Early in the life of this column, I attempted to pack an enormous amount of cognitive information regarding how I view the evolution of tradition based on individual masterworks into a few paragraphs under the heading of the masterpiece phenomenon. The main theme there was the impossibility of uniform valuation, due both to the necessary mental process of selecting information as well as the effects of interactions over time. With the intervening forty thousand words of context available here, plus the simple passage of column-time itself, it becomes possible to explain some of the "technical" terms introduced there and to provide the entire discussion with a more relaxed foundation.
First it should be clear mathematically that the cardinal number of the full set of musical instantiations, whether in writing or sound, as mediated by the set of available conscious observers is a large finite number. It becomes unbounded only if we admit all possible future events, but is to be restricted here to all such events up to a specific time. The time can be stepped forward from some point in the past to form a time series. Clearly the size of the musico-perceptual set only increases with time, as we remark that preferences once posited retain a conditioning effect on subsequent events, whether mediated by oneself or by others. Or, in short, dead people still count, and very much so, as we all know. Any finite set can be ordered, and we could arbitrarily rank all music on this basis. Perhaps more helpfully, we can associate a perceptual ordinal with each musical instantiation, and collapse these instantiations in various ways. We could, for instance, regard all performances of Beethoven's 5th Symphony as one abstract musical entity (and of course we do). If we were to do something such as poll sets of people over sets of music, we would not find uniform preferences. In other words, we do not need to consider the preferences of everyone at any particular time, because many of them will have the same preferences. They still must be weighted in some way, but I tend to visualize this phenomenon on the projective plane of geometry, such that they do not require quantification. We can be quite aggressive by considering "fuzzy" preferences, as measured by a pattern of agreement, as a sort of two-headed composite entity. The result is what I call granularity, a relatively smaller set of more intense clustered perceptual entities. We can define a category of "perceptual algebra" by relationships among preferences, such as "if someone likes one item she (fuzzily) won't like some other one," and use this to yield an even smaller (although arbitrary) "spanning set" of irreconcilable preferences.
I call the resulting perceptual clusters masterpieces, and a somewhat different orientation or spanning set will yield a somewhat different view. In any proper survey of repertory, however, the full set should be spanned. What might not have been clear in the earlier article is that the threads are the discretizations (the musico-perceptual set was never really a continuum, but in some ways it is easier to view it as such) as described and then stepped through a time series. At various points, these threads bifurcate as alternate masterpieces are added within a particular perceptual framework. At other points, threads die out as they cease to produce a contemporary influence. A closely entwined mesh of threads is how I will define a tradition in these terms. The unstable situation with regard to something such as medieval music is therefore clear, because it derives from bifurcations in traditions of younger music and attempts to graft itself onto the shadow of vanished threads as well. The way that previous preferences are reinjected into the formation of new preferences is primarily what I call resonance in this model, and it is clear that this is a nonlinear phenomenon which essentially destroys a democratic view of the process (this is key, because we can extract the same resonances for arbitrary linear transformations of the original perceptual weights). The musical preferences of composers are more influential for the way in which they can consciously extend threads, etc. The same can be said for critics who can define threads, because a thread once defined becomes visible to all and consequently set in sharper focus & intensified. Such resonances can go so deeply as to affect how individuals form their preferences at a basic level, and completely realign threads. It is possible we are in the midst of such a large-scale event right now, as technology merges world traditions closely in various domains. Unfortunately, it is perceptually impossible for us to perceive such events directly, and so we cannot know e.g. how many such shifts have occurred since the medieval era, although we can take a decent guess.
People have a natural need to relate to more complex circumstances via a smaller number of specific instances. One can see this daily in popular culture with its cult of celebrity, and also in classical music with various "best of" compilations and discussions. What an analysis of this process of selection yields is an understanding of the fundamental way in which the act of selection conditions perception. We cannot sensibly hear a piece of music without some knowledge (perhaps implicit) of its context, and we cannot develop that context without a process of discretizing undifferentiated musical utterances. Once outlined in this way, and tangibly instantiated, threads of style become real actors by dictating rules of right & wrong (i.e. resonance). This arises first from the cognitive necessity of the idea of masterpiece and then from the commonalities & influences of those masterpieces strung together. What we see in turn is a rush to predesignate "masterpieces" and then a confusion resulting from the clash between those artificial designations and the phenomenon itself. Threads which might have appeared to run one way suddenly look very different, and the act of looking backward to perceive them allows the nonlinearities to condition the entire model. In short, judgements reinforce themselves until they no longer do (i.e. the phenomenon is metastable). How we might "want" things to align revolves both around the self-referential preferences themselves, as well as broader ideas on the purpose of music. However, constructing a hierarchy a priori, and making it last, is too complex to contemplate.
With these more specific descriptions in place, and hopefully not unbearably tedious or hopelessly vague, I intend to continue in two loosely related directions to explore the ideas of constraint and falsifiability.