Katherine Balch

New Geometry takes its title from a scene in Tom Stoppard’s play, Arcadia. In this scene, young Thomasina Coverly discovers a recursive function that allows her graph the intimate design of an apple leaf, which she calls a “New Geometry of Irregular Forms.” Thomasina’s math allows her to zoom into the miniscule veins and fine details of a shape that appears very simple to the naked eye. In my piece, I play with the opposite process: zooming out from and amplifying compact gestures through the harmonic trajectory of the piece, which passes from microtonal to chromatic to diatonic landscapes. The harmonic broadening loosely guides simultaneous trajectories of registral expansion and rhythmic diminution. But most critically, this exploration is not so bound to a process as mundane as Thomasina’s recursive math. As Valentine Coverly later remarks in reference to Thomasina’s graph, “real data is messy”, and ultimately, in the search for mathematical truth “it’s all very, very noisy out there, very hard to spot the tune…the unpredictable and the predetermined unfold together to make everything the way it is.”

– Katherine Balch