Let's Calculate Bach: Applying Information Theory and Statistics to Numbers in Music by Alan Shepherd (review)

T he music of J. S. Bach has long been the subject of numerical investigations, from the work of Arnold Schering and Friedrich Smend in the early twentieth century to more recent scholarship involving duration, tempo, and compositional architecture. The matter of numbers in Bach took a new musicological turn in 2015 with Ruth Tatlow’s Bach’s Numbers: Compositional Proportion and Significance. In this work, Tatlow aims to provide documentary and numerical evidence that Bach’s published works demonstrate simple internal proportions of 1:1 and 1:2 in measure counts and/or numbers of movements. The response to Tatlow’s work has been mixed, with some scholars praising her work and others being largely critical. In particular, Daniel R. Melamed suggests that many of Tatlow’s claims about intentional, planned proportions are unsupported by documentary evidence, and the numbers likely result from a combination of analytical choices about counting measures/movements and mathematical chance. It is in the context of these discussions that Alan Shepherd’s Let’s Calculate Bach: Applying Information Theory and Statistics to Numbers in Music has arisen, seeking to answer questions not of musicology, but of probability and statistics: namely,