Ruth Tatlow: Bach’s Numbers

Compositional Proportion and Significance
xviii + 411pp, £84.99
Cambridge University Press, 2015.
ISBN 978-1-107-08860-3

The very subject matter of this book might be enough to send you screaming to the hills. Hand on heart, I am a sceptic. My understanding of proportion in music has been (naively?) based on early musical notions that the circle of perfection represented triple time sub-divided into three elements. When I hear music compared to architecture and how the parts must relate proportionally to the whole, I think (again simplistically?) of the folly of having three consecutive phrases of 5, 17 and 11 bars. Surely things that feel  balanced are  balanced? The notion that Bach sat down like an architect and spanned out not only movements but also entire works (and then collections of works!) based on the number of bars involved would strike me as preposterous. And yet, when you sit down and draw up tables, as Ruth Tatlow has done by the dozen, the numbers stack up to support the theories she passionately advocates.

This becomes all the more clear when Bach revises his works when he is assembling them into sets. He removes entire movements, re-writes others, all seemingly with the sole aim of making the total bar counts match over huge spans of his output. Suggesting that the numbers at the end of his scores representing the bar count is strong evidence for a pre-occupation with such things simply ignores the fact that other composers do it, too – and more often than not professional copyists do the same – quite simply in order to ensure that each of the separate parts they copy out has the same number of bars! I have some difficulty accepting in larger works that Tatlow’s 1:1 and 2:1 proportions are justifiable when the selection of movements that adds up to one or other total is so random within a sequence; make a different selection from the list of movements and the maths does not work. Must we assume that Bach got to the “Dona nobis pacem” of the B minor mass knowing exactly how many bars he had to write? Presumably – since it is a repeat of an earlier movement – he already knew that, so had to be more self-controlling in composing the “Agnus Dei”?

There is a huge amount of information in these 400+ pages and the book is anything but an easy read. In her Appendix (“A theology of musical proportions and Harmony in Bach’s time”), I do not see anything that talks to me of numerical proportion and counting bars; rather it is harmony that is seen as the root of perfection, including reference to numbers (7 is omitted from the sequence of “the whole of Harmony”).

There are some slips that copy editors really should have caught (“Leh-rmeister” at a line end on p. 16 is dreadful, for example; there is also a stray dash on p. 17), but on the whole the book is beautifully laid out and printed.

Brian Clark