Ciaccona φ from Partita #2 in D minor, BWV 1004 by Johann Sebastian Bach
Karen Bentley Pollick – Solo Violin;
Stuart Diamond – Visualization
For centuries, scholars have puzzled over what appear to be mathematical structures embedded in the Ciaccona. The pillars of sonic architecture are cast in three distinct sections that unfold in sets of variations over the same bass line in a triple meter with a Sarabande rhythm. The first section in D minor is comprised of 33 variants, the second section in D Major consists of 19 repetitions, and the third section returns to the home key of D minor with 12 variations. Do the proportions between the Minor and Major modes, the number and nature of variations, and how they interchange, reflect some deeper mathematical or even cosmic meaning? Some suggest that the almost perfect proportions of the 64 variations presented in three contrasting sections mirror The Golden Ratio – a set of satisfying proportions that underlie masterpieces of architecture, paintings, and even in nature itself. That in some way, Bach’s genius allowed him to intuit the very nature of reality, and that his creative mind was so attuned to his own essence that the music he wrote exemplified these structural truths.
Or such conjecture could simply be the arbitrary musings of academics – philosophical meditations that have little to do with the art of a workaday composer, who wrote the work in grief, and perhaps tribute, after returning from a trip to discover that his wife (and the mother of seven of his children) had died.
The visuals fuse geometrical and mathematical representations of The Golden Mean, Fibonacci Series, Pyramids of Egypt, as well as the Greek letter “φ“ that has come to represent this Divine Ratio, creating a tribute to Bach's own motto "Soli Deo Gloria".