Musical A Priori's: An Investigation of Explanatory Strategies

October 1, 1979

Everyone here has, no doubt, at one time or another observed that the language we speak has remarkably strong and intimate connections with the rest of what we experience; in particular, it is remarkable that we somehow manage to use certain slices of discourse as explanations for things which are strikingly unlike spoken language. It is perhaps a reflection of these connections that no theorist of music can be, as one might naively expect, exclusively concerned with isolating the niceties of music. Rather we also find ourselves committed to expressing those niceties which we discover, and therefore spend a large amount of our time dealing with what sometimes appear to be purely methodological problems of language—determining how our utterances can best be made to say whatever it is we think we're trying to say about music.

Now a superficially plausible way of accounting for this situation might be to characterize the primary explanatory role of language as simply reflecting whatever conceptualizations we have in our heads. Thus the strikingly different "explanations of musical things" which we endorse might be said to reflect our different ways of conceptualizing those particular "musical things," as well as our different conceptualizations of what it is to be music. This sort of account of explanations might allow that the process of trying to put whatever one is thinking into words could stimulate one to revise one's thoughts; but essentially the language of one's discourse is thereby regarded as a neutral tool which can be used for reflecting conceptualizations with a greater or lesser degree of skill, depending upon one's linguistic (rather than musical) abilities.

In particular, consider the various ways someone's sense of knowing a piece can be said to have come about: pieces are heard in the form of complicated relational structures which we notice in and impose upon certain successions of sounds; pieces are learned by processing score-notations in certain more-or-less conventional and predictable ways; or new pieces are devised by imagining new music-contexts for familiar music-patterns and vice versa. And a piece might be said to be remembered or recalled in any of several similarly diverse ways. In accounting for such processings of music, it is tempting to assume that the word "piece" refers to something both public and well-determined, and that these things known as pieces are dealt with by the application of certain cognitive things, which one might call "concepts." For example, one might say that one knows or understands the concepts of "closure," of "consonance" and "dissonance," of "phrase," or of "tonality," and that one applies these and other concepts to pieces in order to understand those pieces. If this were considered a satisfactory account of the cognitive processing of music, then one might easily subscribe to a purely interpretive account of language as well; for it would be a simple maneuver to claim that explaining a piece consisted merely of verbalizing how the relevant concepts are applicable and were applied to that particular piece. And it would perhaps come as no surprise that someone who subscribed to this sort of account of "explanations" might well feel that the amount of time some theorists spend on so-called "purely linguistic" matters is excessive.

It seems to me, however, that such an account would be difficult to live with, in considering all but the least sophisticated examples of musical discourse. For surely language does more than just reflect whatever it is that is in one's head; those expressions available to me, those I have grown accustomed to hearing and feel comfortable using—in other words, the language of my explanations—not only limit what I can say, but shape and mold in determinate ways any conceptualization I might try to develop. And, although an interpretive account can capture the sense in which the terms "piece" and "concept" are used in casual discourse, it misses some deeper and more specific senses of those words, in part because of the unproductive assumption that both "concepts" and "pieces" can be regarded as objective things.

Now the idea of pieces existing objectively, that is, independently of their individual processings by individual processers, has problematic reverberations even for our everyday experience as musicians. After all, judging from what we say and do, it is clear to me that my conception of, say, the first of Webern's Op. 10 orchestra pieces is actually quite distinct from anyone else's—that is, I hear a counterpoint of patterns and rhythms which seems to be different from the counterpoint others claim to hear; in fact, as far as I can tell, we all seem to have unique Op. 10/1's in mind. In what sense then is everybody listening to, playing, and talking about "the same piece"? In fact, each of us develops his or her own music-thoughts, using various commonly accessible sources, such as sound-successions or scores, and subsequently classifies and categorizes those music-thoughts as "pieces" in various ways for various reasons. We then resort to certain conventional modes of discourse both to ascertain the extent of correspondence with the pieces constructed from the same sources by other musicians, and to ensure enough correspondence for viable communication using common names for those presumed pieces. In this case it is easiest to assume we identify our various Webern Op. 10/1 pieces by referring to what we take to be a mutually recognizable class of physical objects, namely the class of scores of Op. 10/1.

Even deeper problems arise in considering "concepts" as objective or public entities. For we never ascertain the extent to which someone claims familiarity with some "concept" by actually determining his or her awareness of some public "thing" (such an investigation seems, after all, hardly practical). Our claims to such familiarity are based entirely on our use of language in so-called "concept-suggesting" ways. Thus it seems peculiar to ever bring up these so-called conceptual entities at all in our talk about conceptual matters; questions about conceptualizations can be effectively dealt with by translating them into more accessible questions about language-usage. In fact, those components of our own cognitive equipment which we often label as "concepts" can productively be characterized, not as "things" to be grasped, but rather as abilities to use certain expressions and statements in ways which others seem to understand and appreciate; that is, we can say that "understanding a concept" consists essentially of having a certain linguistic ability. And what we talk of as concepts understood by others might similarly be considered hypothesized correlates to what we sense as our own abilities, according to the way each one of us perceives regularities in the language-usage of others.

A comparable point may be made from a different perspective by appropriating a well-known image devised by Quine: namely that the totality of our so-called empirical knowledge is actually a man-made fabric of interconnected and mutually dependent statements which impinges upon our actual experience only along the edges. Our correlation of certain statements at the perimeter of this fabric with certain experiences can be considered not so much an intrinsic relationship between so-called "descriptive" statements and observable data, but rather, as Quine puts it, "nothing more than a loose association reflecting the relative likelihood, in practice, of our choosing one statement rather than another for revision in the event of recalcitrant experience."1 Certainly anything one says can only loosely be said to reflect the way the world or music is in any objective sense; rather the conceptual fabric constructed by each one of us can be more productively regarded as manifesting that person's own particular way of structuring and theorizing about his or her experience, of characterizing the regularities observed by that person, and of imposing classifications upon that experience.

According to this kind of metaphorical account of empirical knowledge in general, an account of "explanations" as straightforward listings of "things found" and "concepts applied" collapses; for "explanations," "descriptions of things found," and "formulations of concepts" can all be considered to be component and integral parts of the same interdependent array of statements, an array which one might term one's "theory" of the world. Certainly a distinction between "direct observations" of pieces and "explanations" of pieces is difficult to support from this point of view. For even what one might call the most direct of observations would seem to depend as much on the conceptual structure in which it operates as does any "explanation." From this point of view, any statement one might make about a piece can be characterized as "explanatory," in the sense that it is filtered through, aligned against, and revised in accordance with one's prior conceptual scheme, and hence reflects its position within that scheme. And it would be just as problematic to defend an absolute dichotomy along the lines of "things brought to a piece from outside that piece" vs. "things inferred directly from that piece"; it is difficult to isolate anything one might get from any piece which is not preconditioned by what is brought to that piece, that is, by the structure of one's prior theorizing about music and the world.

Now a possible counter-argument to all of this might go as follows: granted that whenever one resorts to language in explaining music one is immediately subject to a vast array of prior conceptual filters, both in oneself and in one's audience, can't one gain direct access to music-conceptualizations via music, that is, by having someone perform some "piece" according to his or her conception of it? After all, it is certainly true that the most well-established means for the making public of music-thoughts is by means of successions of sounds. However, the sense in which sounds provide direct access to conceptualizations eludes me; for a listener can only pick up relations and patterns in sounds according to limitations determined by his or her own predilections, preconditionings, and expectations, and then can only assume that the patterns actually picked up were what the performer intended to get across. Communication by means of verbal language may at best be indirect and inferential, but using sounds for communication is, if anything, even more profoundly filtered by individual conceptual schemes. It seems to me that sounds are better thought of as potential analog models of music than as intersubjective telegrams about specific music-thoughts.

Of course, treating questions about the conceptual underpinnings of musical explanations as questions about the language of those explanations does not in itself provide any easy answers; but one does avoid some of the pitfalls of trying to objectively discuss "things" with which we never have any musically relevant objective contact. Thus to examine the sorts of slots in conceptual schemes that one sees a statement as occupying is to isolate the sort of questions in response to which that particular explanation is produced. And to examine the determinacy of some explanation is to examine the usage by musicians of the specific expressions involved in that explanation; specifically, it is to characterize the possible statement-contexts of any particular expression as relatively fluctuant or relatively stable.

Now there appear to me to be two types of questions to which most musical explanations can be considered responses; these can be termed, appropriately enough, why-questions and what-questions. Why-questions (of the sort I'm going to discuss now) seem to reflect what one might describe as a search for generalizations, that is, an essentially scientific or utilitarian search, which presumably has the pragmatic goal of predicting future occurrences of comparable events. Thus we might ask, "Why do avocados fall when you drop them?", and presumably our answer, if we find one, will reflect on any such future experience with avocados, as well as on a wide range of other events, if that answer is formulated broadly enough. To deal with such a question we hypothesize certain regularities based on other statements in our conceptual schemes (or refer to familiar regularities already hypothesized, by ourselves or others). Although regularities invoked in generalizing explanations are often referred to as "laws," they are, rather, merely component statements of more comprehensive conceptual schemes, and as such are as open to revision as any such component. That such regularities are also referred to as "inductive" points out their shaky empirical status, in that they are purported to be generalizations about all cases even though they are "inferred" by hypothesizing some common features in a finite set of observations.

Perhaps the most obvious musical why-question in search of an answer is something like: "Why is this piece successful as it is?" (This assumes that the "piece" in question has been more-or-less well-determined, at least to the satisfaction of the musicians involved.) "Why" in such a question often seems to imply a need for justification, asking "why is this a coherent or even valid piece"; it may even be implied that close relatives or variants of the piece in question will automatically be less "coherent."

A class of possible generalizations for use in this sort of why-explanation might go as follows: "If a piece P contains a certain set of features (specifically delineated somehow), then P is coherent." Such a generalization is clearly inductive and might be used for predicting future dealings with pieces. However, because of the specificity required for this sort of condition to be viable, one clearly runs the risk of acquiring a set of so-called generalizations which cumulatively assert: "If P is contained on the list of pieces . . . , then P is a coherent piece," or, rather, "The following is a list of coherent pieces: . . ." Furthermore, it is difficult to see how to productively test this sort of generalizing explanation; given any such generalization which doesn't merely list the pieces to which it's applicable, it's not difficult to imagine writing a thoroughly awful piece which, however, satisfies the given conditions.

In fact, it might be argued that this sort of theory of coherence, in that it seeks merely to divide the set of all possible pieces into two distinct subsets, say the "coherent" and the "incoherent," is less a theory than a decree, and as such is hardly worth our attention. Certainly it is difficult to imagine ever arriving in such a way at some statement which convincingly answers the original question: "Why is this piece coherent?" In fact, I suspect that notions like "coherence" may be too elusive and personal to be pinned down by objective or public generalizations of any sort. That is, one's sense of the "coherence" of something may be more productively considered a reflection of particular statements about the "things" involved, within the context of particular conceptual schemes. Then, just as an investigation of pieces is nothing less than an investigation of the particular processings of music which get variously lumped together and categorized as "pieces," an investigation of a claim of "coherence" must be treated as an investigation of the details of the particular processing which led to that claim.

I suggest then that absolute standards of "coherence," even if realistically constructable, are irrelevant to musical explanation. For the primary point of explanations in analysis seems more compellingly described as "pinning down what it is that the analyst finds interesting or coherent in a piece." Thus, if standards of coherence and the like can be said to exist at all, they can hardly be anything other than individualized, subjective habits, tendencies, or preferences; and their invocation to justify an analysis can hardly be expected to strengthen the already quite reasonable claim that "this analysis is valid because it shows what I find interesting and coherent in this piece."

Of course, we don't have to limit our investigations of music to considering only our separate determinations about what is found to be interesting in each of, say, several hundred pieces. For it is certainly possible to devise more reasonable theories of coherence, by investigating how particular musicians go about their music-conceptualizing; that is, we can investigate what they seem to or claim to hear as "coherent," as well as what it is that they appear to consider instrumental to that "coherence." It might even be possible to devise specific generalizations for such theories by noting that certain musicians appear to share conceptual strategies (a point we often assume to be true to some degree of musicians with some musical experience in common, such as having had instruction in linear analysis). That is, we can observe whether musicians appear to listen for certain kinds of things in what we take to be certain pieces; or at least whether they often try to characterize the salient details of their individually considered versions of those "pieces" by using comparable expressions and statements. But even such theories don't produce a picture of musical behavior that is in any sense objective; any theory of coherence that I can manage to come up with will be colored at the very least by my particular way of slicing up music-thoughts into "pieces" and my particular way of using the expressions and statements involved.

Considering the particular expressions used in music-explanations leads one into the much broader conceptual territory of the answers we formulate to what-questions. Such questions are not completely removed from why-questions, of course, even in everyday discourse; for example, I may point to someone and ask "What is he doing?" and you may respond "He's conducting an imaginary orchestra"; although you have not explicitly invoked a generalization to answer my question, in producing a statement which necessarily reflects its position in your conceptual scheme you have indirectly reflected lots of generalizations known by you and upon which your answer depends, including as only the most trivial examples, "Conductors wave their arms just as he is doing now" and "Orchestras make their presence known, if not aurally, then visually." One might characterize the immediate focus of some questions as particularizing rather than generalizing, however, if such a question seems to reflect curiosity about something rather than a desire to predict comparable events—a curiosity, that is, to clarify the nature of a thing or to elaborate conceptual contexts into which that thing can be fitted. And in attempting to satisfy this curiosity, we produce statements containing, in addition to the basic language of logic and communication, expressions which we usually regard as connected in various ways with the "thing" being particularized and clarified, that is, expressions which we characterize as "referring" to various aspects of music and music-processing.

Now it seems to me that one can make a loose but still useful classification of such expressions, based on what might be called their "determinacy." One way of arriving at such a classification is by looking at the "things" we consider these expressions to "refer" to; that is, we can ask to what extent an expression is used to "refer to" the same or the same sorts of musical events by different speakers; one might call this a consideration of extensional determinacy. A second approach will be to consider the specific statement-contexts of an expression; in determining the kinds of substitutions musicians seem to be willing to make, we can hypothesize the sorts of positions within conceptual schemes any given expression or statement occupies; call this intensional determinacy. Loosely speaking, then, extensional determinacy is a question of consistency of what is "referred to"; intensional determinacy of consistency of what is actually "meant." The interaction of these two ways of considering determinacy produces an interesting three-fold categorization of expressions appearing in particularizing explanations.

First, consider expressions which are neither extensionally nor intensionally determinable, that is, expressions whose specific references to musical events we can't predict securely, and for which we have no way of delimiting viable statement-contexts. Such expressions I will call, for lack of a better term, "metaphors." Actually, this usage of the term "metaphor" complements a more traditional characterization of what it is to be a "metaphor," namely that which considers it as an expression "borrowed" for one statement-context or theory from another in such a way that some secondary connotations of the expression in question can be considered "transferred."

For example, if someone characterizes Webern's Op. 10/1 as "directed" or as "manifesting closure," it is clear that only secondary connotations of these expressions are intended, not the primary connotations of certain three-dimensional physical-space properties; it is equally clear that I cannot be sure what particular events this person considers as manifesting this "directedness" or "closure," nor can I really predict to what other pieces or events he or she might choose to apply the same expressions. Presumably, such matters could be specified; but if one surrounds a metaphor with such a specification, then in what sense is the metaphor still the carrier of the information? So what then is the point, if any, of using such expressions?

It seems to me that the primary role of "metaphorical" expressions in most musical discourse is one of summing up an array of statements containing more determinable expressions, and of signalling to one's audience the lines along which an inquiry has produced some interesting analytical observations. Thus if I announce that I find Op. 10/1 "directed," you might well interpret that remark along the lines of: "I have found some interesting large-scale patterns in what I take to be Op. 10/1, it is noteworthy that these patterns subsume the entire time-span of this piece, and you can probably enhance your own Op. 10/1's by looking for such patterns yourself." If I should characterize this piece in terms of "momentum," you might construe this as: "I have found a large number of mutually supportive and reinforcing patterns, so that I now find that almost every event of this piece has a niche in what I hear as a particularly compelling counterpoint of patterns." If I call this piece "static" on the other hand, read this perhaps as: "I have managed only to find a few large-scale patterns, so that I am essentially hearing the piece as a too straightforward succession of not unlike segments (even though these segments may well be internally differentiated)." And if I sum up my analytical findings by using expressions like "progression," "prolongation," or "balance," I am similarly directing your attention to and informing you of my interest in those findings.

"Metaphors" then seem a poor substitute for analytical observations, since they can, at least theoretically, be in some sense replaced by more elaborate statements containing more determinable expressions. However, metaphorical discourse offers a useful way of conveying one's interests and of obliquely suggesting large slices of more precise discourse in very few words—if one can only manage to avoid getting hooked and heeding the call of evocativeness to the exclusion of determinability.

Much of the work we do as theorists is explicitly concerned with expressions of the second kind, which I will call "presumptives"—those expressions whose referents are relatively clear and predictable though their exact senses remain obscure. For example, the expressions "rhythm" and "rhythmic": there is seldom any serious disagreement as to whether a passage is "rhythmic" or not; and if someone points to a spot in a piece and announces, "That's a rhythm," we may think that statement a bit strange but would probably not regard it as "wrong." But can any one of us really claim to be able to arbitrate the "real" or "objective meaning" of the word "rhythm"? The notoriously disparate statement-contexts in which these expressions occur seem to reflect distinct and incomparable senses of "rhythm": some people talk of "rhythms" as if they are equivalent to patterns of durations in general; others talk of "rhythm" and "meter" as distinct aspects of the durational and dynamic organization of music; and another view, one which I happen to consider more interesting, is to avoid any distinction at all between the expressions "rhythmic organization" and "musical organization."

The most striking aspect of such presumptives is the extent to which they have led to the construction of theoretical systems. For theorists, in an attempt to pin down precisely the viable contexts of such expressions, have devised formulations using what are intended to be more determinable expressions. What has been most clearly demonstrated by this activity is just the disparateness in the usages of the expressions involved. Consider, for example, all the different formulations of what it is for a piece to be "tonal," even the variations within a single "macroschool" of thought on the subject, such as the students and interpreters of Schenker.

Those presumptive expressions which have been subjected to the most elaborate systematizing also turn out to be those which have had the most pervasive effect on musical thinking at large, perhaps as a result of the general commitment to that systematizing. Thus, whichever "tonal" notions you happen to subscribe to, that system has no doubt acquired almost the force of a linguistic convention for you, so that you may even find it impossible not to apply the system to certain pieces—hence the widespread feeling that certain "pieces" not only are usually processed as "tonal," but actually are "tonal." Thus, such systems come to reflect not only dispositions about language-usage but expectations about music as well; we find many of our various theories of coherence strongly oriented toward explicating what it is we try to hear in music in terms of those systems we are presumed to know.

In the systematization or conventionalization of certain presumptives, especially those of "tonality," it is notable that a large number of expressions more naturally regardable as "metaphors" under this sort of classification have acquired some of the flavor of presumptives. In other words, I claim no ability to predict the application of, say, the expression "phrase" to a piece such as Op. 10/1 (unless it is made clear that this expression is meant to be temporarily substitutable for the expressions "instrumental part" or "events subsumed under certain notated articulation marks"). However, there may well be some general confluence of opinion about where the "phrases" are in Chopin's E major Prelude; and presumably what confluence there is derives from our various ways of processing this Prelude as "tonal," many of which seem to yield comparable large-scale slicings of this string of events.

Two other metaphors which have acquired unusual stability in certain contexts are the expressions "strong beat" and "weak beat." One can assume that it is essentially predictable that a Western musician will look for pervasive durationally-regular patterns of the sort we call "meters" in what he or she considers "tonal" pieces (although the characteristics of such patterns are notoriously difficult to specify); one of the principal factors behind such a strategy is, of course, the fact that most "tonal" scores are notated with just one "meter" throughout. In pieces where such a "meter" is so notated or where it is otherwise predictable that someone will hear such a "metrical" patterning, we can feel reasonably certain what events will be referred to as "strong beats," at least within what we consider the "measures" of that pattern. But what about the sorts of large-scale "metrical" patterns which many theorists pursue, that is, in searching for such things as "hypermeasures" or "structural downbeats"; in what non-metaphorical sense does the term "strong beat" refer to event-slots within such a large-scale patterning? In what sense can one characterization of an event as a large-scale "strong beat" be inherently more correct than some other characterization? And what about non-tonal pieces; do we really get a more-than-metaphorical sense from talking about "strong beats" in, say, a piece by Stravinsky?

For such reasons, I find that these system-colored metaphors are still most productively considered as metaphors, even in what one might consider their more determinable contexts. For the primary role of such expressions still seems to me to be characterizable as indicating or suggesting more specific things to be looked for, rather than getting at the details of what's being heard. Even the "phrase"-division we all might agree on in the Chopin Prelude is merely one slicing-up of that piece; we may agree that this segmentation is productively considered, especially in counterpoint with other segmentations and patterns, but "phrases" per se have no absolute status over competitive slicings. And surely it is the sense in which some event can be considered the "strong beat" in some "metrical" pattern which we are most interested in expressing, that is, the particular patterns in which that event figures in counterpoint with its "metrical" role.

The third category of expressions is relatively straightforward: those which fluctuate only relatively little in reference or in specific usage from person to person—for example, the expressions "pitch," "interval," "time," "duration," "order," "succession," "timbre," "loudness," "equivalence," and so forth. In addition, it is not unreasonable to include here expressions which, though perhaps not in common usage, can be supplied with explications straightforward enough to permit of this kind of determinable usage in musical discourse by anyone who cares to do so: for example, "event"—if used to mean an irreducible component of a piece, "note"—meaning the notational manifestation of an event in a traditional score, "pattern," "segmentation," and so forth. One might call this category of expressions the category of "assumptives."

To close, I will just mention three questions which seem to me even more pressing from this point of view than they might otherwise appear. First, the question of sophistication: is an account of a piece using presumptive expressions "more sophisticated" than one using primarily assumptive expressions? Or is it the other way around? (I have heard it claimed both ways.) Or is the notion of sophistication a valuable measure of explanations at all? I suspect that it may not be, or rather that the notion of sophistication, like the notion of simplicity, may be so difficult to specify, that is, so reflective of personal conceptual schemes, as to be little more than a loosely metaphorical standard. But this is only a guess.

Second, the question of satisfactoriness or adequacy, notions which are more obviously relevant; but again how to specify standards of adequacy in any public way? Our traditional distinction between explanations and mere descriptions (like, say, program notes) seems to reflect opinions about satisfactoriness, especially if you grant my claim that any statement about a piece is in some sense explanatory. Clearly, satisfactory explanations are not limited to just those statements utilizing only assumptives, or only assumptives and presumptives, or all three types of expression. If public criteria are formulable for explanatory adequacy, they are bound to be much more complex than this; and of course they lead one directly from the characterization of particularizing explanations to the formulation of generalizing explanations about the musicians doing the particularizing.

Finally, the question of priority: all of the expressions and theories briefly outlined here can be described as "a priori's," in that they constitute the conceptual equipment one brings to a piece; and certainly pictures of music which one would develop without any such equipment would be remarkably featureless and barren, if indeed they could be called pictures at all. What I have in mind then is not the question of what do pieces depend on, but rather the question of what do pieces necessarily depend on, in the sense of which of these expressions, abilities, theories, or even concepts is music inconceivable without. I confess that I have a strong inclination to claim that music may in fact be at least conceivable in terms of assumptives alone, but this question seems much too deep and problematic to be adequately resolved by any such off-the-cuff pronouncement.

1W.V. Quine, "Two Dogmas of Empiricism," Philosophical Review, 60/1 (January 1951); reprinted in From a Logical Point of View (Cambridge: Harvard University Press, 1953; 2nd ed., 1961), p. 43.

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