"The Aesthetics of Music".

Some dozen years ago, I was riveted by a report in the press about the findings of a study that investigated what male Americans enjoy most in their lives. As best as I can recall, the candidates included work, family, sex, and music. The winner, hands down, was music. But why was this the case? What is distinctive about the musical experience? The study in question was predictably silent on these matters, but the English philosopher Roger Scruton is not in his important new work, The Aesthetics of Music.(1) This book is aptly described on its cover as "the first comprehensive account of the nature and significance of music from the perspective of modern philosophy, and the only treatment of the subject to be extensively illustrated with musical examples."

But what exactly is the "aesthetics of music" as a field of study? In Scruton's view, it amounts to an investigation of what makes music special as a human endeavor, that is: what are the defining properties that make music music? His book makes a significant contribution to our understanding of this question. But surely there is another equally important question lying at the heart of musical aesthetics, one going back to the original insights of Plato and his colleagues: what makes a particular composition especially beautiful? Why at the deepest level is it that people obtain such great pleasure from compositions by Bach or Beethoven, or songs by Bob Dylan, when measured "objectively" on an applause meter? Recall in this regard that the Greeks did not instruct us to understand harmony and rhythm merely as "properties" of music. Rather they spoke of eurhythmy, where the prefix eu- designates "good" or "successful" Remarkably, Scruton's allegedly comprehensive treatise sheds almost no light on this deeper question.

Why is this the case? Is Scruton simply another modernist who believes that such value-laden normative issues cannot and should not be addressed? Quite the contrary. He argues explicitly that the analysis of values is inextricable from the enterprise of serious musical aesthetics. Rather, the answer may well be found in the type of philosophy upon which Scruton draws: modern Anglo-American analytical philosophy. As will be suggested further on, the level of logic used in this type of philosophy intrinsically limits the ability of philosophers to deal with precisely such questions as "What makes x more beautiful than Y, and why?" The logic is typically verbal (mere "word games," some critics allege), and insufficiently mathematical for serious theory construction.

Interestingly, precisely this deficiency of analytical philosophy revealed itself earlier in this century in the fields of ethics and political theory. Extensive discussion about the meaning of justice via verbal analyses-of-meaning produced precious little of interest during the first half of the century. Progress started to be made in the 1950s when the Berkeley philosopher John Harsanyi drew upon modern decision theory and social-choice theory and succeeded in axiomatizing Utilitarianism in 1955. This work contributed to Harsanyi's being awarded the 1994 Nobel Prize in economics. A bastardized and problematic version of this early work would later lie at the heart of John Rawls's 1971 Theory of Justice, arguably the most celebrated modern work in political theory.

The ecstatic response to this decidedly non-"analytical" work suggested to many that analytical philosophy had failed in its most essential task of imparting a superior account of justice and fairness. The paradox here is that, despite its pretensions to analytical rigor, analytical philosophy has proven to be insufficiently analytical to produce robust results. The situation in aesthetics (and not just musical aesthetics) is analogous.

Let us begin, however, by accepting Scruton's restricted conception of musical aesthetics at face value. What does he contribute to the question of what it is that makes music so special? Plenty, and it makes for jolly good if somewhat taxing reading. He succinctly summarizes a good portion of the argument set forth in the first two-thirds of his book on page 344. To paraphrase this useful summary:

1. Music is not "representational" as many forms of the applied and decorative arts are. Specifically, music does not--with rare exceptions--represent particular objects or actions.

2. Nevertheless, music is often very meaningful, in the strong sense that there is something to be understood in it.

3. The act of listening to music is an expression of aesthetic interest, and music is primarily understood through the aesthetic experience of listening to it.

4. Musical truth cannot be decoded in a highly structural manner through any "generative syntax." Scruton contrasts this state of affairs in music with that in linguistics where (some believe) linguistic truth across many languages can be apprehended by applying (in Noam Chomsky's phrase) rules of "transformational grammar." Scruton is very critical of musical "structuralists" such as Leonard Meyer and Heinrich Schenker, and he usefully criticizes not only their particular theories, but also the very aspiration of locating aesthetic truth in the form of "deep structures."

5. The expressive and emotive qualities of music form the most important part of its content.

How successful is Scruton in establishing these points, and how original are they? His most original contribution centers on point three above. He develops a novel account of musical meaning as "the intentional object of an imaginative perception?' He writes that

   The correct approach to aesthetic description, I believe, is to distinguish
   clearly between the intentional object of aesthetic interest, and the
   material object in which it is located. Aesthetic description is an attempt
   to characterize the intentional object--that which we see, hear, or
   understand in the work of art. The terms deployed in aesthetic description
   do not describe the material reality at all, but express, and also
   recommend, a particular response to it.

In this context, Scruton insists that the truest and possibly the only path to aesthetic understanding lies in the act of listening, and in responding to what we hear in whatever (subjective) way we do.

Scruton's extensive analysis of this concept is convincing--as far as it goes. The problem is that his account does not provide a sufficient basis for a comprehensive aesthetics of music. While Scruton's analyses of the other four points are not as striking as his theory of aesthetic description, he admirably succeeds either in usefully rebuking or else in extending the ideas of others in each case. And he does so with originality. Indeed, a pleasant dividend of reading this book is the extent to which it permits the interested reader to discover what philosophers have been saying about musical aesthetics throughout this century and before, and to learn with Scruton's assistance how unsatisfactory much of this work has been.

In the final portion of his book, Scruton is at his best. He happily pushes beyond his somewhat academic discussion of the history of musical aesthetics and in chapters on "Value" and "Culture" (Chapters 12 and 15 respectively) succeeds in doing precisely what philosophy should do for us lay-people. He engages the overarching and all-important issue of music's relationship to social values and indeed to culture as a whole. The combination of the intrinsic interest of this subject with the power of Scruton's mind generates an analysis that is reminiscent of--yet that surpasses--Allan Bloom's discussion of rock music in The Closing of the American Mind.

Among other things, we learn that there can be no value-free aesthetics of music, that taste matters not only to the individual but also to the collective body politic, and that both classical and pop music have recently fallen into rapid decline. Moreover, we learn why this is so via deep arguments stemming from first principles. This is philosophy at its best. A brief sampling of Scruton's discussion will illustrate these virtues.

In correctly identifying the delicious interplay of rhythm, harmony, and melody as the distinguishing feature that makes music so compelling to the listener, Scruton writes:

   Nobody who understands the experiences of melody, harmony, and rhythm will
   doubt their value. Not only are they the distillation of centuries of
   social life: they are also forms of knowledge, providing the competence to
   reach out of ourselves through music. Through melody, harmony, and rhythm,
   we enter a world where others exist besides the self, a world that is full
   of feeling but also ordered, disciplined but free. That is why music is a
   character-forming force, and the decline of musical taste is a decline in
   morals. The anomie of Nirvana and REM is the anomie of its listeners. To
   withhold all judgement, as though a taste in music were on a par with a
   taste in ice-cream, is precisely not to understand the power of music.

We are left at the end of the chapter on culture with the realization that most of today's rock music is devoid not only of melody and harmony, but even of anything more than mechanical rhythm. For the most part, all we have left is beat, and beat is at best a reductio ad absurdum of rhythm. Just contrast the monotonous beat of disco music with the insinuating rhythms of Ravel's Bolero.

The Aesthetics of Music, then, is a book possessing many virtues. If it nevertheless fails to fulfill its main ambition of being comprehensive, that is because of the fundamental inadequacy of the theory of aesthetic intent that Scruton sets forth. The central problem also lies in his point three above, namely that structuralism is both unnecessary and misguided in aesthetics. It is neither. As the Greeks first realized, any satisfactory aesthetics of music must combine a proper theory of structure with the kind of "experiential" theory of aesthetic intent that Scruton himself has helped to create.

Where does he go wrong? In my view, Scruton gets himself into trouble by making two fundamental mistakes. First, while justifiably criticizing the existing structuralist theories of Schenker and others, Scruton makes the logical error of assuming that since the particular theories that he reviews are inadequate, no adequate theory is either possible or necessary. But this is not the case, as I shall indicate below with a constructive counterexample.

Second, and far more fundamentally, Scruton violates what philosophers of science call "The Correspondence Principle." This rule states that when a theory is propounded to replace an earlier theory that works in certain contexts, the new theory must reduce back to the earlier one in appropriate limiting cases. For example, the ten metrical field equations of Einstein's general relativity reduce to the single potential function equation of Newton. In this important sense, Einstein's theory did not oust Newtonian physics, as many think, but rather generalized it.

The situation should be the same in aesthetics. A purportedly newer and better theory should build upon and extend those of yesteryear. In this regard, it is odd that Scruton proffers a theory with little if any relationship to the great tradition of aesthetics focusing on harmony, balance, and proportion. This tradition originated with the Greeks and flourished ever since, as Matila Ghyka's classic book The Geometry of Art and Life (1946) makes clean Ghyka's book also reminds us that such classical principles as the Golden Section and eurythmy were intended to apply to all forms of art, music being but one special case.

It is also odd that, in ignoring this tradition, Scruton should be silent on what is perhaps the deepest challenge confronting aesthetics: the clarification of what exactly it is that makes a great work of art great, whether the work be music, painting or sculpture, or architecture. What is it that all such objects have in common? Or, to restate this in Scruton's language, what exactly is it that people share while experiencing the performance of a composition they all agree to be "very beautiful and moving"? It is my belief that Scruton cannot address these broader issues because he rejects the possibility of meaningful structural analysis. For to the extent that the enterprise of aesthetics attempts to explain what it is that unites differing objects of aesthetic interest sharing the same property--namely, beauty--then the enterprise is necessarily structural.

It should be helpful to illustrate this contention with a counterexample to Scruton's structuralist pessimism--one that suggests in the process that meaningful structural analysis is possible and indeed desirable in aesthetics of all kinds. Among other things, this counterexample will demonstrate that Scruton's most serious misgiving about structuralist theories is misplaced. For it will show that such theories can capture what he calls the "context-dependence' of structural properties, whether rhythmic, harmonic, or melodic. Scruton argues that they cannot do so.

To begin with, note that any object of aesthetic interest--ranging from a Bach fugue to a curvaceous Chippendale armchair--can be formally represented via a decomposition of its component parts into two disjoint sets. First, there is the set of themes, e.g., the subjects of the fugue, and the basic design element of the armchair which will typically be Hogarth's line-of-beauty "S-curve". For simplicity, let us assume there is a single theme. Second, there is a set of transformations of this theme that generates the remainder of the musical composition or the work of art--its "echoes;' in effect. In the case of the fugue, these transformations will include such familiar operations as inversion, stretto, transposition from major to minor key, etc. In the case of the armchair, they will include the rotation, straightening, stretching, reflection, shortening/lengthening of the design element, etc. Jointly, the combined structure of a theme and its transformations fully represents the object.

Note that at least one such decomposition is always possible. For any identifiable portion of the work can be designated to be its theme, and every other portion can be generated by some transformation of this theme. Think of these other portions as "echoes" of the theme. Sometimes, there will be some natural theme(s) and an associated set of transformations. Obvious cases here would be a Bach fugue with its explicitly designated themes and subthemes or Mozart's theme and variations on the tune known in English as "Twinkle Twinkle Little Star." But there need be no obvious theme.

As a next step, let us consider the idea of the relative complexity of the theme and, separately, the relative complexity of the transformations, both of which can be given in formal mathematical terms. In the case of the "theme" or design element of the chair, an appropriate measure of the complexity can be objectively given as the degree of the polynomial equation representing the graph of the S-curve. This equation is cubic, so it is of degree 3. In the case of a kitchen chair with slats across the back, it is of degree 1 since the equation of a straight line (a slat) is linear.

The relative complexity of each transformation can be defined analogously, e.g., via what is called the "index" of the operator defining the particular transformation. In a geometric object like the chair, both a ninety-degree rotation and a reflection symmetry are relatively simple operators, whereas a convolution (twisting) is complex. The more work necessary to transform a particular theme into some "echo" of it appearing elsewhere in the chair or fugue, the higher the index value. Advances in mathematics make such a characterization possible regardless of whether the transformations involved are static, as in furniture or architecture, or dynamic, as in music. (In this context, it is worth recalling Schelling's description of architecture as "frozen music.")

Armed with these concepts, we can offer an account not only of the relative amount of order and balance to be found in an object of interest, but also of the degree of satisfaction that we derive from it. To understand this point, first consider that maximal harmony corresponds to the combination of a simple theme and simple transformations thereof, e.g., a straight-backed kitchen chair or a simple Gregorian chant. Maximal disorder corresponds to a complex theme and complex transformations thereof, e.g., much Victorian furniture and contemporary atonal music.

Now a high degree of satisfaction will typically result when the right balance between order and disorder is achieved, that is, when an "optimal tradeoff" has been struck between the two different complexities. If the theme is simple, then we are satisfied when its echoes are complex ("interesting"), and vice versa. This account makes it possible to clarify and indeed to quantify one of the deepest principles of aesthetics: the fact that people apprehending works of art are bored if there is too much simplicity (the kitchen chair, certain Gregorian chants), and overwhelmed if there is too much complexity (much atonal music, and pastiche Victorian furniture). They wish to be optimally challenged by experiencing the right amount of complexity. Another way to state this is that there is an optimal amount of symmetry (equivalently asymmetry) that is a necessary (yet certainly not sufficient) condition for a work to be found "pleasing". This is a principle running throughout aesthetics from the Greeks on down.

Three final points should be made about this theory of aesthetics as "structural success". First, it can be shown to subsume as a limiting special case the myriad relationships centering around the celebrated "aesthetic number" 1.618. For centuries, this algebraic number has been used to account for the aesthetic appeal of such diverse entities as the golden rectangle, the structure of the human body (observed by da Vinci), the Gothic cathedral, the arresting spiral of the nautilus shell, etc. By subsuming all this, the proposed theory satisfies the Correspondence Principle and makes it possible to unify much of aesthetic theory.

Second, this account is fully context-dependent. To see this, suppose we substitute straight arms for S-shaped arms in the Rococo chair. Then we obtain the following paradox: while a straight arm is much more simple than an S-curved arm, the chair that results is much more complicated--too complicated to be pleasing in fact. This is because too much "aesthetic energy" must now be expended in mentally transforming a complex S-theme into the simple straight line of the arms of the chain The "tradeoff" measure lying at the heart of this theory fully captures this: it accords a "lower" aesthetic value to the chair with straight arms than to that with S-shaped arms. This form of context-dependence is similar to that lying at the heart of general relativity theory in physics: the degree of complexity of a given design element is continuously rescaled according to its context, exactly as the strength of the gravitational field is rescaled by the degree of space-time curvature at each point in the space-time manifold. All this is possible because both theories are nonlinear in the fundamental sense that everything is mutually coupled--that is, everything depends upon everything else. Scruton is right to insist on context dependence in structural analysis, perhaps more right than he realizes.

Third, and finally, while structural success as defined here is usually a necessary condition for an object to possess great aesthetic interest, it is certainly not sufficient. Additional consideration must be paid to the issue of which subsets of themes (e.g., melodies) strike us as beautiful, as well as which transformations are most pleasing. That is, why is the theme of the last movement of Beethoven's Ninth Symphony universally appealing? And why are the cadences in the middle of the first movement of Beethoven's Fourth Piano Concerto or at the end of Bach's Toccata in F for organ so pleasurable? In my view, these questions can be partially answered by the same kinds of formal analysis sketched above, in particular the theory of transformation groups in abstract algebra.

Were Scruton's account of musical aesthetics to be extended to include these complementary structural dimensions of aesthetics, we would then come close to a truly comprehensive account of what it is that we actually "experience" in listening to good music, and why we like it. It will turn out that much of our satisfaction derives from an apprehension of latent structures, whether we are aware of these, or not. Yet an understanding of why this is true will require much more rigor than analytical philosophy has given us to date.

Roger Scruton replies:

Horace Brock raises an important question concerning my book The Aesthetics of Music, identifies what he takes to be a damaging lacuna in its argument, and offers an approach to aesthetics which promises, in his view, to make good the deficiencies in mine.

The important question is this: to what extent can "analytical philosophy" in the Anglo-American tradition, provide answers to fundamental questions of aesthetics? Mr. Brocks view is that this kind of philosophy--of which my book, he assumes, is an instance--is limited to conceptual and verbal enquiries, and cannot avail itself of the quasi-mathematical theories which the questions of aesthetics require. I reply as follows:

1. My perspective on philosophy owes as much to Kant and Hegel as it does to Wittgenstein and Frege (to name but four). I am not sure that I know what "analytical philosophy" is, but I do know that it is something more than word games.

2. Mr. Brock mentions the failure of analytical philosophy to make any progress in the field of ethics and political philosophy, until John Rawls, in A Theory of Justice, introduced concepts and theories from the mathematical discipline of decision theory. My view is that the borrowings from decision theory and game theory in Rawls are of little significance compared with his deeper borrowing from the moral philosophy of Kant, and that they do nothing whatsoever to overcome the difficulties that bedevil the Kantian enterprise.

3. I do not think that all the questions are answered by theory-building--certainly not theory-building of the kind favored by Mr. Brock. It is part of the philosophical naivete of utilitarianism (with or without Harsanyi's formalization) that it commits itself to solving moral problems by a calculus.

Mr. Brock thinks that I do not seriously attempt to solve the most important question of which he gives several versions:

1. What makes a particular composition especially beautiful?

2. Why at the deepest level is it that people obtain such a great pleasure from compositions by Bach or Beethoven, or songs by Bob Dylan, when measured "objectively" on an applause meter?

3. What is it that makes a great work of art great, whether the work be music, painting or sculpture, or architecture?

4. What exactly is it that people share while experiencing the performance of a composition they all agree to be "very beautiful and moving"?

Most philosophers would say (and surely rightly) that there is not one question here but at least four. And they would say, again rightly, that Mr. Brock has not sufficiently distinguished questions of psychology--What goes on when people listen to music?--from questions of criticism--What is it in the music that merits their attention?--and from questions of philosophy--What is aesthetic appreciation, and when is it well-grounded? Only by running these three kinds of question together can Mr. Brock create the impression that a single theory will answer all of them, and that this theory will provide the key to aesthetic value. But the theory he offers is not merely utopian in its generality and deceptive in its spurious claim to rigor. It is a theory which leaves the questions of aesthetics exactly as they were. At best it would offer a psychological explanation as to why some people (perhaps the majority) take pleasure in certain kinds of music and visual arrangements. But it would provide no basis for the aesthetic judgment that they are right to take such a pleasure, or for the critical judgment that there is a meaning and a value in the objects that produce it.

It is easy to envisage a psychological explanation of the characteristic pleasures of the pop-fan: the surrender to beat at the expense of rhythm, the lapse into repetition, and the loss of thought that comes from a music without inner voices, generated entirely by an electronic pulse. But such a theory would not begin to tell us how and why we might criticize the taste which it describes. Nor could it possibly answer question three above.

Consider a parallel instance. A sociobiologist could provide a theory which explains moral judgment, in the following terms: societies which uphold certain prohibitions (against murder, incest, marital infidelity, theft, etc.) acquire an evolutionary advantage over societies which do not. Hence, in the struggle for survival, they are likely to win out. Hence any deep structure in the human brain which favors such prohibitions will be reproduced. So it is likely that moral conformity, of the kind we observe, will emerge in the long term. That theory could be true, for all I know. But it is surely preposterous to suppose that it is an answer to the question posed by Kant--namely, what are the grounds for the judgment that "Thou shalt not kill"? The fact that we are disposed by nature to make a certain judgment is no grounds for its truth--or else the earth is flat.

Mr. Brock argues that I violate the "Correspondence Principle"--namely the principle that a theory which replaces a refuted theory must generate the refuted theory as a limiting case. But this principle applies only to scientific theories--theories which provide causal explanations of observable phenomena. It has no application to philosophical theories, which are concerned not to explain but to justify. By binding himself to the Correspondence Principle, Mr. Brock ensures that the theory which he eventually discovers will be a theory of the wrong kind.

Mr. Brock is right in suggesting that I have not given an answer to the deep question of aesthetics--the question how aesthetic judgments are justified. It is a question that lies beyond theories of the kind that he is attached to--as I have tried to show, in connection with that wretched number 1.618, in The Aesthetics of Architecture. Nevertheless, in my book on music, I go some way to answering the question. My suggestion is that music involves the creation of an imaginary movement in an imaginary space, and that our response to this movement involves the mental rehearsal of gestures, passions, and actions which have their moral reality in the social sphere. Great music leads us into a higher and nobler world of feeling, where love, commitment and self-sacrifice are given their imaginative embodiment. We enter that world through an act of imaginative understanding, and the purpose of criticism is to get us to focus on the features of music that we must hear if we are to hear with understanding. The difference between great music and bad music is, in the end, the difference between virtue and vice--but recreated in the imaginary realm of fictive movement.

Aesthetic value is certainly objective, just as virtue is. But I don't believe it can be measured by an applause meter, or that it is equally to be found in Bach and Bob Dylan.

(1) The Aesthetics of Music, by Roger Scruton; Oxford University Press, 550 pages, $39.95.

Horace W. Brock is the president of Strategic Economic Decisions, Inc.

Roger Scruton's most recent book is On Hunting (Yellow Jersey Press).