On the notion of "Furcations"...
As you all may or may not know, I've been working on a larger piece for some time now - a Double Viola Concerto. The concept upon which the whole piece is based is that of "Furcations," which is a bit of a bastardization of a generally scientific term for "split into parts" or "forked." Merriam-Webster defines it here. The most common uses are in medicine - especially dentistry - and biology, where an oyster is a "bifurcate mollusk." Rivers are often "bifurcate" when geologists are too proud to just say "forked."
The concept grew out of trying to figure out how to make two of the same instrument work together/against/individually whilst retaining the need for two of them in the first place. The piece is in four movements, each a different group of ways to split the components of the piece - ensemble/orchestration, form, chord structure, pitch/key areas, motivic/melodic material, and even the drama of storytelling. Each movement divides these things in as many different ways as possible, especially the first two - Bifurcations and Trifurcations - which divide in two and three, respectively. There was and continues to be much planning, writing, drawing, and staring into space that goes into this process, as well as awkward moments on the subway when a thought occurs and I accidentally spill my coffee all over someone while trying to write it down (okay - that one hasn't happened *yet* but it's a frequent fear during rush hour).
From an aural and visual perspective, as if from the audience, the first movement was relatively easy to conceptualize - two parts (and two soloists standing there), everything more or less equal, in tandem or at odds, balanced as a scale at the butcher shop; it is very obvious to observe that a system, even an aural one, is binary. However, dividing in three proved an extra peculiar challenge, especially when there are only two obvious parts. The question finally became "how do I divide two soloists into three?" and, save for the aforementioned butcher shop, it's pretty much impossible to get three people out of two, but even in a concert hall, the eyes and the ears can play tricks on us. I decided I needed what I termed the "ghost third" - an aural representation of what you see when you cross your eyes, the Pythagorean-comma-version of the way things in your visual field shift depending on which eye is closed. This idea ended up playing out in more ways than I expected, not only as a solution to the problem of illustrating Trifurcation, but also as the seed to the third/cadenza movement, entitled "Naughtifurcation." This is clearly a word I made up, but if you like surreal absurdity, googling its sibling "zero-furcation" yields this internet gem, and exploring further will make one wonder what people in England might be smoking and how one can get one's hands on it... This movement is nothing but the "ghost third," as it is every algebra teacher's worst nightmare: division by zero. (Note: more accurately, it is division into zero, but that doesn't quite make *mathematical* sense either, unless there's cake involved - then its division swiftly followed by zero.)
This "ghost third" concept is quickly becoming the core around which the entire piece is built, and while I'm not yet sure what the final movement will sound like (if you haven't guessed, it will be "Unification" cuz I'm a Disney kid so, at least on the surface, every tale has a happy ending), I'm sure the GT will play a major role in its construction and sound world. But more to the point is this: as I was free-associating the concept of furcations, other versions appeared and attempted to maneuver themselves as focal-points. One of these (that was useful for organizing ideas, but had no structural significance) was the idea of artistic perspective: two-point, three-point, zero-point, and one-point, following the order of the movements. Another that performs a real-world-application function to keep me from pulling a Wachowskis and focussing on the worlds I'm building and not the story I'm telling (looking at you, Matrix Revolutions), is what I've been calling "working ______ each other." That is, "how are these divided parts interacting?" Bifurcations finds the two parts working against each other. Trifurcations involves two of the parts working independently of each other, with the ghost third as the barrier between them.
The logical next question returns us to the cadenza movement, which is not only mathematically paradoxical as one cannot divide by zero, but also, with this new perspective, a musical representation of an imaginary boundary between two other musical entities. What does that even mean? What does it sound like? How is this illuminated in a way that not only means something in context, but also translates outside the piece itself? And, as any human being would, one then asks "how does this reference back to me?"
Now, I've got my ways of illustrating this and have a good idea of what this movement will sound like and how it will make sense, both as an individual and as a part of the entire opus. But the reference back to "me" bit is still a question that exists in the world; to help answer it, I pose three statements and allow you, dear reader, to draw your own musings and conclusions:
1) No problem is ever completely polarized, and therefore no solution is ever completely polarized.
2) The recent (last 50-60 years) upswing in countercultures becoming mainstream has fractured our cultural consciousness.
3) The Hegelian dialectic, a distillation of the construct of societal evolution, demands that every new "thesis" must have an "antithesis."
More musings and provocations to come, as well as an update on the piece's progress. :)
Thanks and love, dear readers...