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Science Connections

The Structure of Musical Revolutions

Edward Slowik investigates Kuhn’s philosophy of science through an analogy.

One of the most important and influential developments in 20th century philosophy of science has been Thomas Kuhn’s theory of scientific revolutions. Its popularity has spread way beyond the relatively narrow confines of philosophy of science, having become a staple topic of discussion and investigation in all areas of the arts and sciences. The term ‘paradigm’ has even entered the vocabulary of the general public. Nevertheless, the precise details of Kuhn’s theory are often glossed over in the brief presentations one frequently encounters. This is an unfortunate consequence of its popularity. An accurate assessment of any theory depends on a careful elaboration and analysis of its underlying assumptions and its essential concepts. Yet a thorough examination of Kuhn’s theory can be difficult for the layperson: the book that introduced Kuhn’s ideas, The Structure of Scientific Revolutions (1970), revolves around a number of elaborate case studies in the history of science.

In this essay, I will present one method of avoiding this problem. I will use an analogy from outside the realm of science which will help explain the nature and purpose of Kuhn’s philosophical concepts, especially his notion of a scientific paradigm. The non-scientific topic that I’ll employ is the history of musical styles and the structure of musical compositions.

Music and Science

The concept of a paradigm is the key component in Kuhn’s philosophy of science. Briefly, a paradigm is a guiding framework of theories or ideas which fundamentally shapes and determines our understanding of the world. Newtonian mechanics, Freudian psychology, Darwinian evolution, are a few instances of a paradigm to Kuhn. For example, an evolutionist will likely interpret the data accumulated from molecular biology as confirmation of the Darwinian view which says that species have evolved over millions of years according to a mechanistic process of genetic variation and natural selection. Conversely, using a different paradigm, a creationist will regard the same data as vindicating their theory that God simultaneously formed all the distinct species about 10,000 years ago. In short, the paradigm you hold largely determines your scientific ‘facts’, since the ambiguity and vagueness inherent in a lot of scientific experiments and observations routinely admits numerous conflicting interpretations – and it’s this conjunction of observation and theoretical interpretation which creates our ‘facts’.

The separate functions of a paradigm are as follows:

1) The paradigm describes the entities of the particular science (planets, atoms, etc.),

2) How these entities behave,

3) The questions that can be legitimately asked concerning them,

4) The techniques used to answer these questions; and finally,

5) The criteria for success and failure of the various answers.

Any comprehensive belief system, regardless of whether or not it is scientific, currently runs the risk of being dubbed a ‘paradigm’. But in fact there are many non-scientific subjects which are particularly amenable to a paradigmatic interpretation. Music is a good example.

The classical sonata form practiced by Haydn and Mozart admirably demonstrates this point. Introduced in the middle of the eighteenth century, the sonata form gave composers a solid framework on which to construct and arrange their musical ideas. Basically, it’s a mold into which composers can pour their thoughts.

The sonata form incorporates a definite pattern: a short introduction; the exposition (wherein are presented the main ‘subjects’, or melodies and themes of the piece); the development (which explores these ideas, often in dramatic fashion); the recapitulation (a repeat of the exposition); and a short concluding coda. The classical sonata form also involves the use of a specific type of key relationship (not to mention the fact that the work is built on the diatonic scale). During the Classical period in music (1750-1820), the first and most important movement of a multi-movement work (symphony, string quartet, solo sonata, etc) usually employed sonata form.

The sonata form in its classical incarnation was a perfect vehicle for the organization and structuring of musical ideas. In this way it served many of the same functions as a paradigm. First of all, the sonata form furnished and described the entities with which the composer worked (first subject, second subject, exposition, development, etc), as well as the ways in which those entities behave (for example, the first subject could be traumatic or tragic in mood). Likewise, the sonata form provided the (compositional) questions that could be legitimately asked, such as “Can we introduce a new theme into the development?” as well as the techniques and standards of evaluation for answering such questions: “Yes, you can introduce a new theme, but only as long as it doesn’t undermine the recapitulation or upset the balance of the movement as a whole.” Overall, analogous to the case of science, a musical paradigm such as the sonata guides and controls the musical thoughts of the composer.

Classical music is not the only source of musical paradigms. Most popular musical forms possess their equivalents of sonata structure. In rock songs, for instance, one can detect a set of stock entities, such as themes, melodies, riffs, etc. The function of these musical ideas, as well as for example the standards of acceptable composition, are no less circumscribed or enforced in rock music than they are in classical. The experience of songs, and possibly entire records, that ‘don’t work’ or ‘don’t sound right’ is strong testimony to the latent power of musical paradigms to shape and determine our musical expectations and our musical experiences. Indeed, in this sense, popular music may exhibit paradigmatic behavior even more successfully than classical, because most classical listeners these days are only exposed to the great masterpieces of the classical repertoire, and not the many mediocre and poor compositions which constitute the vast majority of classical works. In contrast, mediocre contemporary music is a constant reminder of the enormous difficulties that face successful rock composition, both in the matter of structural form and in inspired content.

Returning to our classical music analogy, the sonata form also resembles Kuhnian paradigms in the manner of training/education in the paradigm. Like scientists, composers perfect their trade under the tutelage of accomplished masters, often in an apprenticeship lasting many years. The teachers of classical sonata form handed down this style and all the entities and standards it entails to their pupils in the same fashion that it had been handed down to them (or as they had developed it). For example, Haydn, who helped to invent the sonata form, handed down this technique to his greatest student, Beethoven. Apprentices of this musical paradigm soon learned to channel their musical thoughts through this form, much as scientists learn to construct their hypotheses within the framework of well-confirmed theories and sanctioned methodologies. The classical music teachers, furthermore, offered many musical ‘exemplars’ which they expected their students to study and emulate in their own compositions. In the end, the teachers hoped that their students would go out into the musical world and extend the scope and domain of the styles they had taught them – that is, within the paradigm of classical sonata form, or at least within classical style as a whole. Thus, students should help refine and extend the paradigm, but not reject it. This is identical to the goal of advancing understanding within a scientific paradigm, which Kuhn calls ‘normal research’.

Other Kuhnian Ideas To Adopt

Another way in which music resembles Kuhn’s paradigm theory is with respect to the concept of ‘meaning dependence’ or incommensurability. According to Kuhn, the meaning of a term is determined by the paradigm; so that the term ‘mass’ for example, has a quite different meaning in Newtonian mechanics than it does in Relativistic mechanics. Likewise, musical concepts such as ‘theme’ or ‘chord’ receive a precise meaning from the classical sonata form paradigm. As with physical theories, you have to know and understand the relevant paradigm, classical sonata form, to know what these words stand for in this context. In fact, ‘theme’ or ‘chord’ can take on very different meanings in the context of different musical paradigms; say, romantic opera as compared with baroque concerto form. More often than not, the style and usage of the things that the term (eg ‘chord’) refers to changes drastically when viewed in a different paradigm. Kuhn draws the lesson from the history of scientific thinking that a strict or exact comparison of similar terms from different paradigms is an impossible task in principle. He dubs this ‘incommensurability’.

Kuhn’s other ideas about scientific revolutions can also be adapted to the study of musical history [and possibly to any history of ideas, including the philosophy of science... Ed]. In scientific revolutions, an old paradigm is replaced by a new one, eg creationism by evolution; but the shift is ultimately really only a matter of choice (or so at least some passages in Kuhn seem to read: see pp.150-151). Kuhn believes that no scientific paradigm can lay claim to the ‘truth’ in an absolute, final sense.

Although there are some general rules of thumb for comparing the relative merits of paradigms, such as, simplicity, consistency and precision, these cross-paradigm criteria are not fixed and inviolable themselves. Rather, any method for comparing paradigms can itself be revised or rejected in the course of practice.

This incommensurability of entire scientific paradigms (as opposed to the incommensurability of identical terms from different paradigms) appears to have an analogue in music as well. We cannot compare the music of the baroque period with the music of this century, another paradigm, to discover which one is ‘better’. The entire core of values within these paradigms are different, sometimes radically so. We cannot compare, for instance, a sonata form movement of Mozart with a modern composition from Cage. We have no basis for the comparison; therefore neither one can authoritatively be said to be better. And try comparing Bach with Nirvana.

At this point you may want to reject the analogy between musical and physical theories. Your reasoning may run along the following lines: while science is concerned with trying to understand ultimate physical reality, music only aims at the production and study of aesthetically appealing experiences. In other words, scientific judgement deals with facts and ‘truths’ about our world, whereas music only involves, at best, someone’s idea of what constitutes good aural art. A hard-core relativist who accepts a radical “absolute truth does not exist” interpretation of Kuhnian philosophy would likely retort that the acceptance of a scientific theory is equally a matter of aesthetics or personal taste, as value-driven as, say, choosing your favorite rock band. Since all scientific theories are underdetermined by empirical evidence (ie they haven’t been definitively proven), they argue, there must be either personal or social factors responsible for the choice of any scientific theory. The realists (myself included) will find these assertions perplexing, if not downright false. Was the choice of the Copernican theory of the Solar System over the Ptolemaic merely a matter of taste? Does the same hold for creationism versus evolutionism? It might be argued that whereas personal (or social) opinion seems a perfectly legitimate explanation of musical revolutions (ie significant historical changes in composition and general musical taste), mere opinion does not accurately reflect all the factors involved in the scientific community’s choice of competing scientific paradigms. Objective data counts: one of the competing scientific paradigms will ultimately fit the evidence better than the other. This does not occur in the case of musical paradigms, since there is no evidence to fit.

There are other aspects of Kuhn’s thesis that do not translate well to our musical analogy. (The two types of understanding are incommensurable, perhaps.) One mismatch centers upon the concept of an anomaly, which is an observation or experiment that conflicts with the prevailing paradigm. It is evidence which doesn’t fit. According to Kuhn, unresolvable anomalies are one of the primary agents that precipitate scientific revolutions. If enough anomalies accrue to a paradigm which the paradigm’s way of thinking is unable to resolve, a revolution usually entails. Unfortunately, there is no musical equivalent of a scientific anomaly, at least not in the way that anomalies function in science. On the whole, experimental evidence does not play a large role in music: it is quite difficult to come up with a case where observations or experimental evidence led to a musical revolution [He hasn’t heard me sing – Ed]. A musical revolution would appear to resemble more an internal development than an external conflict of evidence and theory. There are no external, empirical anomalies, ie bad evidence, to judge a musical form by. What apparently happens in music instead, is that composers feel the need to express themselves in a different, unique fashion. This process constitutes a somewhat different type of revolution from scientific revolutions, for the composers might be said to be generating their own (taste) anomalies, rather than waiting for nature to present them.

Some of the difficulties with Kuhn’s theory of scientific revolutions are also reflected in our musical analogy. Kuhn seems to suggest that revolutions come in quantum steps, with abrupt transitions between world views; as in the transition from Newtonian to Einsteinian mechanics. Many critics have alleged that this view of scientific revolutions is not supported by the historical record, or, at least, is not typical of most theoretical transitions in the sciences. Musical paradigms reflect these critics’ argument: musical revolutions (say, from Jazz to Rock ’n’ Roll) do not occur all at once, in complete steps: rather, music culture evolves over long periods of time in short, careful steps. Even the most revolutionary works of composers such as Beethoven or Stravinsky were foreshadowed and based upon either their own earlier, less-radical works, or the more conventional works of other composers. In many ways, it is impossible to establish a strict dividing line between musical paradigms (and periods). Contrary to Kuhn’s belief, the same is largely true of scientific revolutions. Copernicus is often credited with overthrowing Ptolemaic astronomy, but his use of the perfect circular orbits of that earlier tradition in his new sun-centered redescription of the world has often led to his being branded ‘the last of the Ptolemaic astronomers.’ Likewise, Kuhn’s notion of the incommensurability of scientific terms is not exempt from criticism. Just as a scientist can understand and relate the different meanings of ‘mass’ in Newtonian as well as Relativistic theory, so can a composer understand and relate the different meanings of ‘chord’ in say, romantic and baroque music. Therefore, a radical interpretation of Kuhn’s doctrine of term incommensurability is not supported by the historical evidence (as Kuhn would agree, p.202).

Ed Slowik is an Associate Professor at Winona State University, MN.

Musical Paradigms: Classical Sonata Form // Rock’n’Roll

1) Entities: (classical) Theme, chord, development, exposition, etc. (rock) Theme, chord, riff, guitar solo, chorus, etc.

2) Behavior of entities: (classical) First theme in exposition is in main key. (rock) Guitar solo is in middle of song after presentation of main melodies.

3) Legitimate questions: (classical) Can a new theme be introduced in the development section? (rock) Should the song conform to a standard verse/chorus, verse/chorus, bridge, verse/chorus format?

4) Techniques for answering questions (and standards of success): (classical) Yes, but as long as it doesn’t undermine the recapitulation. (rock) Yes, but don’t expect radio air play or TV exposure for prog rock.

5) Exemplars (successful previous application of theory): (classical) A sonata form movement by one of the acknowledged master, such as Haydn, Mozart, etc. (rock) A hit song by one of the great rock bands, such as the Beatles, the Rolling Stones, etc (insert your own choice).

6) Incommensurability: In classical sonata form the ‘theme’ is designed for maximum development capacity, and is (usually) in either the tonic or the dominant key In rock music the ‘theme’ is usually designed for maximum melodic capacity, and must allow the lyrics to be set to the theme. May not strictly follow the tonic-dominant tonal scheme.

Scientific Paradigms: Evolution // Creationism

1) Entities: (evolution) Species, animals, plants, genes, etc. (creationism) Same entities, but with a supernatural designer (God).

2) Behavior of entities: (evolution) Genetic variation, natural selection, plus possible unknown natural mechanisms. (creationism) God’s creative act, with limited genetic variation and natural selection.

3) Legitimate questions: (evolution) How did this species evolve from this earlier species? (creationism) Why did God create this particular species? How does this demonstrate God’s design skills?

4) Techniques for answering questions (and standards of success): (evolution) Are there relevant structural, genetic, anatomical, spatial (location), temporal (in geological strata), etc, similarities between species? (creationism) Is it Biblical? What use is this species to humans or the environment (possibly not answerable by humans)?

5) Exemplars (successful previous application of theory): (evolution) Observed genetic variation and natural selection in living species (fleas, moths, etc); anatomical and genetic similarities in species; fossil records. (creationism) Fossil records; other evidence that allegedly disproves evolution, such as eyes, cellular complexity etc.

6) Incommensurability: In evolutionary theory ‘human’ means an animal species that has evolved over time through a process of genetic variation and natural selection (not designed). In creationism ‘human’ means a species designed by God to be masters of planet earth.