I am not a music scholar. I enjoy listening to music, and I enjoy playing music. But I have never taken the time to study music as much as I might like. My introduction to J.S. Bach did not arise listening to his music. I learned something about part of his musical oeuvre while reading Douglas Hofstadter's book Godel, Escher, Bach twenty or more years ago. Hofstadter's interest in Bach is the canon and fugue, and specifically Bach's The Art of the Fugue and The Musical Offering. Admittedly, I struggled reading Hofstadter's book. I was not familiar with Kurt Godel, and, except for his name, I was not familiar with J.S. Bach either. Only the prints of M.C. Escher, which fascinated me, had I had some prior exposure to. And Godel, Escher, Bach is not really about Kurt Godel, M.C.Escher, or J.S. Bach. Their ideas or works are mere tools for Hofstadter to talk about the coherence of the brain --- what some refer to as the "binding problem" --- which refers to the brain's ability to simultaneously receive several sensory inputs, triggering many different neurons in different parts of the brain, perhaps triggering a memory and/or a mental image of something about to happen, resulting in a unified conscious experience. Godel, Escher, Bach was a heady reading experience, even if I did not understand it all at the time, and I have often thought that it deserved a re-read a couple of decades later.
But our subject here is J.S. Bach. Hofstadter caused me to listen to The Art of the Fugue. I was probably lured into thinking that a Bach fugue is just as inventive and interesting as an Escher print. The sensory experience is different. Escher is a visual experience that confounds all experience. For a Bach fugue, you can close your eyes and make the fugue primarily an auditory experience. Best heard and listened to with a set of headphones, the meaning of fugue comes alive in Bach's exposition. If this is Bach, I thought, I am sold. I listened to The Well Tempered Clavier and The Goldberg Variations as well and discovered the same experience. What the listener is experiencing is polyphony: multiple voices, sometimes "speaking" at the same time, often responding to an earlier voice, but nevertheless speaking harmoniously and recursively. This is referred to as counterpoint. Among contemporary composers, the music of Steve Reich is an example of counterpoint. In harmony and recursion, there is a sense of coherence that simulates in part the kind of coherence that the binding problem speaks to.
Music and mathematics have been associated with each other since antiquity, and there is a "mathematical" feeling to Bach's music, not only its metre, but its harmony as well. This has been noted by others, including Hofstadter. Where music, like the compositions of J.S. Bach, present patterns and harmony, it is not surprising that we should find a relationship between numbers, functions, and rhythm and harmony. In contrast, I think of a work like Ornette Coleman's Skies of America, which for lack of a better word seems "chaotic," inspired by that aspect of life where patterns are disrupted and dissonance prevails. It is still music, but the mathematical beauty that some find in canons and fugues seem to break down in a composition like Skies of America. In the liner notes to Skies of America, Coleman writes, "Skies of America is a collection of compositions and the orchestration for a symphony orchestra based on a theory book called The Harmolodic Theory which uses melody, harmony, and the instrumentation of movement of forms . . .The writing is applied to harmolodic modulation meaning to modulate in range without changing keys. There are eight themes and a harmolodic movement for each theme." But harmolodics, admits Coleman, is an expression that is "freed from tonal limitations, rhythmic pre-determination, or harmonic rules." Fugues and canons, which are constrained by tonal limitations and harmonic rules, do not march to the harmolodic theory. It may not be the case that all forms of music share an affinity with mathematics.
The affinity between music and mathematics must be derivative of the physics of sound and how sound is managed by the auditory cortex in the brain. Pascal Boyer points out that the architecture in the brain's auditory cortex evolved to allow humans to to hear specific frequencies for vowels and consonants, and this capacity has predisposed our species to detect, produce, remember and enjoy music. "This is a human universal," he writes in Religion Explained. "There is no human society without some musical tradition. Although the traditions are very different, some principles can be found everywhere. For example, musical sounds are always closer to pure sound than to noise. The equivalence between octaves and the privileged role of particular intervals like fifths and fourths are consequences of the organization of the cortex. To exaggerate a little, what you get from musical sounds are super-vowels (the pure frequencies as opposed to the mixed ones that define ordinary vowels) and pure consonants (produced by rhythmic instruments and the attack of most instruments). These properties make music an intensified form of sound experience from which the cortex receives purified and therefore intense doses of what usually activates it. So music is not really a direct product of our dispositions but a cultural product that is particularly successful because it activates some of our capacities in a particularly intense way."
Boyer's view that music is an outgrowth of our capacity to hear speech and communicate is not a universal view; others believe that music is a prototype communication system connected to our emotional wiring. In short, some form of music, preceded linguistic communication. In Mapping the Mind (see November 6, 2011 post), Rita Carter describes a "tingle factor" associated with music triggering an emotional response --- relaxation, arousal, tension, relief --- because sound is processed in parallel by the limbic system, which notes its emotional tone, and perhaps recognizes a similarity between a musical tone and vocal signals that carry emotional messages. J.S. Bach's fugues and canons generate an emotional tug that primarily triggers relaxation in my view, and certainly a sense of order within the world. The emotional connection may explain a close correlation between music and religion, particularly where rapture is a component of the religious experience.
In reading a biography of J.S. Bach (1685-1750), by one of the leading Bach scholars, I thought I might learn more about the fugue and counterpoint. I did not. I probably learned more about counterpoint from Hofstadter. Wolff's book assumes a level of knowledge of music and Bach's music that I do not yet have. But I did learn much more about Bach the composer and the man then my limited experience with his most familiar fugues and canons, which are perhaps the most secular pieces of his ouevre.
Bach is a musician of the 18th century Enlightenment, and not surprisingly his music is inspired by his belief in his god, and the influence of the Lutheran Church in central Germany is huge in both his life and the life of the community in which he lived. Bach is the composer of many sacred works that I am totally unfamiliar with, but I suspect that true Bach aficionados are undoubtedly rapturous about. Just as religion and the State were joined at the hip, religion and the arts had sponsors in common, if not unified interests as well. Religion likely embraced music because it did "tingle" emotions and, as others have opined, music can be a shared community building experience that institutions, whether religious or not, have deployed in the recruitment and retention of adherents. To the extent that religion is a transcendent experience, music can be transcendental as well. A tour of any major art museum around the world to look at the paintings of leading painters prior to and even during this era reveals the close relationship between art and religion. Even in the 17th century Dutch and Flemish paintings of landscapes, seascapes, and ordinary life that does not transparently wear some religion on its canvas, there is nevertheless the theme that no event, however small in the cosmic scheme of things, is not one of god's creations. In science and math, Newton and Leibniz were both wedded to their religions and the governing political-religious authorities. The interesting side of this relationship is that the arts are substantially funded by the political or religious authorities. On the payroll of the communities in which he lived, Bach was essentially a public servant, and his professional obligations included providing for church music and music at other public events. True, there were some private, secular gigs on the side at coffee houses and other venues that provided remuneration, but composing and performing sacred music for church services was the priority of his employment. For musicians today whose music might be said to be inspired by the sacred, funding from political and religious authorities or sources is not all that significant. One has to wonder, however, whether the world would ever know Bach's canons and fugues if it was not for that system of public funding of the arts that existed in centuries past.
An aspect of Christoph Wolff's biography of J.S. Bach that intrigues the reader is the intellectual candor of the author. One of the learnings from this biography is that Bach's life, while documented in some ways, is not well-documented in other important details. Furthermore, much of Bach's written musical scores have not survived. Bach himself did not write down much about his life. And Wolff admits in his preface, "Thus, conjectures and assumptions are unavoidable, and this book necessarily calls for numerous occurrences of 'probably,' 'perhaps,' 'maybe,' and the like." If only the writers, editors and redactors of the Bible and its commentators --- Hebrew and Christian portions alike --- had the courage to muster that kind of intellectual courage to admit that their sources were not so well documented and could not bring themselves to confess that they were forced to speculate and conjecture, and that some of what they were retelling was, quite frankly, "probably" the stuff of fiction. There are a lot of "probablys," "would haves," and "perhaps'" in this telling of the life of J.S. Bach. Still, it is a credible biography; there is enough of a contemporaneous historical record about his life, and the written works he left behind that support the telling of this story, despite what is missing.
A highlight of Bach's life in music, in my view, is his constant rewriting and even "morphing" of earlier musical works. One could only learn this from an expert on Bach. Wolff refers to this as Bach's constant pursuit of musical perfection. This is not all that unusual in modern times: songs written in today's musical genres do not always sit still; they have ways of evolving. Bach evolved his music to suit different instruments and perhaps a different listener. His secular music borrowed from his sacred music. Wolff conjectures that in borrowing from previous compositions, Bach was economizing in meeting his obligations to his employers, essentially saying that there was no way that Bach could truly create a novel composition week-in and week-out for decades without borrowing from earlier investments of creative time. Wolff is probably correct. This fact also allows Wolff to conclude that while we do not have every written composition that Bach created, we probably have the core of his work, enough to conclude that, for his time, Bach was the most inventive musical composer of his time, whose works resembled no other composer.