Bach’s Numbers: Compositional Proportion and Significance by Ruth Tatlow (review)

In Bach scholarship there is a distinct department concerned almost exclusively with finding numbers in Bach’s compositions. Some look for evidence of his use of number symbolism intended to be noticed by God alone, while others more modestly and cautiously seek the obvious, such as the ten entries in the pieces that deal with the theme of the Ten Commandments (e.g. BWV 77/1, 635, and 679), or consider more sophisticated implementations of the idea, such as how the concept of the Trinity is manifest at various conceptual and structural levels of the Clavierübung III. What is common to most of these attempts is that little effort has been made to establish a solid historical basis for interpretation. After all, how can one be certain that these numerical references were truly meant by the composer, and if they were, what additional value can one draw from such findings? Ruth Tatlow attempts to address these critical oversights, and offers a host of fresh tools for the analysis of the process by which Bach composed, compiled, and polished many of his works—and much more, as we shall see below.

The book is divided into two parts. Part I, ‘Foundations’, begins with a brief assessment of number studies of the past, and carefully establishes what the author calls ‘historically informed methodology’: through an in-depth survey of carefully selected contemporary literature, the author identifies important issues and concepts that become her theoretical and theological foundations. Emerging from this is a complex concept that Tatlow calls ‘proportional parallelism’: it is a flexible idea to implement, and was, according to her, widely shared among deep thinkers of the past. In Part II, ‘Demonstrations’, the author excavates Bach’s works for evidence of his active use of proportional parallelism. The information is presented in the form of tables with numbers, suggesting an image of Bach counting the number of bars at every possible opportunity to perfect his works. Making use of the results of recent Bach source studies, she introduces many new and exciting hypotheses regarding the plans that Bach may have had for his compositions. These emerge in part from the finished article—Bach’s autograph fair copies and the original prints—but can also be traced in the way Bach seems to have developed and perfected his compositions by adjusting the number of bars as he worked on them from the early stages.

While it may be a side issue for the author, one of the most valuable insights I gained from Part I was the meanings of certain words and concepts in the eighteenth-century literature, including ‘harmony’ (ch. 3, esp. p. 93), ‘musical triad’ (p. 77),’proportion’ (Verhältnis, p. 108), and ‘unity’ (p. 75 f.), all of which appear to have had much richer meanings and different nuances than they do today. Numerous citations are translated and commented on from the perspective of eighteenth-century music theorists, each of which demonstrates how important it is to decipher properly the complicated and hidden concepts and shadings behind these words.

Part II is particularly significant for Bach scholars. Although many of the reconstructions remain hypothetical due to the lack of definitive proof, they nevertheless offer important new insights into Bach’s compositional processes, gleaned from a new methodological approach. Supporting Tatlow’s hypothesis are three key ‘checkpoints’, discovered through her analysis of his compositions: (1) that the bar totals in Bach’s polished works are almost always a multiple of 10, frequently 100 and sometimes 1000; (2) the presence of layers of parallel proportion; and (3) the presence of a self-referential allusion either in the total number of bars or in the overall key pattern B–A–C. Tatlow concludes that ‘all the collections and multi-movement works that Bach published or left in fair copy demonstrate the characteristics of proportional parallelism’ (p. 367).

To substantiate her claims, she discusses a wide range of works...