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

Abstract

Reviewed by: Let's Calculate Bach: Applying Information Theory and Statistics to Numbers in Music by Alan Shepherd Robert L. Wells (bio) Alan Shepherd. Let's Calculate Bach: Applying Information Theory and Statistics to Numbers in Music (Cham, Switzerland: Springer, 2021). xxxiv, 352 pp. The 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.1 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.2 The response to Tatlow's work has been mixed, with some scholars praising her work and others being largely critical.3 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.4 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, [End Page 155] how likely is it that numerical results in Bach's works appear by chance versus as a product of conscious planning? Let's Calculate Bach opens with an introductory chapter laying out the main goals of the book: to use computers to understand the extent to which numbers are relevant to the music of Bach and other composers. Significantly, while Shepherd promises to explore numerous quantitative approaches to Bach, he states that there will be a special emphasis on Tatlow's theories of "proportional parallelism."5 The next five chapters lay the foundation for applying information theory to music. Chapter 2 begins by introducing the basics of information theory and numeric codes, including the notions of bits, bytes, symbols, messages, and "gematria," where letters of a word are converted to numbers and then summed to yield a single, representative value ("G-Value") (13). Shepherd emphasizes that in most cases, G-Values produce ambiguous results, so that a single numerical value could "decode" to many different words. In chapter 3, Shepherd exhaustively considers the ways a composer might encode symbols into their music, from oft-explored examples (numbers of notes, measures, and movements) to more obscure ideas (encoding via rhythm, figured bass, and Hertz frequencies). While these explorations might initially seem excessive, Shepherd is attempting to avoid bias by not eliminating any symbolic possibilities before they have been fairly considered. He also highlights the "true" coding present in a musical score, where dots on a page represent sounds to be performed (36)—a reminder that the score is, at its heart, a set of "codes" for performers. Chapter 4 considers the aforementioned problem of ambiguity in gematria and "G-Values," in which a single number might "decode" to multiple words. For instance, using the Latin Natural-Order alphabet, where A = 1, B = 2, and so forth (but I = J = 9), the word "Bach" would encode to 2 + 1 + 3 + 8 = 14. However, numerous other words could also encode to 14, such as "an" (1 + 13) and "beg" (2 + 5 + 7). The most striking result in this chapter is a set of histograms that show the number of words associated with each G-Value based on the modern dictionary, the Luther Bible, and Bach's cantata texts. All [End Page 156] cases result in a bell-like curve in which mid-range numbers produce a high level of ambiguity, while smaller or larger numbers correspond to fewer possible words. For instance, in the Luther Bible, which only contains words that would have existed in Bach's lifetime, Shepherd finds that the average G-Value represents 74 words in the Latin Natural-Order alphabet (44–45). The G-Value's high level of ambiguity leads Shepherd to...