In the course of a lecture delivered in 1938, Sir Donald Tovey made the following observation:
A modern master of popular scientific exposition—that is to say, an eminent man of
science—has remarked that when the phenomena compel a scientific theory to become
fantastically complex we may foresee that we are observing the phenomena from the
wrong point of view: as, for instance, when the motions of the planets require a tangle of
deferents and epicycles, so long as we try to explain them as seen from a fixed earth instead
of from a central sun. The whole trouble of the official theory of sixteenth-century har-
mony lay in the fact that the theorists retained the point of view of purely melodic scales
long after these scales had become inveterately harmonic, as well as melodic, phenomena.1
It is a great pity that Tovey, exasperatingly and typically, neglects to give the name of the 'eminent man of science', since that gentleman was clearly anticipating Thomas S. Kuhn's theory of 'paradigm shifts' by several decades. As the latter explained in The Structure of Scientific Revolutions (1962), scientists, to function at all, need what he called a 'paradigm': that is to say, a frame of reference that can support their theories, plausibly explain their findings, and guide them towards further research. In many respects, such a paradigm is the scientific equivalent of a religious faith.
It is characteristic of a successful new paradigm that it works splendidly. During the phase of what Kuhn calls 'normal science', researchers make rapid advances, all appearing to confirm its validity. But soon gaps begin to appear between theory and observation. Attempts to bridge these deprive the paradigm of its pristine simplicity. Then, as contradictory findings pile up, it becomes ever more elaborate and implausible, till at last the science reaches a 'crisis', to be resolved only by the supervention of a new and radically different paradigm—at which point the cycle begins again.
In the above quotation, Tovey describes just such a crisis in the musical theory of the sixteenth and seventeenth centuries. It was resolved by the 'paradigm shift' that received classic expression in the second sentence of Rameau's Traité
1A Musician Talks (1941), pt. 2: Musical Textures, 8–9.