Bach’s proportional parallelism

Ruth Tatlow is researching the phenomenon of “proportional parallelism”, a hitherto unknown element of Johann Sebastian Bach’s compositional. The research project is funded by Vetenskapsrådet (The Swedish Research Council).

A Breakthrough in Bach Research

Tatlow’s theory of proportional parallelism asserts that all Bach’s revised fair copies and published collections have three characteristics in common: the total number of bars are a multiple of ten, one hundred, and sometimes one thousand; there are perfect proportions such as, 1:1 or 1:2 on at least three different levels; and there is an embedded signature.

For example, the total number of bars in the six Brandenburg Concertos is exactly 2220, Concertos 4, and 5 having an exact total of 1110 bars, and Concertos number 1, 2, 3, and 6 also with 1110 bars, creating a a parallel 1:1 (1110:1110 bars) in 1:2 (4:2 concertos). These parallel proportions cannot be found in his composing drafts or early versions. He created them when he revised his works and collections in preparation for publication by adding few bars to movements and movements to collections.

The theory has been empirically confirmed through source data and is considered a significant breakthrough in international Bach research. For decades, musicologists have asked themselves why Bach made these small changes to early versions since they appear to have no clear musical objective. Proportional parallelism now provides an explanation for Bach’s revisions. Bach was motivated to make these changes because of what proportions and parallels meant in Lutheran Germany at the time.

Investigating Other Composers

The current research project intends to widen this investigation to include the numerical structure of composers in Bach’s sphere of influence, with the goal of forming a more complete picture of the historical development of the phenomenon of proportional parallelism. Did it exist before and after Bach’s time? The research will be undertaken along two main tracks: 1) the phenomenon’s origins and 2) its use after Bach’s death.