The idea of "musical complexity" has already been raised here in passing. Especially today, it is a significant one and merits further examination. There are now poles of compositional style for which complexity is a parameter; but more than that, the vast array of music available to us suggests further correspondences in this dimension. If we prepare to articulate more concrete thoughts on the subject, the first inescapable conclusion is that complexity is frequently in the ear of the beholder. Something which we do not understand sounds like an amazing tangle of thorny sounds and obtuse relationships, whereas the exact same piece might sound "normal" to even a child in another culture. The first challenge is to separate these aspects so that complexity across styles can be related in a meaningful way. It is not a simple procedure, but I am pushed along by the simple fact that I tend to hear a similar level of "complexity" in the music I like best, one which ceases to change with increasing familiarity.
The motivation is simple asymptotic perception, in the sense that incremental study yields diminishing changes to the apprehension of a piece. This is a concrete phenomenon which any of us can observe, and when combined with the notion that we are actually following what is going on, the amount of perceived action is the notional complexity. While further acquaintance can yield more appreciation, there is a level after which this perception of complexity remains constant. The primary element to this resolution is the apprehension of basic material & technique in some way analogous to that of the originating mind. This idea is necessarily vague, and perhaps merits future examination, but the simple example of theme & counterpoint are clear and so is its extension in the 19th century. Similar divisions apply in other music, and there is a very concrete point at which one perceives what is being done with what. Many questions remain, many of them interesting, but this basic apprehension is fundamental to notions of complexity. Without it there is no sense of stability for any metric, and of course that is the point of several notable postmodern attempts to conflate these ideas. Those exercises can be interesting on their own terms, and even helpful toward an understanding of the basic issues, but here they must be treated as an anomaly of contained scope.
With that posited, certain conclusions are inevitable and commonplace. Popular music is generally less complex than classical music; twentieth century classical music is more complex than eighteenth century; some world traditional styles are more complex than others, etc. We can also perceive that a composer such as Brahms or Mozart tends to maintain a consistent notional complexity throughout his oeuvre. Other composers such as Beethoven escalate during their careers, whereas many fall somewhere in the middle. There are even examples of the reverse, although that tends to occur in one large jump. Complexity can be expressed in counterpoint, in rhythm, in melodic nuance, or even in timbre. Some people have a tendency to consider monophonic music as inherently less complex, but I disagree. In fact, a more elaborate vertical organization has historically enforced simpler melodic contours. While my tastes in complexity tend to be noticeably higher than the "typical classical musician," I don't personally prioritize it to the extent that I seek out the most complex music. In short, there is complexity which is more than I enjoy, even if I do value the music in more limited doses. Analogously, I do try to restrain my own thought processes from becoming too convoluted. Nonetheless, in many areas, I will naturally enjoy the more complex music more, even after the degree of apprehension described above has been reached. Prior to that, I admit toward a possibly pathological drive to understand things which I otherwise do not.
Complexity does not necessarily relate only to simultaneous elements, and in fact duration can be a significant aspect. For instance, a fourteenth century motet frequently has a nearly overwhelming instantaneous density, but is short enough that it becomes possible to wrap one's mind around it in one sweep. If such a density had been carried out to the length of a Mahler symphony, it would be overwhelming indeed, and of course that is the sort of level some modern composers have adopted. I don't mean to make a value judgement there, but merely to note the fact. Such a piece can become exhilarating to perceive. A contrasting notion is that some music has its ideas stretched out over a longer span of time... ideas which might be presented more compactly in other styles are developed more leisurely, thus lowering the complexity. This is a contrast, for instance, between Hindustani and Carnatic classical music. Here there seems to be a certain threshold above which lengthening actually increases the complexity, because it requires more memory. The idea of "movements" and cadences in general is certainly related to this phenomenon, and provides a point at which the mind can wrap itself around the preceding moments. The origin of the "movement" is a potentially interesting topic in this regard, as it was also spurred by a desire for variety and the simple difficulty of mixing simultaneous forms. To this end, I prefer performers not to gloss over pauses without a good reason.
In Western art music, the trend has usually been toward increasing complexity. And why not? After all, a musician who has learned previous music will naturally find a slight increase in complexity to be a pleasing way to express a new personal style. The reciprocal decrease has been generally confined to specific downward jumps at the beginning of new stylistic eras, with the most recent major one at the beginning of the "classical" period. The twentieth century has seen a major bifurcation, with extremes in both directions. Perhaps the most significant example is the advent of mass-market popular music. In many ways, the extremes of complexity in various academic traditions serve as a counterweight to this phenomenon. While our age seems naturally drawn to extremes in all areas, perhaps because endpoints of a linear scale require less sensitive judgement to appreciate, there have also been various modern approaches which adopt a middle ground for complexity, not to mention the postmodern approaches which conflate it. An obvious solution to innovation without increased complexity is to find different basic material and technique. World traditional music provides a natural prospecting ground for such things, although most of the transplants in Western music have been rather superficial thus far. Another interesting approach, which involves something of a conflation, is to make the basic material & technique itself more "complex", such as in the music of Xenakis. Issues of complexity remain fundamental to musical style, as they condition audience constitution and response as strongly as any factor. The many orthogonal directions of the present provide ample means by which to innovate without increasing complexity, but it is after these combinations have been tested that the question will arise again with full force.
Administrivia: One week vacation. Next column in three weeks.