|
COPYRIGHT 2000 University of Washington
I. THEORIES OF COMPOSITION AND THE HYBRID SYSTEM [1]
THEORIES OF COMPOSITION (i.e., theories for the generation of musical structures) form a spectrum whose range illustrates to what degree a theory determines [2] the organization of a composition's musical surface. At one end of the range, lie aleatoric theories, such as those developed by John Cage and employed in compositions such as Music for Piano (1952--56). [3] Since the materials and/or the procedures for organizing the materials are randomly produced with indeterminate composing theories, the specific nature of the musical surface cannot be predicted from the theory. [4] At the other end of the range, lie deterministic or algorithmic composing theories, such as those employed by, Lejaren Hiller, Larry Austin, and others. Since the materials and/or the procedures for organizing the materials are algorithmic, "once certain variables specified by the theory have been defined, a piece of music will emerge." [5] Tonal composing theories, such as the rules of counterpoint or the syntax associated with harmon ic progressions, lie somewhere in between the middle and the deterministic end of the range, because these theories determine many details of the compositional surface but they do not produce pieces. [6] Twelve-tone theories of composition are scattered throughout this spectrum of choice. A simple or minimal twelve-tone theory that only specifies an ordering for the twelve pitch classes along with a set of operations, such as transposition, inversion, and their retrogrades, does not specify how one row relates to any other. Since this theory determines very little about the organization of these musical structures (sequentially, polyphonically, or by any other musical parameter), very few details of a composition's musical surface (i.e., its score) can be predicted from the theory. Therefore, its position on the spectrum would be closer to aleatoric theories. A twelve-tone system incorporating a theory of hexachordal combinatoriality would move it closer to the middle of the spectrum, since the constraints im posed by hexachordal combinatoriality would limit the sequential and polyphonic organization of the twelve-tone rows on a composition's musical surface.
Theories of composition could also form a spectrum whose range illustrates to what degree a theory determines the organization of structural levels relating the musical surface to some background structure. At one end of the range lie completely bottom up approaches to composition, such as motivic composition. [7] Since motivic theories only generate surface structures, they say nothing about background structures or the relation of the surface to a background. At the other end of the range would be theories, such as a rational reconstruction of Schenker's analytical methodology, that would specify at every level the transformational relationships connecting the musical surface to a background structure. [8] Once again, a simple or minimal twelve-tone theory simply producing an ordering of the twelve pitch classes along with a set of basic operations determines very little about the organization of structural levels relating the musical surface to a background structure, presumably a single row form. Consequ ently, its position on the spectrum would be closer to the bottom up approaches to composition. A twelve-tone theory incorporating a theory of array structures, such as Morris, Composition with Pitch Classes, would move it closer to the middle of the spectrum, since it would specify more precisely the organization of structural levels relating the musical surface (the faster unfolding columnar aggregates of the array) to the background structure (the slower unfolding twelve-tone rows forming the linear aggregates of the array).
The hybrid compositional system, which will be outlined in this paper, lies somewhere in between the middle and the algorithmic end of the range of theories that specify the organization of a composition's musical surface, because the theory determines many details but it does not specify every detail of a composition's structure. The hybrid compositional system also lies somewhere in between the middle and the end of the range where theories specify at every level the transformational relationships connecting the musical surface to a background structure, since the system contains a set of transformational relationships connecting most of the musical surface to a background structure. The system is a composing language that combines structural elements from nontonal theories, such as twelve-tone arrays and self-deriving rows, and aspects of tonal theories, such as structural levels and prolongation. The system facilitates constructing complex and coherent musical structures, some of which function in a mann er similar or analogous to the musical structures in tonal systems.
Although the concept of incorporating structures usually associated with tonal music into nontonal systems appears contradictory, the contradiction is nominal, rather than structural. [9] If the diatonic set generates the tonal system's structural elements and relations, and if it is one member of a system of sets classified by their [T.sub.n]/[T.sub.n]I types, and if some sets in the system do not generate tonal structures, then in one sense, the labels tonal and nontonal simply denote sets possessing different structural properties. However, the labels do not imply or lead to the conclusion that differently labeled collections cannot generate similar or equivalent structures, and the labels do not imply or lead to the conclusion that every member of the system does not or cannot generate similar or equivalent structures. Discovering a syntactic connection between the tonal interpretation of the [T.sub.n]/[T.sub.n]I set [0,1,3,5,6,8,10] and other members of the [T.sub.n]/[T.sub.n]I system, and constructing a system based on those commonalties, would be a method of incorporating tonal structures into systems based on set classes other than the diatonic. David Lewin suggests this method of incorporating structures usually associated with tonal music into nontonal systems in his article "A Formal Theory of Generalized Tonal Functions." [10] Lewin transforms the arrangement of tonic, dominant, and subdominant triads linked by common tones (see Example 1) into an expression for constructing systems of tonal functions given a tonic pitch-class T, a dominant interval d, and a mediant interval m.
Each system consists of tonic, dominant, subdominant, mediant, and submediant triads. Lewin's generalization is not limited to any particular dominant or mediant interval, such as perfect fifth and major and minor thirds. Example 2 illustrates the triadic system determined by the ordered triple (C, 3,1) (d = 3 and m = 1). In the (C, 3,1) system, all the triads are [T.sub.n]/[T.sub.n]I [0,1,3] type trichords. Thus, Lewin shows a way to generalize tonal functions to sonorities not usually considered tonal.
Even if the tonal interpretation of the [T.sub.n]/[T.sub.n]I set [0,1,3,5,6,8,10] shared no syntactic features with sonorities not usually considered tonal, the diatonic set may not determine every syntactic property of the tonal system. [11] Since some structures, such as those associated with Schenker's conception of tonality, may be token representations of more general syntactic properties, another method of incorporating tonal structures into systems using [T.sub.n]/[T.sub.n]I sets might be creating a functionally analogous system based on generalizations of Schenkerian tonal syntactic features and interpreting those features within the context of a particular [T.sub.n]/[T.sub.n]I set type. For, example, concepts such as neighbor-note, passing note, prolongation, structural level, and Ursatz, may not be limited to the triads generated by the diatonic set. On the other hand, musical structures traditionally thought of as nontonal, such as tone rows and arrays, may be adapted to simulate tonal functions, or their structure could be the basis of determining tonally analogous functions.
The hybrid system integrates generalized tonal concepts with tone rows and arrays. The background structure of the system is a special type of array structure that contains a limited number of trichordal set classes (from 2 to 4 different classes) in the array columns. The array determines the background or long range voice-leading motions in a composition. The hexachords of the row underlying the array are independent "harmonic" areas, so during the course of a composition the large-scale "harmonic" motion moves from one area to its complement and then back to the original area. The transformations linking the background structure to the musical surface come from a modified and expanded version of John Rahn's definitional reconstruction of Schenker's analytical theory. The definitional portion of the theory generalizes tonal concepts, such as neighbor-note, passing note, prolongation, and structural level, so they can be incorporated into a system that has tone rows and arrays as its foundation.
Before proceeding from this brief overview of the hybrid system to a detailed investigation of its components, I would like to address several metatheoretical issues this theoretical approach to composition raises. Whether formalized or not, music theories are systems used to model (i.e., interpret the structure of) music. While formal logistic systems are concerned with preserving truth, music theories are mainly concerned with producing structural descriptions. Theories not only determine a structure's sense, but they also suggest how the elements of music, such as pitch classes, can be "sensibly" structured. To paraphrase Boretz, "[theories] constitute universes of "all the "things" that things can "be," and, in turn, they constrain (by implication) "all the things that can be a "thing." [12]
Theory's two different functions suggest that compositions and models of compositions are different sides of the same coin, since both view structure through a lens called theory. Either one starts with a theory and models a compositions's structure in the theory or one may create a compositional structure with an interpreted theory in mind. It is possible that a single theory could function as both a composing and parsing theory facilitating the creation or analysis of a composition. [13] The methodological distinction between composing and parsing functions is one of direction. In practice, the theory modeling a composition's structure is not always the same as the theory used to compose a work. Since structure can be viewed from different angles by a single theory, or viewed from each perspective by different theories, misconceptions can arise about the extent of a theory's parsing or composing functions, the connection or lack of connection between theory types, and theory's relationship to the composing process.
While some theorists may falsely conclude that parsing theories accomplish more than they do (leading to the belief that musical "laws" have been discovered), some composers falsely concluded that parsing theories have no connection with, and therefore nothing positive to offer, the composing process. [14] Since parsing and composing theories approach music from different directions (i.e., applied to structure as opposed to generating structure, or top-down versus bottom-up), the methodological distinction can be seen as an impenetrable barrier; like oil and water, the two types of theories do not mix.
A gap similar to that separating composing and parsing theories can also divide composing theories, which can be either one of two types. If the composing procedures are "intuitive," "bottom-up oriented," or partially specified (i.e., the procedures only reveal the most basic features of some undefined musical system), then the composing theory is "unexpressed." If the theory is explicit, "top-down oriented," or speculative (i.e., the systemic relations outlined in the theory apply to nonexistent compositions whose stylistic components are not specified by the theory, but, as Rahn states, the theory is presented "as an interesting possible way of organizing possible views of possible things"), [15] then the theory is "expressed." Some composers only favor the "bottom-up" or unexpressed approach, because composing with an expressed theory is seen as "theory" or "reason driven." [16] Sessions expressed this opinion in his discussion of Krenek's Uber neue Musik: [17]
creation--the end--is a subconscious process, while technique--the means--is the conscious or superconscious one; musical theory therefore that is before the fact can have no conceivable value to the musician, and can only be poisonous to him if he allows himself to be really exposed to it . . . musical theory is valid for the musician only insofar as it is practical and not speculative . . . it [Krenek's Ober nene Musik] stands fatally before the fact; its principles are, quite frankly and from the beginning, based on abstract reasoning rather than on concrete and demonstrable experience of effect.
The plausibility of concluding that expressed theories play a subordinate role in the creative process because compositional practice is antecedent to theory, or that music could be created without some theoretical notions, appears to be founded on three misconceptions. First, because unexpressed composing theories are not formalized, composing with an unexpressed theory fosters the illusion of "theory free" or intuitive composition. Second, the historical evidence supporting the popular notion that "theory always follows practice" is misinterpreted. Since parsing theories have a tendency to appear historically after the music that is intended to be modeled in the theory, the historical antecedence of compositional practice easily leads to the conclusion that theory does indeed follow practice; therefore, compositional practice does not employ theory. However, the popular aphorism could, perhaps, be more precisely stated as "parsing theories always follow unexpressed composing theories. "Finally, expressed c omposing and parsing theories might appear to be functionally identical, because they both appear to be "top-down" processes, which creates the illusion of equivalence between their very different functions.
Perhaps the equivocation of the processes results from the fact that since expressed composing theories move from theory (i.e. theory of structure) to the generation of a composition (i.e., the generation of structure), they are categorically more similar to parsing theories, which move from theory (i.e. theory of structure) to the analysis of a composition (i.e., the analysis of structure), than to "compositional practice" (i.e. unexpressed composing theories), which begin with data and no apparent theory of how that data is to be structured. In expressed composing theories, the move from theory to composition appears deterministic in the same way that a parsing theory determines what structures are available for analysis. On the other hand, unexpressed composing theories appear unrestricted by theoretical constraints, since the composing process only appears driven by data, with no a priori awareness of a relationship to a theory that structures the data. Although each type of composing theory appears to a pproach structure from opposite directions (theory versus data or top-down versus bottom-up), their apparent methodological differences should not be equated with the top-down/bottom-up methodology that identifies a theory as either parsing or composing. Parsing theories are top-down in that they are applied to an already existing structure. Consequently, the goal of parsing theories is to achieve as best they can a one-to-one relationship between theory and composition. For each structure posited by the theory a corresponding, structure will exist in the group of compositions under investigation. Ideally, the group of compositions should not contain structures unaccounted for by the theory. Furthermore, a by-product of parsing theories is they often specify the stylistic component of the music under investigation.
Unexpressed and expressed composing theories are both bottom-up, however, in the sense that they both generate a particular structure. Therefore, the goal of an expressed composing theory does not have to be achieving a one-to-one relationship between theory and composition. In fact, the relationship between expressed composing theories and composition is often a many-to-one mapping. The theory presents a range of possibilities from which the specific structures of a particular composition will emerge. Expressed composing theories simply either narrow the range more than unexpressed theories or they simply make the range of possibilities known. Unfortunately, an expressed composing theory is considered top-down, because the first step in the composing process is the theory's...
Read the full article for free courtesy of your local library.
|
Bookmark this article
Print this article
Link to this article
Email this article
Digg It!
Add to del.icio.us
RSS
