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http://www.jstor.org Music and the a Priori Author(s): Thomas Clifton Source: Journal of Music Theory, Vol. 17, No. 1, (Spring, 1973), pp. 66-85 Published by: Duke University Press on behalf of the Yale University Department of Music Stable URL: http://www.jstor.org/stable/843118 Accessed: 13/08/2008 16:58 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/action/showPublisher?publisherCode=duke. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit organization founded in 1995 to build trusted digital archives for scholarship. We work with the scholarly community to preserve their work and the materials they rely upon, and to build a common research platform that promotes the discovery and use of these resources. For more information about JSTOR, please contact support@jstor.org. 66 MUSIC AND 1. Introduction In our time, certain attempts at theory construction seem to be dangerously confusing the ideal of objectivity with the un- real of anonymity. For example, it is part of the business of a theory to define its terms. Sometimes the definition is cast in a suitable metalanguage and formalized beyond the reach of space, time, and culture. Such a definition is set up as a norm for logical discourse rather than as a guide for musicalexperi- ence. The result is familiar: the validity of the theory itself can be tested only by referring back to the truth value of its defining statements. Under such circumstances, theory and THE A PRIORI THOMAS CLIFTON experience follow separate paths. There seems little reason to doubt that this state of affairs expresses the intentions of the theorist. But the irresistible urge to formalize and generalize is met head on by the immovable presence of music as a social phe- nomenon, that is, something to which people listen in order to have musical experiences and exhibit musical behavior. So that if someone wants a theory of music to be formal and gen- eral, he should also want to refrain from depersonalizing the theory. Is this possible? What slight-of-hand is required to juggle the formal with the material, the general with the partic - ular, and the universal with the personal? What is the terrain like which lies between a synthetic (for Kant) a priori state- ment such as 7 + 5 = 12, and the very particular musical situa- tion whereby, for some person, seven tones plus five tones do not necessarily add up to 12 tones? These questions relate to a rather well-worn but still misunder- stood problem: the problem of the reciprocity between music, as a process existing independently of a person, and a person, whose attentive presence is needed to make a musical process meaningful. Without the exploration of both poles of this re- ciprocal relation, a theory of music will tend to overstress its objective or subjective portions. The result is either anonym- ity or autobiography. One way to avoid these detours is to adopt a broader interpretation of the a priori than was formu- latedbyKant. We are not "subjects" who impose laws of thought onto the experience of objects; we are people at home in the world and in bilateral dialogue with it. Nor can we be satisfied with assigning the a priori to a purely formal domain: the do- main of logically necessary and universally valid propositions. Such propositions are not proofs, but results of reflective rea- soning. But music is not something about which a proof need be supplied, nor is musical behavior the result of reflective reasoning. Music is the justification of reasoning, and as such, it is presupposed in all reasoning about it. II. A General Description of the A Priori We listen to a musical work and experience its sense. In the presence of a musical idea, we think and feel musically. Some- times the musical thought is crystalized into a precise melodic theme or subject, sometimes it is presented in a more general manner, involving textures, colors, or gestures whose identity would not be seriously jeopardized if their individual atoms were rearranged or exchanged for other atoms. We listen to these things, and sooner or later conclude that whatever the musical message might be, it did not come to us as the result of a laborious and systematic thought process, even when that process involves a detailed study of compositional technique (itself the result of someone's systematic thought processes, and not necessarily the composer's). As with logical discourse, an understanding of compositional technique presupposes an understanding of music. This is verified by considering that the class of people who understand music is larger than the class of people who understand compositional technique. (It won't do any good to try to rebut this by arguing that there are kinds and degrees of understanding, since, in any case, this is precisely the point.) What I am approaching is something which is not a presupposi- tion to musical understanding, but the foundation, the Ursatz as it were, of all presuppositions. This foundation, which grounds all logical discourse as well as the experience which is the presumed correlate of a meaningful discourse, is called an a priori. In this section, it must be demonstrated that there is no essential conflict between what is empirically given and what must be given as an a priori condition of musical being. Furthermore, certain characteristics of the a priori itself must be developed to show how it differs from a generality, a rule, or an innate idea. This last suggests that, while the a priori significance of music may not be teachable, it is learnable. This, in its turn, tells us something about the relation between the a priori and history, which brings us back full circle to the a posteriori of historical facts. When it is recognized that the Kantian dichotomies between concept and intuition, man and nature, reason and perception, and fact and meaning are di- chotomies of language and not of existence, the a priori itself takes on a new relevance, especially to the relatively unex- plored regions of musical experience. A. The A Priori and Experience Kant started his Critique of Pure Reason bravely enough by saying that "There can be no doubt that all our knowledge be- gins with experience. " * But he didn't follow through. He immediately distinguished a priori knowledge as that which is not derived from experience but from a universal rule. It was set in opposition to a posteriori knowledge, that is, empirically derived knowledge. To rejoin this unfortunate division, one must first say that knowledge not only begins with experience, but ends in experi- ence. The a priori is for the a posteriori. This statement is especially significant for the arts, whose forms are sensual and given in perception. Secondly, one must consider the way the word "necessary" is used to characterize both the a priori and the a posteriori, thus blurring their distinction. To grasp the meaning of the opening bars of Mozart's C Minor Piano Sonata, it is necessary to hear the tones as members of an ascending line. The perception of "ascending line" is at least part of the meaning ofthe opening gesture. Expressions like "ascending" and "line" are necessary, irreducible aspects of the experience of this sonata. Such words do not refer to facts, since there is nothing literally ascending, and the room is not 70 suddenly invaded by lines. The science of acoustics has nothing to say about ascending lines, nor is it its business to say any- thing about them. It can talk about certain proportions of in- creasing frequencies, and the fact that certain tones appear discretely in a certain time sequence. But if this "ascending line" is not, strictly speaking, in the room the way tables and chairs are in the room, neither is it in me. The experience of "ascending line" is my experience, but it is not a purely private experience. Another person can report that he also experienced this "ascending line. " Three important points should be considered before going fur- ther. First, the a priori is not dependent upon a consensus of opinion about whether a certain state of affairs is the case or not. As an a priori, "ascending line" exists independently of any given number of people, in the sense that their presence does not create the ascending line, nor does their departure destroy it. The second point is to realize that "ascending line" is a meaning and not a fact. As such, it may be a necessary conditionto an authentic musical experience, but it is a neces- sity which is not necessarily given all the time. Presumably, its meaning is not necessarily given to an infant, an Australian aborigine, or, for that matter, a great many members of the contemporary North Atlantic community. In fact, music itself is not necessarily given, in the sense that it is not recognized as such, on many occasions. Musical meaning is not neces- sarily guaranteed, but when it does present itself, it does not do so as the conclusion of an elaborate and systematic mental process. In this sense, it can be said that music gives its meaning immediately. This does not mean that musical mean- ing is given to everyone, or that it is always given at once, at first hearing. "Immediate" here means without the mediation of mathematical, logical, or otherwise symbolic methods. These methods follow from, and render explicit, the immediately given musical meaning. (This to be read with tongue in cheek and fingers crossed.) The final point is implicit in the above statements. That is, the a priori of "ascending line" is im- manent in the musical otject itself. One must carefully note the direction of the logic of experience. It proceeds from the object, rather than being imposed by the subject. The ascend- ing line is "in" the object, it is a necessary appearance of the object. But since there are no formal criteria to guarantee a musical experience, the a priori finds its main function in pro- viding a basis for deciding upon the objective factors of a mu- sical experience, when it occurs. Suppose it is true that the opening two measures of Mozart's C Minor Piano Sonata pre- sent the rhythmically active gesture of an ascending line, a 71 feeling of controlled force, an atmosphere of some degree of tension, terseness, and expectation. . . . (The description could be infinitely refined.) Well, if all these statements are true - and their evidence is that of self-validating experience, not of inference and proof - then they are true, a priori, and we at least have a basis for continuing the discussion. This is a very brief sketch of what is entailed by the word "necessary" as it applies to the a priori. It is only fair to give equal time to the urgent claims of the posteriori. Certain em- pirical conditions cannot be denied: The experience of this sonata necessarily entails either the physical presence of a person, playing upon a musical instrument which is capable of producing a sound spectrum, and in a sound-conductive atmos- phere; or, the remembering, imagining, or anticipating of such a performance. The person engaged in these acts must nec- essarily be capable of perceiving, at least pre-predicatively, psychologically discriminable intervals, tone color, intensity, volume, etc. Certainly an equal-tempered interval is a mat- ter of empirical history. For that matter, so was Mozart. The meaning of this sonata cannot be dissociated from all his other compositions, the compositions of his contemporaries and predecessors, and the social conditions of the time. These are all attendant contingencies to actual experience; something else could have happened. But if something else did happen, then our experience of this sonata might well be different. For example, what if it were Mozart's only extant piano piece? What if it were the only 19th-century composition to begin with an ascending arpeggio? We can only conclude that Mozart and Vienna (where he wrote the C Minor Sonata) were necessary to each other, which is to say that style, or manner, is not a superficial covering draped over an essential structure. As the result of the interaction between a man and his empirically given environment, style can also be regarded as an a priori necessity for the experience of a concrete and particular com- position. Still, the necessity of both the a priori and the a posteriori does not create a reversible interaction between them. Facts and meanings necessitate each other, but the attempt to make one the genesis of the other appears to be misguided, because they reside on different and not necessarily connected levels of human behavior. No amount of factual information can con- vince a person that the object under consideration is a musical object having musical significance if he has never experienced that significance. In this case, facts remain opaque instead of assuming their proper transparency. Musical significance is 72 not in the facts themselves, but is experienced through them; intervals, as acoustical facts, are not music. Music is heard shining through the intervals, but this does not mean that any- one who can hear intervals can hear the music, or that anyone who can experience the music can name the intervals - if any. Thus, it is similarly difficult to move from the meaning to the fact. The significance of the Well-Tempered Clavier is not that it provides examples of equal temperament. The opening of Mozart's C Minor Sonata is not essentially an arpeggio, al- though it pleases us to call it that since meanings are more elusive to name, being more real. Bearing all these things inmind, as well as a number of details that must be left unsaid for now, it becomes difficult to synop- size the relation between the a priori and experience. In the first place, a technical word has to be brought in: the term "transcendence." We say that the a priori is given in experi- ence, but that it transcends any particular experience. In one way, then, it is evident that the a priori is not dependent upon experience. On the other hand, the fact that the necessary conditions of the a priori are not always revealed suggests that the transcendental itself is made knowable only through experi- ence. Perhaps this dualism can be resolved by considering the relation between general and specific modes of experience. Meanwhile, I take refuge again in Mozart. The opening gesture of the C Minor Sonata has been described as an "ascending line, " etc. The transcendental aspects of this description include the following: 1) its significance tran- scends any particular performance (although a bad performance might fail to reveal any significance); 2) the sonata's signifi- cance is independent of the mode of experience, be it perceiving, imagining, judging, anticipating, wishing, etc.; 3) the experi- ence of "ascending line" involves not only cognition but re- cognition. Insofaras "ascending" may be predicated of other experiences, it is not limited to this or any particular musical appearance. The implications of this statement are significant for any descriptive theory and bear closer examination at this time. B. The General and the Particular One might get the impression that the a priori, as a transcend- ental meaning, is too general to be of any use. After all, the experience of "ascending line" invokes the general notions of space, time, and motion. These notions seem to be presup- posed in any conscious referring to a particular instance, since, 73 clearly, we have to know beforehand what "ascending line" is an instance of. Yet if the a priori strikes one as a generality, he cannot be satisfied to let it remain so. In this, the differ- ence between the general and the abstract can be observed. The former is always found in a situation, always attached to the world we know. It is not only possible to give an example of a general concept, it is absolutely necessary to do so if we are to refrain from idealism. Implicit here is a distinction between that which is abstracted and the concept of the abstract itself. There is nothing abstract about "ascending line, " al- though, for purposes of exemplification, "ascending line" is temporarily abstracted from its setting. Furthermore, the general-particular relation is not quite like a genus-species relation. Thus Dufrenne feels justified in saying: The a priori possesses the generality of a meaning which may belong to very dissimilar objects and which introduces a special relationship between them: a correspondence of analogy more powerful than resemblance. The diversity of examples. . . attests that they are not the species of a genus or the members of a species- i.e., objects sub- sumable under one and the same definition. They are rather objects animated by the same meaning. *2 I canperceive ascending lines in a painting as well as in a mu- sical composition, not because I have performed an induction, moving from an examination of X number of individuals to the general concept which embraces all of them. This similarity of meaning, which is apprehended in both the painting and the music, is presented without mediation, intuitively, and as such, it constitutes the beginning of knowledge. Woltersdorff has schematized the relation between the general and the particu- lar with considerable linguistic precision. 3 Adapting his scheme for our own purposes, it can be said that: 1) "ascend- ing gesture" is a case of the general concepts of space, time, and motion; 2) space, time and motion are exemplified in Mo- zart's C Minor Sonata; 3) "ascending gesture" is an aspect of Mozart's C Minor Sonata. Now, it has been argued that general concepts (or non-individ- uals) enjoy at best only a purely verbal (nominal) existence. The tragic, the joyful, the comic, are only words, whereas what really exists is Hamlet, Beethoven's Ninth Symphony, or Charlie Chaplin; that is to say, individuals. However, the problems arising from this attitude border on the perverse. For one thing, it seems to me that one is left without any justi- fication for experiencing that this sonata which I remember is 74 the same one whose performance I expect to hear next week, or that this sonata which was mutilated by an inept performance last month is the same one whose performance I enjoyed last night. What indeed wouldwe ever mean by a goodperformance or a bad one? But we can take an example of something even more personal: the case of our own bodies. How could I, as myself, maintain my identity through the birth and death of millions of cells of which my body, as an object, is made? True, in a certain sense, it can be said that I am not now what I was thirty years ago, but this only compels the distinction between an I as a person and an I as a body. My person is what I mean to myself and to others, and as such it is given immediately as an a priori. My body, on the other hand, is indeed this physical object composed of organic materials. My person is that which is more or less truthfully revealed to me and to others, while my body is what I and others have to learn about. The situation in music is similar. We not only have to distinguish between music and notation, but have to realize that music is a "person" which addresses us, and with which we engage in dialogue. Just as the surgeon's knife can never find my person in my body, since my person is what motivated the knife in the first place, the analyst will never find music's person in its body, since it is the music which motivates the analysis. Analysis does not verify music. (This is not to say that analysis is pernicious, but only that its aims and limita- tions should be clarified.) The moment we consider a composition as only an individual, it loses its individuality, since it would lose itself in the proc- ess of its own coming-to-be. Such an individual would be like one of those sub-atomic particles whose creation demands its destruction: it has an instantaneous, homeless existence. On the other hand, the pure generality is not even allowed to seek a home. It is the result of an attempt to interpret the world from above it, or from outside it. It is standpointless, without perspective, foreground, or background. It is indeed in this sense unreal. But these problems exist only because people are unable to speak contrapuntally. Actually, the general and the specific comprise a kind of counterpoint whose lines are dependent upon, and ihteract with, each other. At the root of the separation of the general and the particular lies the separa- tion of concept and intuition. But writers of various philosoph- ical allegiances have shown considerable unity in bridging this separation. Piaget, for example, suggests that the radical separation of intuition from logic or axiomatics has never been achieved in practice; and in fact, is un- 75 attainable in principle. . . . The "schema" formed by formal logic always retains traces of intuition, while the primary intuition requires some degree of schematization in order to possess a structure. * 4 My understanding of Mozart's C Minor Sonata is limited neither to an intellectual accounting of certain of its sonic properties, nor to a raw and uninterpreted perception of those properties. I do not attach a metaphorical image derived from visual ex- perience onto a collection of discrete pitches in order to call the result an "ascending line." Finally, I do not experience musical space as an empty container which I proceed to fill with this "ascending line. " The gesture presents itself as a meaning for which thought and action have collaborated, so that the experience of "ascending line" is not so much a matter of what I think, but of how I act. I have "carnal knowledge" of this gesture because my eyes and hands have learned what such a gesture "feels" like, and if it is empirically true that my senses are distinct, it is a priori true that they are unified, and that they can teach each other. We not only hear motion, in the form of lines, bands, curves, and angles, but we hear colors and textures as well. However, this world of musical space is too vast a topic to be explored here. I want to move now into a brief consideration of the difference between the a priori and the theory of innate ideas. C. The A Priori as an Aptitude The distinctionbetween the a priori and innate ideas is a rather complex one to make, and a clarification of the one is usually made at the expense of the other. Piaget refused to consider space and time from the standpoint of the a priori because of his commitment to experimental psychology, yet his conception of the a priori appears tobe limited to that of a universal rule. However, to identify the a priori with innate ideas would be to repeat the error on the side of the person himself by making him out to be a kind of universal subject, removed from his personal development and environment. Once these errors are penetrated, it will be seen that there is no fundamental disagreement between genetic epistemology and the existential view of the a priori. Nowhere does Piaget claim that the child creates or invents time and space, but only that he constructs time and space. But even so, this is not quite accurately ex- pressed. It is not time and space itself which the child con- structs, but only the interpretation of their actualization in em- pirical circumstances. This is more in line with the fact that we grasp the sense of an individual musical composition before 76 we fully understand what music is, or that we learn to speak before we know what language is. There is always a first time in which we experience a musical composition as such, although we may not be able to call it that. Still, the dated occasions on which we experience musical compositions also serve to awaken the a priori meaning of music itself. Even Piaget con- cludes that Musical rhythm is, in fact, the most intuitive of all time measurements and is certainly not imposed on us from outside. The same is true of stress in common speech and quite particularly of metre in poetry. Here, too, it was not the theorists who invented the metre but the bards, thus showing that there is no contradiction between ele- mentary arithmetic and the expression of rhythm in inner life. *5 Genetic epistemology has made its contributions in the descrip- tion of those conditions whereby the a priori is awakened. This awakening is not felt by everyone in the same manner, nor is it developed to the same extent by all people. If different cul- tures and nations produce different musics, still it is the a priori which enables a person of one culture to say, about the music of another culture, that "it sounds strange," since the notion of strangeness is grounded on some resemblance, how- ever slight, to the music one is at home with. It is for this reason that education, habit, and environment play an essential role in the clarification of the a priori. Is it not curious that this brief description of the a priori thus ends with a consideration of the nature of habit? But we have to question two alleged characteristics of habits: that they are acquired, and that they are determinate. (A third characteris- tic of habit, whereby the present is made the slave of the past, will not be discussed here.) Of course it is true that habit is an acquisition, but one must also consider that it might be a predisposition as well. One acquires the habit of playing an instrument because he possesses a certain capacity, an apti- tude, to do so. Viewed in this light, habit is understood not as a diminution of one's individuality but as formative of it. Indeed, it is through a study of habit that we realize that the activity of making sense out of music is neither automatic (since not everyone experiences music the same way), nor the result of conditioning (since I am free to accept or reject any particular way of experiencing music). The development of certain listening habits does not determine, once and for all, that I will forever experience Mozart's C Minor Sonata exactly 77 the same way. It does not have to have any significance for me at all, as when I hear it being played by someone down the street while I am engaged in conversation with a friend, or it can have a kind of negative significance, as when it is played to a starving man whose only thought is for more substantial nourishment. The very plenitude of contingent circumstances which one can imagine would either inhibit or reveal the a priori significance of this sonata seems to argue against these circumstances as the efficient cause of its significance. Once again, then, a priori significance is referred back to the per- son whose habits vitalize the aptitude to attune his body to some circumstance which acquires meaning in a specifically musi- cal way. Quite possibly, in the absence of this aptitude, one would not be able to benefit from, or even develop, the habits which determine whether this or that circumstance is a musi- cal one. So the a priori is not an innate idea, if by the latter is meant a kind of knowledge. Rather, the a priori is access to knowledge, and as such, it is something to be known, as well as a condition of knowledge. Before going any further, let me synopsize this description of the a priori. First, we can still retain the idea of a formal a priori by regarding it as the form of an object, not the form of a logical statement, and by regarding "object" as a meaning rather than a matter of fact. Since it is thus formative, the formal a priori may be co-extensive with a number of physi- cal objects. The formal a priori, interpreted as the form of meaning, is that which links existent objects - not merely thinkable objects - so that we may have multiple experiences of a single object as well as a unified experience of many ob- jects. But Dufrenne has described many other kinds of a priori, some of which have been informally discussed here. For ex- ample, it has been pointed out that the a priori is anchored in particular experiences, yet independent of them. We thus come upon a material a priori, which can be regarded as a form necessary to a particular object - not an object-in-gen- eral - if that object is to appear at all. The formal a priori does not have to specify a content, but the material a priori is always concerned with the meaning of this "X". "Ascending line" is therefore both a formal and material a priori: it is formal because it transcends the particular matter of Mozart's C Minor Sonata, and it is material in being a form necessary to this sonata. But let me clarify that "ascending line" is not a mere item in an intellectual inventory of qualities, but a con- crete appearance (inthe object itself) of a transcendental mean- ing. Because the material a priori is bound up withparticular objects or events, it can be expected to show considerably more variety than the formal a priori. We shall soon see that this is indeed the case. The materiality of the a priori, together with the merging of intuition and conception, suggest a third kind of a priori: that which is given in perception. "Ascending line" is something which I perceive, and perceive immediately if I perceive it at all (using "immediate" in the sense defined above). The link- age of the perceived with the a priori raises a host of problems which Dufrenne himself deals with. Let me suggest that one problem - that of regarding perception as lying wholly within the field of the empirical - can be avoided by considering that perception is never simply perceiving what is empirically given. Perception is essentially ambiguous because it is simultan- eously complete and incomplete. The perception of the opening of the C Minor Sonata is a complete one; I have no wish to hear either something else or something more. Yet perception is incomplete because it is never an isolated act, but it is always accompanied by acts of imagination and understanding, feeling and volition. Furthermore, perception is incomplete because the object of perception is never completely given, so that while we perceive the given, we experience the not-given of the object as well. Its not-givenness is by no means to be equated with non-existence. The whole sonata exists, which is why we perceive it as unfolding in time. The final type of a priori intimated here is what Dufrenne calls acorporeal a priori. Two sides of the corporeal a priori can be summarized here: the person as meant to himself, and the world as meant to the person. The person is a meaning to himself (and possiblyothers) which far transcends the value of his flesh. He is given to himself in an immediate way, so that, even in the dark, he does not first have to solve a problem in coordinate geometry before he can bring one hand to touch an- other. Secondly, the person is the general vehicle of musical comprehension. We can speak meaningfully of musical move- ment because our bodies know how to move. My body is a nec- essary condition for the personal knowledge of such musical- topological relations as betweenness, nextness, enclosing, en- closed, separation and order. Bearing these distinctions of the a priori in mind, we can now turn to some examples of the a priori as they are presented in music. III. The A Priori in Music A twofold purpose motivates this section: to name and describe some (not all) musical a priori, and to distinguish them from 79 meanings which belong more on the side of the empirical. In this way, we should be able to develop some criteria for de- ciding whether a certain musical meaning is a priori or not. Musical time is an a priori, but tempo is not. Time is a tran- scendental, since it is a necessary aspect of the world. How- ever, tempo is that aspect of time which we must learn to measure. The same person who can experience the a priori relation between time and feeling also must learn to play in tempo. Tempo is a performance problem, and it becomes more of a problem the further back we go in history. But mu- sical time is not that kind of problem. Rather, it is the foun- dation of all problems of tempo; it becomes problematic only when we try to describe its varieties. Even then, time itself is not problematic, but only the attempt to catch the word which will best describe its appearances. However, we have no trou- ble talking about tempo. "Play this piece at J = 80mm," is a perfectly clear, complete statement. This suggests that the relation between time and tempo is one of ends to means. Time is the meaning which only a correct tempo can present. Harmony is an a priori, but a supertonic triad is not. The harmonious - that is, a balance of contrasts - presents itself without mediating operations. No "if. . . then. . ." procedure involving the collection of elements, their addition, and their final inspection, is required to deduce the meaning of harmony, since harmony is not deducible. On the other hand, a super- tonic triad is a fact, not a transcendental meaning. "Super- tonic triad" is not a term describing the experience of a cer- tain harmony; it is a member of a vocabulary of technical terms attached to, and explicative of, a system imposed by the mind on the harmonious object. In identifying supertonic triads, we only demonstrate that we have learned the system, not that we have learned anything about music-as-harmonious. Dissonance and consonance are a priori, but the ratio of vi- brating strings is not. Dissonance, as an appearance of in- stability and disunity, not only transcends pitch relations in music, but music itself. For example, "dissonance" has be- come a sociological term used to describe certain human re- lationships. What makes so much of early music theory rather dreary to read are the repeated legislations enacted by theorists to make intervals dissonant because ( ! ) the vibration ratios are 9:8, 16:15, or what have you. Acoustical facts can never be the efficient cause of dissonance or consonance as experienced. At most they can provide the setting for such experiences. Polarity and opposition are a priori, but sonata form is not. Sonata form is a particular way of celebrating these a priori, which also make their appearance at the heart of the drama, in certain play forms and other ritualized behavior, and in certain myths. The appearance in history of sonata form had to wait until the elements of polarity and opposition could be structured in particular ways, both synchronically (e.g., fig- ure-ground relationships) or diachronically (e. g., contrasting ideas presented in a temporal sequence). As general forms, polarity and opposition become inhabitable by drawing from a matrix containing (but not limited to) the following characteris- tics: 1) conflict, which appears not only in music but in cer- tain sports and battlefield maneuvers; 2) resolution, which may take the form of either a conjoining of previously opposed ele- ments (as in the closing measures of Mozart's "Jupiter" Sym- phony), or an overcoming of opposingelements (as in the myths of rebirth or resurrection); 3) transformation, which has both internal and external applications. (Here, transformation means any operation performed on elements to effect a varia- tion of some kind.) An internal transformation of opposing elements within a particular work may either intensify (as in the case of Schubert's posthumous Bb Sonata) or neutralize (as in the case of Beethoven's Sonata Op. 101) the opposition. Ex- ternal transformations may be observed in the identity or si- milarity of structure of sonata forms exhibiting a wide variety of styles, instrumental media, tempi, etc., so that it becomes meaningful to say that both the first movement of Mozart's C Minor Sonata and Brahms' G Minor Rhapsody are in sonata form, only if we consider the transformations of the form which make Mozart's music different from Brahms's. The point be- ing made here is not subtle: learning what sonata form is, as a lived experience and not as a scheme, involves self-knowl- edge, or, more precisely, the recognition of ourselves in the sonata. Polarity and opposition are meaningful in sonata form because they are already meaningful as forms of bodily be- havior. Order is an a priori, but a twelve-tone row is not. If the state- ment, "I experience order in this composition, " is true, it is a priori true, and not because other statements of a stipulative nature are true. Twelve-tone rows are not the cause of order in a twelve-tone composition, but the experience of order can justify the analysis of that composition. An ordered experi- ence implies an objectof that experience, but that object is not likely to be found on the level of, say, foreground invariances of dyads. Order does not necessarily come out of the com- poser's workshop. It is not necessarily the result of the per- formance of a score, but of a listener's performance, the ac- tive-passive behavior which he elicits as the constitutive agent of musical significance. It is for this reason that the following sentence by Milton Babbitt is guilty of the genetic fallacy (here, of making empirical objects the cause of states of conscious- ness): Among any events in [Moses und Aron] coherence and con- tinuity are effected through set forms, transpositional levels, melodic, harmonic, and rhythmic motivic ele- ments, individual and composite rhythms, timbre, texture, and the interrelation of all these factors with the ideational and sonic structure of the text. *6 Here, I assume that coherence and continuity are states of consciousness, not words capable of being rigorously (mathe- matically) defined. In any case, a defined order is not nec- essarily an experienced order. Therefore, probably the best lesson we have learned through music's brief flirtation with serialism is that the difference between a composer and a lis- tener is not what we usually think it is. The responsive lis- tener does not create the composition, but he constitutes it as meaningful for him, and if the composition created by the com- poser is not quite the same as that constituted by the listener, still itis the listener's composition which counts for him. In short, order is constituted a priori by the listener, not im- posed by the composer. If we experience order in a composi- tion, it is probably because the composer has also been listen- ing - to himself and to his composition. These examples of musical a priori are too few to serve even as an introduction; they merely state the problem. An investi- gation of the a priori forms of musical space, for example, would result in at least a monograph. But perhaps enough has been outlined to identify various kinds of a priori at work, and to distinguish them from their empirical associates. All the examples presented have this in common: Musical a priori are meanings given immediately in a musical context. Rather than thinking of the a priori of time, harmony, dissonance, etc., as universal conditions for the very being of music, these a priori are regarded as immanent in music and accessible to perception without the mediating operations of logical proofs. The very quantity of musical a priori suggests that we consider them as residing within a matrix, and capable of being pre- sented in various combinations under agreeable circumstances of time and place. As to the kinds of a priori themselves, it can be said that time is a formal a priori, in the sense that it is formative of the musical process as perceived. Nevertheless, a certain kind of musical time may be described as a material a priori, if it is considered to be an essential aspect of a particular composi- tion. The notion of temporal overlap, for example, as it appears just before the recapitulation in the first movement of Beeth- oven's Third Symphony, seems a reasonable candidate for a material, temporal a priori. (The future, that is, the rest of the movement, and the past, the development section, momen- tarily slide into one another.) If one is still thinking of harmony as chords, then the appro- priate a priori form would be that of space. Space, like time, is formative of music while transcending it. But again, like time, spatial a priori may be materialized by the essential ex- periences of line, surface, volume, and color. Harmony, how- ever, can also be considered as attunement (as in Stockhausen's Stimmung), in which case it would seem more precise to con- sider it as a corporeal a priori, as a feeling located in the body which is present to, and engaged in, a musical situation. However, these are distinctions which emphasize certain a priori but which do not separate them from other a priori. Time, harmony, dissonance, consonance, polarity, opposition, and order are all perceivable, self-validating experiences, so that no single a priori can be isolated from, or given prefer- ence over, all the other kinds. The a priori cannot be separ- ated from one another any more than the faculties of a person can be separated, or the a priori "I" from other "I's. " But what about tempo, chords, sonata form, and twelve-tone rows? Don't they apply generally to at least the music of a particular culture, and do they not therefore transcend particu- lar instances? These questions call for a further distinction between the formal and the material, based on the realization that the formal and the material are not always a priori. Of course it is necessary to play a piece at the correct tempo, but this necessity does not seem to be directed towards itself as its own end. There is a reason why we try to play at the right tempo, and this reason I take to be an a priori. It is not my reason; it is the music's reason. Similarly, there is a reason why a certain chord or row form is thought to be neces- sary, but they are not necessary for themselves. A twelve- tone row can be said to obey the laws of thought, but I men- tioned before that the a priori does not depend on what we think. It is the other way around; what we think depends on the kind of a priori being presented. I have a certain obligation to at- tend to these a priori, and this obligation is different from the constraints which I impose on the musical object ("Avoid par- allel fifths"). The problem is to conjoin the form of thought to the a priori meaning in the work itself. Caution is therefore needed if we are not to confuse the a priori, as the logic of experience, with either physical requiredness (as in the case of vibrating strings) or the requiredness of mathematical or logical propositions. Chords and row forms have a purpose very similar to doors: they are meant to be opened and passed through. In addition to the judgment which identifies ends and means, another criterion whereby a priori meanings can be distin- guished from empirical meanings is to consider the different meanings of words like "learning" and "education." I take it that learning, whatever else it may entail, is more than the accumulation and recycling of facts, and I interpret education in its root sense: as a leading-out or uncovering. In any case, it is not contradictory to speak of the a priori and a certain kind of learning in one breath. The feeling of polarity and op- position is a meaning which may have had to be learned - I really do not know - but still, when I experience these feelings, they arrive unannounced, although they may be reflected upon later on. Not so with sonata form. I had to learn about that. Furthermore, one does not "know" sonata form until all its elements and relations have been grasped. In the one case, a self-validating experience precedes elaborative understand- ing; in the other, it is the elaboration of facts which precedes understanding. A final criterion for distinguishing a priori meanings from em- pirical meanings is to consider more carefully the notion of evidence. It has been argued here that an a priori meaning is an irreducible, self-validating meaning. This meaning is a content of and for consciousness. I could not, in truth, say that I experience an ascending gesture at the opening of Mozart's C Minor Sonata if I were not certain of this experience in con- sciousness. Thus it is consciousness, or subjectivity, which provides evidence for the truth of a priori statements. But I do not for a moment think that my experience of this ascending gesture reveals some perceptual maladjustment, nor do I equate my experience with my opinion. Neither of these conditions exhausts the significance of subjectivity. My consciousness, and the object of my consciousness, are felt as individuals, but this doesn't render them hermetic. The possibility of "as- cending gesture" being experienced by other people is not to be excluded. However, I feel under no compulsion to equate my consciousness of "ascending gesture" with factual condi- tions of existence. The move from "I experience an ascending gesture," to "There is an ascending gesture, " is one which I feel can be indefinitely postponed. No last minute subversion is intendedhere; it just seems that such an isomorphism is not necessary. But one cannot afford this luxury with empirical meanings. It would be nonsense to say, "This piece is in so- nata form, " unless it were verified that such a piece actually exists and is indeed in sonata form. But with empirical mean- ings, verification is a posteriori: it follows from the facts, beingdependent upon their investigation. Thus empirical veri- fication presupposes that the object being investigated actually exists. The conclusion to these remarks is likely to sound somewhat paradoxical. It is precisely because the a priori is grounded in subjectivity that we experience a world - a world of objec- tive meanings. To say that "It's all in the mind, " is to com- pletely miss the point of these remarks. On the other hand, empiricism naively supposes that theworld adjusts to the forms of thought, thus giving us a world of subjective facts. This apparent paradox can be resolved in two ways: by using facts as means to an end, and by breaking the subject-object dichot- omy with the realization that each is necessary to the other. Mozart's C Minor Sonata is an object which has meaning for me, and as such, it is part of the environment which I consider as "mine, " and which contributes to the definition of my in- dividuality. Similarly, the sonata has a certain hold over me. It is in this area of mutual possession where the a priori are likely to be discovered. REFERENCES 1 Immanuel Kant, Critique of Pure Reason, trans. Norman Kemp Smith (London: Macmillan, 1964), p.41. 2 Mikel Dufrenne, The Notion of the A Priori, trans. Edward S. Casey (North- western University Press, 1966), p. 93. 3 Nicholas Woltersdorff, On Universals (University of Chicago Press, 1970), passim. 4 Jean Piaget, The Child's Conception of Space, trans. F.O. Langdon and J. L. Lunzer (New York: Norton, 1967), p.448. 5 Jean Piaget, The Child's Conception of Time, trans. A.J. Pomerans (New York: Ballantine, 1971), p. 303. 6 Milton Babbitt, "Three Essays on Schoenberg," Perspectives on Schoenberg and Stravinsky, ed. Benjamin Boretz and Edward T. Cone (Princeton Univer- sity Press, 1968), pp.57-58. Article Contents p. 66 p. 67 p. 68 p. 69 p. 70 p. 71 p. 72 p. 73 p. 74 p. 75 p. 76 p. 77 p. 78 p. 79 p. 80 p. 81 p. 82 p. 83 p. 84 p. 85 Issue Table of Contents Journal of Music Theory, Vol. 17, No. 1, Spring, 1973 Front Matter [pp. 1 - 149] Tonal Coherence in a Motet of Dufay [pp. 2 - 64] Music and the a Priori [pp. 66 - 85] The Origin of the Coniuncta: A Reappraisal [pp. 86 - 109] The Fibonacci Series in Twentieth-Century Music [pp. 110 - 148] French Modal Theory before Rameau [pp. 150 - 163] Book Reviews untitled [pp. 164 - 167] untitled [pp. 168 - 171] untitled [pp. 172 - 174] Letters [pp. 175 - 176] Books and Articles [pp. 177 - 184] Back Matter [pp. 185 - 186]
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