DISSONANCE AND HARMONY: RESPONSE TO DANIEL R. MELAMED

I am grateful to Daniel R. Melamed for taking the time to reviewmy work, and for his conclusion that ‘This is scholarship that deserves close and respectful attention, but I do not think that its results can be taken at face value, however attractive they appear’ (‘“Parallel Proportions” in J. S. Bach’s Music’, Eighteenth-Century Music / (), ). That Melamed is not convinced by the results is, of course, fine by me. What I am concerned about, though, is his misleading representation of the theory that could deter new readers from Bach’s Numbers: Compositional Proportion and Significance (Cambridge: Cambridge University Press, ), or sow doubt for those who have found it inspiring. There seems to be a dissonance in the article that makes it hard to discern Melamed’s aim. Is it designed to take the discussion forward, or to discredit the theory of proportional parallelism? As Melamed is a valued colleague, I trust his desire is to open discussion of the topic, regardless of his opinions. For the readers’ sake, therefore, I will now comment upon aspects of his article that, in my view, misrepresent the theory. Throughout the article there is a troubling oversimplification of the nature and scope of proportional parallelism, including several statements that imply serious misreading or misunderstanding of my work. For example, Melamed writes: ‘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  Dresden Missa, and his own tallies do not agree with those in the theory’ (); ‘we have to acknowledge that there are multiple ways to count’ (); ‘There aremultiple ways to assemble the various choices, but only the ones that work are presented: others are silently rejected’ (). These, and similar phrases, give a distorted view of my theory, and could imply to the unsuspecting reader that I had not considered how to count bars and movements, had disregarded the evidence in Bach’s manuscripts, and was unaware of the multiple ways of counting. As anyone who reads Bach’s Numbers can see, this is simply not the case. The section ‘Foundations’ (chapters – of Bach’s Numbers, – ) lays out systematically every element of the source-based theory: how Bach and his contemporaries used and counted the bar, how they planned and laid out compositions, scores and manuscripts, how and why I selected data, how and why I chose the methodology, how numbers in music and the arts were understood and practised in Bach’s time, and much more. These first chapters include numerous seventeenthand eighteenth-century sources not previously seen or examined in Bach scholarship. Together they provide our discipline with a solid foundation on the basis of which numbers and compositional ordering can be discussed with integrity. The theory of proportional parallelism has been evolving for decades and continues to do so. One unexpected development since the publication of Bach’s Numbers was the discovery in  that Chopin used Bach’s proportional ordering as the basis for his own collection of twenty-four preludes (see Tatlow, ‘Symmetry and a Template: Bach’s Well-Tempered Clavier, and Chopin’s Preludes, Op. ’, in Bach and Chopin: Baroque Traditions in the Music of the Romantics, ed. Szymon Paczkowski (Warsaw: The Fryderyk Chopin Institute, ), –). This startling feature of the score shows that Bach’s proportional ordering had been noticed by Chopin himself in /, long before Eighteenth-Century Music /, – © The Author(s), . Published by Cambridge University Press