The music of JOHANN SEBASTIAN BACH has often been likened to computational logic and algorithmic thinking (most famously, perhaps, in “GÅ¡del, Escher, Bach,” by Douglas Hofstadter, which won the Pulitzer Prize in 1980). The particulars of these comparisons are sometimes rather odd, but generally speaking, there is some value in them: it must be admitted that music is almost always bursting with patterns, and computers… computers are patterns, from top to toe. The music of Bach, from the large scale organization of sets of works down to the carefully notated ornaments, contains nest upon nest of fearfully patterned musical thinking (“fearful symmetry’, as in William Blake).
The “Ciaccona’ from the Partita in D minor for Violin Solo is remarkable for many reasons, but perhaps most remarkable for doing so much with so little. Not only is it an absolutely vast work for a single (and portable) instrument, but it is laid over an incredibly simple structure. It is, among many other things, an unbelievable efflorescence of algorithm. The whole piece can in a sense be reduced to the repetition of a four-bar falling bass line with a leaning dance rhythm. If portability and efficiency were an issue, it could be described in the bottom of the first four bars (above). From this, the “Ciaccona’ folds further and further out, all the while using only a violin, with Bach finding any number of variations in figuration and violin techniques to continue the lines of thought. Even when the bass line is not literally played, it is palpably present, a controlling force.
That said, the repetition is not of a mechanical type at all. In fact, it in some sense allows a hearer (or player) to understand the musical distances being traveled without actually measuring them. And the repetitions are not artificially (that is to say, mechanically) created or remembered; they seem, rather, to create the desire to remember. In a way having as much to do with desire for escape as desire to remember, the patterns around its core are both center-fleeing and center-seeking. Many conceptual, religious, alchemical, numerological, and psychological ideas have been fruitfully applied to it as matters for interpretation. The binary-minded among us, for example, might take its 256 (that is 2^8, or 4^4 , or 100000000) + 1 measures as a significant clue. But all of these are just more variations. Its extraordinary core, its world contracted to a span, remains inarguable, and endless even when it ends.