=== === ============= ==== === === == == == == == ==== == == = == ==== === == == == == == == == = == == == == == == == == == ==== M U S I C T H E O R Y O N L I N E A Publication of the Society for Music Theory Copyright (c) 1996 Society for Music Theory +-------------------------------------------------------------+ | Volume 2, Number 6 September, 1996 ISSN: 1067-3040 | +-------------------------------------------------------------+ General Editor Lee Rothfarb Co-Editors Dave Headlam Justin London Ann McNamee Reviews Editor Brian Alegant Manager Robert Judd Consulting Editors Bo Alphonce Thomas Mathiesen Jonathan Bernard Benito Rivera John Clough John Rothgeb Nicholas Cook Arvid Vollsnes Allen Forte Robert Wason Marianne Kielian-Gilbert Gary Wittlich Stephen Hinton Editorial Assistant Ralph Steffen Cindy Nicholson Nicholas Blanchard Musical Example Designer William Loewe Midi Consultant David Patrick Watts All queries to: mto-editor@smt.ucsb.edu or to mto-manager@smt.ucsb.edu +=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+ 1. Target Article AUTHOR: Grauer, Victor A. TITLE: Toward a Unified Theory of the Arts KEYWORDS: aesthetic, semiotics, negative syntax, positive syntax, antax, gestalt, negative field, positive field, tonality, atonality, disjunction, multireferentiality, poststructuralism, modernism, Cubism, Mondrian, Schoenberg, Webern, Baumgarten Victor A. Grauer No academic affiliation 5559 McCandless Avenue Pittsburgh, PA 15201 grauer@pps.pgh.pa.us Abstract: My essay, "Toward a Unified Theory of the Arts," originally published in the Journal *Semiotica* [see details below], outlines the essential ingredients of a theory intended ultimately to encompass all art forms, traditional and modern, Western and non-Western, within the purview of an approach to semiotics which also does justice to *aesthetic* (*not* "aesthetics") as a fully independent "logic" of sensory experience. For practical purposes, I have confined myself to two areas only: the pictorial arts and music. The theory is divided into two opposed but complementary sets of principles, the first concerned with the unifying syntactic or "positive" field of traditionally conceived semiosis, the second with the disjunctive "antactic" or "negative" field established in certain works of modernist art and music which disrupt semiosis. In order to clarify, for the readers of this journal, the relation of my ideas to certain issues in the theory of music, I have added a Preface and Postscript. Accompanying files: [refer here to the files containing the eight figures, or, if you prefer, "examples."] [0] Preface [0.1] From 1979 through 1981 I labored on a book length monograph dealing with modernism, semiotics and poststructuralism as they pertain to cinema, painting, music and (prior to the final revision, which required drastic cuts) poetry. My volume, recommended for publication by Thomas Sebeok in his Advances in Semiotics series, was ultimately turned down by the publisher as not sufficiently marketable. For many years I contemplated a more readily publishable essay that would convey the essentials of the new approach to a theory of the arts which lay at the heart of this work. As its treatment of already difficult material was quite complex, I believed for some time that such a condensation was not possible. Finally, after having put the matter out of my mind for some years, I decided that such an essay *could* work if I were content to limit myself to painting and music only, and simply outline my ideas with only minimal explanations, arguments and references, so a reasonably knowledgeable reader could at least get the gist of what I had in mind. [0.2] The resulting paper, "Toward a Unified Theory of the Arts," published in the journal *Semiotica*,(1) turned out better than I thought it might, as it forced me to concentrate on basics, thinking through certain issues more deeply than before. As *Semiotica* is not the sort of journal regularly studied by music theorists, I am most grateful to *Music Theory Online* for making my essay available here, to a group of scholars already experienced in dealing with theoretical issues pertaining to the arts. I do not, however, expect easy sailing over the already famously stormy seas of music- theoretic argument. Even for highly informed readers, the paper's necessary condensations can be puzzling and even irritating. A prime concern has been that my quick run- throughs of certain complex historical developments and theoretical issues might appear superficial, dogmatic or both. I am especially grateful, therefore, for the opportunity to prepare my readers in this Preface and flesh out some especially difficult aspects of my theory in a concluding postscript. ========================================================== 1. See *Semiotica* (vol. 94-3/4),1993, pp. 233-252. ========================================================== [0.3] Theories attempting the "unification" of two or more art forms are hardly a novelty.(2) What sets mine apart and makes it, if I may say so, particularly timely, is the fact that it "unifies" only in so far as it is able to establish a radical break, an "abyss" at the heart of that-which-is-to-be-unified. Paradoxically it is this break which enables me to posit "unification" in the very teeth of the currently fashionable "postmodern" view that "grand unified theories" are now and forever after passe.(3) Had I wished to cater to this view, I could well have titled my work "*Against* A Unified Theory of the Arts," or "Toward A *Dis*unified Theory of the Arts." (It could certainly, in a sense, be described as a "grand *dis*unified theory.") But, as you shall see, I am no postmodernist. In fact, my theory challenges certain basic tenets of one of the driving forces of postmodernism: poststructuralism. ========================================================== 2. Among the better known works, out of a great many which could be brought together in this rather vaguely defined category: Richard Wagner's *Art Work of the Future*; Wassily Kandinsky's "On the Spiritual in Art," and "Point and Line to Plane," in Kandinsky, *Complete Writings on Art*, (New York: DaCapo Press, 1994), pp. 114-220 and 532-699 respectively; Joseph Schillinger's incomplete and somewhat simplistic, but nonetheless remarkable *The Mathematical Basis of the Arts*, (New York: Philosophical Library, 1948); and Marshall McLuhan's *Understanding Media*, (New York: McGraw-Hill, 1964). Almost any work on general semiotics would also be relevant, a good example being Umberto Eco's comprehensive *A Theory of Semiotics*, (Bloomington: Indiana University Press, 1976). The field of Comparative Literature has, over the last twenty years or so, extended its reach to various other arts, an interest reflected in the 1983 edition of the *Yearbook of Comparative and General Literature*, no. 32, devoted to "Interdisciplinary Aspects of Comparative Literature." Included in this volume is Steven P. Scher's "Theory in Literature, Analysis in Music: What Next?," a useful survey of some cross-disciplinary research of that time. More recently, Scher has edited *Music and Text: Critical Inquiries*, (Cambridge: Cambridge University Press, 1992), which includes, among other thought provoking essays, Marshall Brown's "Origins of Modernism: Musical Structures and Narrative Forms," pp. 75-92, a study which, like my own, relates semiotics, dialectics, modernism and music. An especially important work in this genre is Lawrence Kramer's *Music and Poetry* (Berkeley: University of California Press, 1984). Interdisciplinary studies involving literature and visual art and/or cinema abound, especially among poststructuralists such as Roland Barthes, Deleuze and Guattari, Julia Kristeva, Jean Baudrillard and Jacques Derrida, but studies involving music are, with some trivial exceptions, rare in this milieu. 3. See Jean-Francois Lyotard, *The Postmodern Condition*, trans. Bennington and Massumi (Minneapolis: University of Minnesota Press, 1984). ========================================================== [0.4] Fundamental to the poststructuralist view is the notion, derived from structural linguistics and semiotics, that "everything" consists of systems of "empty" codes, referring only to one another; that there is nothing "outside" such signifying systems, no "metaphysical presence" that could conceivably transcend language, no prior perceptual or even sensory "givens" that could serve as its building blocks; that there is, in "fact," no "reality" "out there" for all the many "signifiers" to be either made from or "signify." For musical scholars, the notion that music, like language, is made up of "empty" codes, that there is no "reality" for music to signify, will for obvious reasons, not be a matter of serious concern. But hand in hand with this goes the notion that there are no musical "givens," no "neutral level" (to invoke Nattiez(4)), no ultimate reality either "out there," for the notes to "mean," or "in here," for the notes to "be," as purely auditory objects. ========================================================== 4. For the music-semiotics of Jean-Jacques Nattiez, the neutral level, a vital one-third of the "semiological tripartition," is the level of the "text," stripped of the intentions of its creator (poietic level) and the culturally determined perceptions/interpretations of the listener (esthesic level). Nattiez, without explanation, refers to the neutral level as a "trace," possibly reflecting the influence of Derrida. See Nattiez, *Music and Discourse: Toward a Semiology of Music*, trans. Carolyn Abbate (Princeton: Princeton Univ. Press, 1990), pp. 10-16. ========================================================== [0.5] Simple as they are, the musical examples presented at the outset of my paper illustrate an important aspect of what is at stake: that we cannot normally hear musical passages outside a kind of tonal "force-field" not unlike that which produces, for language, what linguist Ferdinand Saussure called "value." Music, like language, must thus be regarded as "a system of interdependent terms in which the value of each term results solely from the simultaneous presence of the others..."(5) Thus, from the poststructuralist viewpoint, heavily indebted to Saussure, what we "perceive" when we "listen musically," is not really given as "audible" sounds, but is the result, as with verbal language, of a system of differences articulating an "etic" (physically measurable) soundstream into "emic" (culturally determined) *classes*.(6) Thus, we hear music *virtually*, in terms of essentially mental semiotic *fields* (gestalts produced by systems of differences), not in terms of the material, purely sensory experience of something we might want to call the "sounds themselves." The sensory is *repressed* by such fields, to be experienced, if at all, in terms of something like what Derrida has called "the trace."(7) ========================================================== 5. See Ferdinand de Saussure, *Course in General Linguistics*, trans. Wade Baskin (London: Peter Owen Limited, 1959) p. 114. 6. The "etic"/ "emic" opposition, drawn from the linguistic terms "phonetic" and "phonemic," is an important part of the music-semiotics of Nattiez, though he does not draw the distinction along quite the same lines as I. See *Music and Discourse*, op. cit., especially p. 61. 7. Derrida's "trace" turns up in many places in his extensive writings. Among the earliest and most important is *Of Grammatology*, trans. Gayatri Spivak (Baltimore: Johns Hopkins University Press, 1974). To give something of the flavor of Derrida's *problematization* of this term, I quote the following: "The trace is *nothing*, it is not an entity, it exceeds the question *What is?* and contingently makes it possible" (p. 75). ========================================================== [0.6] A basic premise of my paper is that the poststructuralist view 1. must be taken very seriously, as it has been rigorously argued; 2. precipitates a crisis for theory of the arts, as it demands that any such theory be totally subservient to an (already shaky) theory of the sign function. In other words, to accept such a position would be to regard music, painting, sculpture, cinema, architecture, dance, etc. as languages which can be "read" and fully analyzed, "deconstructed," what have you, in essentially literary terms. [0.7] The first part of my paper presents a framework within which both music and pictorial art can be understood more or less in such terms. (Extending the approach to cinema, drama, dance, sculpture, architecture, the literary arts, etc. would certainly have been possible, but would clearly have taken me beyond the limits of the essay format.) Central is the notion of the *syntactic field*, a conflation of the most general semiotic and gestalt principles, understood as a fundamental ground of all traditional discourse. The second half is an attempt to go beyond the poststructuralist position by demonstrating how certain modernist artists and composers have *subverted* the syntactic field to promote a *negative* field essentially beyond the reach of verbal discourse, poststructural or otherwise. Such a field can serve as a ground of the *trace* or, equivalently, promote it to the status of ground. Serious consideration of either possibility would certainly be the postmodernist equivalent of heresy. [0.8] My discussion of the relation between the traditionally conceived *syn*tactic field and the completely untraditional *an*tactic field of the modernists, is, to use a much abused term, heavily "dialectical." What makes any such argument difficult is that certain terms can never really be "defined," as their meaning can change and indeed often reverse itself during the course of the argument. Thus the meaning of certain oppositions, such as foreground/background, continuous/discontinuous, unified/ disunified, perceptual/ logical, must be continually reconsidered according to the changing context of the presentation. Unless one follows the thread quite carefully in this manner it is easy to misinterpret what I am saying. [0.9] Another possible sticking point is what may appear a cavalier tendency on my part to draw analogies between visual art and music. It is, indeed, all too easy to come up with loosely defined analogies of all sorts between and among any number of fields. I must, therefore, underline the fact that almost all my analogies are firmly grounded in one fundamental analogy, which can be considered well established: traditional music, like traditional visual art (and, indeed, semiosis itself), is subject to principles of gestalt perception.(8) Once the fundamentally gestalt/anti-gestalt basis of my position is understood, most of the other analogies can be seen as derivations, or necessary extensions, of it. Thus, once we understand that *negative space* is a necessary consequence of figure/ground relations, the necessity for notions such as *negative tonal space* (negative tonality) and *negative time* becomes apparent. ========================================================== 8. Leonard Meyer's *Emotion and Meaning in Music* (Chicago: University of Chicago Press, 1956) is the classic treatment of the gestalt foundations of musical perception. ========================================================== [0.10] A relation between my theory and certain aspects of the writings of Derrida has been noted and deserves some comment here. When the theory was first conceived I had never heard of him. At the urging of an editor, who felt that my book required some consideration of recent developments, I undertook an examination of certain works of, among others, Jacques Lacan, Julia Kristeva and Jacques Derrida. To my amazement, much of what I read seemed quite relevant to (though hardly in complete agreement with) my own ideas and, as a result, I added a chapter to the book. Kristeva's approach to the "poetic language" of modernist poets such as Mallarme and Artaud has much in common with aspects of my theory, as acknowledged in an all too brief reference in my paper. Derrida's *differance* and *trace* always seemed tantalizingly close to some of my own ideas, but these "non- concepts" are shielded by such an array of paradoxes and circumspections that I was unsure what to think. At this time, while still unsure, I feel I have at least some understanding of *trace* (see above). As for *differance*, I am now willing to speculate in public that it might bear some relation to my notion of *passage*. For those intrigued by such parallels, I might add that one could claim a strong relation between my "syntactic field" and what Derrida calls "metaphysical presence." Finally, the negative syntax I find in the work of certain modernist masters seems to have something in common with, and might some day even be shown to have been in some sense a model for, *deconstruction*. Now that I have stuck my neck out very far indeed, I will pull it all the way back in again by insisting that none of the central points of my essay is in any way dependent on an "understanding" (mine or yours) of Derrida. This is fortunate, for, by its very nature, his "position" is also a "non-position" and can neither be easily understood nor in any sense "equated" with anything else. [0.11] I hope the above has served as a reasonably helpful preparation for what follows. I have added a concluding Postscript, addressed to those who, having read the essay, may well feel the need for more detailed explanation. For every point that has been clarified, of course, many others, which themselves might require further clarification, have been introduced. This cannot be helped, as the matter is, indeed, complex. [1] Toward a Unified Theory of the Arts by Victor A. Grauer [First pubished in *Semiotica* 94-3/4(1993), pp. 233-252. Reprinted with permission of Mouton de Gruyter, a division of Walter de Gruyter & Co, Berlin, Germany.] [1.1.1] With the great successes of structuralism, semiotics and poststructuralism during the past three decades, the theory of the sign-function and the ideological issues associated with it threaten to dominate the entire realm of aesthetic discourse. This paper presents the essential ingredients of a unified theory of the arts which, while reflecting the very real insights of structuralism and its offspring, seeks to move beyond them to a realm where the aesthetic can find a meaningful place. The theory is "unified" in the sense that it is intended ultimately to encompass: 1. any and all art forms; 2. the full historical and ethnological range of artistic expression, non-Western as well as Western, modernist and postmodernist as well as "traditional"; and 3. semiotic as well as aesthetic principles. [1.1.2] A complete elucidation of such a theory would be beyond the scope of this paper. For now I would like simply to define and discuss certain fundamental principles and possibilities with respect to two important areas: the pictorial arts (painting, drawing, etc.) and music. The reader should bear in mind that my intention, in this context, is simply to convey a clear idea of the general outlines of the theory, not present a carefully reasoned set of arguments in its defense.(9) ========================================================== 9. An extensive, carefully argued treatment and defense of crucial aspects of the theory can be found in Victor Grauer, *Montage, Realism and the Act of Vision* (Unpublished monograph, 1982). ========================================================== [1.2] An Analogy [1.2.1] Consider Figure 1. From an iconographic point of view, the most we can say is that it is rhomboid, essentially geometrical and flat. [1.2.2] Adding some lines (Figure 2) we can immediately recognize the sign, however crude, for "house." Our rhombus has become one side of the house. It is, moreover, no longer perceived as flat, but polarized in a particular direction with respect to three dimensional space: rearward to the right. [1.2.3] Consider the variation in Figure 3. The same rhombus is now perceived as polarized in a completely different direction: rearward to the left. [1.2.4] Now let us attempt to combine the two (Figure 4). Something is clearly wrong. The Figure contains all the elements of the sign for house, but does not make sense. The difficulty centers on the original rhombus, which can no longer be perceived as having an unambiguous spatial orientation of any kind. The result can be described as "ungrammatical." [1.2.5] Withholding, for the moment, any attempt at analysis, let us move to what seems an entirely different realm. Imagine listening to the unaccompanied musical line of Figure 5. [1.2.6] Harmonized in the key of G Major (Figure 6), the line is clearly polarized in a particular *tonal* direction. Note how the final "A" sounds "up in the air." Figure 7 presents the same notes polarized toward a completely different tonal center (A Major), giving them a musical meaning very different from that found in Figure 6. In this context, the line ends with a sense of finality and repose. [1.2.7] Finally, in Figure 8, which superimposes the two previous settings, we have something that sounds, from the "common practice" point of view, wrong, "ungrammatical." Unrelated to any key, the line cannot be oriented in tonal space. Its musical meaning is therefore unclear and, from a traditional standpoint, it sounds out of place. [3] The Syntactic Field [1.3.1] While the above visual and musical situations may not strictly parallel one another, there is a close analogy nonetheless. In the pictorial examples, a particular figure took on a different meaning and a different appearance depending on its apparent orientation within pictorial space. In the musical examples something very similar happened, but this time in the context of what we must call "tonal space." In both cases, instances which could not be understood within any given "spatial" context seemed in some sense to violate a "grammatical" rule and were understood as meaningless.(10) ========================================================== 10. The so-called "abstract" nature of music should not confuse the reader into thinking that because musical notes or passages cannot be translated into words they cannot have meaning. We need not look for lexical meanings in music any more than we would look for musical meanings in language. To say, for example, that a certain passage functions as a "cadential figure" is already a perfectly sufficient statement about its signification within musical discourse. ========================================================== [1.3.2] Similar examples could doubtless be drawn from, say, "color space," the "space" of musical time ("metric space"), sculptural space, architectural space, cinematic space, cinematic time, etc. What they would all have in common can be summarized in the following, which I call the "first *semio-aesthetic* principle": *any object of perception can signify (take on meaning) only in relation to a controlling syntactic field*. [1.3.3] The notion of *syntax* is appropriate for more than one reason: it is associated with the rules of "grammar" to which we have already referred -- in this sense pictorial or musical "space," by analogy with linguistic syntax, can be regarded as the source of a set of rules determining pictorial or musical signification; the term implies a purely formal, structural entity, functioning independently of any possible content; the derivation of the word suggests the useful notion of a structure (*tax*) which brings-together (*syn*) -- in this sense a syntactic field must be understood as having a unifying function. [1.3.4] The notion of a syntactic *field* should not present serious problems. A field is a kind of invisible controlling spacelike region or extent within which certain types of activity have the potential to take place. In the physical sciences, prior to the field idea, bits of matter and the forces between them were considered fundamental. For Faraday, followed by Maxwell and Einstein, what is fundamental are the fields (e.g. electromagnetic, gravitational) through which forces and matter can be understood to operate. Similarly we can consider a syntactic field as a controlling, determining fundamental entity or function by means of which syntax and signs can be understood to operate. [1.3.5] Principle one does not, of course, follow inevitably from our analysis of Figures 1-8. However, these examples do provide simple, readily apprehensible illustrations of the workings of syntactic fields in the pictorial arts and music. In Figure 2, a spatial syntactic field is produced from a few carefully placed lines just as an electromagnetic field would be produced by a small burst of electrical current. A differently oriented field is produced in Figure 3. Figure 4 is "ungrammatical" simply because it cannot be unambiguously oriented within a field. Since the differences between Figures 2 and 3 relate to orientation in depth, we know that these fields are equivalent to three dimensional spaces. Since the Figures have been drawn on a two dimensional surface, the fields in question can only be understood as *virtual*, that is essentially mental, imaginary. The most highly evolved example of this sort of thing can be found, of course, in perspective space, where invisible "lines of force" control the syntactic field of an entire picture. [1.3.6] Figures 6 and 7 produce analogous syntactic fields in *tonal* space. Since the difference between the fields produced by the two keys cannot be accounted for with reference to one dimensional (high to low) pitch "space," the tonal field must also be regarded as virtual. In its most highly evolved form, the "common practice" tonal system of Western culture during the Eighteenth and Nineteenth centuries, virtual "lines of force" deriving from the Circle of Fifths control the syntactic tonal field of an entire musical composition. [1.3.7] The same tradition has produced an equally systematic method of controlling musical time. Virtual "lines of force" in the form of *measures* orient each note within a *metric* field. Thus, for example, a note occurring on the first beat of a measure will sound different and carry a different musical meaning from the same note occurring on the second beat, even if both are played in exactly the same way. [1.3.8] A second principle arises naturally from the first: *before any perceptible can function as a sign, it must be apprehended as a gestalt, i.e. a form or figure perceived against a ground*. [1.3.9] In other words, insofar as a syntactic field is also a perceptual field syntax must be first and foremost organized according to the laws of gestalt psychology, where figures are perceived against grounds and wholes are greater than the sum of their parts. The field itself functions as the ground within which sign-gestalts are placed. It would, indeed, be difficult to imagine how one would attempt to describe or deal logically in any way with a sign that was not also perceptible as a gestalt. [1.3.10] In the rush to establish semiotics as a theory of everything this rather obvious point seems to have been lost. (There is no reason, however, to deny to semiotics the complementary notion: every gestalt must signify.) [1.3.11] Gestalt principles are, of course, the basis for the traditional pictorial art of the West and many other cultures as well, as reflected, for example, in relations between shapes and backgrounds or, in more modern terms, positive and negative space. While not so obvious, analogous relations are found in traditional Western music, where, for example, various kinds of figurations and motives generate gestalts, as do points of closure such as cadences.(11) ========================================================== 11. For a thorough treatment of the role of the gestalt in music, see Leonard Meyer, *Emotion and Meaning in Music*, Op. Cit. ========================================================== [1.3.12] A third principle is the result of poststructuralist insights: *every syntactic field is a construct with an ideologically determined basis*. [1.3.13] In other words, there is no such thing as a passive or even neutral ground. The fields associated with all signifying processes are the products of culture and reflect ideologically determined value systems enforced by explicit or implicit rules. [1.3.14] Principle four: *in the absence of a clearly defined syntactic field, there arises a context of free floating, ambiguous implication which functions as though a syntactic field were present*. Thus one cannot defeat the ideological effect of the syntactic field simply by breaking the rules, invoking rhetoric or bricolage as a substitute for logic, making random marks or random sounds, etc. While such devices may not unambiguously signify, they will always imply the existence of some transcendent field within which their ambiguities can be resolved and a kind of mystical sign function can arise. This is undoubtedly the source of the special appeal of Surrealism. [1.4] Signification vs. Aesthesia [1.4.1] Let us pause for a moment to ponder some issues raised by the above. The examples with which we began illustrate how pictorial and musical meaning is related to a process of signification within a syntactic field. What is most remarkable and disturbing about this process is the fact that the shifts in *meaning* produced shifts in the way our figure and our notes were actually *perceived*. When understood as "side of a house," our rhombus is *seen* as a rectangle oriented in a certain direction. When understood as "in the key of G," our melodic line is *heard* as ending "up in the air." Indeed, in such a context meaning and perception can hardly be distinguished. [1.4.2] For traditional semiotics this sort of thing reveals a surprisingly intimate connection between signification and perception. For the more radical poststructuralists it leads to a profoundly disturbing metaphysical gap. From this point of view all perception is completely dependent upon codes of signification -- we literally cannot see or hear anything that is outside a signifying process. [1.4.3] In terms of the principles outlined above, we could say that all perception is dependent upon syntactic fields and, since such fields are controlled by ideologically determined thought processes, we are inherently incapable of perception *per se*. In more radical terms, not only perception, but reality itself falls away in favor of a purely mental process devoted exclusively to the decoding and encoding of "empty" signs. [1.4.4] In the present context we can leave aside the difficult metaphysical issues raised by this position. We cannot, however, avoid an obvious question: in view of the total absorption of perception into signification, what is the status of the work of art or, more specifically, how does the art work differ in kind from any other coded entity? [1.4.5] Let us recall that the word *aesthetic*, derived from the Greek *aesthesia*, originally meant "of or pertainable to things perceptible by the senses, things material as opposed to things thinkable or immaterial."(12) Indeed, the Eighteenth Century philosopher Alexander Baumgarten, in establishing aesthetic for the first time as an autonomous field of study, specifically relates the term to "things perceived" as opposed to "things known"(13) (Baumgarten 1954:78). We will be using the word in this original sense throughout the remainder of this essay. Though the provenance of this term has broadened considerably since Baumgarten, it would be difficult to imagine an aesthetic theory in any sense of the word which excluded the sensory world. ========================================================== 12. *The Oxford English Dictionary* second edition, volume one (Oxford: Clarendon Press, 1989), p. 206. 13. Baumgarten, Alexander, *Meditationis philosophicae de nonnullis ad poema pertinintibus*, trans. by K. Aschenbrenner and W. B. Holther (Berkeley: University of California Press, 1954) p. 78. ========================================================== [1.5] Signification and its Other [1.5.1] Semiotics, poststructuralism, "deconstruction" etc., in denying the ultimate validity of sensory experience, remove thereby any basis for an autonomous theory of the arts. If perception is reduced to a mode of signification, aesthetic must simply take its place within a system of essentially linguistic codes, hardly distinguishable from an intensified rhetoric.(14) ========================================================== 14. Such is the impression given by the discussion of art in Umberto Eco's *A Theory of Semiotics* (=Advances in Semiotics) (Bloomington: Indiana University Press, 1979) pp. 261-276. Eco treats the "aesthetic text" as a means of "overcoding" and/or "code-changing," categories that appear as part of the more extensive discussion of rhetoric which follows [see pp. 276-298]. Julia Kristeva, in an attempt to carve an independent place for the "poetic language" of modernism in a spirit very close to our own, nevertheless concludes that it must posit "its own process as an undecidable process between sense and nonsense, between language and rhythm . . ., between the symbolic and" that which is prior to symbolization. Essentially, her notion of poetic language involves a process of continual mutation within signification, a function hardly distinguishable from that of rhetoric. [See "From One Identity to Another" in Julia Kristeva, *Desire in Language* (New York: Columbia University Press, 1980) pp. 124-147.] Further arguments for rhetoric as the basis of aesthetic experience can be found in Paul De Man, "Semiology and Rhetoric" in *Textual Strategies*, ed. Josua Harari (Ithaca: Cornell University Press, 1979) pp. 121-140.. ========================================================== [1.5.2] While it is not our intention, here, to "deconstruct" poststructuralism, it is necessary to put this issue in historical perspective. The conflict between perception and signification is an old one and, consciously or unconsciously, has always posed a problem for the artist. The issue came to a head with the development of naturalist painting in late Nineteenth Century Europe, which entertained the naive hope of a perfectly straightforward, unmediated representation of the material world. [1.5.3] Naturalism came to grief during a remarkable period when artists such as the Impressionists, Cezanne, Braque and Picasso delved progressively farther into the most fundamental problems of observation and representation. Finally, in the crucible, or should we say "cyclotron," of Cubist art, aesthetic and semiotic collided, the atom of cognition was split, and a new sensibility was born. Structuralism and modern semiotics can trace much of their ancestry to the Russian Formalist school of linguistics, born as a response to this sensibility as expressed in Futurism and Constructivism, direct outgrowths from Cubism.(15) ========================================================== 15. For documentation of the links between the artists and poets of the Futurist/Constructivist school and the linguists of the Russian Formalist group, as well as the latter's influence on the development of structuralism and semiotics, see Steiner (1984). ========================================================== [1.5.4] In our view, the remarkable group of paintings and constructions produced by Picasso and Braque in the years 1908 to 1914 already encompass the central issues not only of semiotics but also deconstructionism. As a result, these works, which became the foundation stones of modernism (and postmodernism), also provide a key to the functioning of "traditional" pictorially based sign-systems. [1.6] Disruption of the Sign [1.6.1] Space does not permit an adequate analysis of the Cubist achievement in these pages. I will make do, instead, with a few comments which, if they are so brief as to appear dogmatic, will at least, hopefully, clarify my point of view. [1.6.2] Cubism begins as an extension of the project of Cezanne, i.e., the use of painting as part of a relentless struggle to observe the material world directly, free of any representational scheme (such as perspective). Like Cezanne, the Cubists proceed by breaking up pictorial space to do justice to the unique space generated by each object. The various contending spaces are linked by areas of "passage," a time-honored device in which painters have traditionally linked foreground and background elements in order to create vague areas of transition that could, among other things, mask spatial discrepancies. As Cezanne learned, extreme use of passage leads to distortion. Seeking to resolve this problem, the Cubists radically fragment space into ever smaller "facets," so that each can absorb some of the distortion. [1.6.3] Extreme fragmentation and passage, coupled with devices such as reverse perspective, cause forms to disintegrate, details to be emphasized at the expense of the whole. As a result, the syntactic field breaks into its constituent signs and sign-parts. No longer visible as gestalts, however, these fragments cannot fully signify. At this point Cubism becomes a self-referential meditation on the relation between perception and signification, playing a thousand different games with the now defused signs for spaces and things. [1.6.4] With the disruption of the three dimensional syntactic field, areas such as the rhombus of Figure 1 can no longer be "read" as polarized in *any* direction and begin to reveal themselves simply as patches of color on an intensified surface. A new kind of space begins to emerge from such areas and the areas of passage surrounding and infiltrating them: "negative space," the space between forms. [1.6.5] As Cubism moves into its so-called "synthetic" phase, fragments of negative space resolve into large, flattened areas of solid color or collage, punctuated by forlorn, thoroughly deconstructed sign fragments. As Cubist energies wane, the project is taken up by Mondrian, who methodically eliminates all reference to signification in an effort to equilibrate the newly acquired space through control of proportion. With Mondrian, the realist ambition ultimately becomes transformed into the project of determining perception itself. [1.7] The Musical Analogue [1.7.1] Parallels with the development of music over a somewhat broader time span are striking. Musical "modulation," a transitional device linking more or less distant keys is, of course, analogous to pictorial passage, which links more or less distant spaces. Modulation is usually characterized by the use of "pivot chords," ambiguous harmonies which have a function in both the old and the new key. [1.7.2] During the Nineteenth Century, as composers seek to incorporate farther ranging tonal relationships, increasing emphasis is placed on a group of dissonant, inherently ambiguous pivot chords which can afford ready "passage" to distant keys via *enharmonic* relationships: the chord of the diminished seventh, the "French," "Italian" and "German" Sixths and the so-called "Tristan" chord. By the late Nineteenth Century, these and other transitional harmonies are enabling composers to fragment tonal space through frequent, almost routine, modulation. In the process, as with painting, forms begin to disintegrate and details, in the form of a host of new, highly colored dissonant harmonies, increasingly appreciated in and for themselves as *sounds*, begin to assert themselves at the expense of the whole. [1.7.3] Finally, in the work of Arnold Schoenberg, the tonal system itself breaks down. With Schoenberg's "emancipation of the dissonance," the ambiguous chords which originally functioned as musical "passage" take on a new role as stable, unambiguous landmarks of a new "negative" tonality: *atonality*. [1.7.4] The new musical space, designed to prevent any one note from becoming a stable tonal center, defeats the tendency, illustrated in Figures 6 and 7, for every note to be polarized in a particular tonal "direction." Notes and chords begin to be heard, not in terms of musical "meaning," but as *sounds* with unique and interesting properties of their own. [1.7.5] Atonality, in which the notes *repel* one another, initially functions as a fundamentally disruptive strategy, comparable with analytic Cubism. The systemization of atonality by Schoenberg's twelve tone method, by analogy with synthetic Cubism and the later work of Mondrian, *builds* a completely new, multipolar "space" in which all elements (notes of the series) are in equilibrium.(16) ========================================================== 16. Additional, equally relevant developments should also be mentioned: Stravinsky's tonal bipolarities and rhythmic fragmentations disrupt the tonal/metric gestalt as effectively as atonality; Schoenberg's ironic, self-referential treatments of traditional musical materials in, for example, *Pierrot Lunaire* or the *Serenade* , mirror the "semiotic" playfulness of Cubism; likewise Stravinsky's *Le Histoire du Soldat* and, of course, all his subsequent neoclassical work. ========================================================== [1.7.6] Despite his radical break with the tonal system, Schoenberg is reluctant to completely do away with rhythmic and motivic gestalts. The final break comes in the work of his disciple Anton Webern, whose opening out of the motive- gestalt, liberation of *timbre* and rhythm, and acceptance of the ephemeral, eventually inspire the most influential compositional movement of the Twentieth Century: total serialism. [1.7.7] The serialists, led by Pierre Boulez and Karlheinz Stockhausen, continue the process of radical fragmentation, increasingly emphasizing (as in "moment form") the ephemeral part at the expense of the transcendent whole, the audible "surface" (the "sound object") at the expense of tonal "depth" and (as with Mondrian's treatment of space) attending carefully to the proportional division of musical time.(17) ========================================================== 17. Interest in sound for its own sake drew Boulez to the concept of the "sound object" [see Andre Hodier, *Since Debussy* (New York: Grove Press, 1961) pp. 136-142]. For a discussion of moment form and its role in the proportional determination of time in the work of Stravinsky, Messiaen and Stockhausen, see Jonathan Kramer, "Moment Form in Twentieth Century Music," in *Musical Quarterly* 64(2), 1978, pp. 177- 187. ========================================================== [1.8] Negative Syntax [1.8.1] The striking parallels between the pictorial and musical developments outlined above encourage us to draw up a set of principles which might clarify this new situation: [1.8.2] Principle five: *a syntactic field is always associated with an opposing, usually hidden field, which, by analogy with negative space, we will call the negative field*. [1.8.3] As demonstrated by Cubism, negative space is more than simply the space between forms. The latter is only a fragment of a larger entity, repressed by the syntactic field which it threatens. As Cubism develops, this new space, first perceived as a distortion of three dimensional "positive space," emerges as a "negative field" of the surface, functioning in direct opposition to the gestalt structure of the more familiar "positive" syntactic field. [1.8.4] Principle six: *while the syntactic field is virtual, i.e., fundamentally conceptual, the negative field is material, i.e., fundamentally sensory, defined in terms of what Kant has called "Transcendental Aesthetic," the "two pure forms of sensuous intuition": *space and time*.(18) ========================================================== 18. Emmanual Kant *Critique of Pure Reason*, trans. Max Muller (New York: Doubleday, 1966) pp. 22,23. ========================================================== [1.8.5] In painting, the negative field is the two dimensional space of the canvas itself, which must be suppressed to permit representation in depth. In this context, negative space, if noticed at all, is always perceived as part of the material (sensual) two dimensional surface, never as part of the virtual (mental) three dimensional space-in-depth. [1.8.6] In music, the negative field is the simple, one- dimensional pitch "space" of the sound-spectrum (as opposed to the multidimensional syntactic "space" of the tonal system, with its functions and class identities) coordinated with the time of simple duration (as opposed to the multi-leveled time of the metric system, with its hierarchically structured periodicities).(19) The "negative times" of music (analogous to the "negative spaces" of painting) are the actual durations of sounds or the silences between them as opposed to the "figures" created by attack-points.(20) ========================================================== 19. See Jonathan Kramer op. cit., pp. 181-183, for a convincing analysis of temporal "flattening" in certain modernist compositions. 20. Note how effectively a piano arrangement of any traditional Western art music conveys its essential "logic" or "meaning" despite the instrument's very limited ability to sustain. The greater part of Twentieth Century music, which places more emphasis on "negative time," where the release is as important as the attack, would *not* be well served by piano arrangements, and in fact they are rare. ========================================================== [1.8.7] We must be careful to distinguish (as Kant did not) between the virtual, abstract space and time of the syntactic field, and the space and time of the negative field, perhaps best described as *experiential* or even *existential*. [1.8.8] Principle seven: *the negative field disrupts signification -- to the extent that sign elements are present in a predominantly negative field they will be multireferential*. [1.8.9] While its value to purely aesthetic experience should never be minimized, the negative field also has an important role to play in the opening out of the ideological forces behind the signifying process. Unlike simple ambiguity, which only tends to mystify the sign, the negative field, in defeating gestalt perception, totally disrupts the sign, revealing the rich, multiple play of interconnected, often contradictory, channels of reference hidden within the apparently straightforward message of any "text." It should thus be of interest to the poststructuralists, whose attack on semiotics is based largely on the latter's neglect of the "polysemic" implications of the sign-function. [1.8.10] Principle eight: *the negative field, normally suppressed by the process of signification, can only be liberated by a structural principle in direct opposition to syntax -- we can refer to this principle as negative syntax (or antax)*. [1.8.11] Though we have left it for last, negative syntax is especially important, the key to the liberation of the negative field. Its operation has, to some extent, already been described in our earlier discussions of the development of Cubism and serial music. Initially, negative syntax is a repellent force, working against the tendency of *positive* syntax to promote gestalt perception and unify the syntactic (positive) field. Negative syntax opens the gestalt, promotes the part at the expense of the whole, perception at the expense of signification, disunifying the (positive) syntactic field while, at the same time, unifying the (negative) aesthetic field. Ultimately, after its *analytic* moment has been supplanted by a *synthetic* moment, negative syntax is equivalent to what can be called the "aesthetic determination" of the negative field, a pure sensory play of rhythm, proportion and surface. [1.8.12] The above description of this extremely complex and revolutionary structural principle is only partially adequate. To pursue the matter further, we must take a detour into the past. [1.9] *Ars Analogi Rationis* [1.9.1] Strangely enough, the position we have arrived at via the practice of some of the most advanced minds of our century betrays a remarkable affinity with the thought of an obscure Eighteenth Century metaphysician, the aforementioned Alexander Baumgarten. Usually considered the founder of aesthetics as an independent discipline, Baumgarten is nevertheless so rarely read his major work has apparently never been translated from the original Latin. [1.9.2] For Baumgarten, *aesthetica*, the knowledge of the "lower" faculties of cognition (i.e., the senses), cannot be reduced to the categories of logical thought, but must be treated independently, as an *ars analogi rationis* ("art of the analogy of reason"). Reversing the priorities of his rationalistic forbears, he concentrates not on the clarities of the mind, with its distinct, "intensive" categories, but the clarities of the senses, with their potential for apprehension of conceptually confused but vividly observed "extensive" particulars. It is in the "lower" faculty that we can find the "perfect sensate discourse" of "the poetic," analogous but opposed to the "perfect conceptual discourse" of "the rational."(21) ========================================================== 21. See Baumgarten, op. cit., especially propositions 3, 9, 14, 15, 17, 19, 22, 112, 113. My summary of Baumgarten owes a good deal to Leonard P. Wessel's "Alexander Baumgarten's Contribution to the Development of Aesthetics," in *Journal of Aesthetics and Art Criticism* 30(3), 1972, pp. 333-342. ========================================================== [1.9.3] While the greater part of Baumgarten's argument is all too heavily indebted to the rationalism (and artistic taste) of his day, its core remains remarkably fresh, providing us with a valuable insight into the meaning of the very similar analogies we have drawn. Indeed, negative syntax can be understood as in some sense equivalent to Baumgarten's *aesthetica*. Both seek to balance the cognitive equation. [1.10] The Aesthetic Function [1.10.1] Baumgarten, in treating *aesthetic* as an artifice or construct, not, as did his contemporaries, an inborn faculty for direct, unmediated knowledge *a priori*, places the object of his concern beyond the reach of the perennial debate over the status of the "real." Instead of attempting, as have so many others, to use sensory experience as both an empirical given of thought and that which can only be redeemed by thought, he opens for sensory processes a balanced, symmetrical relation to mental processes in which neither is given, neither exists as anything more (or less) than a *function*. [1.10.2] Taking our cue from Baumgarten, we must define negative syntax as a function analogous to (though also in opposition to) logic. As logic can be said to determine thought, so negative syntax (aesthetic) can be said to determine perception. Thus negative syntax promotes perception by determining it, not valorizing its supposedly privileged position with respect to "reality" or "presence." [1.11] Axioms of Perception [1.11.1] Moving deeper into our analogy with an analogy, we are faced with some difficult questions. If negative syntax is, indeed, *ars analogi rationis*, then: 1. what aspects of negative syntax resemble what aspects of logic? 2. how does a "logic" operating in opposition to logic work? 3. how can such a "logic" determine *sensory* experience? While an attempt to provide more or less complete answers to such questions would take us far beyond the limitations of this essay, let us suggest some paths of research which might prove fruitful. [1.11.2] Of all the visual artists whose work we have thus far discussed, the only one to make a serious theoretical contribution was Mondrian. An important clue to the workings of negative syntax can be found in his notion of *dynamic equilibrium*, "a dynamic rhythm of determinate mutual relations which excludes the formation of any particular form."(22) While Mondrian's meanings are often far from clear, it is possible to distill from his writings, as a key to dynamic equilibrium (and negative syntax), the following sequence: neutralization of representation through abstraction; opening of forms (i.e., gestalts, which, even when abstract, can still signify) to space; determination of equilibrated proportions in space (equivalent to the determination of perceptual space itself). ========================================================== 22. Piet Mondrian "Plastic Art and Pure Plastic Art" In Mondrian *Plastic Art and Pure Plastic Art* (New York: Wittenborn, 1945) p. 58. ========================================================== [1.11.3] In "logical" terms, this could be equivalent to: abstraction (e.g., dealing with logical symbols or numbers rather than, say, apples); analysis (the basic tool of logical thought); *ratio* (the traditional term for reason itself, apparently conceived as a proportioning of logical "space"). [1.11.4] Studying Mondrian's artistic development, from the earliest influence of Cubism in 1911 to the period just before his emigration to America in the early Forties, we see his principles at work in a process of reduction and distillation leading to a group of paintings that can, in fact, be characterized as *axiomatic* with respect to perceptual experience. The result is a dynamic, balanced interplay of line, plane and color which cannot be perceived in terms of figure-ground and contains no gestalt. [1.11.5] As a logical axiom is a single thought, self-evident to the mind, an aesthetic axiom must be a single (non- hierarchical) image, "self-evident" to the senses. Aided by his theoretical principles, Mondrian simplifies to the point that he can determine proportions (and, of course, colors) exclusively by eye, with no recourse to logic, representation, geometry or system of any kind. We can compare this to the process with which Euclid arrived at his axioms by a similarly reductive, purely *mental* process, with no need for empirical (perceptually confirmable) input. [1.11.6] The musical equivalent of Mondrian's axiomatic paintings would undoubtedly be the highly reductive, extremely brief works of Webern's early, pre-serial period (e.g. the *Five Pieces for Orchestra*, *Six Bagatelles for String Quartet*, *Four Pieces for Cello*, etc.). [1.11.7] The tone row itself can, in a different sense, also be regarded as a kind of musical axiom. A twelve tone series is an essentially disjunctive, equilibrated arrangement (proportioning) of the twelve pitch classes which, as the basis for an extended composition, functions as an axiom. As with a logical proof, the entire construct inherits the properties of the axiom(s). Thus in a well made twelve tone work, the entire piece inherits the disjunctive tonal space of the row, in addition to any special motivic/harmonic characteristics a particular row may have. While in the hands of many composers the row can function conjunctively as a substitute for positive tonal syntax, this is not the case for Webern, whose treatment of the row always remains a fundamentally disjunctive system-for-the-disruption-of-system. [1.12] Negative Syntax, Art and Signification [1.12.1] From the point of view presented here, contrary to the conventional wisdom of the "postmodern" era, the modernism of the Cubists, Mondrian, Schoenberg, Webern, etc. is more than a style period to be followed by the next style period.(23) It represents the founding of a new sensibility, a new mode of awareness and, like all fundamental paradigm shifts, alters our view of past and future alike. ========================================================== 23. For an extended discussion of the meaning of postmodernism with respect to some of the issues raised in this paper see my essay "Modernism/Postmodernism/Neomodernism" in *Downtown Review* 3 (1 & 2), 1982, 3-7. ========================================================== [1.12.2] The modernist attack on the sign-function reveals the presence, in the words of Mondrian, of "liberated and universal rhythm distorted and hidden in the individual rhythm of the limiting form".(24) Thus negative syntax does not produce something completely new, but liberates that which has always been present but repressed.(25) ========================================================== 24. Piet Mondrian, "Pure Plastic Art," in *Plastic Art and Pure Plastic Art*, op. cit., p. 31. 25. A remarkably similar point of view is revealed in Julia Kristeva's notion of the *chora*. See, for example, Kristeva op. cit., pp. 133-137. ========================================================== [1.12.3] We must think, therefore, of negative syntax (aesthetic) and positive syntax (logic, representation, signification, semiosis) as two poles of a dialectic which must pervade any but the most thoroughly sublimated sign system. In substituting a dialectical, *semio-aesthetic* process for a monistic, rule-based semiotics, we may even be able to win back for systematic theory a portion of the territory now claimed by deconstructionist *bricolage*.(26) ========================================================== 26. The paradoxes of a purely semiotic (i.e. logic-based) attack on the ideology of the signifying process are discussed in Jacques Derrida, "Structure, Sign and Play in the Discourse of the Human Sciences," in Derrida, *Writing and Difference*, trans. A. Bass (Chicago: Chicago University Press, 1978) pp. 278-293. Derrida argues that ideology can only be "deconstructed" by an informal, anti-systematic process of disruption-from-within which he calls *bricolage*. ========================================================== [1.12.4] A complete elaboration of a semio-aesthetic theory of expression/communication would, of course, be a major undertaking. At the present time, we must be satisfied with the following somewhat disconnected thoughts: [1.12.5] 1. In most cases of more or less traditional expression, negative and positive syntax may be seen as opposing (or, in another sense, complementing) one another on many levels. On the lowest level, negative syntax produces the disruptions that articulate (analogous to, say, the "phonetic" stream). Positive syntax pulls these articulations together to produce the next ("phonemic") level. On higher levels, the same process is repeated, negative syntax opposing the positive field just enough to make *perceptible* the differences which positive syntax will bring together to produce *thinkable* (meaningful) gestalts on the next level. [1.12.6] 2. The above dialectic resembles the workings of the Japanese game of *go*, where each side tries to incorporate space previously carved out by the other. In all but modernist discourse, positive syntax always wins. Thus, in traditional works of art, all the space, even that once occupied by the negative field, ends by belonging to the positive field. The negative is usually present only in repressed, all but subliminal form. [1.12.7] 3. Whenever negative syntax is incorporated into the process of signification by the unification of its disruptions through positive syntax, the portion of the negative field that has been (provisionally) revealed is then "understood" as having some sort of expressive value or adding to the impact, vividness or drama of the result. The stronger the pull of negative syntax, the more dramatic the effect will be. (Of course, negative syntax that has not been incorporated by positive syntax will not be understood at all and will convey only the notion that either "something is wrong" or "this is modern art.") [1.12.8] For example, many Futurist paintings incorporate the extreme spatial fragmentations of Cubism, but use geometric structure (positive syntax) to pull the fragments together into an ultimately positive totality. Such paintings, essentially far more conventional than those of the Cubists, have a very exciting, hyperdramatic quality, gained through appropriation of a powerful negative field. [1.12.9] More traditional works are replete with less extreme, but very similar effects, where distortions, spatial disruptions, coloristic anomalies, etc. are understood as "expressive" where and when they are comprehended positively on a higher structural level. Negative syntax also contributes to the degree to which local relationships or particular details hold their own with respect to the whole. [1.12.10] 4. Negative syntax must be distinguished from weaker *ad hoc* devices that can have a disruptive function. Negative syntax is a structure, albeit a structure which disrupts structure. The key to differentiating a structure from a simple device is that the former is always associated with a field. [1.12.11] 5. Of all expressive means, language alone is not fully grounded in either space or time, hence lacks a true negative field. This is not to say that the sounds of spoken or the marks of written language do not exist in time and space, but that they are not precisely defined therein. As soon as one attempts to be precise with the time of spoken language one begins to turn it into music (e.g., chant). As soon as one attempts to be precise with the space of written language it becomes visual art (e.g., concrete poetry). The precisions of language exist exclusively within the realm of signification and the logic (positive syntax) which grounds it. [1.12.12] Thus, while a truncated form of negative syntax is certainly present in language and can even manifest itself strongly (e.g. Mallarme, Artaud, Joyce, Stein), language based art forms can never completely resolve onto a negative ground, thus can never move beyond essentially rhetorical devices such as *overcoding* or *code shifting*.(27) This may be the reason why structuralists, semioticians and poststructuralists, primarily linguists or literary scholars, have tended to either explicitly or implicitly place all artistic expression within the realm of rhetoric. ========================================================== 27. Umberto Eco, *A Theory of Semiotics*, op. cit., pp. 261- 275. ========================================================== [1.12.13] The limitation of language with respect to the negative field has consequences for the deconstructionist enterprise, which uses language in an attempt to negativize the signifying process from within (rather than outside itself, from the realm of the senses, as is the case with, say, Cubism). This essentially ungrounded, self-reflexive strategy can result in a fascinating, if unending, play of paradoxes and witty "openings" of the sign, but can never resolve, as, lacking a negative *field*, it lacks any ground but that of the logic it seeks to demystify.(28) Consequently, what begins as a bid for expressive freedom ends with reincorporation within the bonds of the positive. Postmodernist art operates according to essentially the same model, choosing to ignore or minimize potential negative fields in favor of a play of mutually negativising positivities. ========================================================== 28. See Derrida op. cit., pp. 278-281, for the classic statement on this founding paradox of deconstructionism. ========================================================== [1.12.14] There is a certain advantage to be gained from such play, which, by traveling in circles, need never fear reaching a "dead end." But it is unfair and, indeed, repressive of the deconstructionists, on the basis of the limitations of language, to insist that all expressive forms share the same limitations and that, as a result, logic (ideology) can be attacked only from within itself. Such a policy leads to mystifications as disturbing as any deconstructionism seeks to overcome. [1.12.15] 6. While positive syntax always reflects culturally accepted and controlled procedures and values (ideology), negative syntax seems to work against them, toward a universal experience which is not culture bound. Initially, of course, negative syntax opposes positive syntax and, in so doing, becomes a kind of image (albeit a negative image) of that which it has engaged. Ultimately, however, negative syntax disrupts the ideologically controlled signifying process in favor of a liberated sensory play. The extent to which this play will reflect socially determined value systems can, of course, only be decided by examination of its function in a variety of cultural settings. [1.12.16] If, as it would seem, negative syntax *is* resistant to such local variation, it would be extremely valuable as a tool for isolating universals in cross-cultural studies of the arts and communication. Negative syntax may, indeed, have something to do with the fact that all art forms with the exception of those that are language-based may be appreciated, if not understood, trans-culturally. In fact, the crucial difference between the *appreciation* and *understanding* of a work of art may derive from the distinction between negative and positive syntax. [1.12.17] (7) The discourse of the traditional Western arts, with their elaborate hierarchical structures, would seem to be far more heavily positivized than that of non-Western or "folk" cultures. Would careful study of the arts of these "simpler" societies reveal a compensatory development of the negative? [1.13] Summary [1.13.1] Semiotic and poststructuralist theory argues that all aesthetic experience must take its place within the essentially language-based, ideologically controlled codes of the signifying process. While acknowledging the validity of much of this argument, we have taken exception to the notion that the world of the senses cannot be independently grounded. Determining that any signifying process must be based on what we have called a "syntactic field," we found, in certain modernist paintings and musical compositions, a structural principle which disrupts this field to promote sensory experience and multireferentiality: *negative syntax*. [1.13.2] Following the lead of Alexander Baumgarten, for whom *aesthetic* is the basis of perception, we have attempted to understand negative syntax as, in his words describing aesthetic, "*ars analogi rationis*." Indeed, certain paintings of Mondrian seem to function as "axioms of perception," and certain examples of twelve tone music operate, like (anti)logical proofs. [1.13.3] While negative syntax was first revealed in, and can help us to analyze, modernist art, it also clearly plays an important role in traditional art, if not all forms of expression and/or communication. In this regard, we have attempted to speculate on the manner in which negative and positive syntax operate dialectically within "normal" communication and the meaning such a dialectic might have cross-culturally. [1.13.4] These speculations are intended to stimulate further thought and should, of course, be regarded as provisional. Sorting out the role of *aesthesis* vis a vis *semiosis* in traditional Western art and discourse, not to speak of the traditional arts of non-Western cultures, is bound to be a technically difficult, intellectually challenging and time consuming task. Perhaps this paper will convince some readers that such a task would be worthwhile. 2. Postscript [2.1] I'd like to take the opportunity here to clarify and, to a limited extent, amplify, certain points which may remain unclear to readers of the above. As is appropriate in the present context, I will confine myself, for the most part, to topics of interest to musical scholars. [2.2] My "first semio-aesthetic principle" is indeed a "first principle," or even in some sense an "axiom." Thus the notion of a *syntactic field* must be regarded as, for all practical purposes, "given." Any attempt to derive it from anything more fundamental would force me to sound far too much like Hegel or Heidegger for my own or anyone else's good. The most I can say is that, as I indicated in the Preface, it is intimately related to the notion of the *gestalt* field. All the following principles, in one way or another, follow from this. [2.3] The definition of "meaning" as solely a function of a *syntactic* field, with no regard for semantics, may seem odd.(29) Such a definition is necessitated primarily by musical considerations. If semiotics can ever hope to establish itself as a truly general discipline it must come to terms with the problem of music's apparent lack of a clearly determined semantic dimension. Since even totally non- referential music can clearly be meaningful, meaning must have its source in something prior to semantics.(30) ========================================================== 29. My *principle one* is certainly no more cryptic than Nattiez' quite similar "meaning exists when an object is situated in relation to a horizon." See *Music and Discourse*, op. cit., p. 9. Also similar, in spirit, is John Covach's "*Musical understanding arises when we are able to situate a particular piece within a musical world, and musical meaning arises as we appreciate the particular way in which the work is situated*." See Covach, "Destructuring Cartesian Dualism in Musical Analysis," in Music Theory Online 0.11 (1994): 19. 30. The fact that music *can* and very often *does* carry explicit reference testifies to what I would call the semantic "valence" of musical syntagms, the readiness with which they can attach themselves to semantic entities. Since musical signifiers can thus be said to *imply* the existence of possible signifieds, even when none can be explicitly invoked, music appears to have at least a potential sign function. Some of the more penetrating treatments of the issue of musical meaning in the literature are Meyer, *Emotion and Meaning in Music*, op. cit., especially pp. 33-40; Victor Zuckerkandel, *Sound and Symbol*, (New York: Pantheon, 1956), pp. 67-71; Nattiez, *Music and Discourse*, op. cit.; Eero Tarasti, *A Theory of Musical Semiotics*, (Bloomington: Indiana University Press, 1994); Rosario Mirigliano, "The Sign and Music: A Reflection on the Theoretical Bases of Musical Semiotics" and Raymond Monelle, "Music and Semantics," both in *Musical Signification: Essays in the Semiotic Theory and Analysis of Music*, edited by Eero Tarasti (Berlin/NY: Mouton de Gruyter, 1995). Many others could be added to this list, yet the issue is far from being fully resolved. ========================================================== [2.4] The notion of "tonal space" functioning as a "field" deserves further comment. Among the simplest examples would be the pitch classes of any scale, each of which could be understood as uniquely "colored" by its orientation within the "field of difference" produced by the scale itself. More generally, the term "field" relates to both the gestalt principle, in which vision and hearing are conceived as taking place within "perceptual fields," and the "vector fields" of physics, in which the direction and strength of "forces" at any given point can be symbolized by an arrow and a number. The tonal system can be understood as a conflation of the two, a perceptual "force field," with implied "vector arrows" associated with the harmonic "orientation" of each pitch class, the size of the arrow indicating the strength with which, at a given moment, one hears it as attracted to any other pitch class. For example, we could, in the penultimate chord of a perfect cadence, attach to the "leading tone" an especially large vector arrow pointing toward the tonic. If the tonic note, at that point, were not the same as the key note of the movement, it too would have a vector arrow pointing toward this more fundamental tonic. (Such a system of analysis exists, at the present moment, only in principle, and would certainly not be easy to construct. The vector arrows could by no means be determined empirically, but would, as in Schenkerian analysis, reflect the tonal intuition of the individual analyst.) [2.5] My field approach is not inconsistent with accepted theories, especially that of Schenkerian analysis, which already has certain field characteristics. However, the notion of a tonal vector field has the potential to take us beyond traditional paradigms, toward an examination of questions such as, for example, why it is that composers such as Wagner and Debussy, who so often share the same harmonic vocabulary, have such a different sound. For, if the first chord of the Tristan *Prelude* sounds utterly different from essentially the same chord at the opening of Debussy's *Faun*, this difference could well be ascribed to the totally different vector fields within which each chord appears.(31) ========================================================== 31. The similarity of Debussy's harmonic vocabulary with that of Wagner, particulary the Wagner of Parsifal, is exhaustively demonstrated in Robin Holloway, *Debussy and Wagner* (London: Eulenburgh Books, 1979). What Holloway fails to notice is the totally different sound identical chords can have in the work of each composer. ========================================================== [2.6] Milton Babbitt's notion of "time-point class," conceived as a very untraditional tool for the serialization of rhythm, can help us understand the workings of the syntactic field of traditional common practice musical time. Just as each pitch class within a given scale or key has a unique tonal "coloration," determined by its place in the vector space of the tonal field, so any such sound will take on a certain *metric* "coloration" depending on its time-point class, which determines its place in the *metric* field (similarly conceivable as a vector space).(32) As time-point class membership depends solely on point of attack, not duration, *impulse*, not *substance*, the rhythmic figurations of common practice music, like the notes themselves, can be regarded as virtual. ========================================================== 32. The principles of time-point class theory are set forth in Milton Babbitt, "Twelve-Tone Rhythmic Structure and the Electronic Medium," in *Perspectives on Contemporary Music Theory* (New York: Norton, 1972), pp. 148-179. My references to time-point class reflect a very different usage from that of Babbitt and, though based on his theory, should not in any way be taken as representative of his thought. ========================================================== [2.7] As theorists such as Cooper, Meyer and Cone have suggested,(33) the theory of metric relations can, in some sense, be expanded to encompass entire musical forms. Thus musical structure itself could be considered a function of a large scale "metric" field. Among the many advantages of this paradigm would be the way in which structural landmarks, temporal proportions, etc. could be understood as simply taking their place as part of the determination of a field, rather than as a series of interrelated moments which must be subject to psychological processes of memory and recognition. ========================================================== 33. See Grosvenor Cooper and Leonard Meyer, *The Rhythmic Structure of Music* (Chicago: University of Chicago Press, 1969) pp. 144-167 and Edward T. Cone, *Musical Form and Musical Performance* (Norton, NY, 1968) pp. 25-26. ========================================================== [2.8] Ultimately we would want to combine the tonal and temporal fields into what could only be called a "field of musical motion," a "master" field in which the various aspects of the tonal/metric system would be considered *in toto*. [2.9] Principle three, "every syntactic field is a construct with an ideologically determined basis" encapsulates a great deal. Such fields are not simply entities embedded in a "text," but complexes produced by interaction between the text and each individual involved with it. The manner in which what I have called "syntactic fields" manifest themselves and the effects they can have will vary enormously in terms of culture, society, history, class, gender, ethnicity, individual psychology, etc. Since such matters have already been treated extensively in the poststructuralist literature, from Lacan, Barthes and Althusser to Kristeva, Derrida, Lyotard, Baudrillard, etc. I felt no need to elaborate. [2.10] Some have assumed that the references to randomness in my discussion of principle four are aimed specifically at John Cage. Nothing could be farther from the truth. While randomness is, in itself, not capable of fully resisting the pull of the positive field, Cage's work is not simply "random," but would be more accurately described as a highly systematized treatment of randomly derived elements. Cage's great sensitivity to the requirements of the negative field is revealed in a great many decisions which have nothing to do with randomness: 1. emphasis on *duration* as opposed to attack; 2. foregrounding of silence as an expression of negative time; 3. negation of motivic and melodic formations; 4. refusal to distinguish foreground from background (negation of the musical gestalt); etc. [2.11] I'm afraid my encapsulations of late nineteenth and early twentieth century art and music "history" may be misconstrued as more dogmatic than I intended. I have no argument whatever with the postmodern view that there can be no such thing as a "definitive" history, a single, unbiased standpoint from which the past may be transparently observed. When I discuss the manner in which Cezanne's project is taken up and developed by the Cubists, or describe how the enharmonic pivot chords of the late nineteenth century "gave way" to the "emancipated" dissonances of the twentieth, I am simply attempting to demonstrate that certain aspects of my theory can be understood historically. I make no claim that this is simply what "really happened," that there are no other meaningful ways of describing such an extraordinarily complex set of musical and historical relationships. Nor, in fact, do I make such a claim for the theory itself, which will stand or fall by virtue of its consistency and explanatory power, not its validity as some sort of "deeper" truth about the way things "really are." [2.12] My encapsulated "music history" has been taken to task for claiming that 1. modulations are analogous to pictorial passage; 2. in atonality the notes "repel one another"; 3. total serialism is "the most influential compositional movement of the twentieth century." The last, relatively trivial, point has seriously annoyed some readers. I'll take it first, to get it out of the way. [2.13] Please notice that I refer to a "movement," not a composer or even a style. Of other such movements that could be named, such as impressionism, nationalism, *verismo*, Gebrauchsmusik, neo-primitivism, the "music hall" esthetic of *les Six*, the "Tudor revival," dodecaphony, *folclorismo*, indeterminism, electronic music, *musique concrete*, minimalism, the first two were indeed highly influential, but essentially of the previous century, while the others (some of which may not really be movements in any case) seem to have been strictly limited in provenance. In my view neoclassicism is too loosely defined to count as a movement (as is the current trend toward neoromanticism), but if it were, it would be the only one I can think of that had nearly so wide an influence during the twentieth century. Total serialism was a truly international movement, with important branches in both Europe (Boulez, etc.) and the USA (Babbitt, etc.). It flowered at a moment when increased interest in musical composition in the academic world was leading to unprecedented bumper crops of composition majors, MA's and Ph.D's, so that a list of the "serious" composers of today, the great majority of whom have been (how could they not have been?) influenced in one way or another by total serialism, would undoubtedly be far longer than at any other time. The movement began in the late Forties and persists, in some circles, to this day, a span of close to fifty years (yes, we *are* getting older!). Even among composers who rejected it, such as Xenakis, Ligeti, Penderecki, Riley, Young, Reich, Glass, etc., etc., its influence (or counter-influence) has been considerable. And its influence on the way music is taught has been, I should think, even greater. So, yes, I think my statement is defensible. [2.14] The question of whether modulation is analogous to pictorial passage can be treated adequately only by the kind of careful analysis of historical developments which I presented fully in my book, but had to drastically encapsulate in my paper. This analogy is the product of a dialectic in which procedures such as passage and modulation, designed to promote continuity by covering over structural breaks, ultimately become promoters of the discontinuity they originally were intended to obscure. Once one sees how this can happen in painting, the parallels with music should not be difficult to accept. We are talking, as with so much else in my paper, not so much about painting and music, as about gestalt principles and the ways in which such principles (and their subversion) can be manifested in different media. [2.15] The notion of atonal notes "repelling" one another can also best be understood dialectically. If we can say that the "force-field" of tonality promotes mutual attractions among the notes, we ought to be able to say that the subversion of this field (atonality) causes them to repel one another. To put it in somewhat milder terms, the notes could be said to "stand out" from one another in an atonal context, as opposed to the "harmonious" blending promoted by the tonal system. In any case, "repulsion" is characteristic only of earlier phases of the dialectic, when the negative field is defined in terms of its opposition to the positive. At a later phase, beginning, I suppose, with Webern's dodecaphony, we can speak of the notes being in a state of "dynamic equilibrium" (to borrow Mondrian's phrase). [2.16] Principles five through eight are concerned with the *negative field*. This, the heart of my theory, is admittedly a difficult and certainly controversial topic. Painfully aware that any efforts at clarification may well raise more questions than they settle, I will nevertheless venture the following. [2.17] As far as common practice music is concerned, there is little if anything in principles one through four that is incompatible with traditionally accepted theories and modes of analysis, from Rameau through Riemann and Schenker to the latest forays into the arcana of musical semiotics. But it would be a serious mistake to assume that a theory of the *syntactic field*, or any other "unifying" approach, can account for everything of importance. Even in the common practice realm, not to speak of "early," "ethnic," "modernist" and "postmodernist" music, the notion that all elements necessary to a successful work of art can be smoothly integrated within the operations of a single, unifying "field," "concept," "semiosis," "*Ursatz*," what have you, is not only inadequate, but repressive. In terms that will be familiar to students of Derrida, the contradictions smoothed over within all such doctrines make them ripe for "deconstruction." [2.18] At this point in my paper, one might indeed expect the deployment of some form of poststructuralist "strategy" along deconstructionist lines. For me, such an attempt, while certainly valid and potentially quite valuable, would not be sufficient. Space does not permit me to treat with any degree of adequacy the manner in which poststructuralism, like the positive field of which, willy nilly, it is a part, functions in an ultimately repressive manner with respect to artistic experience. Associating perception with either "metaphysical presence," or the ephemeral, ungrounded, "trace," this critical practice effectively places all art "under erasure" (to (mis)use Derrida's phrase), treating it as "readable," not perceptible, analyzable only as a form of rhetoric. In my view, the poststructuralists, virtually all absorbed in literary pursuits of one form or other, have simply failed to notice that certain painters, sculptors, composers, filmmakers, choreographers, etc. of our century have already engaged in highly successful "deconstructions" of their own, without benefit of a theory of the "text."(34) The *negative field* and *negative syntax* are the product of my attempts to come to terms with the true (no quotes necessary thank you) achievement of these remarkable artists. ========================================================== 34. The only well known poststructuralist figure who, to my knowledge, has produced a major study of modernist aesthetics is Julia Kristeva, whose viewpoint, as expressed in *Revolution in Poetic Language*, trans. Leon Roudiez (New York: Columbia University Press, 1984) and other works, has, I feel, much in common with my own. ========================================================== [2.19] The question of the nature of the negative field, what it actually *is*, can take us easily into the sort of metaphysical/antimetaphysical issues that would quickly return us to all too familiar poststructuralist controversies. To say, for example, in the spirit of modernist art critic Clement Greenberg, that this field can ultimately be equated with the physically tangible, flat, surface of the painted canvas, would be to risk the reinstatement of "metaphysical presence." To totally deny it would be to imply that the negative field is not material but, like the positive field, virtual. And how, in such terms, could we deal with music, which is certainly not presented on a tangible flat material surface? Principle six therefore defines the "material" in terms of sensory experience which, in turn, must be understood as grounded in the precise determination of space and time. Ultimately, therefore, in the "purest" of negative structures, it is the special nature of the *proportions* (of a Mondrian, say, or a late Webern) which establish such works as fundamentally material. (Such proportions must not, however, be confused with the geometrical, harmonic or metrical proportions common in traditional art and music. Negative proportions disrupt such structures to determine an *experiential* space and/or time which is uniquely sensory.) [2.20] One might suppose that I regard the negative field as representing a "hidden truth" or the "reality behind" the positive field. This would be a mistake. The negative field does *not* transcend or in any way deny the validity of the positive field, but simply subverts its hegemony within the realm of the sensory. Since neither field is more fundamental than the other, the two can be regarded as *complementary*.(35) ========================================================== 35. In a fascinating study, *Complementarity: Anti- epistemology after Bohr and Derrida* (Durham: Duke University Press, 1994), comparing the ideas of Derrida and noted physicist Niels Bohr, Arkady Plotnitsky identifies Bohr's notion of *complementarity* as a key to understanding both. I feel that this term, possibly the only one which can effectively relate the profoundly disjunct terms of a "negative dialectic," is applicable to my theory as well. ========================================================== [2.21] Principle seven raises the issue of "multireferentiality," which might be confusing. The negative field disrupts signification but often there will be a residue of what could be called "liberated" reference. For example, consider a Cubist collage in which bits of wallpaper or newspaper appear. They can no longer signify in the traditional sense, but they still contain what might be called "empty" reference, which, as part of the negative field, can be interpreted in a variety of different ways. Such interpretation is "multireferential" in that, since there is no longer any unifying structure there to "tell" the viewer what to think about what is being seen, he or she can pick and choose freely among various interpretations. Something similar occurs in, for example, works as different (and not so different!) as Stravinsky's *L'Histoire* and Schoenberg's *Septet-Suite* Opus 29 (other works by either composer could also be cited), both of which abound in explicit references to various types of music -- we are free to hear them *as* such references, or simply as part of an abstract musical structure, or both. Multireferentiality is part and parcel of the process which enables Stravinsky's neoclassic works to simultaneously invoke the past and keep their distance from it. [2.22] *Negative syntax*, the structural principle which promotes the negative field, can be understood as possessing two dialectical "moments," which we can call (in terms of the well known and quite apt Cubist terminology) "analytic" and "synthetic." Initially negative syntax, in opposing the positive field, pulling it apart "analytically," is radically disjunctive. Ultimately, as the analytic gives way to the synthetic, *disjunction* with respect to the positive field gives way to *unification* of the negative field. (Note that this is an absolutely unique form of "synthesis," not at all comparable to that of traditional dialectic, in which the original oppositions are resolved on a higher level. The unification of the negative field does *not* resolve the positive-negative opposition but in fact maximizes it.) [2.23] Musical negative syntax is most clearly exemplified by certain works of Stravinsky, Schoenberg and Webern. Due to lack of space I will have to be very general, glossing over all sorts of exceptions and subtleties. Stravinsky's approach to tonal structure in his pre-serial works (and to an extent the serial ones as well), can be regarded as "dialectical," as it so often involves the opposition of two disjunctive tonal areas.(36) While this "bipolarity" permits traditional formations, such as triads, seventh chords, diatonic scales, etc., any tonal field they might tend to produce is usually nullified or at least severely weakened by juxtaposition with similar formations from the opposing area.(37) While many of his works may favor a particular pitch class or chord, such entities are heard as important structural landmarks, not really tonics or even tone "centers." Stravinsky's famously disjunctive rhythms and accents clearly disrupt the metric field by continually redefining, thus negating, time-point class, thereby encouraging us to listen in terms of experiential time, i.e., *durationally*. In the absence of an overall controlling tonal or metric field, and despite a veneer, in the neoclassical works, of conventionalized form, his pieces tend to break down into static, self contained sections. ========================================================== 36. The prototype for Stravinsky's "dialectical" approach to harmonic structure can be found, of course, in the second movement of *Petroushka*, equilibrated harmonically by the polarization of two tonal fields, dominated respectively by C and F#. It should go without saying that I completely disagree with the non-dialectical view of Arthur Berger and Pieter van den Toorn, which rejects "bitonality" and finds in the octatonic scale some sort of occult unifying force for this, as well as most of Stravinsky's other work [See Arthur Berger, "Problems of Pitch Organization in Stravinsky," in *Perspectives on Schoenberg and Stravinsky*, ed. Boretz and Cone (Princeton: Princeon University Press, 1968) and Pieter van den Toorn, *The Music of Igor Stravinsky* (New Haven: Yale University Press, 1983)]. In this matter I side wholeheartedly with Richard Taruskin, who, in the very process of demonstrating Stravinsky's indebtedness to Rimsky's octatonicism, nevertheless insists, in response to Berger and van den Toorn: "We are meant [in Petroushka] to hear C and F# in terms of an active, not static, polarity -- as competing centers, not merely as docile components of a single, static octatonically referable 'hyper-harmony' . . . " [Richard Taruskin, "*Chez* Petroushka: Harmony and Tonality *chez* Stravinsky," in *Music at the Turn of Century*, ed. Joseph Kerman (Berkeley: University of California Press, 1990)]. In a paper more broadly aimed at certain underlying principles in Stravinsky's work as a whole, "Cross-Collectional Techniques of Structure in Stravinsky's Centric Music" [in *Stravinsky Retrospectives*, ed. Haimo and Johnson (Lincoln: University of Nebraska Press, 1987)], Paul Johnson affirms the importance of the octatonic collection yet at the same time emphasizes the role of disjunctive intervals in the establishment of tonal polarizations in Stravinsky's work as a whole. 37. We must be careful not to confuse Stravinsky's bipolarity with the dialectic of traditional music, where conflicting tonal areas (e.g., tonic and dominant) are ultimately resolved in a unifying "synthesis." The musical dialectic of the composers we are considering here never really resolves, thus is closer, perhaps, to the "negative dialectics" of T. W. Adorno (who was, not surprisingly, inspired by Schoenberg). [See Adorno, *Negative Dialectics* (1966), trans. E. B. Ashton (New York: Continuum, 1994).] ========================================================== [2.24] Concerning Schoenberg and Webern, I must also be far too general. Schoenberg's journey toward negative syntax was much longer and more gradual than that of Stravinsky. Especially meaningful with respect to the early phase is the following statement from "Composition With Twelve Notes:" "In the works of Strauss, Mahler, and, even more, Debussy... it is already doubtful... whether there is a tonic in power which has control over all these centrifugal tendencies of the harmonies... I do not have to be ashamed of producing something of this sort myself."(38) The tension between this "centrifugal" force and the "centripetal" pull of tonality dominates virtually all of Schoenberg's mature pre-atonal work. The theoretical issue is encapsulated in the following words (based on her reading of the *Harmonielehre*) from a recent study by Silvina Milstein: "At the centre of Schoenberg's harmonic theory lies the notion that tonally interesting progressions often exploit the fact that chords can be reinterpreted as simultaneously belonging to several tonal areas. The functional ambiguity afforded by the reinterpretation of tonal triads and their interaction with tonally evasive chords and non-tonal formations led Schoenberg to conceive an all-embracing monotonal system based on the twelve tones of the chromatic scale."(39) Milstein applies this insight to aspects of the first three movements of the Second Quartet, where "we can observe that the reinterpretation of function through common tones applies not only to chords but to motifs. At the large-scale level this is manifested in the reappearances in different harmonic contexts of the untransposed opening motif."(40) In terms of the analogy developed in my paper, "the reinterpretation of function through common tones" can be understood as *passage* from one harmonic area to another,(41) not only locally but "at the large scale level," not only in terms of notes and chords, but motifs as well. The notion of notes, chords and motifs sharing the same function leads directly to Schoenberg's collapsing of the two tonal "dimensions" (melodic and harmonic) and from there to the notion of a harmonic "field." Thus, we can speak not only of "pivot chords," but "pivot motifs" and "pivot fields," which can function "centrifugally," in a manner analogous to Cubist *passage*, to disrupt tonality. It is, moreover, not too difficult to see in the "reappearances in different harmonic contexts of the untransposed opening motif" a precursor of both the row itself (the same motif in different contexts) and the serial device known as "invariance" (the *untransposed* motif in different contexts). We can see, in other words, how musical "passage" can take us from modulation and "reinterpretation of function," to the row itself and, moreover, an important device for organizing serial relationships: invariance. ========================================================== 38. "Composition With Twelve Tones," in *Style and Idea*, rev. ed., ed. Leonard Stein (London, 1975), p. 245. 39. Silvina Milstein, *Arnold Schoenberg: Notes, Sets, Forms* (Cambridge: Cambridge University Press, 1992) pp. 44, 45. 40. Ibid., p. 45. 41. See Ibid., pp. 45-47, where Milstein's illustrations of "the stabilization of a dissonant event in terms of overall structure" can be equally understood in terms of musical *passage*. Her entire analysis of portions of the Second Quartet in this section is highly relevant. ========================================================== [2.25] With the appearance of the tone row, we arrive at the famous "method of composing with twelve tones related only with one another" - one another, that is, as opposed to being related to a tonic. Despite the currently widespread view that Schoenberg's serial works are "really" in some sense tonal, the definition quoted above must, in my opinion, stand. Certainly Schoenberg very often emphasizes certain notes at crucial structural junctures or favors certain row transpositions which appear to mimic tonal practice. Nevertheless, in terms of the theoretical context presented here, for tonality to be unambiguously present a tonal *field* must be established. The favoring of certain note complexes or the deployment of certain row transpositions is not enough. To produce a syntactic field all these things and many others as well must relate to and reinforce one another. Moreover, if one looks carefully at the type of note complexes which receive emphasis one will see, time and again, that they are disjunctive (the tritone) or tonally neutral (augmented triad, whole tone complex, diminished seventh chord). Often in fact we find in Schoenberg's supposed "tonality" something more closely resembling Stravinsky's "bipolarity," with the opposing foregrounded elements functioning more like structural landmarks than tonics. There are indeed many types of bipolar disjunction to be found in Schoenberg, including, of course, hexachordal combinatoriality. [2.26] As far as Webern is concerned, I'd like to begin by quoting a 1955 statement by Pierre Boulez, whose words might still, to many, be as surprising as when first published: "Webern -- via Debussy, one might say -- reacts violently against all inherited rhetoric, in order to rehabilitate the powers of sound... He has even been found cerebral to the exclusion of all sensibility -- so it is well to realize that his sensibility is so radically new that it indeed runs the risk of appearing cerebral at first."(42) Webern, in my view, is not necessarily so "radically new" as Schoenberg. However, in carrying certain of the latter's innovations to their logical conclusion, thus moving from "analysis" to (negative) "synthesis," his work reaches a point where the relation of negative syntax to "the powers of sound" is more readily apparent. To understand this connection we must, first, consider his treatment of pitch and pitch-class. His frequent disjunctive leaps of a major seventh, minor ninth or greater are particularly difficult to hear in terms of interval class, calling attention to the pitches as such, rather than their pitch class identity. To Henri Pousseur the *structural* weakening of pitch class is already apparent as early as Opus 9, where certain pitches an octave apart function "no longer as possible octave transpositions of the same note but as *absolutely different notes*."(43) In Webern's serial compositions, the fixing of pitches at certain absolute points for sections at a time becomes quite common. This, combined with his use of invariance, much more common and clearly delineated than in Schoenberg, can give such pitches enormous structural weight in and for themselves rather than merely as pitch class tokens. Since the series is based on pitch class identity, the notion that such identity could be disrupted in and through the strict application of serial principles is indeed a paradox. Since pitch class identity as a source of musical semiosis (see paragraph 0.5 of the Preface) is intimately bound up with the workings of the positive field, the disruption of the "vector arrows" of pitch class is a significant measure of the degree to which Webern has succeeded in establishing a negative field.(44) ========================================================== 42. "The Threshold," in *Die Reihe*, Anton Webern issue (Bryn Mawr: Theodore Presser, 1955) p. 40. 43. "Webern's Organic Chromaticism," in *Die Reihe*, op. cit., p. 54. Especially relevant from my point of view is Pousseur's "The Question of Order in New Music," in *Perspectives of New Music*, Vol. 5, No. 1, Fall-Winter 1966. I want to take this opportunity to acknowledge Pousseur's influence, as theoretician and teacher, on my own thinking regarding the structure and aesthetics of modernist music. 44. Stravinsky's tendency to emphasize certain musical events which return always at the same pitch level and with the same instrumentation has a similarly disruptive effect with respect to pitch-class. Examples abound, the most notorious being the remarkable opening chord of the *Symphony of Psalms*. ========================================================== [2.27] Next, we must turn our attention to Webern's treatment of musical time. Analytic Cubist paintings and early Mondrians contain many disjunctive linear "accents" which, while in some sense still "figures" against a ground, nevertheless tend to disrupt the figure-ground gestalt. The similarly disjunctive accents of Stravinsky and early Webern have an analogous effect. The later, "classic" Mondrians equilibrate figure-ground without such accents, as do certain later Webern works, notably the Symphony first movement, where each note has a "planar" rather than a figurative quality and release can be as important as attack. A work such as this can serve as an excellent demonstration of the profound difference between a music based on time-point classes, where release is far less important than attack and time is experienced virtually, and a music based on durations, where attack and release are of equal importance and time is experienced materially. Such duration based music anticipates what Karlheinz Stockhausen has called "moment form." For Stockhausen, "a given moment is not merely regarded as the consequence of the previous one and the prelude to the coming one, but as something individual, independent, and centered in itself..."(45) In disrupting the continuities, the "flow," of *positive* time, Webern's *negative* time similarly places maximal structural weight on local relationships and ultimately, individual notes. ========================================================== 45. "Momentform" (1960) in Seppo Heikinheimo, *The Electronic Music of Karlheinz Stockhausen* (Helsinki, 1972) pp. 120, 121. Jonathan Kramer's excellent essay on moment form also contains much that is relevant to my theory. See his "Moment Form in Twentieth Century Music," in *Musical Quarterly*, vol. 64, no. 2 (April, 1978), p. 177. ========================================================== [2.28] From the viewpoint of my theory, the field of positive musical syntax (tonality) can be regarded as a structural background which, in a manner roughly equivalent to that described by Schenker, controls what we hear "from behind the scenes," unobtrusively unifying musical space and time. Negative syntax, in its analytic "moment," disrupts this field and, in so doing, brings structure "up" from the background onto the "surface" of our awareness. Thus it can be said that certain atonal works, especially certain very brief works of Webern, lack any sort of structural background at all, with everything of importance directly present to the listener. I have described such works, along with the equally reductive classic canvasses of Mondrian, as "axiomatic," in the sense that structure has been reduced to bare essentials, to the point of "self evidence." [2.29] Once one accepts the opposition between positive syntax as a systematic, unifying background and negative syntax as an anti-systematic, disruptive foreground, Webern's serialism can come as something of a shock. For once again we have a unifying system which has retired into the background. Thus Webern's completion of the dialectical movement from the analytic to the (negative) synthetic goes beyond that of Mondrian in a truly remarkable way, establishing, as I characterized it in paragraph 1.11.7 of my essay, a "system- for-the-disruption-of-system," in which Webern's serial procedures systematically unify the negative field as thoroughly as they disrupt the system of the positive. When Webern claims, therefore, as he so often does, that "unification" is the primary goal of his patently disjunctive structures, I can wholeheartedly agree. Only he is, perhaps without fully comprehending it, speaking from the other side of the "looking glass," from the viewpoint of Baumgarten's *Ars Analogi Rationis*. [2.30] The final section of my paper is concerned with an especially intriguing but difficult question: what, if any, is the relation between negative syntax and positive syntax in the operation of "traditional" discourse? It is possible that there is none at all, that the disjunctions we find in the normal course of things have nothing to do with the disjunctions of modernism, that the latter's evolution from the former does not necessarily reflect back upon it. This seems unlikely, but in terms of the "abyss" opened in my essay, it can certainly remain an "open" question. If such a relation does exist, and I strongly suspect it does, we can already find many important clues to the nature of its operation in the existing literature on linguistics, semiotics, psychology and, most of all, psychoanalysis and rhetoric, both of which have been explored with some zeal in poststructuralist circles. And, as I have already speculated, the work of Kristeva and Derrida seems especially relevant here. As far as music is concerned, I find much of interest along these lines in Lawrence Kramer's work, particularly *Music and Poetry*, where, in the chapter "Generative Form"(46) he examines the relation between disruptive and integrative forces in both Beethoven and Wordsworth in truly dialectical terms. Some recent works published in Music Theory Online, notably Richard Cochrane's "The Phases of Fire"(47) and John Covach's "Destructuring Cartesian Dualism in Musical Analysis"(48) also seem relevant. ========================================================== 46. in Lawrence Kramer, *Music and Poetry*, op. cit., pp. 57- 90. 47. Music Theory Online 1.1 (1995): 1-11. 48. John Covach, op. cit. ========================================================== 2. Commentaries AUTHOR: Bent, Margaret TITLE: Diatonic *ficta* revisited: Josquin's *Ave Maria* in context KEYWORDS: Wibberley, counterpoint, ficta, diatonic, accidentals, mode, notation, hexachords, Josquin, Obrecht REFERENCE: mto.96.2.5.wibbrly.art Margaret Bent All Souls College Oxford, OX1 4AL England margaret.bent@all-souls.oxford.ac.uk ABSTRACT: Roger Wibberley in MTO 2.5 has criticized a version I published of the sequence from Josquin's *Ave Maria*, on grounds that it flouts Glarean's modal classification. Cristle Collins Judd has already challenged Wibberley's construction of mode, and I further deny Glarean's relevance on chronological grounds. The first part of my article restates and revises some of the premises (ignored by Wibberley) which provided the context for my discussion of the Josquin piece; the second part extends my original discussion of that passage, and offers some comments and questions in response to Wibberley's paper. ========================================== *A mind is like a parachute. It only works if it is open.* [1] I am grateful to Roger Wibberley and other correspondents following his article in MTO(1) for airing some important questions and providing me with an incentive for this reply. I do plan eventually to produce a more fully revised and corrected expansion of the thesis I set out in "Diatonic *ficta*" (henceforth DF),(2) incorporating replies to Karol Berger and Peter Urquhart, but this may serve as a partial, interim statement.(3) ========================================== 1. Roger Wibberley, "Josquin's Ave Maria: Musica Ficta versus Mode," *Music Theory Online* 2.5 (1996). 2. Margaret Bent, "Diatonic *ficta*," *Early Music History* 4 (1984), 1-48. 3. Karol Berger, *Musica ficta: Theories of Accidental Inflections in Vocal Polyphony from Marchetto da Padova to Gioseffo Zarlino* (Cambridge: Cambridge University Press, 1987), especially 43-8; Peter Urquhart, "Canon, Partial Signatures, and 'Musica Ficta' in Works by Josquin Desprez and his Contemporaries," Ph.D. dissertation, Harvard, 1988; Urquhart, "Cross-Relations by Franco-Flemish Composers after Josquin," *Tijdschrift van de Vereniging voor Nederlandse Muziekgeschiedenis* 43 (1993), 3-41. Their paraphrases have been invaluable in showing where my formulations need to be strengthened. ========================================== [2] Cristle Collins Judd began her posting of July 23 to mto-talk ("Wibberley, MTO 2.5," mto-talk 23 July 1996) by addressing not so much Wibberley's solution but his modal premises. In order to restore premises rather than symptoms to the centre of the discussion, I shall first set the Josquin aside. Since some readers may not be familiar with DF and the context in which I used that example, and since none will be able to infer it correctly from Wibberley's article, it might be helpful if I now restate and amplify some parts (only) of the thesis particularly germane to this discussion, and take this opportunity to adjust some areas where my presentation may have proved incomplete or too elliptical. [3] Since I invoke counterpoint so strongly, I had better explain the specific sense in which I use the term. Counterpoint, as defined in DF from Tinctoris and earlier theorists, is concerned not with lines or vague general attributes but with *two-voice* progressions--what *we* might call two-part or *dyadic harmony*.(4) At least up to the late 15th century, the handling of more than two parts was treated by theorists as an extension of those dyadic principles. It is in respecting and reconciling melodic principles and the rules of counterpoint that ficta is necessitated; I have tried to show that ficta needs to be viewed in the context of counterpoint as a whole, and not informed just by precepts specifically labelled as ficta. The list discussion has referred to the need to set priorities in cases of conflicting principles (Judd, 23 July: "the challenge to Bent's solution of the passage in question comes not from modal theory, but in relation to how one interprets horizontal and vertical priorities in determining ficta." Just so.). I did indeed attempt(5) to draw from theorists a set of primary guidelines for applying contrapuntal precepts (melodic and "harmonic") precisely with a view to setting priorities when those precepts come into conflict, though there is still a long way to go in spelling out qualifications, exceptions and licences to those primary considerations, some of which have been addressed by Berger and Urquhart. ========================================== 4. Richard Crocker, "Discant, Counterpoint and Harmony," *Journal of the American Musicological Society* 15 (1962), 1- 21. 5. In DF 23-29; also in my "Accidentals, counterpoint and notation in Aaron's *Aggiunta* to the *Toscanello in Musica*," *The Journal of Musicology* 12 (1994), 306-344 (Festschrift issue for James Haar: Aspects of Musical Language and Culture in the Renaissance), henceforth ACN. See especially 324-5. ========================================== [4] A fundamental difference between renaissance notation and ours is that, then, "not to notate accidentals is not to misnotate the music." Notated accidentals were truly accidental. No more or less importance attaches to their prescriptive power or indeed to their absence than would, say, to that of sporadic fingerings in some early keyboard sources. We may be glad of help, however occasional or eccentric, but notation should not be viewed as incomplete or inaccurate when lacking such accidental indications. When we transcribe old music into a notation in which accidentals have become essential, we tend to read the notation thus transcribed as a stronger default than it ever could have been, one from which "deviations" have to be justified and to which accidentals have to be added, or notes inflected. It is we, *not they*, who "add accidentals," depart from the notation, and make inflections. They had no term to distinguish our F flat from F: if a note was F according to the clef, it was still "F," even F fa ut, *even if* it had become our "F flat" by local contrapuntal operations. This is what I shall mean by the term "contrapuntal descent" (see [8]), as distinct from a descent caused by tuning. [5] It is the modern transcription that has traditionally been treated as our default, as when we refer to "the notation as it stands," or at "face value," despite changing standards in editorial practice. After considerable editorial experience, it is now my conviction that so to treat it is a greater disfigurement and source of misprision than to start from the other end, as I now advocate. It is obvious that *their* starting point for these determinations, *their* access to the music, was not from a modern transcription but rather through singing from their manuscripts and prints. Early notation provided a weak intervallic default organization by clef and signature, but because it was incompletely prescriptive of pitch (hence "weak default"), the performer expected to arrive at actual sounds by some means besides prescriptive notation. Modes and hexachords (see [18] below), while very important for other purposes, run on separate tracks from each other and are at best marginally relevant to the realization of counterpoint and the determination of ficta. The most important key to successful realization of weakly prescriptive notation is to complement it as they must have done, armed with an approximation of the elementary training shared by composers and singers, and which composers presumed in their singers when they committed their compositions to notation, namely, for these purposes, practical training in counterpoint. Taken in partnership, notation and counterpoint create a more strongly prescriptive basis for realization. Like them, we should develop the (for us very different) musical skills that are dictated by singing from the original, acquiring an awareness of the constraints and freedoms inherent in the notation, as well as a sense of the violence done by putting weak-default (early) notation (without the complement of a strengthening counterpoint training) into a (modern) form that demands to be read by the standards of modern notation as a "strong" default. DF grew out of a recognition that the answers to many of these questions follow naturally from the experience of reading and singing from original notation instead of from conceptually different modern translations. If this is a counsel of perfection, we need at least to learn (by doing it) to *simulate* that experience so that in using modern scores we can make all allowance for their inherent distortions, as one glimpses the original language through the shortcomings of a translation. It is those earlier habits that (echoing Crocker 1962) we need to recover, by reading their books (musical and theoretical) rather than ours, by observing what they don't say as well as what they do. [6] Armed with the rudiments of mensural and contrapuntal skills (correct realization of perfect simultaneities and cadential approaches in discant-tenor pairs, and perfection of melodic 4ths and 5ths unless prevented), one *reads* one's own part in a state of readiness to re-interpret, of readiness to change one's *expectation* of how to read the under-prescriptive notation (not to *change the notation!*) in prompt reaction to what one *hears*. The "default" of the line you *see*, together with the melodic articulations you expect to apply (perfecting linear fourths, making cadential semitones) is controlled and sometimes over-ruled by the counterpoint you *hear*. The "default" that is "changed" is not the *notation as transcribed*, but the *expectation* of how the original notation is to be realized.(6) Once the new (i.e. old) habits of listening and adjusting aurally have been internalized, most solutions follow naturally, and almost never require the lengthy discussions that arise when singing from transcribed score. I fear that I am now as skeptical of the authority of assertions about what is and is not possible in early polyphony, from those who have not acquired fluency in reading in this way, as I would be reluctant to accept literary correction from someone who read a language only in translation. The weak default of under- prescriptive notation becomes a strong default when coupled with contrapuntal training, but it is a different strong default from modern, mostly white-note, notation "as it stands," and the inherent status accorded accidentals by current editorial conventions. ========================================== 6. See also my "*Resfacta* and *Cantare super librum*," *Journal of the American Musicological Society* 36 (1983), 371-91, and "Editing early music: the dilemma of translation," *Early Music* 22 (August 1994), 373-394. ========================================== [7] We are still free to treat results so obtained as a default that can or must be departed from, but this default is as different as it could be from that of a modern transcription. We will approach their thinking and musicianship more closely by trying to do it their way (the Kon-Tiki principle of testing whether the expedition is possible using the original equipment), even if the results turn out to be very different from what we have grown used to by doing it from the opposite, unquestionably anachronistic direction, and even if we then decided (on grounds *yet to be determined*, since "modal fidelity," *pace* Wibberley, will no longer do) that the new results need further adjustments of a different kind. [8] Our musical culture has raised the definition of frequency and pitch-class to a high status, for analysis, editing and performance. My reading of a range of early theorists leads me to posit a slightly fuzzier status both for what we would call pitch-class and for frequency, a status that places pitch closer to the more flexible view of durations and tempo that we still have. This reading rests partly on conspicuous circumlocutions and the late arrival of precise language, notation and measurement, partly on a pervasive Pythagorean mentality expressed in the tuning system, partly on my understanding of counterpoint and the internal evidence of some paradigmatic pieces, *not* the Josquin. We routinely make *rhythmic and durational* analyses on the basis of notated values even though we know that performance fluctuations, some necessary, some elective, expected but elusive to precise definition, are ignored by the analyst. We are not necessarily shocked if an analysis disregards the fact that a piece, any piece, may end slower than it began. A terminal ritardando needn't affect certain kinds of analysis; nor need the ritardando of pitch caused by a logical downward sequential spiral (Obrecht) shock us. I do not assume, as Wibberley seems to impute [2], that for the "Obrecht piece to begin on F and end on Fb was of little if any consequence for the singers." By suggesting that if they *knew* they were spiralling for reasons either of tuning or counterpoint (if I understand him correctly) they would have found a way not to do so, Wibberley subscribes to a rigid frequency stability which, however well established it became in the keyboard-reference era, did not, I believe, govern earlier music (see especially [13] below). Without cumbersome advance planning, I maintain that it is virtually impossible to sing the Obrecht *Libenter gloriabor* Kyrie (and about 30 other pieces) from original notation in any other artful way than to let the sequence, indeed, wind smoothly down in its *contrapuntal* operation (irrespective of the tuning used, even if that were equal temperament). This happened in one of our singing sessions when someone innocent of its notoriety brought a facsimile along. We read it, it descended, as everyone was (and always would have been) well aware as it was happening. The sequence of descending fifths and rising fourths F B E A D G C F is notated only with a few encouraging B and E flats, but its smooth counterpoint locks it into -- in our terms, F Bb Eb Ab Db Gb Cb Fb (see DF, 34-40). Another of us, who had previously been sceptical of "my" solution on paper, exclaimed with surprise that it sounded fine. That is precisely the point. Try it! [9] Nor need such a spiral impinge on, *pace* Wibberley, a modal analysis. The work by Powers and Judd on Aaron's modal assignations(7) makes it clear that Aaron in the *Trattato* was indeed making those assignations "on paper," in such a way as to permit two startlingly different-sounding pieces (such as *Mon mari m'a diffame* by De Orto and *E la la la* by Ninot le Petit, nos. 12 and 27 in Canti B) to receive the same classification. (How, for example, does Wibberley deal with such witness or advocacy of mode?) This is closer in time to Josquin than Glareanus and should restrain Wibberley's construction of the relevance of (his perception of Glarean's view of) mode to the sound (= contrapuntal realization) of a piece. The relatively higher status we now accord to sounding pitch definition is reflected in the facts that we (not they) have made accidentals essential, and that we fix frequency and pitch class much more sharply than we do metronomic values. Pitch, in short, has a higher status for us than rhythm. Skilled singers *of course* would be aware of changes, both at the micro-level of tuning, shifting commas of intonation, and at the macro- level of occasional contrapuntal spiralling sequences such as I believe to be indisputable in the Willaert and unavoidable in the Obrecht examples. ========================================== 7. Harold Powers, "Is Mode Real? Pietro Aron, the octenary system, and polyphony," *Basler Jahrbuch fuer historische Musikpraxis* XVI (1992), 9-52; Cristle Collins Judd, "Reading Aron reading Petrucci," Early Music History 14 (1995), 121-152. ========================================== [10] Berger (in *Musica ficta*) was unwilling to accept the evolution of his "renaissance" view of a keyboard-like repertory of available pitches from my free-standing, vocally-conceived, Pythagorean, pre-keyboard "medieval" view of pitch, tuning and vocal counterpoint. Indeed, he (like Wibberley) is reluctant to accept any possibility of fluctuation, by tuning or counterpoint, and there we differ. I believe that Berger's view is broadly valid for a later period and with different qualifications from those to which he applies it, and that it can at some point be reconciled with mine, though not as a background to music before 1500, where I judge it to be anachronistic. I wrote: "Musica recta is not an arsenal of fixed pitches but denotes a set of relationships to a notional norm of pitch stability that is more like a flotilla at anchor than a Procrustean bed or a pre-tuned keyboard. The 'operation of *musica ficta*', that is, the substitution at any point, for contrapuntal reasons, of a tone for a semitone (or vice versa), could mean that the absolute frequency of the As, Bs, Cs that follow may not be the same as they were before, although the local interval relationships of small segments will remain intact. The taking of a *conjuncta* (substitution of a tone for a semitone or vice versa) anywhere in the system may change the actual pitches following that point, without changing the relationships except at that point. The value of a semibreve may be changed by proportional operation or mensural change; the contextual relationships of that semibreve will continue to be observed after the point of change even if the absolute durations represented by the same symbol in the same context are different from before. Both for mensuration and for pitch, the values are achieved through local context and without reference to long-term absolutes." (DF p. 10, and passim.) Especially since the Powers-Judd illumination of renaissance views of mode, it has yet to be shown that there is any basis other than modern prejudice for claiming such absolutes with respect to sounding pitch, as distinct from notated status, for a musicianship that was not yet, before the 16th century, bound by keyboard-like reference. It is the notion of frequency volatility of both these kinds that has already educed the loudest howls of protest (e.g. from Berger, p. 45). This is a genuine point of disagreement, much more fundamental than the Josquin example. That singers were aware of these shifts does not prove (again, *pace* Wibberley and Berger) that they would have found them undesirable or striven to avoid them. Before about 1500, and often afterwards, there is nothing to constrain a piece to a fixed frequency or, in certain special circumstances, to a fixed constancy irrespective of tuning, for a letter-name-plus-hexachord syllable point on the gamut, these fixities are what I see as coming in with the rise of the keyboard as instrument of practical and theoretical reference. They would have been as ready, I believe (as we are not), to redefine a frequency or, as in the Willaert, to adopt a changed but logically-approached pitch for E, as to accept (as we can without special pleading) a new value for a semibreve beat after a proportional shift, whether specified or otherwise necessitated. [11] Diatonic (and hence also chromatic) status was defined *melodically* in the 16th century and earlier.(8) The presence of sharps and flats does not necessarily render music chromatic; diatonic status then, as later, is not confined to "white notes." F-F# is a chromatic, F#-G a diatonic semitone, *irrespective of the size or tuning of the interval*. F#-G-Ab presents two adjacent *diatonic* semitones. This or any melodic progression that proceeds by diatonic intervals (e.g. the tenor of the Willaert duo) is diatonic. Most ficta is diatonic, hence "Diatonic ficta." I did not intend the apparently paradoxical title as a label for exotic procedures;(9) rather, I used some unusual pieces to illustrate how far diatonicism can go, in order to demonstrate how some modern scholarship has misused the term in relation to early music, and to bring out the different underlying assumptions and the different prescriptive power of old and new notation respectively. I am pleased to note in the recent discussion that most correspondents avoid indiscriminately calling sharps and flats chromatic, and thus tacitly acquiesce in the view that, except for specifically chromatic intervals such as F-F#, ficta was largely diatonic. ========================================== 8. James Haar, "False Relations and Chromaticism in Sixteenth-Century Music," *Journal of the American Musicological Society* 30 (1977), 391-418. 9. As Wibberley, [2] and [10]. ========================================== [12] I have read with interest the mto-talk postings of Nicolaus Meeus on tuning and intonation ("Wibberley, MTO 2.5," mto-talk 19, 26 August 1996). He rightly surmises that I believe some kind of just intonation (with pure 5ths and 8ves) applied to *a cappella* vocal counterpoint "with pure intonation, Pythagorean in principle [Meeus and Lindley also use this qualification], but probably with justly tempered thirds in practice" (DF p. 18). However, Meeus's view of tuning is so clearly anchored to a sophisticated keyboard-equivalent that, in setting a standard of reference for a piece or a passage, it comes at the discussion from the opposite direction from mine. As for adjustments *on* dissonances, the frequent pitch redefinitions that result from a Pythagorean approach (as I understand it; see next para.) result in no bumps, no audible local dislocations. [13] It is highly significant that there was no standard *starting point* for tuning the Pythagorean monochord. In DF I presented Pythagorean tuning as the antithesis of keyboard reference: "even if two monochords were tuned with true Pythagorean ratios, their resulting frequencies could be slightly different if those ratios were applied from a unison by a different route through the spiral of fifths." (See DF, especially 3-7.) The monochord was unsuitable as an accompanying instrument; apart from very elementary pedagogic use, it was a representation of Pythagorean ratios rather than a proto-keyboard for an individual performance; this of course allows for the kind of disciplined frequency movement I believe to be endemic to their thinking, hence the Pythagorean spiral, not circle, of fifths. The monochord *represented* the proportions that yielded those sounds, but in practice (by pure 5/4 thirds) may have been on a slightly different track from them (separate tracks, yet again). I believe that the view of a constantly redefining Pythagorean application overcomes the rejection (by Meeus, mto-talk 26 August, and implicitly by many others) of Pythagorean tuning throughout the very period where it is prevalent, and the point of theoretical reference for proportions of all kinds. Indeed, the better in tune a performance sounds in terms of its local progressions (with pure thirds and fifths), the more likely it is to move down, as several professional performers confirm. It is a short step from here to believe, as I do, that Pythagorean intonation was *constantly redefinable* around new central notes in the course of a piece. The arrival on each new true fifth sonority would then be the new point of departure for purposes of tuning calculations, thus achieving local perfection and a smooth, gradual descent by comma increments. This rules out a notional keyboard standard for performance; any performance *with* a keyboard necessitated compromises, a fact that exercised several 16th-century theorists. The final sequence of a piece like *Absalom*, in which (I believe) pure (Pythagorean) fifths would, ideally at least, have been mediated by pure 3rds (5/4) which in turn anchor the next pure fifths of the sequence, is almost bound to end at a fractionally lower frequency unless it is (artificially, and irrelevantly for this discussion) disciplined by adherence to a pre-tuned keyboard standard or repertory of available pitches (Berger's view). [14] If you believe, with Lowinsky, that frequency must have been constant, a musical absolute (as if to be accompanied on equal-tempered or fretted instruments), then obviously pieces such as the Willaert duo and Greiter's *Fortuna* can be regarded, as he did, as precocious manifestos for equal temperament.(10) He was prepared to accept *contrapuntal* descent under certain conditions, but not frequency descent. By contrapuntal descent, I mean pieces like the Obrecht and Willaert examples (see DF) and the Greiter where *even with constant frequency* the "F" at the end is, by purely contrapuntal spiralling, one or more semitones lower than the "F" at the beginning. If you believe, with me, that (1) such logical *contrapuntal* and melodic descent through the spiral of fifths in these pieces is inherently Pythagorean in concept and (2) that Pythagorean *tuning* of 5ths in practice, with pure 3rds (5/4), was predisposed to result in comma slippage, pieces which thus descend *contrapuntally* can be construed as (in these cases, late) manifestos of Pythagorean conception and execution, as posited above. Rejection of *any* degree of frequency volatility obviously makes it harder to overcome resistance to contrapuntal descent, despite the existence of pieces (Willaert, Greiter) where all are agreed that it *must* happen. Otherwise, the tuning consideration need not be an impediment to considering other premises of this argument (notably contrapuntal correction) independently of a specific tuning system.(11) ========================================== 10. E.E. Lowinsky, "Matthaeus Greiter's *Fortuna*: an Experiment in Chromaticism and in Musical Iconography," *Musical Quarterly* 42 (1956), 500-519, 43 (1957), 68-85. 11. Of course, transcriptions of these or any pieces *can* be sung in equal temperament, but I disagree with Lowinsky that they *must* be; indeed their spiralling and fifth- based conception makes it most unlikely that this would have happened in a locally well-tuned vocal performance. ========================================== [15] Now for a confessional review of some miscalculations in DF, and a further unpacking of some ellipses. First, it was misleading to present my examples in modern score. I should never have expected readers to accept, even hypothetically, a paradigm shift that emphasizes the radical difference between old and new notation while at the same time transcribing the examples in such a way as to imply that they are equivalent, and exposing them to all the shock of unfamiliarity, and to conceptually foreign analyses of their tonality and tuning. As I put it, "neglect of some primary musical facts has led us to tolerate the aural dissonance of intolerable intervals before we accept the merely graphic dissonance of an intolerable-looking modern score." (DF p. 48.) My examples in DF should, rather, be seen as "phonetic" approximations, into a different language, of what might be sung from the original, or might be at least the first default so derived. But it is hard to know what else to do. It is unrealistic to assume that readers will have the training or time to get together to sing examples from parts, the counsel of perfection spelled out above, thus simulating the *process* by which contrapuntal training was applied to notated music, but modern scores might at least be read with that awareness. [16] Since DF I've had the benefit of reading and discussing recent developments in work on mode, especially by Powers and Judd, and I would now reformulate some of what I said about mode in the light of that, though the basic disconnection, on which Judd and I agree, is not much affected. For the moment, I will confine myself to quoting her clear statements to the mto-talk discussion: (23 July) "there is simply no need for mode or ficta to impinge one upon the other because they occupy different conceptual and theoretical realms," and, after quoting Wibberley's "Only by this means [retaining some diminished fifths in performance] would it have been possible to remain faithful to the mode on account of the actual notes Josquin composed in the particular combination chosen by him," Judd continues: Wibberley's "conclusion is based on a modern understanding of mode as tonal system. Nowhere is such a view articulated by Glarean. Such a view fundamentally misrepresents the very nature of musica ficta in seeking to fix pitches in a way that Renaissance musicians clearly did not. Although Bent's solution is not one that I would adopt for this passage, there is nothing in the Glarean passage quoted by Wibberley in para. 9 to argue against it. Wibberley is imputing to Glarean an "internal" view of the modes, but nothing in Bent's solution changes the final or range (i.e. the external criteria by which the mode is recognized), hence Bent's view that her solution does not disturb "modal coherence." [17] While I do not think that I am "mixing up"(12) performance and understanding, I do see that this is something that needs to be addressed, and one way in which I hope to advance the formulations of DF is to make that distinction a bit clearer. I hope I have done so by introducing the "default" element into paras [4-7] above. Having advocated even more separation of tracks than I did in DF, I see that here I have not gone far enough, and that certain rare conundrum passages like the Josquin that are capable of a perfect contrapuntal realization might in practice not receive it. Just as there might be a reading of a piece that was perfectly consonant with the traditional (Wibberley's) modal-scalar ideal, but a reading that one would not choose in practice, so there may be passages like the Josquin sequence where the perfection of the counterpoint would have been tempered in practice. This is where my discussion above of a "default" concept may be helpful. While I in no way withdraw from "my" version of the Josquin as an exercise in contrapuntal perfection, I am perfectly prepared to accept the possibility of a more cautious compromise (see below), if only to direct attention to the premises by admitting that they need not stand or fall by an "extreme" example. I chose examples that would make vivid the radically different conceptual underpinnings of old and new notation, rather than to illustrate the much subtler consequences that this understanding brings in practice for most "normal" pieces; but if we can now agree to recognise the Josquin as a special case, the way may be open for broader acceptance of what I have outlined above. ========================================== 12. As Berger alleges, *Musica ficta*, 46. He also rebukes me for not keeping in mind letter-plus-solmization designations, a charge directly contradicted by DF 7-12. ========================================== [18] In an attempt to set out the main tributaries of a proposed radical shift in *understanding* the basis of notation (not necessarily or always entailing a shift in the sounding *results*), I inevitably overstated or understated some aspects, largely by insufficiently freeing myself of some modern prejudices. In attempting to formulate the complementary nature of notation and counterpoint, I may have overstated the weakness of the default, leading others to impute a less disciplined relativism than I actually intend. I hope that the default element helps here. I seem to have *under*stated my position on the role of hexachords and solmization, and hence misled Daniel Zager and some others about how mastery of solmization relates to ficta.(13) I never meant to claim (as Zager implies but does not state) that solmization can resolve counterpoint/ficta problems. I do not share his dependence on solmization to determine counterpoint. Rather the converse: contrapuntal decisions, once made, can be expressed in terms of solmization, the nearest they had to a precise language in which to conceptualise and name sounds. But since they stretched the system to cope with all eventualities, so that anything could be solmized by extensions and disjunctions, the criterion of easy solmization is not a valid arbiter of which sounds are or are not possible. To argue a particular solution *from* solmization is to let the tail wag the dog. I wrote: "Hexachords provide a functional context for semitone locations which have been predetermined by musical considerations, but they do not in themselves determine what the sounds will be. The hexachordal *voces* are the means by which those sounds become practically accessible in vocal polyphony, just as, by analogy, fingering is the means by which small groups of notes are physically negotiated on instruments." Hexachordal thinking permeates their terminology. It guides us away from the notion of "inflections" of individual notes and into that of small scalar segments (sometimes projected as tangents from the *scala* of *musica recta*) that accommodate and articulate semitones, the need for which is *pre-determined* on contrapuntal principles. It cannot in itself solve individual ficta problems just as, conversely, no ficta solution can be rejected on grounds that it can't be solmized. Nor, as Judd agrees, can modal theory solve ficta questions, whether Aaron's or Glarean's. What I have proposed is the beginnings of a system drawing simple rules and priorities from counterpoint theory, principles whose development, exceptions and qualifications will have to venture beyond the point where theory helps us and be derived in turn from actual composed music; but they can be projected homeopathically in the direction indicated by that theory (rather than antibiotically from our alien perspective), and fleshed out from a practice stripped of some modern varnish (such as the notion of modal fidelity as an arbiter of tonal stability, and of modern notation "as is"). Some of these precepts are strong and binding. Some are weaker and open to alternatives and competing priorities. All of them can be accepted without the obligation to choke down my Josquin example whole as a prescription for *practice*. That is negotiable. ========================================== 13. Daniel Zager, "From the Singer's Point of View: A Case Study in Hexachordal Solmization as a Guide to Musica Recta and Musica Ficta in Fifteenth-Century Vocal Music," in *Current Musicology* 43 (1987), 7-21, referred to by Wibberley. Urquhart (p. 368) invokes awkwardness of solmization against my version of the Josquin. ========================================== [19] Having thus slightly rearranged the furniture to permit (I hope) constructive discussion, now to the Josquin. I should add to my list of miscalculations that I ought to have saved that example until a later time, in order not to distract attention from the premises, or at least I should have continued the argument, which I will now try to do. It *is* an exceptional puzzle, and has been so recognized by several writers, notably by Dahlhaus, with the rather different conclusion that "der Tonsatz abstrakt konzipiert ist und dass sich Josquin ueber die Unentschiedenheit, wie er zu realisieren sei, hinwegsetzte, da sie ihm gleichgueltig war." ("the composition is conceived in the abstract, and that Josquin disregarded the inconclusiveness as to how [the composition] was to be realized, because he was indifferent to [the inconclusiveness.") Dahlhaus thus posits *the composer's indifference to the actual resulting sounds*, and argues that counterpoint thus abstractly conceived may have lacked either prior aural imagination of such sounds or, indeed, any musically acceptable realization.(14) To this view Berger and I join in taking exception, if for different reasons.(15) Josquin's sequence *is* a conundrum, of a fairly rare type. In the disputed measures, he gives us not just one text-book sequential "cliche" chain of fifths and sixths, but *two* superimposed contrapuntal pairs, discant and tenor, tenor and bass,(16) *both* of which, (not just the upper pair, *pace* Wibberley [13]), have claims to perfection *and* place constraints on the other. Dahlhaus gave up on the passage. Lowinsky favoured B natural in bar 48 because it fitted his sense of the piece as being *tonal* as well as (*nearly* pure) Ionian.(17) Urquhart accepts Bb at bar 48, but avoids my version by accepting the simultaneous false relation of a B *natural* against it in the treble.(18) Wibberley also accepts the Bb, but his compromise has a melodic augmented fourth *and* a simultaneous diminished fifth at 48-50.(19) The conundrum is that, *pace* Dahlhaus, I have shown that Josquin wrote a passage that *is* capable of contrapuntally perfect realization, whether we like it or not, and this intervallic perfection has been acknowledged by Wibberley (n.7) and by others in the list discussion. Let us call it "a" solution but not necessarily "the" solution. In the context of DF, I was frankly more interested in its Janus-like status as a theoretical conundrum than in making a binding performance prescription. I would now prefer to call that version a contrapuntally-defined default, a *starting-point* for negotiation or compromise. I was exploring the implications of counterpoint, not primarily fixing up a piece for performance--perhaps I did not make this clear enough (in DF n.49), but it is clearer to me now. ========================================== 14. Carl Dahlhaus, "Tonsystem und Kontrapunkt um 1500," *Jahrbuch des Staatlichen Instituts fuer Musikforschung preussischer Kulturbesitz* 1969, ed. D. Droysen (Berlin, 1970), 7-17, especially 15-16. 15. Berger, *Musica Ficta*, 166-70. 16. I give "text-book" sources for this sequence from Hothby and Aaron in DF 29-30. 17. E.E. Lowinsky, *Tonality and Atonality in Sixteenth- Century Music* (Berkeley and Los Angeles, 1961), 20. 18. Urquhart discusses the *Ave Maria* example on pp. 368-69 of his dissertation. His solution, couched in an often seriously misleading report of my premises, is given in his article cited in n.3, especially pp. 25-8, and also in a paper to the American Musicological Society, November 1995. 19. Wibberley states [13]: "Since it is impossible to render the Josquin passage in any way other than that proposed by Bent without failing to eliminate all diminished fifths otherwise occurring between notes of the upper voices (such an elimination being her prime motive)." I invite him to re-read the way I set up the Josquin example. If any fifths, by Wibberley's criteria, are to be regarded as "where perfect consonances were to be attained," they are surely these. See [22] below on diminished fifths, and [27] on Aaron. ========================================== [20] The provocation, therefore, is not mine but Josquin's. It remains interesting and inescapable that he set up this sequential passage of two superimposed contrapuntal pairs in such a way that an intervallically flawless reading,(20) if not a perfect solution, is possible. Josquin's conceit deserves better than that we retreat from it on anachronistic grounds based on notions of white-note supremacy or modal chastity. Wibberley has attempted to make the case for doing so on modal grounds, but for reasons given by Judd, and because of the irrelevance to Josquin's personal arsenal of the later testimony of Glarean, let alone Zarlino, it will be clear that I do not think he has succeeded. We have to choose in practice whether to depart from that particular kind of perfection-- indeed, whether Josquin was provoking us to do just that, rather than whether to depart from the notational translation of a modern score. That is the nub of the "default" aspect of my hypothesis. Bach chose occasionally to break "rules" about parallels or leading notes; we must be prepared for Josquin to do likewise, and to imply that we need to realise certain passages imperfectly. But we had better have a reason more firmly grounded in what we can discern of the musical practice of Josquin's contemporaries than simply disliking something that differs from what *we* have--perhaps mistakenly--grown used to. Addled by years of hearing and seeing under-inflected performances (of the notation "as it stands") with too many flat leading-notes and proto-tonal diminished fifths, our mistrained ears are not reliable arbiters. That "we haven't tried it because we don't like it" (to quote the old Guinness advertisement) is a self-fulfilling prophecy. ========================================== 20. Before someone raises it on the mto-talk discussion list, I explain in DF (29-34) why the altus part, for internal and diagnosable reasons, takes a low priority in this passage, and why the sequence, as "pure" counterpoint, can be contemplated separately. But the altus may yet be the best way into arguments as to how one might depart from a contrapuntally pure default. ========================================== [21] I am pleased to see that there has come to be acceptance of the bass Bb in bar 48 by Wibberley and Urquhart, despite other disagreements.(21) This note was ubiquitously rendered as B natural in the Josquin *Werken*, in Miller's edition of Glareanus, by Lowinsky, and in most recorded performances. Good, for that Bb seems to me the one non- negotiable point, and reflects new acceptance of a strong priority that we can perhaps all agree on. The B natural was earlier seen as a kind of first-inversion dominant seventh anticipating the leading-note that takes us back to the bright radiance of C major or, if you prefer, Glarean's likewise anachronistic hypoionian. The Bb in bar 48 *both* avoids a linear tritone *and* a simultaneous diminished 5th in a standard sequential progression, and thus claims priority on two counts. But that Bb is the thin end of a wedge; that there *can* be an ideal solution but no perfect solution makes it very difficult to define how far is too far, now that we have removed anachronistic tonal harmony, simplistic modal restraints, and, I hope, the misapplication of modern notation as defaults. ========================================== 21. See DF n.48, where I comment on the source status of the bass B flat. Wibberley however places it in parentheses in "my" version, while stating: "By the accepted rules of consonance, the bass b must be flattened to b-flat in order to provide a perfect consonance with the tenor" (Wibberley [4]). ========================================== [22] Except for the bar 48 Bb, alternative compromise solutions can be entertained in performance, including the different ones of Wibberley and Urquhart (and see DF n.49). Since there is no good solution, the actual performance choice is much less interesting, because to some extent arbitrary. I have summarized the most important rules and priorities, (see above, n.5) but there are many caveats, and a much longer discussion is necessary, especially of the circumstances where diminished fifths may be permitted, and where there is some common ground between my views and those of Berger and Urquhart. I could, for example, more readily tolerate an--albeit unnecessary, and denied by a notated B flat--diminished 5th in the different context of bar 43 (with B* natural below F contracting to a third on C and E between the lower parts) before Wibberley's example begins: [discantus] D C B [tenor] F E D [bassus] D B* C G The fifth at bar 48 on the other hand does not contract but forms part of an ongoing sequence and must, as we seem to agree, be perfect. But how do the following limbs of the sequence differ in the constraints that are placed on consonance and contrapuntal perfection? Wibberley cites Aaron in support of his claim [15] that "None of this means, however, that diminished fifths were to be completely banned from composed music; it simply means that perfect consonances did not admit them, and that where perfect consonances *were to be attained* [my emphasis] such intervals had to be eliminated." If *this* chain of fifths is not a prime, and literally text-book, candidate for "where perfect consonances were to be attained," I don't know what is. Having accepted the Bb in 48 by the rules of consonance [4], his version presents both a linear tritone and a simultaneous diminished 5th in a standard sequential progression, and thus merely pushes further on the crisis that was avoided at bar 48. He invokes a lower status for the relationship between the upper parts, which might be acceptable when the main contrapuntal relationship was between the lower two. Indeed, diminished fifths sometimes occur either, as Wibberley puts it, between upper parts that are supported from below, or, as I would more often prefer to put it, when the primary contrapuntal cadence, the 6th to 8ve between the lower parts, has an added part above, e.g.: [discantus] F E [2nd discantus] B C [tenor] D C But he fails to recognise that the Josquin passage does not meet those criteria, because its unique feature is that *two* primary and non-cadential contrapuntal progressions are superimposed, and that the upper part therefore cannot be treated as subsidiary. [23] In light of Judd's postings to mto-talk it is almost superfluous for me at this point to deny the relevance of Glarean's twelve-mode system (or for that matter Zarlino's counterpoint theory(22)) to discussion of constraints and freedoms that might have applied in Josquin's mind and his expectations of performance. Glareanus says nothing relevant to counterpoint and ficta. His 12-mode system is no more germane to how *Josquin* might have classified the *Ave Maria* than would be a roman numeral analysis to his harmony. Wibberley would be mistaken to assume that my silence on Glareanus was for any other reason (see DF 45). Judd published a modally-based analysis of the motet, not mentioned by Wibberley;(23) in principle, her and my statements can co-exist without disagreements affecting our different approaches: "there is simply no need for mode or ficta to impinge one upon the other because they occupy different conceptual and theoretical realms"("Wibberley, MTO 2.5," mto-talk 23 July 1996).(24) Judd further commented in the same posting: "Wibberley's straightforward mapping from composer to theorist (and vice versa) highlights an even more problematic issue. I find his view of theorists as "witnesses" difficult to sustain. Aron, Glarean, and Zarlino are, after all, advocates of their own agendas as well as witnesses." Then Wibberley ("Wibberley, MTO 2.5," mto-talk 19 August 1996): "The presumption underlying my article was that the Josquin motet WAS [Ionian tonality], especially since Glareanus said so." and ("Wibberley, MTO 2.5," mto-talk 5 August 1996): "What is clear to me is that Glareanus is telling us something quite definitely about the way the COMPOSER has composed the music, rather than about the way others might have performed it." Does Wibberley not distinguish between subsequent comment and classification on the one hand, and what could have been in the composer's mind, on the other? It is indeed a big leap to go from a subsequent theorist (especially Glarean) with his own axe to grind to make the assumption that because this was in his mind it must have been in Josquin's more than 50 years earlier. ========================================== 22. Wibberley [29] "Josquin would seem, in the example under consideration, to have arrived at Zarlino's "impasse," but Bent has not followed Zarlino's advice in finding a suitable way around it." Why should I have taken the advice of a theorist 100 years later whose theoretical world, including his use of terms like diatonic, is entirely different from Josquin's? 23. "Some Problems of Pre-Baroque Analysis: an Examination of Josquin's *Ave Maria... Virgo Serena*," *Music Analysis* 4.3 (1985), 201-239. 24. Why, incidentally, does Wibberley so dislike Zager's term "modal purity" and how does it differ from his own "modal fidelity" [13, 26]? He complains "If, by "modal purity," [Zager] has in mind a succession of notes and harmonies that arise only from the pure diatonic notes of a particular scale," but in his own n.8 Wibberley refers to "the use of notes outside the diatonic notes of that mode." ========================================== [24] Finally, some further comments and questions for Wibberley. Why is it acceptable for *Absalom* to "modulate" (a modern term and concept) and, as Wibberley would have it, to "remove the harmony from its base," but not (by his standards) for the Josquin or indeed the Obrecht? By what standards does he judge such "removal" not only permissible but "very successful" while other comparable pieces are not similarly favoured?(25) Indeed, we cannot be sure exactly what Glareanus means by his "without removing the harmony from its base,"(26) invoked by Wibberley against excessive fictive adjustments. Glarean's language and context *may* suggest some connection with Aaron's *distonata via* and Tinctoris's *distonatio*, neither of which easily lends itself to the construction Wibberley would wish to place on it. This is a difficult area, yet to be explained; Wibberley jumps too readily to the conclusion that it must mean removal from defaults of modern, not of renaissance, imposition. ========================================== 25. Wibberley, mto-talk 5 August. His reference to this as a "powerful rhetorical device" suggests that he might be following Lowinsky in demanding extra-musical reasons for what they both call "modulations," a position that can lead to great inconsistencies of treatment between musically similar constructions. Consider the arcane lengths to which Lowinsky went to defend his Secret Chromatic sheep against the musically similar goats who did not qualify by virtue of their texts. See also DF n.47. (NB the *Absalom* "modulation" is not *dependent* on notated accidentals and would have to occur, even without them, as in the Willaert and Obrecht pieces.) 26. I plead innocent to the mind-boggling charges packed into sentences such as Wibberley's [10]: "The whole point of Margaret Bent's solution is that the harmony is, via the "necessary" application of diatonic ficta, "removed from its base." And I don't know what Wibberley means by claiming [7] that I see "modal coherence as a close relative of pitch stability," citing DF 45-47, where I wrote: "Modal theory does deal with some kind of long-term tonal coherence, but not necessarily such as can be equated with pitch stability--another distinction that has lost its force for us." There are numerous examples in Wibberley of discourteously careless reporting, not only of my alleged views but also Bonnie Blackburn's, astoundingly misrepresented. ========================================== [25] That Wibberley accepts *some* "ficta additions" (I would prefer to call them contrapuntal adjustments) is clear in his posting of 8 August ("Wibberley, MTO 2.5 mto-talk 8 August 1996). Are all of these consonant with his view of mode in pieces classified by Glareanus (or indeed Aaron), or with the way that these theorists *would have* classified them? Up to what point does he accept "inflections," and which ones, on what criteria and authority, and why no further? How does he reconcile the constraint he draws from Glareanus with explicit and incontrovertible text-book examples of ficta from the early 16th century, such as offered by Ornithoparcus and Listenius?(27) Are works classified by Glareanus to be given different treatment in order that they can conform with Wibberley's sense of what Glarean means, irrespective of any musical characteristics that may suggest otherwise? He also accepts ([13]) that my example is consonant. He sometimes invokes the rules of consonance, though he does not make it clear where he departs from the notational-contrapuntal premises of DF--where indeed? It is on (albeit anachronistic) modal grounds that he determines that the rules of consonance may here be broken. Wibberley adopts the Bb in the bass at bar 48 "by the accepted rules of consonance," but it was not widely accepted before I spelled out those rules (see above, n.5). Wibberley and others think that my Josquin example takes the application of the rules too far for practical purposes, and I might even agree with them, but they (and I) have yet to define precisely at what point and why the "accepted rules of consonance" become unacceptable. Does Wibberley have a view on this? ========================================== 27. These and others are cited in E.E. Lowinsky, "Secret Chromatic Art Re-examined," *Perspectives in Musicology*, ed. B. Brook et al. (New York, 1972), 91-135. ========================================== [26] Wibberley [21] and n.11 is unclear about the status of the fourth. When the fourth appears in composition treated *not* as a dissonance, it is because it is not part of the primary contrapuntal pair. In this case there will be a fifth or a third below it: [discant] F# G [contratenor] C# D [tenor] A G Another and more medieval way of explaining this would be that *each* of the upper parts formed a contrapuntal pair, cadencing on a 5th and 8ve respectively, with the lowest part, when that part is functionally the tenor at that moment. When the fourth occurs between the primary dyadic pair--that is what Tinctoris means by "in counterpoint"-- it must be treated as a dissonance, i.e prepared and resolved. Wibberley's citation of Tinctoris's "Hence it is rejected [as a consonance] by counterpoint" (n.11) means just that. He misinterprets Tinctoris's statement as meaning generally in the musical texture, but counterpoint clearly must be understood specifically here, or it doesn't make sense, and Wibberley has to labour to do so. He confuses the issue by bringing in acoustics ([15] and n.15). Acoustic perfection is on a separate track (again!) from contrapuntal perfection. Later instructions for the behaviour of a third or fourth voice are also ancillary to the primary dyadic counterpoint. [27] A substantial portion of Wibberley's article [paras. 14-19] is devoted to the examples in Aaron's *Aggiunta* to his *Toscanello*. I have discussed these examples and rules,(28) and invite interested readers to compare my explanations with Wibberley's for some of the features he observes. He fails to point out [14] that Aaron's discussion of partial signatures relates them to mode; see ACN p. 321. See ACN p. 324 for a discussion of Aaron's bias to the lowest voice. In para 18 Wibberley raises Orto's *Ave Maria*, used as an example in Aaron's *Aggiunta*, and says that the only reason for the diminished 5th in the preceding bar is that there is a G in the bass beneath it. Not so. The Bb above E contracts to a third, but this E is making a discant-tenor 6-8 cadence with the bass. This is one case for possible exemption for diminished fifths (see [22] above). Indeed, a fifth contracting to a third might sometimes be regarded as "exempt" when it is not part of the primary discant-tenor contrapuntal relationship, and it does not always have to have bass support. Aaron's weighing of priorities in the Agnus of Josquin's Missa *L'homme arme super voces musicales* is discussed in DF 26- 28 and ACN p. 312; he allows a mediated melodic augmented fourth (but not in a sequence) in order to avoid a simultaneous diminished fifth, *and* to concord with the cantus firmus. The melodic augmented fourth is here mediated, and is tolerated in the interests of perfecting a simultaneous fifth; Wibberley's solution achieves neither. ========================================== 28. DF 19, ACN (see n.5); for Aaron see also Judd's article in n.7. ========================================== [28] No one these days can deny the importance of language, and the way the terms we use permeate our thought-processes and prejudices. Thus it is surely also important, for our purposes, to flag dangerous short-circuits or short cuts that may symptomise inappropriate matching of concepts and terms, so that, when we have to use modern terms, we can at least be aware that the *absence* of an early term may be eloquent.(29) I pointed out at the beginining of DF that medieval theory had no single word for pitch or for rhythm, but rather *congeries* of differently-shaded words, a powerful symptom of the separate tracks on which, for example, mode, counterpoint, solmization and tuning operate. These tracks are interdependent, but not in the way we imagine when we prioritize not only pitch, but a frequency-biased notion of pitch. ========================================== 29. In view of his reproaches to me for anachronism, I'm surprised to see Wibberley use terms such as root (n.16), tonicization (n.7) and modulation [10]. ========================================== [29] In conclusion: There is still a widespread and under-supported belief that renaissance composers must have stuck largely to "white- note diatonicism" except where we are forced to believe otherwise. This has been supported from modern misprisions of mode (such as Wibberley's), now being unpicked, that were in turn introduced to counter what we now see as the excessively harmonic-tonal approaches to early music by previous generations of scholars. The unpicking of all related assumptions still has a long way to go. Recent repudiation of artificial shackles of "modal purity" (or whatever we call it) invites us to start afresh with open minds about the sound of early vocal polyphony. (The question of tuning is separable, but obviously important, since it is loaded with many of the same modern assumptions. The contrapuntal arguments are not affected by precisely what tuning system they are realized in, but can be made on their own track.) The urgent question remains: if Judd's view that "modal fidelity" poses no constraints on ficta prevails over Wibberley's view that it does, i.e. if it is true that "paper" modal assignations may be disconnected from realized sounds; and if my premises outlined above find even partial acceptance, are we not further overlaying modern prejudices on early music by assuming that in order to be "coherent" it must conform to *our* standards of long-range tonality (and frequency)? Some of the same questions arising from our imposition of value-laden terms have been raised by Richard Taruskin and others for "authenticity," a term of approbation which admits no alternative; I believe we must do the same for "stability" and "coherence." ---------------------- AUTHOR: Walker, Jonathan TITLE: Intonational Injustice: A Defense of Just Intonation in the Performance of Renaissance Polyphony KEYWORDS: Just Intonation, Syntonic Comma, 1/4-Comma Mean-Tone Tuning, Ptolemy, Josquin, Bartolome' Ramos, Zarlino, Bent Jonathan Walker Queen's University Belfast School of Music Belfast BT7 1NN Northern Ireland, U.K. ABSTRACT: Just intonation is commonly dismissed as an impractical, utopian system which could not have had any role to play in the performance of Renaissance vocal polyphony. In the present essay, I attempt to refute this item of received wisdom by providing a theoretical model of a practicable just intonation system, a model which overcomes many of the traditional objections through its flexibility and pragmatism. I argue that other objections result from the inappropriate imposition of a keyboard-based model of pitch on a vocal repertoire. The second section of the essay is devoted to an historical consideration of the counter-claims of Pythagoreanism as the correct intonational system for this repertoire; I argue why there is good reason to believe that a gulf developed between intonation as described by most theorists up to the late 15th century, and intonation in compositional and performance practice. ACCOMPANYING FILES: mto.96.2.6.walker1.gif mto.96.2.6.walker2.gif mto.96.2.6.walker3.gif mto.96.2.6.walker4.gif Prefatory note on notation In order to minimize the number of GIF files for this article, I shall be using notations that remain within the ASCII character-set; while these are probably familiar to the larger part of the readership, they may nevertheless remain unknown to some. The character "^" as in "2^5," is to be read "to the power of." Since ASCII does not include the root sign, I shall be employing an equivalent notation, thus "5^(1/4)" is to be read "the fourth root of 5," while "2^(7/12)" reads "the twelfth root of two-to-the-power-of-seven." "2^-1," "two to the power of minus 1" is equivalent to "1/2," so "2^-2" is equivalent to "1/(2^2)." Having clarified these details, we can proceed to the main body of the article. Introduction "Just intonation can never have had any real *practical* application in vocal music" - Roger Wibberley{1} "Just intonation is a utopia." Nicolas Meeus{2} [1] Just intonation has long been considered a theoretical chimera which could have had no role to play in the performance of Renaissance polyphony. In conscious opposition to this consensus, I wish to argue here that the standard presentation of just intonation by its opponents (and sometimes its misguided supporters) is a straw man, and that a more flexible and nuanced system of just intonation (hereinafter JI) is indeed viable, and suffers from none of the obvious shortcomings present in its straw-man counterpart. While for reasons of space, the main burden of my argument here will be to demonstrate that JI is not an impossible, nor even an impracticable system, I shall nevertheless sketch out some reasons why we should also consider it historically correct. Section I, below, is a largely theoretical exposition of the JI system I wish to defend, while Section II provides evidence to latch theoretical possibility onto historical actuality. ================================================================= 1. Roger Wibberley, posting to mto-talk, 21 Aug 1996 "Re: Wibberley, MTO 2.5"; the issue of just intonation in Renaissance polyphony was one of the topics of the mto-talk discussion that followed the publication of Wibberley's article "Josquin's *Ave Maria*: Musica Ficta versus mode" in MTO 2.5. I should state at the outset that just intonation does not receive any attention in that article. 2. Nicolas Meeus, posting to mto-talk, 19 Aug 1996, "Re: Wibberley, MTO 2.5." ================================================================= [2] For the purposes of this discussion, I shall first introduce a convenient categorization of the possible approaches to tuning theory that have been evident from Greek antiquity to the present. The first approach I shall call the Pythagorean: this clings dogmatically--even mystically--to the number 3 as the basis for musical order; musical intervals should be constructed, accordingly with ratios involving primes no higher than 3.{3} This includes Pythagoras himself, of course, and the Pythagorean cult that grew up among his disciples, but it was also inherited, via Boethius, by the medieval Church, which invested pagan numerology with a new Trinitarian significance; Pythagoreanism is still manifest, perhaps not so mystical, but still dogmatic, in contemporary musicology, not only among specialists in medieval and Renaissance European music,{4} but also, occasionally, in ethnomusicology.{5} ================================================================= 3. Andrew Barker, ed. *Greek Musical Writings, Vol. II: Harmonic and Acoustic Theory*, (Cambridge 1989), pp. 28-35. A concise, witty and polemical account of tuning history in the West is to be found in *Genesis of a Music*, Harry Partch (New York, 1949/1974), pp. 361-397. 4. Wibberley's posting to mto-talk, 21 Aug 1996, in which he defends himself against Meeus's charge that his article assumed JI; in reply, he endorses and articulates a thorough-going Pythagoreanism, and wields this against JI. He states that "[JI's] total incompatibility with medieval and Renaissance theory is manifest in crucial ways." I shall demonstrate later why Renaissance theorists cannot be enlisted en masse to bolster Pythagoreanism. 5. E.g. Mieczyslaw Kolinski, "The Structure of Music: Diversification versus Restraint," *Ethnomusicology* 22/2 (1978). ================================================================= [3] The second approach I shall call the Aristoxenean, after Aristoxenus the deflator of Pythagoreanism, who argued that musical intervals are very much a subjective and arbitrary matter; he also passes muster as the first to adumbrate tempered systems, although this arose partly through his mathematical incompetence, since the Greeks possessed no mathematics of the irrational numbers (Euclid was quick to refute Aristoxenus).{6} Aristoxeneanism is manifest today among those who believe that tuning systems are necessarily and exclusively cultural constructs, based on the accumulation of subjective preferences;{7} I shall include within its compass those who are wont to use the 12-note equal tempered division of the octave as their arbitrary norm for describing other tuning systems. ================================================================= 6. Aristoxenus, *Elementa Harmonica*; English translation in Barker, *Greek Musical Writings*, vol. 2, pp. 119-208. 7. Nicolas Meeus, postings to mto-talk, 19 and 26 Aug 1996. In the latter posting Meeus says, "Roger [Wibberley] writes : 'just intonation can never have had any real *practical* application in vocal music'. Right, but I would be tempted to say exactly the same of the Pythagorean intonation, so many medieval and Renaissance theorists notwithstanding." Meeus also suggests that keyboard tunings are our best source for vocal intonation; part of the purpose of my article is to show that constraints operating upon the closed tuning systems of keyboards (with 12 to 19 notes per octave) had no bearing on unaccompanied vocal music, which allowed infinite flexibility with regard to pitch. Some of Meeus's other comments indicate, however, that we may not entirely disagree. ================================================================= [4] The third approach provides a via media between these two extremes: Ptolemy rejected both the dogma of Pythagoras and the pure subjectivism of Aristoxenus, describing the Greek genera in terms of the lowest-numbered ratios he could judge, by ear, to correspond to the intervals used by musicians;{8} for example, he replaced the Pythagorean description of the major third (to use our term) "81/64" with the simpler ratio 5/4, which he judged to be in accordance with practice. His approach was therefore to account for practice without abandoning the precision of ratio terminology, but to use this terminology without the prescriptivism of the Pythagoreans. My own position is thus Ptolemaic. I shall call upon these three categories wherever they may serve to clarify the argument, but I would ask readers to remember that I am using them as nothing more than a convenience--not as part of a grand thesis uniting Ancient Greek and Renaissance music theory beyond what is historically warranted. ================================================================= 8. Ptolemy, *Harmonics*; English translation in Barker, *Greek Musical Writings*, vol. 2, pp. 270-360. I cannot recommend Ptolemy's *Harmonics* too highly, for its content, the quality of the argument, and for its early demonstration of scientific method at work. Here is Barker's endorsement: "The care with which he undertakes this investigation, and his willingness to modify theory in the light of the evidence of practice, give us good reason to trust the accounts he gives. They are precious evidence, unique in their combination of mathematical precision with empirical good faith, about systems of attunement that Greek musicians really used" (p. 272). This would explain in part why he proved so attractive to Renaissance humanist scholars such as Fogliano and Zarlino. ================================================================= I [I.1] I shall now move on to the expository discussion of JI, as a practicable tuning system. (I would suggest that readers already familiar with the basics of tuning should pass rapidly through this and the next paragraph; I prefer not to omit these elementary principles, lest the discussion become incomprehensible to a few valued readers.) In order to avoid ambiguity, I shall introduce new terminology for the two ratio-based tuning systems described in this section. The octave is, of course, found on the monochord at the point which divides it in two, and successive octaves are produced by dividing the string into 4, 8, 16, 32 parts, etc. All octaves are thus found in proportions involving powers of two only--this introduces the first prime. In order to obtain fifths, another prime, 3, must be introduced, hence the perfect fifth, 3/2, the perfect fourth, 4/3, and the major second, 9/8. In each case the numerator and denominator is always either a power of 2 or 3. [I.2] If we take C as an arbitrary starting point, which we shall call 1/1, then G, D, A, E and B, all within the same octave, will be expressible in ratio terms as 3/2, 9/8, 27/16, 81/64 and 243/128. All the ratios are thus located between the 1/1 starting point and 2/1, the octave; while the numerator ascends in powers of 3, the denominator ascends in powers of 2 such that the denominator is always less than the numerator, but greater than half the numerator. Travelling in the other direction from C, the notes F, Bb and Eb, again moved up within the same octave, have the ratios 4/3, 16/9 and 32/27--the denominator now contains the power of 3, and the numerator is greater than the denominator, but less than half its value. Such a tuning system, based purely on ratios which include only the first two prime numbers and their powers, is most often called Pythagorean (and this accords with Pythagoras' teaching) but the term is ambiguous, if only because the Aristoxenean tendency prefers not to distinguish its two categories of opponent, labelling them all Pythagorean; in any case such a system was already known to the Chinese two millenia before Pythagoras, so it would seem incorrect to call them Pythagoreans. I propose, therefore, a neutral term which carries no baggage: "3-limit system."{9} This also has the advantage of being self-explanatory and easily remembered, now that its context has been set. ================================================================= 9. This terminology is to be found in Partch, *Genesis of a Music*; while I owe much to this work, and value Partch's music highly, the present article is not to be regarded as an extension of his polemic, which was motivated by his compositional project. ================================================================= [I.3] What then of the next prime number, 5, and a corresponding 5-limit system? Using the same principles as above, but now with powers of 2 and 5 forming the ratios, we will take C again as 1/1 , and rise by major thirds to E and G#--these are expressible in ratios as 5/4 and 25/16, with powers of 5 in the numerator. Descending by major thirds, Ab and Fb will be the ratios 8/5 and 32/25. You will observe that the so-called "enharmonic equivalents" of equal temperament are no longer equivalent, since the 5-limit E, 5/4, and Fb, 32/25, are patently not one and the same pitch. But of still greater importance for this discussion is the comparison between this E, and the 3-limit E we had mentioned above: these Es are also distinct, since the 3-limit interval between E and C is 81/64, while the 5-limit interval is 5/4. Which E is higher? If we express both in terms of a common denominator, 64, the 5/4 becomes 80/64, which is clearly a narrower interval than its 3-limit counterpart. In order to find the interval between the two Es, we must divide 81/64 by 80/64; the 64 cancels out, leaving us with the ratio 81/80. The interval expressed by this ratio is the syntonic comma, and it is this which shall be the focus of all my arguments. [I.4] I would invite readers at this point to examine the right-hand section of Fig. 1, which displays a fragment of the 5-limit system.{10} All ratios are expressed in relation to C, and lie within the span of one octave. The letter-name lattice on the left represents the same set of intervals as the ratio lattice on the right. Perfect fifths (3/2) lie along the verticals; just thirds (5/4) lie along the horizontals. "+" raises a note by one syntonic comma (81/80); "-" lowers a note by one syntonic comma. "0" cancels comma inflections. All ratios which do not lie on the horizontal and vertical axes passing through 1/1 (C) combine the primes 3 and 5; for example, to arrive at B, we add a 5-limit major third to a perfect fifth, i.e. 3/2 x 5/4 = 15/8 (remember for other intervals the power of 2 requires adjusting to keep the interval within the same octave). Note that while the 3-limit system is a proper subset of the 5-limit system, I shall use, for convenience, the name "5-limit interval" for those intervals that are not also members of the 3-limit. Both systems are, for theoretical purposes, infinite (which does not prevent one from being a proper subset of the other). The shaded area is the Ptolemy Sequence (as discussed by Zarlino) on C; this area can equally well be regarded as the C major scale, or the Ionian and Hypoionian modes--the identical intervallic structure does not imply identity with respect to any other properties. All the church modes, including Glarean's, together with the major and minor modes are located within the group of letters that bear no syntonic comma or chroma (i.e. flat/sharp) inflections--the final of each mode then takes the place of C as 1/1. ================================================================= 10. Fig. 1 is close in form to the 2 and 3-dimensional lattices employed by the U.S. composer-theorist Ben Johnston as a pre-compositional tool; I have freely generalized Johnston's notations for my own theoretical purposes. Cf. Johnston, "Rational Structure in Music," *American Society of University Composers Proceedings* 11/12 (1976-77). The first movement of Johnston's String Quartet No. 2 combines serialism with the 5-limit system; the music is written in such a way that it will ascend quickly by syntonic commas up to the central point, after which it descends in the same manner, back to the original pitch. ================================================================= [I.5] Just as the Pythagorean comma (3^12/2^19 = 531441/524288) arises through the incommensurabilty of the "2-limit" (i.e. octaves) and the 3-limit, so the syntonic comma arises through the incommensurability of the 3-limit and the 5-limit. To translate these into cents, the Pythagorean comma is roughly 23.5, while the syntonic comma is roughly 21.5 (cents equivalents will always be approximate, except for equal temperament, from which the measure is derived--a cent is the irrational proportion 2^[1/1200] to 1). While the syntonic comma is therefore too small to be of melodic significance in a musical tradition such as Renaissance vocal polyphony, it is by no means too small to lack harmonic significance. The syntonic comma arises through the conflict between the accurate tuning of 3/2 fifths and 5/4 major thirds, and similarly between the accurate tuning of any 3-limit and 5-limit intervals. Referring to Fig. 1 again, observe the interval between C and C#, represented by 25/24, the 5-limit chroma (i.e. the inflection notated by means of a sharp or flat). This is, of course, a melodically significant difference. In general, Renaissance polyphony involves ficta sharps only at cadences, while flats may be required at any point, to avoid undesirable harmonic or melodic tritones; melodically significant chromas are thus restricted to the requirements of ficta practices. What of syntonic commas? The case I wish to make here is that they could be used freely, either as upwards or downwards inflections, since being melodically insignificant, they were not bound by melodic conventions. Nevertheless, being harmonically significant, they were required in maintaining, as far as possible, the accurate intonation of 3-limit and 5-limit intervals. [I.6] Since I am not arguing for a rigid, purely theoretical system, but rather a pragmatic, flexible and ad hoc resolution--in practice-- of the conflicts between 3-limit and 5-limit intervals (this is what I am presenting as JI), I shall deal now with the possibilities offered by specific examples. The passage I wish to examine is the sequence from Josquin's *Ave Maria* which has been discussed elsewhere, for different theoretical purposes, by Margaret Bent and Roger Wibberley.{11} I shall use this passage firstly to demonstrate how JI can operate in detail, and secondly to demonstrate that JI is, strictly speaking, neutral between the Bent and Wibberley versions, which follow very different courses from each other in the application of ficta chromas.{12} ================================================================= 11. Bent, "Diatonic Ficta," *Early Music History* 4 (1984); Wibberley, "Josquin's *Ave Maria*. 12. As it happens, I am persuaded by Bent's argument in "Diatonic Ficta," and am therefore constrained to reject Wibberley's version and the accompanying arguments; I have further reservations concerning Wibberley's version, above all because of the melodic tritone in the cantus between Bb and E, bars 48-50. Nevertheless, since this matter is entirely independent of my advocacy of JI, the readings that I present remain scrupulously neutral. ================================================================= [I.7] Observe now Example 1, which is Wibberley's version of the Josquin, with my syntonic comma inflections added. Notice that in this version, I have used only one extra pitch-class beyond Wibberley's set, namely the D- (Wibberley's Bbs have consistently become Bb-s); all Wibberley's perfect fifths are preserved, while the 5-limit intervals are now also rendered accurately (I realize this was no concern of Wibberley's, but I shall leave this matter until Section II). One of the most important strategies for accurate, but practicable 5-limit intonation is the inflection, mid-way, of a longer note--this occurs in the tenor part, bar 45, and again in bars 46/47; such a move is unavailable where the melodically significant chromas are concerned, but it is generally indispensible for JI realizations, and unavoidable in the present sequence of 5-6 progressions. [I.8] Notice also that the pitch at the close of the passage is identical to the pitch at the opening, whereas one of the chief objections to JI is the supposedly unavoidable accumulation of syntonic comma shifts downwards. The notion that the comma shift can only draw the pitch downwards is to treat commas, by faulty reasoning, as if they must behave like chromas. Not all simultaneously sounding intervals are given equal weight: for example, the eighth-note neighbor-note D in the cantus, bar 50, need not flatten a syntonic comma to form a 4/3 with the A already sounding in the altus--it passes too rapidly for this to be a consideration; and if the D is not constrained to tune from the A, it will then form a correct 6/5 minor third (plus an octave) with the B neighbor note in the bassus part (and leaving rapidity aside, this would surely be a more important consideration). Likewise the passing-note D in the cantus, bar 52, need not be deflected by the bassus A already sounding, again because of its rapidity. [I.9] With these considerations in mind, we can examine the very different prognostication of Nicolas Meeus--namely, that this passage will inevitably shift downwards by five syntonic commas in any JI reading.{13} This would indeed be the result if it were not possible to weigh up the different prima facie demands of 3-limit and 5-limit intervals, and of melodic and harmonic considerations, in a word, to employ the rigid, dogmatic model of JI which I said was merely a straw man. If my license to leave rapid neighbor notes and passing notes uninflected were restored, the pitch of the final in bar 53 would shift three commas downwards; and if my license to move freely upwards as well as downwards by comma inflections was also restored, the pitch of the final would remain unaltered in bar 53. What my JI version requires us to abandon is the notion of a given notated pitch remaining fixed in performance; we have seen, in the worked example, that a notated D should fluctuate in performance, between D and D- (respectively 9/8 and 10/9 from C). ================================================================= 13. Meeus, mto-talk posting, 19 Aug 1996: "... but something odd happens. Consider for instance how the first C in the tenor, m. 44, connects to the second, in the altus, m. 46, by a string of consonances ...The second C ... is a syntonic comma lower than the first... But the phenomenon repeats: I leave it up to you to check that, on the same premises, the C in the altus in m. 52 is five commas, 110 cents, more than a semitone, lower than the first. ... Just intonation is a utopia." ================================================================= [I.10] We may now turn to the version of the same passage that Margaret Bent has produced. Since Bent is quite prepared to countenance an irreversible shifting of pitch (although she doesn't happen to diagnose it in this passage), I shall produce two JI readings of her version: the first (Example 2) leaves the pitch of the final unchanged at the end, but involves the usual local fluctuations required by JI; the second (Example 3) allows the pitch level to sink, irreversibly, by one syntonic comma. The difference between the first and second readings pivots entirely upon what happens in bar 48: the first employs F+s in the middle parts to form 3/2s with the Bbs in the bassus and cantus; the second features the reverse operation, employing Bb-s to comply with the Fs. These three JI readings (Exx. 1-3) should thus serve to demonstrate the neutrality of JI, not only with regard to the Wibberley and Bent versions, but also on the issue of the irreversible sinking of pitch, versus a static overall pitch standard (within which local pitch fluctuations take place); the case for JI can be made independently of these disputes. Again, it should now be evident that the JI system I am describing does not entail that a single correct reading exists for any given passage--on the contrary, it is inevitably pluralistic; indeed, it need not entail that any preference be given to one plausible reading over another. [I.11] In the foregoing paragraphs, I have presented a *theory* of JI in practice; I am certainly not suggesting that singers would have thought of their intonational practices in this manner. It would even be misleading to imagine that singers concentrated on syntonic comma adjustments under that description; their concern was merely to maintain good intonation by listening carefully to themselves and to each other, and it is my contention here that this included not only octaves, fifths and fourths, but also 5-limit thirds (5/4, 6/5) and sixths (8/5, 5/3). While I mentioned that JI is not dependent upon any of Bent's arguments on ficta practices, it runs a parallel course; just as Bent argued against Lowinsky's "secret chromatic art" with her counter-thesis of diatonic ficta, so I wish to avoid any appearance of endorsing a "secret microtonal art." Bent's case contra Lowinsky was based upon pointing out the anachronistic thinking which brought Renaissance vocal polyphony within the conceptual framework of modern notation; an Obrecht passage which moves sequentially from F down to Fb certainly appears exotic in a modern transcription. But Bent argued that this "chromaticism" was only a product of the transcription, since singers (in Obrecht's time) would have been following the purely diatonic contrapuntal implications of the piece (Cb to C-natural is a chromatic semitone, but Cb to Fb is not a chromatic interval at all).{14} Similarly, the addition of "+" and "-" signs to represent syntonic comma "inflections" is purely a matter of achieving clarity within the same framework of modern notation; singers would not have imagined themselves to be applying microtonal adjustments--they would merely have been aiming for good intonation of all the usual intervals. =========================================== 14. Bent, "Diatonic Ficta," especially pp. 34-35. =========================================== [I.12] Before moving on to the historical discussion of Section II, I must add a further qualification, lest I be misunderstood: this concerns the degree of precision to be expected of singers. The various possibilities for performance that I have sketched out are merely an indication of what singers might have aimed for; I am not claiming that they were able to do this with extraordinary accuracy, but simply with enough accuracy in general to aim for a 5/4 major third, rather than for a vague "major-third region" which could as easily have resulted in a Pythagorean 81/64. The fact that equal temperament, for all its benefits, has blunted our sensitivity to 5-limit intervals provides us with no reason to imagine that singers in the 15th and 16th centuries were in the same position. Equal temperament, being based on a slight tempering of the 3-limit which shrinks twelve fifths into the compass of seven octaves, will of course reflect the 3-limit quite accurately (e.g. the 3/2 with only about 2 cents discrepancy). The 5-limit is ill-served however, with the 5/4 represented by an interval almost 14 cents wider, and the 6/5 by an interval nearly 16 cents narrower. Our own acceptance of vagueness in the 5-limit is a consequence of equal temperaments ubiquity today; this was entirely reversed, as we shall see below, in the longest-lived system of keyboard tuning, which was in use during the period under discussion: there the 3-limit was compromised for the sake of pure 5/4s. Tempo and the ambient acoustic are also of importance in considering precision: a slower procession of notes and a more resonant environment would afford greater opportunities to realize subtleties of intonation (and conversely, render any intonational inaccuracy all the more obvious). Exx. 1-3 should be treated no more (and no less) literally than these qualifications allow. II [II.1] My main concern has been to provide a theoretical case for a practicable JI system; nevertheless, without any corroboration from available historical evidence, such a theory could proceed no further than the realm of--perhaps unrealized--possibilities. I shall now sketch out various reasons which would constrain us to believe that such a JI system was not merely possible, but overwhelmingly probable; for reasons of space, this part of the discussion will be all too brief (I hope to expand upon it on another occasion). [II.2] The medieval Church inherited its Pythagoreanism from Boethius, and entrenched the number 3 into its account of musical intervals by evoking Trinitarian symbolism in addition to Pythagoras' own numerological obsessions. Consonance was judged the sole preserve of the 2/1, 3/2 and 4/3 (and their counterparts with an added octave-gap); the 81/64 Pythagorean third was understandably excluded as a dissonance.{15} 1, 2, 3 and 4--the elements earth, water, air and fire were four--when added together produced the mystic Pythagorean Dekad, and the number of the Commandments, and so on. Theorists of music (within the quadrivium) were allotted a privileged position over those who merely practiced the art; the theorist was the guardian of a prescriptive, speculative system, and not the empirical investigator of musicians' practices. There was still the occasional flicker of other possibilities: for instance, Hucbald (840-930) described a 5-limit tetrachord--1/1, 10/9, 5/4, 4/3;{16} but the possibility of a scientific enterprise in the spirit of Ptolemy was ignored for the sake of upholding Pythagorean dogma.{17} ================================================================= 15. Cassiodorus, *Institutiones*, translation in *Source Readings in Music History*, ed. Oliver Strunk (London, 1952), p. 89. 16. Cited in Partch, *Genesis of a Music*, p. 380. 17. Cassiodorus nevertheless pays lip-service to Ptolemy's "excellent treatise" in passing; his medieval followers evidently failed to act upon this recommendation (in Strunk, *Source Readings*, p. 92). A characteristic example of Trinitarian symbolism conjoined with Pythagorean music theory can be found in Jean de Muris, *Ars novae musicae*, in Strunk, *Source Readings*, pp. 173-4. The original text, Muris, *Notitia artis musicae* is to be found in *Corpus scriptorum de Musica*, vol. 17, ed. U. Michels (1972), p. 67. ================================================================= [II.3] A distinct problem emerged when chains of thirds were incorporated into two-part organum, and later in the parallel sixths of English faburden. Walter Odington examined these "concords of discord" (i.e. theoretical discord perceived as concord) and found, by means of the monochord, that singers replaced 81/64 and 32/27 with 5/4 and 6/5 respectively; elsewhere, he states that the proportions of the major triad should be 64:81:96:128, thus acknowledging the normativity of Pythagoreanism.{18} Franco of Cologne is less timid in admitting thirds: besides "perfect concords" (unison, octave) and "intermediate concord" (fifth, fourth), he provides a third category of "imperfect concord," consisting of major and minor thirds.{19} A papal decree issued in 1324 attempted to ban these intervals; it was generally insinuated that they were sensuous, effeminate and worldly. With the passing of another century, the English cultivation of the third--from the "Sumer" canon through to Dunstable and the "contenance angloise"--witnesses eloquently against such dogmatism. ================================================================= 18. Cited in Partch, *Genesis of a Music*, p. 372. The original text is to be found in *Corpus scriptorum de musica*, Vol. 14, ed. F. Hammond (1970). 19. Franco of Cologne, *Ars cantus mensurabilis*, in Strunk, *Source Readings*, p. 153. Franco nevertheless counts sixths among the discords. ================================================================= [II.4] By 1482, Bartolome' Ramos was able to sweep away centuries of doctrine with a casual preamble in his *Musica practica* (note the title): "The regular monochord has been subtly divided by Boethius with numbers and measure. But althought this division is useful and pleasant to theorists, to singers it is laborious and difficult to understand. And since we have promised to satisfy both, we shall give a most easy division of the regular monochord."{20} Ramos then embarks upon a very lucid description of the 5-limit system, based upon his "easy division" of the monochord, detailing the 5/4 and 6/5 thirds, the 8/5 and 5/3 sixths, and the 16/15 diatonic semitone.{21} This work won Ramos much vehement criticism, which continued into the following generation, when his pupil Giovanni Spataro was still being required to defend these monochord divisions. Lodovico Fogliano's *Musica Theoretica* (1529) reinforced and extended Ramos's teaching and by the mid-century, when Zarlino produced his *Istitutioni*, the new ideas were well-established. ================================================================= 20. Bartolome' Ramos, *Musica practica*, in Strunk, *Source Readings*, p. 201. 21. Ramos, in Strunk, *Source Readings*, pp. 203, 4. Curiously, the 5-limit chromatic semitone Ramos offers is the 135/128, which in my Fig. 1 is the interval between C and C#+. This interval is rather implausible, and I can only imagine that Ramos failed to notice the 25/24 (the interval between C and C#); it would seem that Ramos may have been Wibberley's source, since he also presents the more cumbersome ratio as the chromatic semitone (mto-talk posting, 21 Aug 1996). ================================================================= [II.5] Leaving aside Zarlino's contribution for a moment, it is worth considering developments in keyboard tuning, which provide irrefragable evidence of the 5-limit intervals' importance in music as practiced. Arnold Schlick's *Spiegel...der Organisten* (1511) described the practice of mean-tone tuning which was clearly already in existence; Schlick also provided adequate formulas for obtaining the tuning. Pietro Aron produced a more throrough analysis of the system a decade later, in the *Thoscanella de la Musica*, which sufficed for all practical purposes. Francisco de Salinas finally provided a systematic, mathematical account of the mean-tone system in his *De musica*. [II.6] In order to ensure that the implications of this development in tuning are clear, I shall look briefly at its main organizing principle. The mean-tone system is based upon the pure 5/4 third; recalling our earlier discussion of the syntonic comma--as the difference between the 3-limit E+, reached by a chain of four fifths, and the 5-limit E--the mean-tone system narrows the chain of fifths so that they equal the span of two octaves and a 5/4 third. Just as the 3-limit is tempered to fit the 2-limit in equal temperament (by removing the twelfth root of the Pythagorean comma from each interval in a chain of twelve fifths), so the 3-limit is tempered to fit the 5-limit in mean tone temperament (by removing the fourth root of the Pythagorean comma from each interval in a chain of four fifths)-- hence the full name "quarter-comma mean-tone" (i.e. [81/80]^[1/4]). The fifths, now the narrower 5^(1/4)/1, have thus been sacrificed to maintain the purity of the 5/4 thirds. Remembering that keyboards at this time were principally used to play vocal polyphony (albeit decorated) this should be reason enough for us to concede that the intonation of the third as 5/4 must have been well-established among musicians by the early 16th century--indeed they considered the matter so important that they chose a tuning system which gave this third priority over the fifth. This should also cause us to reflect upon the arbitrariness of our own tuning preference for the fifth to the detriment of the third--such preferences are not immutable and universal, but are based upon historical contingencies, and the power of habit.{22} ================================================================= 22. Lest anyone imagine that twelve-note equal temperament would have been adopted instead if only it had been conceived of, it should be pointed out that it is considerably simpler in its mathematics (although the calculations involve more labor). Henricus Grammateus had already drawn up a fairly close approximation in 1518, and Zarlino corrected Vincenzo Galilei's plan for a twelve-stringed equal-tempered lute (Galilei had invoked Aristoxenus as his inspiration in this project). Even though the mathematician and music theorist Mersenne produced a correct and systematic description in 1635, equal temperament was not adopted until 150 years later in Germany and Austria, while Britain and France delayed for over two centuries. In the 17th century, the main alternatives to 1/4-comma meantone were other tempered meantone systems, such as the 1/6-comma, and the 2/7-comma. ================================================================= [II.7] Zarlino is considered the preeminent theorist of JI; *Le Istitutioni harmoniche* (1558) introduces the prime number 5 into the proportions he derives from the senario (1-2-3-4-5-6, in clear opposition to medieval theory): superparticular ratios (i.e. [n+1]/n) from 2/1 to 6/5 were the simplest consonances; "composites" with numerator and denominator up to 6 were next simplest, e.g. 5/3 (composite of superparticulars 4/3 x 5/4); composites with numerator or denominator above 6 were next in rank of consonance.{23} Where medieval theorists had learned that 3/2 and 4/3 are the harmonic and arithmetic means between 1/1 and 2/1, Zarlino went on to demonstrate that the 5/4 was the harmonic mean (on a monochord) between 1/1 and 3/2, and the 6/5 the arithmetic (the harmonic mean between x and y is 2xy/(x+y); the arithmetic mean is xy/2). By extension, he assigned "major" tonality to harmonic proportion--a string and its parts (1/1, 1/2, 1/3, 1/4, 1/5, 1/6), while "minor" tonality was derived from arithmetical proportion--equal parts of a string added together (1, 2, 3, 4, 5, 6). Like Fogliano before him, Zarlino championed Ptolemy, and advocated the "Ptolemaic sequence" as the "natural" scale (this consists of the ratios within the shaded area of Fig. 1). Nevertheless, there was a little of the Pythagorean impulse in Zarlino, since he indulged in occasional mystificatory strategies in order to justify his theories: for example, the fact that a cube had only six sides was offered as an argument for stopping at 6 (Mersenne was later to question Zarlino on the issue of this supposedly natural terminus--he suggested that 7 be included in the proportions of musical intervals, a proposal which later interested both Tartini and Euler). ================================================================= 23. The complete text of the *Istitutioni* (in the original Italian) can be obtained from http://www.let.ruu.nl/C+L/wiering/ The introduction, by Claude Palisca, to *On the Modes*, trans. V. Cohen, (New Haven, 1983), provides a useful overview of Zarlino's achievement as a theorist. ================================================================= [II.8] Section I argued that just intonation is not merely the useless plaything of theoreticians, but on the contrary is eminently usable when treated as a flexible and pragmatic body of strategies. Section II has supplemented this consideration of JI's possibility with a body of evidence that demonstrates its actuality in Renaissance Europe. While both sections provide no more than a brief sketch of the terrain, I trust they will nevertheless serve to persuade, at least partially, those readers who had formed no fixed opinion on the matter, and to place serious doubts in the minds of those who have hitherto been implacably opposed to JI. I have indicated why the testimony of medieval theorists should not be taken at face-value; the depth of the vested interests at stake became evident as the violent controversy over Ramos' "easy divisions" of the monochord continued for decades--it is easy to see Ramos, without too much exaggeration, as a predecessor of Galileo Galilei, who published his work on heliocentric cosmology over a century later. [II.9] Perhaps the most satisfying, but at the same time most discomfiting aspect of historical study is the discovery that we have consistently misinterpreted the evidence before us, because we had failed, through a lack of imagination, to enter more fully into another's conceptual framework. In our case, the convenience of transcriptions in modern notation is also a potential handicap, since it renders the task of shedding our assumptions more difficult-- assumptions concerning what the score determines, and what differences would have arisen in a musical tradition which lacked scores themselves.{24} The convenience of a tuning system adopted for keyboard instruments in the late 18th century, namely equal temperament is a further handicap, which imposes its own conceptual tyranny regarding pitch in general, and tuning systems of a previous age, above all JI, whose every virtue is regarded as a shortcoming within the framework of equal temperament, and vice versa.{25} It is remarkable how blithely we tend to speak of the "circle of fifths," as if the fact that this is merely a product of equal temperament had been cast to the nethermost regions of our memory.{26} We also tend to see equal temperament as the goal of a centuries-long teleological process whereas we ought to be why one particular tuning system, and not another, was used for a given repertoire. Need I say that my purpose in this article is not to condemn equal temperament as the intonational decadence that set in after the glorious purity of JI? Of course we should reject such views, but we should equally guard against any notion that the musicians of past centuries were benighted because they lacked equal temperament, or that they were unwittingly striving towards it all the time.{27} As I have already mentioned, equal temperament was the subject of various 16th century experiments, and its mathematics was completely understood by the early 17th century; composers were not striving towards it--on the contrary, they rejected it. ================================================================= 24. Cf. Bent, "Editing Early Music: the dilemma of translation," *Early Music*, August 1994. 25. The *New Grove* entry on Just Intonation, by Mark Lindley, is conceptually skewed in just this manner: from half-way through the first paragraph, to the end of its two-page spread, keyboard instruments are the sole subject matter (with a passing reference to the guitar, another fixed-pitch instrument). JI's most obvious domain --vocal music--is not touched upon; by contrast, JI is a rather obscure corner in the history of keyboard instruments, with no notable success. As I have argued above, the true keyboard-based progeny of JI was 1/4-comma meantone tuning, which was both very widely used, and enjoyed the longest lifespan of any keyboard tuning to date. It is regrettable that this article should provide the unwary student with a first (and perhaps last) taste of JI. 26. There are further "circles" after 19, 31, 43 and 53 fifths; Vincentino's archicembalo was variously described by its maker in terms of the 31-fifth "circle," and in terms of ratios derived from Ptolemy, while it can perhaps be understood most convincingly as an extension of the 1/4-comma meantone system. 27. Lowinsky, "Matthaeus Greiter's *Fortuna*: An Experiment in Chromaticism and in Musical Iconography," *Musical Quarterly* 42 (1956), 43 (1957). ================================================================= [II.10] I shall close with some historical considerations that might prove fruitful for future research. Most of the positive historical evidence I have adduced dates only from the late 15th century onwards; given that we need not take the Pythagoreanism of medieval theorists as a faithful description of musical practice (since it was never intended to engage in such inquiry), how far backwards should we project the present arguments for JI? For the tuning of faburden sixths, anything other than the 5-limit intervals is, I believe, highly implausible. But neither would I like to assume that the almost unanimous Pythagoreanism of medieval theorists simply ceased to have any impact on composers. These are qustions for further investigation, which is likely to include not only the examining of musical and other documentary evidence, but also the study through performance of later medieval repertoires in order to discern what intonation would seem most appropriate. By the 16th century, the complete absorption of the 5-limit intervals seems certain, while the 10th century evidence on the intonation of organum thirds is hazy. Assuming that Pythagorean, i.e. purely 3-limit tuning was in fact practiced at some stage (and it is always worth stating our assumptions, even when we don't intend to question them), we may slowly be able to deduce where and when it expanded into the 5-limit system, and where it might have enjoyed a resurgence. ============================================================ 3. Reviews AUTHOR: Schaffer, John Wm. TITLE: Review of Peter Castine's *Set Theory Objects: Abstractions for Computer-Aided Analysis and Composition of Serial and Atonal Music* KEYWORDS: atonality, computers, set theory, serialism, Castine John Wm. Schaffer University of Wisconsin-Madison School of Music 455 N. Park St. Madison, WI 53706 jwschaff@facstaff.wisc.edu ABSTRACT: *Set Theory Objects* explores the process of developing a computer program for assisting in the composition and analysis of post-tonal music. The author surveys the set-theoretical literature, and deals with various issues related to the design, development, and implementation of such a program. Included are tables detailing formal definitions for most set-theoretical functions. 1. Contents 2. Group I: Introduction & Overview (Chapters 1 and 3) 3. Group II: The Computer Program (Chapters 4-6, Appendix C) 4. Group III: Set Theory And Serialism (Chapter 2, Appendices A-B) 5. Conclusions ----------------- 1. Contents [1.1] Peter Castine's *Set Theory Objects: Abstractions for Computer-Aided Analysis and Composition of Serial and Atonal Music* (hereafter referred to as STO) actually represents several texts in one. From the author's straightforward discussion of set-theoretical principles to his fascinating look into the process of developing a powerful computer tool for assisting composers or theorists in the manipulation of these set-theoretical operations, the book offers both a broad and informative look into the complex world of cross-disciplinary study in significantly different domains, while at the same time suffering from the difficulties of trying to place two hats on the same figurative hook. [1.2] STO (essentially a reprint of Castine's Ph.D. Dissertation in communications science and musicology from the Technical University Berlin, 1994) is divided into six chapters with three additional appendices covering several rather discrete, yet interlaced, topics. The first and third chapters offer a rather brief, yet interesting, overview of the myriad issues--both historic and current--that the author dealt with in developing his computer project. The second chapter offers a selectively-detailed overview of set-theoretical concepts, enhanced by two appendices presenting a complete set-class table and a compilation of formal definitions and theorems. The last three chapters present a rather detailed, yet incomplete, journey through the actual process of conceptualizing, defining, refining, and implementing a Macintosh-based computer program. A final appendix offers a limited set of programming definitions, primarily useful for those "hard-core" programmers intent on understanding the most fundamental underlying design principles of the project. [1.3] While Castine is to be lauded for undertaking such a multifaceted project, any real attempts on his part to integrate these materials into a cohesive work appear to be absent. As happens all too frequently in many dissertations, Castine appears simply to have avoided the issue by offering his reader a collection of six relatively discrete chapters, which, upon closer examination, actually divided rather cleanly into three rather self-contained groups. This observation is not intended to diminish Castine's work, but finding value from STO demands that the reader treat the work as two very different texts, bound together for convenience under one cover. For most readers their interest in the work most likely will lie in one or the other of the two camps, relinquishing the composite text primarily to those of us similarly involved in melding computer technology with musical inquiry. [1.4] Having said all this, a more substantial look at each of the component chapters of the book clearly is in order. I have chosen here, however, not to present the discussion in chapter order, but rather to base my discourse around chapters sharing related content. ==================== 2. Group I: Introduction & Overview (Chapters 1 and 3) [2.1] Castine, in his rather brief (six pages) introductory chapter, begins interestingly enough by laying out quite clearly just what he believes STO is not about. He writes that, while "it had been [his] intention to include a 'critical evaluation' of set theoretic methods and their application to music analysis," as work on the project progressed he became acutely aware that inclusion of such a discussion "would be of only marginal interest, since the usefulness of set theory has been, frankly, discussed to death" (p. 16). Castine also wants his readers to be very aware of his own self-imposed limits regulating the design and function of his computer program when he states that "This [work does not represent] an attempt to create a program to analyze music without human intervention. Indeed, the fields of computer science (in general) and artificial intelligence (in particular) have made great strides [and computer programs potentially] could produce interesting or even valuable results. There are, however, several reasons why this path was not pursued. . . . [One of these reasons is] aesthetic and philosophical: I am not interested in trying to replace the human being in the musical process; I am interested in giving him tools to allow him to concentrate on his work while making the mechanics of that work easier" (p. 17). [2.2] The author is also concerned that we understand his intended scope and limitations regarding the set-theoretical tools chosen for integration into his work. Castine's project was inspired almost entirely by his desire to expand and enhance an earlier set of computer programs, Contemporary Music Analysis Package (CMAP), developed by Craig Harris and Alexander Brinkman (1987) for MS-DOS and Unix-based computers. While Castine states clearly that "there are significant differences between the work done by Brinkman and Harris and mine, and in certain aspects my objectives have been diametrically opposed to those originally presented in Harris's dissertation," he specifically sets out to document the development of a program that would "provide (at least) the functionality, flexibility, and speed as the original version of CMAP in a form that would be considerably easier to use, that would be available to a far larger number of musicians" (p. 19). [2.3] As part of his rationale for undertaking this project, Castine sets out in chapter three to survey other such projects. By constraining himself, however, to those programs "whose authors have made an effort to disseminate their work beyond an immediate circle of colleagues and students" (p. 76), Castine severely restricts his survey to less than a half-dozen programs, of which only CMAP is privileged with any significant discussion. Given Castine's belief, however, that "None of the programs available for Macintosh provide the flexibility nor comprehensiveness of CMAP" (p. 91), this shortcoming is at least rationalized. ========================== 3. Group II: The Computer Program (Chapters 4-6, Appendix C) [3.1] Castine's discussion of the development of his computer program encompasses the largest portion of the book, spanning three chapters totalling seventy pages. It is perhaps most likely the fourth chapter (Designing User-Oriented Software for Set Theory) from which the reader will gain the most benefit. Castine devotes over thirty pages to exploring and detailing solutions for what many would consider the most important aspect of any useful program: the user interface. The author is careful to consider such factors as the historical nature of the problem, the target audience, the purposeful definition of specific tasks, and the overall basic design of the user interface. Castine's discussions are both thorough and insightful. He clearly knows his topic and has put a great deal of energy into creating elegant and useful solutions for typical interface problems. The author's solution for this project is elegant and simple: he opts for the use of an "analytic scratchpad," a program window based on a spreadsheet-like metaphor that offers a very powerful and simple way to manage a constantly varying number of music objects (sets) linked by any myriad number of different operational relationships. Being able to place sets into cells anywhere on the scratchpad, and then to be able to apply various set-theoretical operation to either individual sets or combination of sets, clearly allows for a wide range of possible analytical paradigms and working methodologies. Castine offers a solution somewhat analogous to a piece of scratch paper with a built in analytical calculator that does not require the user to push many buttons to make it work--the solution is so straightforward and basic as to have eluded any number of programmers for quite some time. This chapter definitely should be read and digested by any programmer even thinking of undertaking such a project. [3.2] The remaining two chapters, while offering some valuable insights, do not really carry through the informational richness presented in chapter four. Chapter five does offer an interesting triptych of the process of actually implementing the program. In the absence of any program code, or charts diagramming some of the basic functionings and design considerations of the program, the materials presented at best can offer little more than a taste of how this undertaking unfolds at select points throughout the development process. [3.3] Chapter six details those things that Castine feels still need to be done to enhance the functionality of his program. In a way, this section presents us with a good lesson in futility, as Castine is so apt to show us--albeit inadvertently--as he begins to explore possible avenues of future program enhancement. Initially, Castine's discussions draw value from their close proximity to the current (i.e., completed) task. Continued musings, however, quickly lead the reader further from the core foundation of the program into a potentially endless abyss. Anyone of us might be able to sit and speculate with a fair degree of fluency as to how this or that of a particular program might be improved, but unbridled flirtations with "what if" scenarios, while they may certainly entertain, will probably offer nothing much new in the end. =================================== 4. Group III: Set Theory And Serialism (Chapter 2, Appendices A-B) [4.1] Chapter two, at around fifty pages, weighs in as the second major component of STO. As a detailed discussion of set-theoretical and serial principles, it is also at best only peripherally related to the other materials of the book, yet it offers the reader perhaps one of the better overviews of the topic--albeit a slightly myopic one--that I am aware of. The materials are not presented in any formal pedagogical manner--Castine opts instead for a decidedly historical perspective. Instead, he presents the basic materials in a concise and well organized descriptive manner. Although Castine's discussion is strongly based on the composite views of many theorists and composers--such as those of Milton Babbitt, George Perle, Edward Cone, David Lewin, and Peter Westergaard--particular attention is paid to ideas expressed in three significant works published at the time of his study: *The Structure of Atonal Music by Allen Forte* (1973), *Basic Atonal Theory* by John Rahn (1980), and *Composition with Pitch-Classes* by Robert Morris (1987), hereafter referred to as CPC. Perhaps most importantly, Castine's discussion is specifically limited (with a few exceptions) to those elements representing the core materials imbedded in CMAP, a fairly comprehensive collection, yet one with significant roots in the three works cited above. Included in this chapter are the following sections: -Pitches, Pitch Equivalence, and Pitch Classes; -Intervals, Interval Equivalence, and Interval Classes; -Ordered Sets, Unordered Sets, Rows, and Cycles; -Set Membership and Cardinality; -Twelve Tone Operations -Properties of Unordered Sets; -Set Equivalence and Set Class; -Set Class Relations; and -Segmentation, and Other Objections. [4.2] Throughout these discussions, the author employs terminologies and formalizations as promoted by Morris in CPC. Specifically, Castine feels that Morris's notational convention "has the advantages that it is as succinct and precise as any: it reflects most contemporary developments in set theory; it adheres closely to conventions used in mathematical set theory; and has found wide acceptance" (p. 23). [4.3] Early in the chapter Castine promotes a notion that "the reader will find roughly equal attention paid to both analytical and compositional aspects of set theory" (p. 23); however, I found no real evidence to support his claim. For the most part, the various discussions are presented clearly and without any sense of bias. The chapter contains several excellent charts, such as the one summarizing basic set operations; and the text is abundantly supported with historically informative footnotes. Castine does occasionally make a few problematic statements, such as regard to enharmonic spelling as being "in accord with standard conventions in atonal music" (p. 25) [italics are mine]. The chapter also contains a rather odd section on "dissonance" in post-tonal music--a topic with no direct correlation to traditional set theory as espoused here. Essentially, Castine offers no real insight on the topic except to conclude that "a general theory of dissonance (or musical tension) compatible with set theory is lacking" (p. 61). [4.4] Two related appendices are also included. Appendix A contains a complete table for all sets of cardinalities one through twelve. The information is presented in tabular form and contains all the basic information found in the original CMAP table for each entry: a Fortean set name, prime form, z-relatedness, m-relatedness, interval-class vector, invariance vector, and adjacent interval vector. Perhaps more valuable as a pedagogical aid is Appendix B, which contains a set of formal definitions and theorems for all the topics covered in chapter two. ====================== 5. Conclusions [5.1] It needs to be expressed again that, to evaluate the effectiveness and usefulness of this book, one needs to be able to see beyond the dual nature of the work. Clearly, the inclusion of two distinctly different topics poses a number of organizational problems that the author seems not to have been able to resolve effectively, leaving a bit of a schizophrenic taste in the mouth of the reader. Each part obviously is more successful by itself, yet the two halves never really join forces. On the other hand, when effectively isolated from one another, the two primary topics each can be of much greater value, particularly depending on individual readers' needs and interests. [5.2] Perhaps most interesting to the larger theoretical audience is Castine's lengthy discussion of set-theoretical issues. He offers the reader a sound, well-documented historical overview that is presented in a clear and concise manner--yet, perhaps at times, a bit too objectively, as topics such as Forte's K/Kh relationships are typically presented with no discussion of the relative merits of such notions. And, readers must be aware of the CMAP bias driving Castine's discussion, particularly noting the omission of many relevant theoretical concepts such as Morris's work with contour-space and pitch-space, or various other authors' work with similarity measures--all of these notions have been well established long before the writing of this book. Nonetheless, despite the problems and omissions of the text, chapter two perhaps could be utilized quite effectively as an introductory body of materials for a graduate-level course in set theory, particularly in light of the excellent reference materials presented in the appendices. But, then again, what do we do with the other five chapters? [5.3] More problematic is the status of computer program itself. All of the wonderful and creative ideas notwithstanding, a well-conceived interface married to a powerful set of analytical tools is of real value only to the user of that program. Unfortunately, much of Castine's work exists only on paper. What is coded and running lives up to the promise of the prose, but is still too incomplete to fulfill its real pledge of offering us a powerful and intuitive analytical tool. As with any large undertaking such as this, the path to success is all too often fraught with worldly pitfalls and obligations. Lest I be blamed simply for casting the first stone, let me first express my sincerest hope that the programming efforts already begun will eventually see the light of day. I have witnessed the beginnings and know that we will all benefit greatly when the end finally comes. REFERENCES Forte, Allen. *The Structure of Atonal Music*. New Haven: Yale University Press, 1973. Harris, Craig R. "Computer Programs for Set-Theoretic and Serial Analysis of Contemporary Music." Ph.D. Dissertation, Eastman School of Music, 1973. Harris, Craig R. and Alexander R. Brinkman. Computer program for Unix and MS-DOS. Vers. 1.0. Rochester, Bitwise Music, 1987. Morris, Robert. *Composition with Pitch-Classes*. New Haven: Yale University Press, 1987. Rahn, John. *Basic Atonal Theory*. New York: Schirmer Books, 1980. Schaffer, John. "Review of *CMAP: Contemporary Music Analysis Package*." *Integral* 2 (1988): 201-214. ================================= 4. Music Theory International AUTHOR: Broman, Per F. TITLE: Report from the Three Seminars on Contemporary Music with Connection to the ISCM World Music Days in Copenhagen, 1996. KEYWORDS: ISCM, Boulez, Pli selon Pli--Portrait de Mallarme, Erling Gulbrandsen, IRCAM, Georgina Born. Per F. Broman Lulea University, Sweden School of Music in Pitea Box 744 S-941 28 Pitea, Sweden per.broman@mh.luth.se ABSTRACT: University of Copenhagen, Department of Musicology hosted a three-day series of lectures in conjunction with the ISCM World Music Days in Copenhagen 1996. The unifying thread running through all seminars was institutionalization of the avant-garde and the concept of pluralism. Of particular interest from a theoretical perspective was the presentation of Norwegian young scholar Erling Gulbrandsen's recent doctoral dissertation on Boulez's *Pli selon Pli*. [1] The ISCM World Music Days is an annual festival for contemporary music and this year's event was held in Copenhagen, the 1996 Cultural Capital City of Europe, September 7-14. In conjunction with the festival, the University of Copenhagen's Department of Musicology hosted a three-day series of lectures featuring Georgina Born (London): "Pierre Boulez's IRCAM. Institution, History, and the Situation of Contemporary Music Today"; Erling Gulbrandsen (Oslo): "New Light on Pierre Boulez and Postwar Modernism"; Reinhard Oehlschlagel (Cologne): "Institutions of New Music: Development, Typology, Problems"; shorter papers were read by a panel including Per O. Broman (Uppsala), Erik Wallrup (Stockholm) Jens Hesselager (Copenhagen), Steen K. Nielsen (Aarhus), and Per F. Broman (Stockholm) and were followed by a discussion. This final session was chaired by Soren Moller Sorensen (Copenhagen). [2] Georgina Born's presentation consisted of a brief review of her recent book *Rationalizing Culture: IRCAM, Boulez, and the Institutionalization of the Musical Avantgarde* (Berkeley: University of California Press, 1995), followed by a new, more elaborate discussion of the cultural policy for supporting composers--a topic hinted at in the final chapter of her book. She argued that big institutions might not be the best way to support composers, that instead scholarships for longer periods of time, maybe for ten years, should be granted. Reinhard Oehlschlagel provided a much more positive description of the present situation in which the contemporary musical institutions (sometimes, according to his definition, consisting of only two persons) contribute to a pluralistic musical discourse. [3] Of particular interest from theoretical perspectives was Erling Gulbrandsen's recent doctoral dissertation on Boulez's *Pli selon Pli*. Based on archive studies, done at the Paul Sacher Stiftung (Basel), of the sketches and of a work that Boulez had rejected, the author traces the work's pitch structures. Although Gulbrandsen spent much time performing detailed archive studies that revealed much of the work's organization, he selected to emphasize the "important role of free choice and unpredictability in the process of composition, strongly indicating the deeper kinship not only with the poetics of Mallarme, but with the romantic-aesthetic categories of judgment, taste, musical articulation, and play." [4] The panel of final day's session "Pluralism--the Cultural Condition," presented critical papers on the institutions of ISCM (Jens Hesselager) and Darmstadt (Per F. Broman). There were also presentations focusing on the alternative aesthetics challenging the modernist traditions: Per O. Broman's reading of electro-acoustic music as a musical subculture with strong affiliation to popular "industry-music"; and Erik Wallrup's and Steen Nielsen's presentations of works and aesthetics by non-mainstream composers such as Karin Rehnqvist, Michael Nyman, and Steve Martland. The ensuing discussion illustrated the difficulties surrounding the concept of pluralism. The participants could not even agree on any consensus in regard to the use of the term, and, indeed, the debate illustrated Soren Moller Sorensen's introductory words: "Pluralism is more than just a truce between conflicting positions and laissez-faire attitudes in political, ethical and aesthetic affairs. To learn to live with pluralism is to learn to live in a world that can no longer be meaningfully organized around a central hub of 'natural' authority." ========================== 5. Announcements Mikropolyphonie is a refereed online journal published on the World Wide Web. It aims to encourage scholarly analysis and discussion in any genre of contemporary music making and research. |----------------------------------------| | | | Check out our demonstration site at: | | | | http://farben.latrobe.edu.au/mikropol | | | |----------------------------------------| Call for submissions ==================== This is a call for submissions for the first online issue of Mikropolyphonie. Its feature section will be on "Musical Futures" in which we invite you to speculate on music beyond 2000. Articles can adopt this theme or any general subject matter associated with contemporary music. Deadline 31st July for expressions of interest. Submissions should be as follows: Text (max 2000 words): html or plain ASCII text. Images: GIF or JPEG format Sound: AIFF format soundfiles, 8-bit, 22kHz sampling rate, mono. The above may be sent to: J.Giovinazzo@latrobe.edu.au as Macintosh-formatted email attachments or on Macintosh-formatted HD floppy disk to: The Editor, Mikropolyphonie Music Department La Trobe University Bundoora, Vic 3083 Australia __________________________________________________ While authors should adopt the Harvard style, we are keen to explore the interactive frontiers possible on the "net". To discuss proposals, articles, or any other editorial queries, please contact: David Hirst (editor) at D.Hirst@latrobe.edu.au |==========================================================| | Mikropolyphonie is a project of the National Networked | | Facility for Research in Australian Music. This facility | | has been made possible through financial assistance from | | the Commonwealth Department of Employment, Education and | | Training. | |==========================================================| ____ __ | / \ | | __ \__/OSEPH \__|IOVINAZZO Mikropolyphonie J.Giovinazzo@latrobe.edu.au ------------------------------------ Ethnomusicology Online http://research.umbc.edu/eol/ Ethnomusicology Online (EOL) seeks scholarly and general submissions in ethnomusicology and related disciplines that take advantage of the multimedia capabilities of the World Wide Web. Articles for the online scholarly journal will be peer-reviewed. General articles on any ethnomusicology subject will not be peer-reviewed. We plan to publish EOL at least yearly on CD-ROM. Reviews, reports, dissertation abstracts, and other contributions will be edited in consultation with authors. Submissions combine text, video, graphics, and audio, and all issues are available free of charge at the web site. Editor: Karl Signell E-mail: signell@umbc.edu ----------------------------------- WORD AND MUSIC STUDIES: ASSESSING AN INTERART DISCIPLINE An International Conference May 29 - June 1, 1997 Graz, Austria Call for Papers It is the aim of this interdisciplinary conference to survey the field of Word and Music Studies, to define its subject, methods and objectives and to describe the field's state of the art. Scholars from various areas of activity in Word and Music Studies are invited to present their views on the shape of the whole discipline from the perspective of their own work, with a strong emphasis on general reflection. Sections of the conference will be devoted to questions of the scope, the critical methodology and the institutional dimension of the field. Ideally, the sessions will combine stumulating position statements with focused discussion. Following an initiative taken at the 1995 Lund conference on "Interart Studies: New Perspectives", it is envisioned to found, at the conference here announced, an International Association of Word and music Studies. Results of the conference are expected to form the basis for the furture work of the Association. Offers of conference papers should be sent to Walter Berhnart at the address below by October 1, 1996. They should include a title, a brief statement on the perspective the presentation will take on the topic of the conference, and an indication of the expected duration of the presention, which should not exceed 30 minutes. The organizers of the conference will be happy to welcome participants at Graz, which is a typical univeristy city of a quarter million inhabitants, near the Alps and near lovely wine-growing areas, with a large medieval town centre and a thriving cultural life. A diversified social program will complement the conference events. Graz University A-8010 Graz, Austria Department of English Heinrichstrasse 36 Section "Literature and the Other Arts" tel.++43-(0)316-380/2478 Chair: Professor Dr Walter Bernhart 2475 2497 fax:++43-(0)326-380-9765 e-mail: walter.bernhart@kfunigraz.ac.at ------------------------------------------------------- EVENT: GAMUT 1997 Meeting HOST: University of Georgia, Athens, GA DATE: February 21-22, 1997 DESCRIPTION: The Georgia Association of Music Theorists will hold it's annual meeting February 21-22, 1997 at the University of Georgia in Athens. Gary Wittlich (Indiana University) will be the keynote speaker. The Program Committee invites papers dealing with any aspect of music theory to be submitted for the meeting, along with proposals for a Friday evening panel session dealing with any aspect of theory pedagogy. Papers may be 30-45 minutes in length, and the panel session should be an hour and a half. Manuscripts should be double-spaced with one-inch margins. Send four copies, including a short abstract to: Professor Leondard Ball, Program Chair University of Georgia School of Music 250 River Road Athens, GA 30602 REGISTRATION DEADLINE: Up to meeting date, 2/21/97 PAPER/PROPOSAL DEADLINE: December 16, 1996 COST AND PAYMENT OPTIONS: $25 for regular members, $30 for dual members (same address, one copy of mailings), $15 for students and retired faculty. Cost includes membership in GAMUT through spring 1998 and a subscription to the GAMUT Journal. TRAVEL AND HOTEL INFORMATION: To Be Announced CONTACT: Kristin Wendland GAMUT Secretary Music Department Morris Brown College 643 Martin Luther King Dr. Atlanta, GA 30314 e-mail: ir002842@interramp.com Phone:(404) 220-0045 Fax: (404) 220-0261 ============================= 6. Employment JOB POSTING COMPOSITION The University of Pennsylvania is pleased to announce the Robert Weiss Chair in Music Composition. The position is at the rank of full professor or associate professor with tenure. The ideal candidate will be an internationally recognized composer with a strong commitment to teaching at both the undergraduate and graduate levels and excellent leadership qualities. (This is a continuation of the search announced in spring, 1996.) Effective date of employment is July 1, 1997. Applications must be postmarked by: October 1, 1996. Please send resumes to: Chair, Search committee, Department of Music, 201 S. 34th Street, Philadelphia, PA 19104-6313; (215) 573-2106; e-mail: music@mail.sas.upenn.edu (No scores or recordings at this time.) EOE/AA; women and minorities are strongly encouraged to apply. Cristle Collins Judd cjudd@sas.upenn.edu ============================ AARHUS UNIVERSITY: CHAIR IN MUSIC The University of Aarhus, Denmark, invites applications for a Chair in Music tenable from February 1, 1997, or as soon as possible thereafter. The aim of the Chair is to develop and strengthen the research profile of the Department of Music. Considerable original academic research of international standing within central areas of the history, theory and culture of Western music is required, including academic work with a broad relevance within and across these areas. Experience with management of research projects, and other management functions will also be an advantage. It should be noted in this connection that present research in the Department covers folk music and popular music as well as classical music. Experience with management of research projects will also be an advantage. Candidates must have extensive teaching experience at university level in the different literary disciplines taught at the Department. Active involvement in all aspects of the work of the Department will be required. Candidates who do not speak Danish will therefore be expected to learn enough Danish to be able to take part in the full work of the Department within one year. The letter of application (marked 1996-211/1-4) should be addressed to The Rector, and sent to the University of Aarhus, Journalkontoret, Ndr. Ringgade 1, DK-8000 Aarhus C, Denmark. Closing date: 23 September, 12 noon (Danish time!). Three copies of the following material (marked as above) should be sent directly to the Department of Music (address below): a) curriculum vitae, including details of teaching and administrative experience and research; b) list of publications and other relevant academic production complete with all biographical information. Please indicate clearly on the list which items are being submitted with the applications; c) the written material which the applicant is submitting (theses, publications, etc.) as indicated on list of publications; d) copies of academic diplomas and documentation of teaching experience. The selecton committee reserves the right to request further material for consideration. Material sent on computer discs will not be considered. Annual salary approximately DKK 382,000 plus pension. A special supplement of up to DKK 37,000 per annum is negotiable, depending on experience and qualifications. Before applying, potential candidates are invited to seek further information about the Department and the post from Karen Juul-Olsen, Head of Department, the Department of Music, University of Aarhus, Wilhelm Meyers All=E9, Building 220, DK-8000 Aarhus C, Denmark; tel. +45 8942 3137. Please mark the application 1996-211/1-4 Submitted to smt-list by: Steen Kaargaard Nielsen musskn@hum.aau.dk ---------------------- FIELD: Music Theory POSITION: Assistant Professor of Music. INSTITUTION: University of Wisonsin-Madison QUALIFICATIONS: Completed Ph.D. at the time of appointment. DESCRIPTION: The University of Wisconsin-Madison invites applications for a tenure-track position (at the rank of Assistant Professor) in music theory to begin September 1, 1997. The search committee is seeking a music theorist who demonstrates a clear promise of making a major contribution to the discipline; preference will be given to those with a record of publication and conference participation. We welcome applications from candidates in all areas of specialization, including those whose work is interdisciplinary or critically informed. Cover letters should discuss the candidate's current research and its significance to the discipline. DUTIES: Instructional responsibilities include active participation in the development of a new, innovative undergraduate curriculum in music theory, supervision of TAs, active involvement in the graduate program, thesis and dissertation supervision. A normal course load is two per semester. SEND: Please send a letter of application, CV, at least 3 letters of recommendation to: Prof. Brian Hyer, Chair Music Theory Search Committee UW-Madison School of Music, 455 North Park Street Madison, Wisconsin 53706 DEADLINE: October 4, 1996. NOTE: AA/EOE; women and minorities are encouraged to apply. Unless confidentiality is requested in writing, information regarding applicants may be made released to the public on demand; finalists cannot be guaranteed confidentiality. CONTACT: Brian Hyer ---------------------------------------------- Music Theory - The Eastman School of the University of Rochester seeks two new faculty in the Department of Music Theory: one senior and one junior (rank negotiable). Preference will be given to those candidates whose experience and expertise complement the strengths of the department's current faculty; doctorate required. We are looking for individuals who will contribute to both our undergraduate and graduate programs, and who will be actively engaged in music research. Positions will be available to begin fall of 1997. Salary dependent upon experience and qualifications. Send cover letter, curriculum vitae, and supporting documentation by November 1, 1996 to Elizabeth Marvin, Chair of Music Theory, Eastman School of Music, 26 Gibbs Street, Rochester, NY 14604. The Eastman School of Music of the University of Rochester is an equal opportunity employer (M/F). ------------------------------------------------ POSITION/RANK: Head, Department of Music; appointment as Full or Associate Professor with tenure, or in a position leading to tenure, Effective 8/23/97 INSTITUTION: University of Connecticut, Storrs CT QUALIFICATIONS: Successful administrative experience at the college level, doctorate or equivalent, and a record of successful college teaching experience, plus outstanding achievement in music performance, theoretical or historical research, composition, or music education. Preference will be given to applicants with experience in a comprehensive program that includes undergraduate and graduate teaching. JOB DESCRIPTION/RESPONSIBILITIES: Serve as chief academic and administrative officer for the Music Department and represent the Department in its relationship with the University Administration and with the public. Provide Intellectual and artistic leadership for the Department, and work with the Dean of the School of Fine Arts, the Department's Directors of Undergraduate and Graduate Studies, and area coorinators in Applied Music, Ensembles, Music Theory and History, and Music Education to further the goals of the Department. Assume significant responsibilities in planning and supervision of Department-sponsored events, recruitment, and outreach activities. SALARY RANGE: Competitive, commensurate with qualifications and experience ITEMS TO SEND: Letter of application, resume and other credentials (including at least three letters of recommendation and list of references). DEADLINE: Open until filled, with preference given to applications received before December 15, 1996 CONTACT: Apply to: Department Head Search Committee School of Fine Arts, Box U-128 University of Connecticut Storrs, CT 06269 For additional information: phone (860) 486-3728 fax (860) 486-3796 email: rbass@finearts.sfa.uconn.edu ---------------------------------------- FLORIDA STATE UNIVERSITY SCHOOL OF MUSIC Position: 9-month tenure-track position in Music Theory Rank: Assistant Professor Qualifications: Completed Ph.D. in Music Theory. Strong commitment to teaching at all levels and to ongoing research and publication in area of specialization. Responsibilities: Teaching responsibilities may include: first and second year music theory and ear training; upper-division counterpoint and classic forms and styles; graduate seminars in area of specialization, advanced Schenkerian analysis, and thesis and dissertation direction. Appointment Date: August 1997 Institution: The Florida State University is a comprehensive research institution of 16 colleges and schools with 1500 faculty serving a student body of 30,000. The School of Music, with 80 faculty and over 900 students, offers a wide range of professional degrees in music, baccalaureate through the doctorate. The University is situated in Tallahassee, Florida's beautiful, wooded capital city. Located in the "Big Bend" area of Northern Florida, Tallahassee enjoys mild changes of season and proximity to the Gulf of Mexico. Procedure: Send resume and three letters of recommendation to: Jon R. Piersol, Dean Music Theory Search School of Music Florida State University Tallahassee, FL 32306-2098 Deadline: October 10, 1996 Submitted by: Jane Clendinning Florida State University jane_c@cmr.fsu.edu ========================================= 7. New Dissertations AUTHOR: Guigue, Didier TITLE: Une Étude "pour les Sonorités Opposées" - Pour une analyse "orientée objets" de l'oeuvre pour piano de Debussy et de la musique du 20è siècle. INSTITUTION: Ecole des Hautes Etudes en Sciences Sociales, Paris BEGUN: October, 1991 COMPLETED: April, 1996 ABSTRACT: Most of analytic tools developed during this century are exclusively devoted to the basic low-level components of music writing : pitches (or pitch classes). It is however an evidence that, at least since Debussy, forming and linking complex abstract sound-objects are, too, decisive composing features. This work exposes the basis of a computer-aided method of information and evaluation of the components of the musical score which may bring out all the necessary data for a neutral -level analysis of the formal functions of these objects. Our experimental analyses of some piano works of Debussy, show how such an object-oriented approach could be included in a more general analytic method. KEYWORDS: Sonic Object; Piano composing in 20th Century; Debussy; Functional analytic method; Computer-aided Music Analysis. TOC: Introduction 8 Première Partie ‹ La composition orientée objets 17 Chapitre 1 ‹ L'objet sonore: une abstraction pour la composition, un défi pour l'analyse 18 Chapitre 2 ‹ Une lecture orientée objets: propositions méthodologiques 50 Chapitre 3 ‹ Composition et Analyse dans un environnement informatique: intégration et interdépendance 85 Deuxième Partie ‹ Une méthode d'évaluation des qualités sonores 96 Chapitre 1 ‹ La sonorité au piano et son contrôle 97 Chapitre 2 ‹ Une modélisation des variables sonores du piano 138 Chapitre 3 ‹ Les objets sonores: un réseau de composants et composés 184 Chapitre 4 ‹ Les composants des caractéristiques achroniques 207 Chapitre 5 ‹ Les composants des caractéristiques diachroniques; évaluations de synthèse 243 Troisième Partie ‹ Éléments pour une analyse immanente de la sonorité dans l'oeuvre pour piano de Debussy 260 Chapitre 1 ‹ Dimensions de l'expression d'une forme archétypique chez Debussy: La Cathédrale Engloutie 263 Chapitre 2 ‹ L'Étude pour les Sonorités Opposées: quelles sonorités, quelles oppositions? 321 Chapitre 3 ‹ La Terrasse des audiences au clair de lune: une quantification des corrélations fonctionnelles entre le geste instrumental, la sonorité et la forme 369 Chapitre 4 ‹ Techniques de prolongations et transformations de sonorités dans Brouillards 397 Conclusion ‹ Vers une analyse fonctionnelle de la sonorité 456 Appendices, bibliographie, références, index, tables 466 CONTACT: Didier Guigue Rua Antônio P. Rocha, 90 58045-380 Joao Pessoa - Pb - BRAZIL Fone/Fax: + 55 83 247 14 73 email: dguigue@openline.com.br --------------------------------- AUTHOR: Hussey, William Gregory TITLE: "Compositional Modeling and Quotation in the Works of Johannes Brahms: An Application of Harold Bloom's Theory of Influence to Music" INSTITUTION: The University of Texas at Austin BEGUN: September, 1995 COMPLETION: December, 1996 ABSTRACT: The extent and manner in which composers are influenced by one another continues to be a concern of music theorists and musicologists. Some analysts such as Kevin Korsyn and Joseph Straus have appropriated Harold Bloom's literary theory of influence for music in an attempt to address these concerns. Although Bloom's theory of influence has been applied in many other fields besides literature, it has been criticized for describing artistic originality as a result of Freudian psychological processes in later artists as well as for the sexist language in which Bloom expresses his theory. This dissertation will attempt to do the following in analyses of works by Johannes Brahms: 1) explore the advantages of Bloom's theory for comparative music analysis between different works without Freudian psychological implications; 2) apply the theory to the finale Brahms's Piano Concerto No. 1 in D minor, Op. 15 as a work structurally modeled upon Beethoven's Piano Concerto No. 3 in C minor, Op. 37; 3) apply the theory to musical quotations from works of other composers as well as by Brahms himself in later works by Brahms; 4) analyze the influence of several works on the finale of Brahms's Piano Concerto No. 2, Op. 83. KEYWORDS: Brahms, Influence, Bloom, Quotation, Piano Concertos, Songs, Solo Piano Works TOC: Chapter 1: Introduction to Bloom's Theory Chapter 2: Compositional Modeling in Brahms's Piano Concerto No. 1 in D minor, Op. 15 Chapter 3: Quotation and Influence Chapter 4: Multiple Influence Analysis on Brahms's Piano Concerto No. 2 in B-flat, Op. 83. CONTACT: 3201-A Maywood Ave., Austin, TX 78703 (512) 302-3861 Email: WGHus@aol.com ------------------------------ AUTHOR: Lowe, Bethany L. TITLE: "Performance as Reception: The Symphonies of Sibelius in Britain 1930-1965" INSTITUTION: University of Southampton Music Department, Highfield, Southampton SO17 1BJ, England BEGUN: October 1995 COMPLETION: August 1998 ABSTRACT: Following the recent work of Laura Gray of Yale University in examining the reception history of Sibelius in the early part of this century, my research focusses on the recorded performances of the Sibelius symphonies released in Britain in this period, in an effort to discover how these inflect, and are determined by, contemporary images of Sibelius. Whilst using empirical methods to examine tempo structure in versions of the first movement of the Fifth Symphony I shall consider how the results obtained relate to analytical writings of the same period; and by examining these recorded sources as sites of reception in a multivalent network consisting also of critical, analytical and historical materials I shall aim to draw out these empirical methodologies into the spheres of critical musicology and theory/analysis. KEYWORDS: Sibelius, performance, recording, reception, Britain, tempo, analysis TOC: still in planning CONTACT: email: bll@soton.ac.uk [no home phone] ------------------------------------------------ AUTHOR: McDonnell, Donald R. TITLE: Roger Sessions' Symphony No. 3, First Movement: Form, Hexachordal Polarity, and Harmonic Language (and) Nexus/Dreamscape for Chamber Ensemble. (Original Composition) INSTITUTION: Brandeis University, Department of Music, Waltham, MA 02254-9110 BEGUN: September, 1991 COMPLETION: February, 1994 ABSTRACT: The first movement of Roger Sessions' Symphony No. 3 is music deeply ramified in the tradition of Symphonic first movements, but speaks to us in a modern harmonic language. This dissertation explores the sonata form of the movement in relation to like forms in tonal music, and draws parallels between the polarity of tonic and dominant with Sessions' treatment of complementary hexachords. Abstract complementary relations between Z-related hexachords at the beginning of the movement create large-scale dissonance, analogous to modulation to the dominant in tonal sonatas. The unity of key in the recapitulation of some tonal sonatas is parallelled by large-scale aggregate-forming relations in the recapitulation of the Third Symphony's first movement. The harmonic language of the movement is rich and diverse, but two primary hexachords provide motivation for large-scale formal procedures and relationships, and are also the source of much of the movements local pitch structure. The first chapter explores the genesis of the Third Symphony, references in the theoretical literature, and gives perspectives on analysis, and the historical context of the work. The second chapter defines theoretical premises to be used in the analysis of the movement. Chapters three and four are the heart of the paper, exploring the form of the movement and hexachordal polarity, and the harmonic language of the movement, respectively. The final chapter draws conclusions, summarizes the important points of focus earlier in the paper, and explores some implications for further research. KEYWORDS: Roger Sessions, sonata form, 12-tone, sets, hexachord, symphony, partition graphs TOC: I. Introduction 1.1 Sessions on the Genesis of his Third Symphony 1.2 References in the Theoretical Literature 1.3 Perspectives on Analysis 1.4 Historical Context II. Theoretical Preliminaries III. Form and Hexachordal Polarity 3.1 Aspects of Sonata Form: Tonal Procedures/Twentieth-Century Procedures 3.1.1 Sessions' Concept of Sonata Form 3.1.2 Style Traits of Sonata Form 3.2 Tonal Polarity/Hexachordal Polarity 3.3 Thematic Articulations of Large-Scale Structure 3.4 Conclusions: the Form of the Movement 3.4.1 Sessions on the First Movement of His Third Symphony IV. Aspects of Harmonic Language and Pitch Structure 4.1 Aggregate Formations 4.1.1 Overview-Prominent Row Appearances 4.1.2 Other Instances of the Row in the First Movement 4.1.3 Summary-The Use of the Row 4.1.4 Other Aggregate Formations 4.1.5 Summary of Aggregate Formations 4.2 Atonal Contexts for the Primary Hexachords and Their Pentachordal Subsets 4.2.1 Hexachord X and its Pentachordal Subsets 4.2.2 Hexachord Y and its Pentachordal Subsets 4.2.3 Summary-Atonal Contexts for the Primary Hexachords 4.3 Subsets of the Two Primary Hexachords 4.3.1 [0146] (4-Z15) 4.3.2 [0137] (4-Z29) 4.3.3 [0124] (4-2) 4.3.4 [027] (3-9) 4.3.5 Summary-Subsets of the Two Primary Hexachords 4.4 Secondary Hexachords: Their Use and Syntactic Function 4.4.1 The Chromatic Hexachord 4.4.2 Hexachord H 4.4.3 Summary-The Function of Secondary Hexachords V. Conclusion Appendix A: Set Class Frequency Appendix B: Subset Content of the Two Primary Hexachords Appendix C: Hexachordal Partition Graphs Select Bibliography CONTACT: Donald McDonnell Faculty Box 121 Berklee College 1140 Boylston Street Boston, MA 02215 e-mail: dmcdonnell@berklee.edu ---------------------------------- AUTHOR: Raickovich, Milos TITLE: "Einstein on the Beach" by Philip Glass: A Musical Analysis INSTITUTION: City University of New York BEGUN: May 1991 COMPLETED: May 1994 ABSTRACT: This analysis deals with the pitch content of the opera "Einstein on the Beach" by Philip Glass. Chapter 1 provides an introduction to Minimal Music. Compositional techniques from the 1960s and 70s by composers La Monte Young, Terry Riley, Steve Reich and Philip Glass are discussed. Chapter 2 describes "Einstein on the Beach" on the macro-form level. Dramatic and visual aspects are compared with the musical themes of the opera. In Chapter 3, the thematic unity of the entire work is defined by the melodic contours of the "Core Motive," present in virtually all sections of the opera. Chapter 4 deals with the ambiguities of Glass's harmonic language. The use of the pentatonic modes within the functional-harmonic context and non-chordal sonorities are discussed. Chapter 5 presents some conclusions about the original aspects of the pitch content of "Einstein on the Beach." KEYWORDS: philip, glass, einstein, beach, minimalism, steve, reich, terry, riley, young TOC: Chapter 1 - Introduction Chapter 2 - Description of "Einstein" and Its Musical Themes Chapter 3 - Thematic Unity: The Core Motive Chapter 4 - The Harmonic Language Chapter 5 - Conclusion CONTACT: http://www.page-me-now.com/milos_raickovich.html milrai@muze.com -------------------- AUTHOR: Robison, Brian TITLE: [working title] *Carmen Arcadiae Mechanicae Perpetuum*: Toward a Methodology for Analyzing Harrison Birtwistle's Music Since 1977 INSTITUTION: Field of Music Lincoln Hall Cornell University Ithaca, NY 14853 BEGUN: November 1995 COMPLETION: May 1997 ABSTRACT: Although Harrison Birtwistle is the pre-eminent British composer of his generation, his works remain underrepresented in the analytic literature. As assorted writers have noted, his music powerfully resists conventional analysis, and the composer himself hasn't expounded at length on his methods. Accordingly, commentators on his music have generally lacked specific technical means to substantiate many of their interpretative claims. The present study investigates Birtwistle's 1977 composition *Carmen Arcadiae Mechanicae Perpetuum* (hereafter simply *Carmen*), beginning with comparatively simple structures and proceeding through increasingly complex ones. Birtwistle's techniques of melody, harmony, motive, and cyclic segments of pitch or rhythm all reveal a highly methodical approach to the creation of varying degrees of disorder. In particular, attention to pitch sets (rather than pitch-class sets) and contour segments of pitch and rhythm reveals a much greater degree of compositional control than has been generally assumed. A concluding chapter demonstrates that the tendencies found in *Carmen* are by no means unique to that work, but recur in many of Birtwistle's major compositions since 1977. KEYWORDS: Harrison Birtwistle, contour analysis, pitch set analysis, contextual equivalence classes, "non-diatonic diatonicism", generalized mode mixture, generalized isorhythm TOC: [working titles] Chapter 1: Introduction Chapter 2: An overview of *Carmen* Chapter 3: Birtwistle's monodies: Interrupted endless melodies Chapter 4: Compound monophony: Harmonic permutation through approximate parallelism Chapter 5: From aleatoric mobiles to motivic permutation Chapter 6: Perpetual songs: Cycles of pitch and rhythm Chapter 7: Summary and synthesis Chapter 8: Birtwistle's music since 1977 Glossary Appendix 1: Misprints and likely errors in the published score of *Carmen* Appendix 2: Passages of compound monophony, with intervallic tables CONTACT: 209 Kline Road Ithaca, NY 14850-2116 Voice: (607) 277-2974 Music Library 225 Lincoln Hall Cornell University Ithaca, NY 14853-4101 Voice: (607) 255-4011 Fax: (607) 254-2877 (attn: B. Robison, Music) ============================== 8. New Books University of Chicago Press UNIVERSITY OF CHICAGO PRESS Saying Something: Jazz Improvisation and Interaction. Ingrid Monson This fresh look at the neglected rhythm section in jazz ensembles shows that the improvisational interaction among drums, bass, and piano is just as innovative, complex, and spontaneous as the solo. Ingid Monson juxtaposes musicians' talk and musical exa mples to ask how musicians go about "saying something" through music in a way that articulates identity, politics, and race. Through interviews with Jaki Byard, Richard Davis, Sir Roland Hanna, Billy Higgins, Cecil McBee, and others, she develops a persp ective on jazz improvisation that has "interactiveness" at its core, in the creation of music through improvisational interaction, in the shaping of social communities and networks through music, and in the development of cultural meanings and ideologies that inform the interpretation of jazz in twentieth-century American cultural life. Replete with original musical transcriptions, this broad view of jazz improvisation and its emotional and cultural power will have a wide audience among jazz fans, ethnomusicologists, and anthropologists. Ingrid Monson is assistant professor of music at Washington University. Chicago Studies in Ethnomusicology DECEMBER 192 p. (est.) 6 x 9 6 line drawings, 19 musical examples 1996 ISBN: 0-226-53477-4 Cloth $35.00tx 1996 ISBN: 0-226-53478-2 Paper $13.95tx ============================= La traviata Melodrama in Three Acts by Francesco Maria Piave Giuseppe Verdi Edited by Fabrizio della Seta Now one of Verdi's most beloved works, *La traviata* was initially far from a success. Verdi declared its 1853 premiere a "fiasco," and later reworked parts of five pieces in the first two acts, retaining the original setting for the rest. The first per formance of the new version in 1854 was a tremendous success, and the opera was quickly taken up by theaters around the world. This critical edition presents the 1854 version as the main score, and also makes available for the first time in full score the original 1853 settings of the revised pieces. For this edition Fabrizio della Seta used not only the composer's autograph an d many secondary sources but also Verdi's previously unknown sketches. These sketches helped corroborate the original readings and illuminante the work's compositional stages. The editor's wide-ranging introduction traces the opera's genesis, sources, a nd performance history and practices; and a detailed critical commentary discusses source problems and ambiguities. Fabrizio della Seta is associate professor of music history at the University of Siena, Italy. Praise for *The Works of Giuseppe Verdi*: "The most significant development in the history of Verdi scholarship." --Donald Henahan, *New York Times* "An achievement for which every conductor, singer, and player should be grateful." --Julian Budden, *Times Literary Supplement* DECEMBER Two-volume set. Score (one volume cloth): 608 p. 10 1/2 x 14 1/2 Commentary (one volume cloth): 6 3/4 x 9 1/2 1996 ISBN: 0-226-85316-0 Cloth $300.00tx =============================== Disciplining Music Musicology and Its Canons Edited by Katherine Bergeron and Philip V. Bohlman *Disciplining Music* confronts a much debated topic: how do musicians and music scholars "discipline" music in their efforts to confer order and meaning on it? This collection of essays formulates questions about music's canons--rules that negotiate cult ural constraints, reconstruct the past, and shape the future. Written by scholars of historical musicology, ethnomusicology, and music theory, many of the essays push the boundaries of these traditional divisions. "Fortunately, in a blaze of good-humored . . . scholarship, [this] book helps brains unaccustomed to thinking about the future without jeopardizing the past imagine the wonder classical-music life might become if it embraced all people and all musics." - -Laurence Vittes, *Los Angeles Reader* "These essays will force us to rethink our position on many issues . . . [and] advance musicology into the twenty-first century." --Giulio Ongaro, *American Music Teacher* With essays by Katherine Bergeron, Philip V. Bohlman, Richard Cohn and Douglas Dempster, Philip Gossett, Robert P. Morgan, Bruno Nettl, Don Michael Randel, Ruth A. Solie, and Gary Tomlinson. Katherine Bergeron is assistant professor of music at the University of California, Berkeley. Philip V. Bohlman is associate professor of music at the University of Chicago. He is coeditor (with Bruno Nettl) of *Contemporary Musicology* and *Anthropology of Music: Essays on the History of Ethnomusicology*, both published by the University of Chicago Press. NOVEMBER xii, 220 p. 6 x 9 1 halftone, 3 line drawings, 4 tables 1992 ISBN: 0-226-04370-3 Paper $15.95tx -------------------------- Oxford University Press Rethinking Dvorak Views from Five Countries Edited by David R. Beveridge 1996 328 pp.; music examples, 7 halftones 816411-4 $60.00 The Dynamics of Harmony Principles and Practice George Pratt September 1996 168 pp.; numerous music examples 879020-1 paper $22.00 Performing the Music of Henry Purcell Edited by Michael Burden 1996 336 pp.; 38 halftones & linecuts 816442-4 $85.00 Music in the English Courtly Masque, 1604-1640 Peter Walls 1996 400 pp.; 15 plates, 10 tables, 57 music examples 816141-7 $70.00 Celestial Sirens Nuns and Their Music in Early Modern Milan Robert L. Kendrick 1996 576 pp.; 5 plates, 2 maps, 100 musical examples 816408-4 $95.00 Born for the Muses The Life and Masses of Jacob Obrecht Rob C. Wegman 1994 (paper September 1996) 432 pp.; color frontispiece, 20 illus., 32 music examples 816650-8 paper $19.95 816382-7 cloth $45.00 Haydn's Keyboard Music Studies in Performance Practice Bernard Harrison, Lancaster University August 1996 400 pp.; 300 music examples, 19 tables, 1 figures 816325-8 $90.00 The Music of Benjamin Britten Revised Edition Peter Evans 1996 608 pp.; 300+ music examples & diagrams 816590-0 paper $21.00 Mozart A Musical Biography Konrad Koster Translated by Mary Whittall 1996 432 pp.; frontispiece, color endpapers, 15 plates 816339-8 $35.00 Richard Strauss's Elektra Bryan Gilliam 1992 (paper 1996) 288 pp.; 4 figures, music examples 816602-8 paper $24.95 313214-1 cloth $75.00 Women Musicians of Venice Musical Foundations, 1525-1855 Named an Outstanding Academic Book for 1994 by Choice Revised Paperback Edition Jane L. Baldauf-Berdes 1993 (paper 1996) 336 pp. 816604-4 paper $24.95 Winner of the Wallace Berry Award of the Society for Music Theory Wagner's Das Rheingold Warren Darcy 1994 (paper 1996) 288 pp.; 67 music examples, 4 figures, 25 pp transcription of Wagner's sketches 8166036 paper $24.95 Franz Schubert A Biography Elizabeth Norman McKay 1996 384 pp.; 16 pp b/w plates, 5 text illus, 1 music example 816523-4 $35.00 Performing Music Shared Concerns Jonathan Dunsby 1995 (paper August 1996) 112 pp.; music examples, 2 figures 816642-7 paper $13.95 ============================== 9. Advertisements INTEGRAL Integral is a juried periodical of articles and reviews on theory, analysis, criticism, and their relationship to composition an performance. It is published annually during the summer by graduate theory students at the Eastman School of Music. Volumes 1-8 include articles and reviews by: Bo Alphonce Robert S. Hatten David Beach Kevin Korsyn Matthew Brown J. Phillip Lambert Allen Cadwallader Elizabeth West Marvin Howard Cinnamon Patrick McCreless Richard Cohn Andrew Mead Edward T. Cone Robert Morris Warren Darcy Massimo Ossi Cynthia J. Folio Alexandra Pierce Richard Kurth Gregory Proctor Robert Gauldin Marie Rolf Robert Gjerdingen William Rothstein Douglass Green Robert Wason Daniel Harrison Mary Wennerstrom Subscriptions and Back Issues $12 individuals $10 students $16 institutions Outside North America, please add $4.00 postage Checks (in U.S. dollars) should be made payable to Integral Please allow four to six weeks for delivery Back Issues: Volumes 1-9 $84 individuals $70 students $112 instituttions Send subscription requests to: Subscriptions Manager, Integral Eastman School of Music 26 Gibbs Street Rochester, New York 14604 --------------------------------- Music Theory Spectrum The Journal of the Society for Music Theory Joel Lester, editor Contents of Volume 18, No. 2 (Fall, 1996): Brian Alegant Unveiling Schoenberg's op. 33b Ethan Haimo Atonality, Analysis, and the Intentional Fallacy Martha M. Hyde Neoclassic and Anachronistic Impulses in Twentieth-Century Music Timothy A. Johnson Chromatic Quotations of Diatonic Tunes in Songs of Charles Ives Herbert Schneider Review of Thomas Christensen. Rameau and Musical Thought in the Enlightenment David W. Bernstein Review of James Pritchett. The Music of John Cage Music Theory Spectrum is sent to all current members of the Society for Music Theory. Regular membership dues: $45 per year, $55 for dual members (two members at the same address; one copy of mailings), $20 for student members, $30 for dual student members (two student members at the same address; one copy of mailings), and $30 for emeritus members. Libraries and other institutions subscribe at the rate of $48 per year. Kindly add $15 per year for subscriptions outside of North America. Applications for membership and available back issues may be addressed to Cynthia Folio, Treasurer SMT Esther Boyer College of Music Temple University Philadelphia, PA 19122 =================================== 10. Communications Editor's Message 1. Electronic Publishing and Scholarly Dialog 2. MTO Reader Survey 3. Music Theory International 4. MTO Hypertext Subscriber Directory 5. Subscriber Services 6. Auto-responder Addresses: Instant Documentation by Email ------------------------------------------------- 1. Electronic Publishing and Scholarly Dialog Publishing has traditionally been a slow affair. From the time new research leaves a scholar's desk, as a journal article or a book, until the time it appears in print, several years may elapse. Yet more time passes until scholars around the world become aware of new findings or perspectives, and can react to them in print. Electronic publishing on the Internet has significantly changed that scenario. For scholarly electronic journals, the time lag from submission to circulation has been reduced from years to months, the lag for peer responses to days, thanks to electronic discussion forums like mto-talk. The last and present issue of MTO are excellent examples of the benefits of electronic publishing. Roger Wibberley's provocative essay on musica ficta in MTO 2.5 stimulated an interesting dialog on mto-talk among Cristle Collins Judd (U.S.), Victor Grauer (U.S.), Nicolas Meeus (Belgium), Jonathan Walker (Northern Ireland), and Wibberley (England). This issue of MTO, appearing only two months later, includes commentaries on the essay by Margaret Bent, whose notion of "diatonic ficta" was a focus of Wibberley's article, and by Jonathan Walker, who pleads a case against the unjust verdict on Just Intonation in performance practice. Electronic publishing may never replace print publishing, but its rapidity, versatility (multimedia) and growing accessibility are clear advantages over print, assuring it a prominent and unique place in the future scholarly world. MTO is pleased to offer subscribers current research and responses. We encourage readers to contribute to discussions on mto-talk, and to submit essays and commentaries for publication in MTO. 2. MTO Reader Survey When MTO began in February, 1993, the chief means of distributing documents on the Internet were email, command-line "anonymous" FTP (File Transfer Protocol), and Gopher. The World-Wide Web was in its infancy, known to few and used by even fewer. Netscape, today the most popular graphical user interface ("browser") for accessing Internet documents, did not exist, and Mosaic was in early development. Now, the World-Wide Web and browsers have become the preferred means of accessing information and services on the Net. FTP servers remain, but the commands that make them work, and the workings themselves, are hidden by browsers. Gopher servers, so prevalent as document retrieval mechanisms only a few years ago, have largely been supplanted by Web servers. MTO has evolved with Net technology. We established a Web server in January, 1995 (MTO 1.1) and began offering documents in both non-graphical plain-text (ASCII) and hypertext formats (HTML), the latter integrating text, graphics, and sound. We have continued to provide plain-text documents of all items, and have maintained mto-serv, our plain-text FileServer, a Gopher and anonymous FTP site for those who do not have the necessary equipment to use the graphically-oriented Web, or who prefer to retrieve MTO in plain-text format. Providing MTO in two formats has always required a bit more work for the small staff, but we accepted that burden in order to ensure that anyone with even the most basic Internet service--an email account--would have access to MTO. Now that the journal has expanded in content with the new Music Theory International department (see below), Advertisements, a New Book section (and perhaps yet another to be announced in MTO 2.7!), the burden of producing each issue of MTO in two formats has grown substantially. We are therefore considering the possibility of offering MTO as a Web-only publication, that is, in HTML format only. Plain-text versions of MTO items would no longer be made available (except for the table of contents, which would still be distributed by email). The burden of providing two versions of all items would be eliminated, shifting some responsibility to our subscribers, who would need to begin using a Web browser in order to read MTO. Those who have sufficient hardware resources would probably want to get and learn to use one of the graphical Web browsers. Those who lack the resources would need to ask the system administrator of their Internet host to install a non-graphical (plain-text) browser such as Lynx. Lynx is very easy to use and is available on most hosts. Those who have relied on mto-serv and email to retrieve and read MTO items may be surprised to discover that they can, in fact, read MTO on the Web by typing "lynx http://smt.ucsb.edu/mto/index.html" at an Internet host's system prompt (and then hitting ENTER). Because Lynx is a non-graphical browser, it can be used with even the most basic terminal emulations (e.g. VT100). Lynx does not display images but does allow users to transfer image files to their Internet hosts, from which the files can then be downloaded to a home computer and viewed offline with a graphics monitor and appropriate software. Robert Judd, MTO Manager, wrote a guide to Web tools in volume 1.3 (www-tools.txt or www-tools.html). Subscribers may want to consult that guide in considering the best way to access the Web. The reader survey distributed last week was designed to help us gauge the readiness and willingness of our subscribers to move to a Web-only MTO. If you have not yet filled it out and sent it in, please do so as soon as possible. The survey is included below in case you cannot find yours. Copy the survey into an email message, fill it in, and send it to mto-survey@smt.ucsb.edu. We hope to have a high response rate so that we know how to proceed. Music Theory Online Reader Survey The MTO editors would be grateful if you would take a moment to reply to this request for information. Our goal is to provide the most effective and useful service we can, while conserving resources as far as possible. Please send your reply to mto-survey@smt.ucsb.edu. Do not send it to mto-list@smt.ucsb.edu. 1. MTO ACCESS a) Do you access MTO via e-mail, gopher, ftp, or the Web? b) Do you normally download/print or do you read online? c) How would you react to eliminating ascii versions of MTO? 2. LYNX a) Are you aware of Lynx Web access at your internet host? b) Have you used Lynx satisfactorily or not? c) How would you feel about switching to Lynx for a Web-only MTO? 2. MTO SERVICES a) What MTO services do you find particularly valuable? b) Are there services you believe could be eliminated? c) Do you know of services we don't provide that ought to be considered? 3. MECHANICS AND CONTENT a) Do you have other comments as to the mechanics or content of MTO? b) Can you suggest improvements to mto-talk? Thanks in advance for taking the time to reply. A report on the responses will appear our next issue (2.7, November 1996). 3. Music Theory International MTO 2.5 introduced a new section, MTO Correspondents, for reports on music theory activities around the world. Our first report was by Peter Castine (Berlin, Germany). In the Editor's Message for 2.5, and in the table of contents, I mistakenly labeled the new section "MTO Correspondents," when in the August SMT Newsletter (Volume 19, Number 2, 1996) I identified the new section as Music Theory International, which from now on will be the title. Since our last issue, we have added two new Correspondents, Roberto A. Saltini (Brazil), and Gerold W. Gruber (Austria). A full listing of the Correspondents appears in the MTO masthead. They are as follows: Per Broman, Sweden Peter Castine, Germany Wai-ling Cheong, Hong Kong Geoffrey Chew, England Gerold W. Gruber, Austria Henry Klumpenhouwer, Canada Nicolas Meeus, Belgium, France Ken-ichi Sakakibara, Japan Roberto A. Saltini, Brazil Michiel Schuijer, Holland Uwe Seifert, Germany Arvid Vollsnes, Norway Per F. Broman submitted a report for this issue on three seminars that took place in connection with the 1996 ISCM World Music Days (Copenhagen). If you live in a country not yet represented, please contact me at the address below if you are interested in serving as a Correspondent, or if you would like to suggest someone. 4. MTO Hypertext Subscriber Directory A plain-text alphabetical directory of MTO subscribers has been available on our home page for some time. The present and future directories will be in hypertext format, where each email address is a hot link. If your WWW browser supports "mailto" links, clicking on the address in the new directory will bring up an email screen with the address of the selected link already filled in. Check out the directory at http://smt.ucsb.edu/mto/docs/mto-dir.html. We hope subscribers will find this new directory useful. An updated copy will appear at the beginning of each month. 5. Subscriber Services When you go on vacation, you should postpone your MTO and mto-talk mail. If your email address changes, you must change your subscription address for both MTO (= mto-list) and mto-talk. These and other options can be set by filling in and submitting a Web form. Point your browser at the MTO home page and follow the link for "Subscriber Services" in the menu near the top of the page. It is much easier, and more reliable, to set subscriber options by submitting the Web form than by submitting email requests to "listproc," our mailing list software. Please report any problems with the Web form to me. 6. Auto-responder Addresses: Instant Documentation by Email Subscribers should be aware that they can receive documentation and short help documents by sending an empty email message to one of several "auto-responder" addresses: - help@smt.ucsb.edu fill in the "Subject:" line with one of the following words general (for general help) subscribe (how to subscribe to a list) unsubscribe (how to unsubscribe from a list) password (changing your list password) address (changing your list address) options (setting mail options) - mto-guide@smt.ucsb.edu (= MTO Guide) - talk-guide@smt.ucsb.edu (= mto-talk Guide) - mto-authors@smt.ucsb.edu (= MTO author guidelines) - issue-number@smt.ucsb.edu (= MTO's current issue number) - mto-dbase@smt.ucsb.edu (= MTO database guide) - addresses@smt.ucsb.edu (= important SMT addresses) - join-smt@smt.ucsb.edu (= form to join SMT!!) - smt-guide@smt.ucsb.edu (= smt-list Guide) - smt-dbase@smt.ucsb.edu (SMT bibliographic database tutorial) Send suggestions for further auto-responder addresses to me. ------------------------------------------------------ Lee A. Rothfarb, General Editor Music Theory Online University of California, Santa Barbara Santa Barbara, CA 93106-6070 U.S.A. mto-editor@smt.ucsb.edu voice: (805) 893-7527 (with voice mail) fax: (805) 893-7194 +=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+ Copyright Statement [1] *Music Theory Online* (MTO) as a whole is Copyright (c) 1996, all rights reserved, by the Society for Music Theory, which is the owner of the journal. Copyrights for individual items published in MTO are held by their authors. Items appearing in MTO may be saved and stored in electronic or paper form, and may be shared among individuals for purposes of scholarly research or discussion, but may *not* be republished in any form, electronic or print, without prior, written permission from the author(s), and advance notification of the editors of MTO. [2] Any redistributed form of items published in MTO must include the following information in a form appropriate to the medium in which the items are to appear: This item appeared in *Music Theory Online* in [VOLUME #, ISSUE #] on [DAY/MONTH/YEAR]. It was authored by [FULL NAME, EMAIL ADDRESS], with whose written permission it is reprinted here. [3] Libraries may archive issues of MTO in electronic or paper form for public access so long as each issue is stored in its entirety, and no access fee is charged. Exceptions to these requirements must be approved in writing by the editors of MTO, who will act in accordance with the decisions of the Society for Music Theory. +=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+ END OF MTO 2.6 (mto.pak.96.2.6)