, you will be on the right track. Mirka begins by establishing the basic system of Penderecki's style by positing certain oppositions in the three fundamental "parameters" of pitch, loudness, and time. But classifying features neatly into discrete sets is not always possible, for our ways of perceiving require mediative terms as well. Mirka takes us then into the land of syntax, understood here to mean "the temporal order of segments in the course of a musical narration," and explores competing arrangements of segments under the aegis of narrative. Just when we thought structuralism was pass�, we find a fresh invocation of it that helps to ground an analysis of style.
 From the foregoing summary it should be evident that framing a discussion of all four papers together presents a formidable challenge. A check list of issues raised reveals a network of affiliation. Elements of that network include historical matters, including the status of music-theoretical treatises (Meeus, Martinez), questions of style and relations between repertoires (Meeus, Mirka and Anku), musical syntax (Anku, Mirka, Meeus and indirectly Martinez), narrative (Mirka, but also, implicitly, Anku in what he says about the master drum), non-Western music (Anku [Africa], Martinez [India]), structuralism and semiology (Martinez and Mirka explicitly, Meeus implicitly) and notions of pitch and rhythm sets (Anku [rhythm] and Mirka [sound masses]).
 What does a respondent do in the face of such heterogeneity?
 Although I was asked to draw lessons for American Theory from the perspectives exposed by our four guests, I find myself at a loss as to what to say. For, as I mentioned earlier, the familiarity of their approaches eliminates any need for pontification on how Others can help us lead our theoretical lives better. But I would like to conclude with two brief observations. The first concerns foundations. Music theory is a foundationalist discipline. Indeed, it is an aggressively foundationalist discipline. One reason for our attachment to foundations stems from the pedagogical imperative that has been entrusted to us in the American Academy. Yet the news from elsewhere in the Academy is of a skepticism about foundations, a rethinking of what they enshrine or exclude, what they enable or disable. In some extreme formulations, we are in a post-foundational phase. Can we begin to imagine a post-foundational music theory? I am not sure whether our guests can help us here, since each of their papers is concerned either with laying down foundations or drawing upon existing ones. Still, it seems to me that a radical questioning of the descriptive and procedural protocol that we have long taken for granted is in order.
 Second and related, when foundations are enshrined in Theory and deployed in something called Theory-based analysis, they do nothing but reproduce themselves. It would be wise, then, in seeking to escape the circularity of theory-based analysis, to return to an issue that exercised several minds as far back as the 1960s, and to consider detaching theory from analysis. Theory is closed, analysis open. A theory-based analysis does not push at frontiers in the way that a non-theory-based one does. Theory is foundational, analysis non-foundational. But analysis is also performance, and its claims are to a different order of knowledge than, say, historical or archival knowledge. Analytical knowledge is non-cumulative whereas theoretical knowledge is cumulative. So it is possible that we would be doing analysis a favor by detaching it from theory in order to pursue both with equal commitment. I would not dare to suggest that the SMT become the SMAT [Society for Music Analysis and Theory]--who knows what some mischievous graduate students will do with that acronym? Nor do I mean to imply that analysis has not always been an essential part of what we do. It has, of course. I mean rather to urge the continuing cultivation of the more speculative kinds of analysis, that we can more decisively call into question the foundations of our discipline, foundations that may well prove ultimately unshakeable. In an ironic way, then, the contributors of our guests serve as valuable pointers to roads not to be taken if the aim is not to return to business as usual.
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