The last two decades have seen the opening of several new paths in eighteenth-century musicology, and Robert O. Gjerdingen has opened one of these: schema theory. Schemata are ‘stock musical phrases employed in conventional sequences’ that function as harmonic, melodic and rhythmic frameworks for musical passages. Evidence of such schematic thinking has emerged through related studies on partimento and solfeggio. Solfeggio practice of the time manifests a schematic way of thinking about music, being mostly based on simple hexachordal patterns which, as studies progressed, could be embellished in different ways. Vasili Byros has addressed the ‘archaeology’ of hearing through reception history, and offered strong evidence that eighteenth-century ears did hear schemata. Interweaving corpus studies on music of the long eighteenth century (1720–1840), contemporary music criticism and reception history, as well as didactic documents from that era, Byros sheds new light on the ways in which schemata were perceived at the time. A recent contribution by Gilad Rabinovitch uses a live improvisation in the style of Mozart by Robert Levin to demonstrate the importance of conventional schemata for historical improvisation.

Recent studies propose that J. S. Bach established ‘parallel proportions’ in his music – ratios of the lengths of movements or of pieces in a collection intended to reflect the perfection of divine creation. Before we assign meaning to the number of bars in a work, we need to understand the mathematical and musical basis of the claim.

First we need to decide what a ‘bar’ is and what constitutes a ‘movement’. We have explicit evidence from Bach on these points for Bach's 1733 Dresden Missa, and his own tallies do not agree with those in the theory. There are many ways to count, and the numbers of movements or bars are analytical results dependent on choices by the analyst, not objective data.

Next, chance turns out to play an enormous role in ‘parallel proportions’. Under certain constraints almost any set of random numbers that adds up to an even total can be partitioned to show a proportion, with likelihoods better than ninety-five per cent in sets that resemble the Missa. These relationships are properties of numbers, not musical works. We thus need to ask whether any apparent proportion is the result of Bach's design or is simply a statistically inevitable result, and the answer is clearly the latter. For pieces or sets with fewer movements the odds are less overwhelming, but the subjective nature of counting and the possibility of silently choosing from among many possibilities make even these results questionable.

Theories about the number of bars in Bach's music and possible meanings are interpretative, not factual, and thus resistant to absolute disproof. But a mathematical result of the kind claimed for ‘parallel proportions’ is essentially assured even for random sets of numbers, and that makes it all but impossible to label such relationships as intentional and meaningful.