It should be clear by now that the task of building and testing music theories is not only a lot messier than we might suppose, but it is also plagued by many of the same methodological problems as the-ories in other disciplines, especially the natural and social sciences.
In very general terms, we have seen that these problems often involve finding effective ways to balance the drive for evidence with the drive for system. Although this all sounds reasonable enough, we can spell out more clearly how such a balance might be achieved. Following, Kuhn, Quine and others, we can invoke sev-eral concrete criteria for doing so: figure I.10 (Six criteria for evalu-ating theories) includes the notions of accuracy, scope, fruitfulness, consistency, simplicity, and coherence.38 The list is by no means exhaustive; other criteria, such as completeness, elegance, or even
‘coolness,’ could easily be added. Figure I.10, however, gives us a good place to start our inquiry. For convenience, the six criteria are divided into two types—those that relate to the evidential basis of theories and those which relate to the systematic aspects of a model. The horizontal arrow at the top of the figure suggests that there may be inherent conflicts between the evidential concerns (accuracy, scope, and fruitfulness) and the systematic concerns
(consistency, simplicity, and coherence). The vertical arrows along the sides suggest that there may be a similar tension between mem-bers of the same type.
The first criterion on our list is accuracy. Since a successful theory should explain why certain phenomena behave the way they do and predict what will happen in new situations, we will surely want the most exact explanations and predictions possible.
Although our theories can never be completely accurate, we gener-ally see increased precision as a virtue, so that, given two theories, we usually prefer the one that is more accurate, other things being equal. And yet, it is by no means obvious how to measure the accu-racy of competing models. Norwood Hanson, Thomas Kuhn, Paul Feyerabend, and others have insisted that since our observations about the world may be theory-laden, decisions about what consti-tutes evidence will be determined by our theoretical prejudices.39 Indeed, to paraphrase Quine, “Our judgments about what there is are always embedded in some sort of theory; we can substitute one theory for another but we cannot detach ourselves from theory altogether and see the world unclouded by any preconception of it.”40 If competing theories reflect widely different values, there may be no neutral grounds for comparing their accuracy. In such cases the two theories are said to be incommensurate. Critics, however, have countered that the problems of theory-ladenness and incommensurability are greatly exaggerated. While it may be true that observations tend to be theory laden, this doesn’t mean that we can never distinguish observational terms from theo-retical terms. Indeed, as Quine points out, “theotheo-retical sentences grade off to observation sentences”; some observations come with
Evidence Figure I.10. Six criteria for evaluating theories.
negligible theoretical baggage, while others come with a lot.41 Compare, for example, the observation that the first movement of the “Eroica” Symphony begins with an E triad with the claim that the movement is “in” E. Whereas the former involves few theoretical assumptions and is readily apparent to most listeners, the latter is highly theory laden and presupposes an elaborate the-ory of key relations.42
But even though many of our observations are biased, theo-rists working with different frameworks are still able to reach some degree of consensus in specific cases. In this respect, the main issue is that of intersubjective testability rather than of objectivity per se. This notion of intersubjective testability through bias is most remarkable when the various biases are not only different, but also contradictory. I refer to this as ‘The Hostile Witness Prin-ciple.’ Very simply, this principle suggests that a particular claim gains force when it is confirmed by theories that are directly opposed to one another. Such situations often arise because, as Richard Boyd points out, “A particular experiment can be con-ducted on the basis of a methodology that—however theory-dependent—is not committed to either of the two contesting theories.”43
The second criterion in figure I.10 is scope. Just as we want our theories to be as accurate as possible, so we also put a premium on their breadth of coverage. This means that, given two theories, we normally prefer the one that covers the larger array of pieces or wider range of properties, other things being equal. Perhaps the most common way to expand the scope of our theories is by sub-suming hitherto separate theories under a single scheme. This is known as ‘Theory Reduction.’44For example, if we proposed a the-ory of functional monotonality that subsumes the thethe-ory of tonal voice leading with the theory of functional monotonal harmony, then we should prefer it to a rival theory that explains only the behavior of tonal voice leading or that explains only the behavior of functional monotonal harmony. This does not mean, however, that generality is always a good thing; on the contrary, some theories are so general that they lose their explanatory force. That’s the snag with Anne Elk’s theory of the brontosaurus.45While it may be true that the only thing common to all brontosauruses is that they “are
thin at one end, much, much thicker in the middle and then thin again at the far end,” this account is so general that it is trivial. The notion of ‘Theory Reduction’ has likewise been questioned. While there are certainly situations in which the model seems to apply, it does not explain every option. Kuhn, for example, has suggested that explanatory scope can expand through conceptual innovations or paradigm shifts, rather than the addition of new laws or the reduction of one theory into another.46To overcome these difficul-ties Philip Kitcher and others have advocated the notion of ‘Theo-retical Unification.’ According to Kitcher, the success of theories depends on “minimizing the number or patterns of derivation employed and maximizing the number of conclusions generated.”47
When evaluating the success of our theories, we do not simply want to keep duplicating results in familiar pieces; we also want to use our concepts, laws, and procedures to predict how things will behave in other, perhaps novel, works and disclose new phenomena or previously unnoted relationships among those already known.48 To do this, we must be able to predict every consequence and not merely a smattering of special cases.49This idea represents the third criterion in figure I.10, namely fruitfulness. Very simply, given two theories of functional monotonality, we prefer the one that makes the more fruitful predictions, other things being equal. According to Kuhn, the criterion of fruitfulness “deserves more emphasis than it has yet received.”50 Just as it is hard to measure the accuracy of rival theories, it is also difficult to assess their fruitfulness, especially if the theories draw on widely different bodies of empirical data.
This issue is troubling because successful theories often evolve considerably over time; it may take a long while for theorists to appreciate just how fruitful a theory may be and even longer to con-sider all of its ramifications. As a result, fruitfulness may not play a significant role when a theory is originally presented to the world but will become more significant as that theory matures.
Whereas our first three criteria concern the drive for evidence, our fourth criterion concerns the drive for system. When formulat-ing a music theory, we will want it to be as internally consistent as possible, other things being equal. Inconsistencies are bad because they prevent us from making concrete predictions; if we cannot make concrete predictions, then we cannot subject our work to
rigorous testing, especially by other people. It is important to stress, however, that even internal consistency is a matter of degree; the more comprehensive our theories become, the less likely they are to be internally consistent. For example, although Schenker insisted that the process of composing out is bound to the laws of tonal voice leading and harmony, his graphs often violate the law prohibiting parallel perfect octaves and fifths. As we will see in chapters 2 and 3, this inconsistency has enormous consequences for understanding various tonal phenomena, especially sequences.
Assuming one has satisfied the preceding constraints, the drive for system often prompts us to evaluate rival theories according to their complexity; as a rule we prefer a simple theory to a compli-cated one, other things being equal. This fifth criterion from figure I.10 is commonly known as Ockham’s Razor or ‘The Principle of Parsimony’ and is almost as old as theorizing itself.51 The rationale is obvious enough: the simpler the theory, the easier it is to apply and the less prone it is to error.52Nevertheless, Ockham’s Razor can leave some scars. Simplicity is, to some extent, in the eye of the beholder; if taken to extremes it can end up being a downright liability.53 As we will see in chapter 1, the theory of functional equivalence seems to run afoul of this very issue. By restricting tonal harmonies to just three basic functions (tonic, dominant, and subdominant), the theory oversimplifies the richness of many tonal progressions. In such cases simplicity comes into conflict with other values, especially accuracy and scope.
Finally, we come to the sixth criterion from figure I.10. Suppose that we are faced with two theories that are equivalent empirically and systematically, that is, both are equally accurate, both have a similar scope, both are fruitful, both are consistent to the same degree, and both are comparable in their level of simplicity. What grounds, then, do we have for picking one theory over the other?
One answer is to see if they are coherent with theories in related disciplines, other things being equal.54If, for example, one theory of functional monotonality is coherent with current theories of music cognition, whereas the other is not, then we have good reason for preferring the former to the latter. Conversely, if our theories cannot be embedded or made compatible with known principles of music cognition, then we have good reason to be suspicious of them.
Of course, coherence between theories in different domains is an extremely difficult thing to achieve, especially since the two spheres of inquiry may have such different methodological bases; it is no easy task to find appropriate bridge laws that bind one discipline to another. Nevertheless, coherence is still a goal worth striving for.
So far, we have sketched some general reasons for invoking the six criteria given in figure I.10. We have also seen that these crite-ria are often at odds and that theorists are often forced to trade one off against another. These last ideas are significant because they help us to explain how different theorists can reach a consensus on certain methodological issues without agreeing on the particulars of any given theory. The reason for this is simple: music theorists might evaluate theories according to the same criteria, but weight each one differently in any given context. Take, for example, the differences between Schenker’s original theory and that of his student, Felix Salzer.55As we will see in chapter 1, Schenker put a premium on the accuracy of his model. He went to great lengths to make sure that he could explain the minutest details of tonal voice leading. But, to achieve such a high degree of precision, Schenker confined himself to functional monotonal music of the Common-Practice Period. Felix Salzer, meanwhile, focused his attention on explanatory scope; he wanted to explain the tonal properties of a broad spectrum of music from the Middle Ages to the Twentieth Century. To do this, Salzer had to modify many of Schenker’s ideas, thereby sacrificing much of their accuracy and predictive power. History has shown that Salzer’s trade was not worth the price. As time has gone by, music theorists have generally found Schenker’s approach more robust than Salzer’s. This seems in keeping with the general notion that theorists value accuracy most highly among the evidential values; once accuracy is gained, theo-rists are unwilling to relinquish it without a fight. Just as theotheo-rists seem to value accuracy over scope and fruitfulness, so they also seem to value consistency over simplicity and coherence. Again the rationale is clear. Consistency guarantees that claims can be tested inter subjectively; and inter subjective testability is one of the hallmarks of rational discourse. Simplicity, meanwhile, is an advantage in application, but it is ultimately much better to be complex and consistent than simple and inconsistent.
Besides providing us with a mechanism for evaluating rival theories, we can also use the preceding model to explain how music theory might progress as a discipline. Now, there can be little doubt that “progress” has become something of a dirty word in musicological circles these days. Indeed, as Richard Taruskin notes, “Few historians today subscribe to overtly teleological or deterministic models.”56 The reasons for this are not hard to find. Recent scholarship has tended to focus on those properties of music whose significance depends on historical or social context. Once music is treated as a social construct, the notion of progress simply smacks of anachro-nism and cultural imperialism. Change, yes; progress, no. Yet, even if we balk at the idea of progress in musical composition, we may still accept the notion of progress in music theory. The two things are, in fact, quite different. Whereas the former is concerned with producing aesthetic experiences, the latter is concerned with pro-ducing knowledge and understanding. Knowledge and understand-ing are two thunderstand-ings that can clearly improve. They progress when a community of theorists acknowledges that a new cluster of con-cepts, laws, and procedures is more accurate, more expansive, more fruitful, more consistent, more parsimonious, and more coherent than its predecessors. It is for these reasons that Schenker’s theory of functional monotonality is superior to its precursors. And we have every reason to suppose that even more successful theories of tonality will be developed in the future.