Refracted Across Infinity

Listen to the work here!
 
Refracted Across Infinity is a study on minimalism and process composition, written for a mixed trio of instrumentalists: Bb Trumpet, Piano, and Woodblock. This piece is inspired by two categories of numbers, infinite and infinitesimal, which when combined with the real number line created a number system called the hyperreal numbers. An infinite number is defined to be a positive number which is greater than any natural number (the natural numbers are those which can be put into the infinitely long ordered list 1, 2, 3, 4…). Similarly, an infinitesimal number is one which is closer to zero than any positive value (similarly characterized as being smaller than ½, ⅓, ¼,...). Familiar notions of arithmetic must be altered when working with hyperreal numbers, but they do have a purpose in the study of modern algebra and number theory, in particular allowing for the well-defined notion of division by zero, something that is impossible in the real numbers.
 
In translating this mathematical concept to a character study for three voices, I wanted to look at how the basic melody, repeated multiple times in the trumpet part, may be played in augmentation which surpasses the length of the piece (like the extension of real numbers into hyperreals). This is how the notes for the right hand of the piano part were determined: by wrapping the notes trumpet’s melody around the form of the piece four times to produce a four-note set to accompany the melody in each section. The harmonies presented by the piano’s left hand are similarly cyclical, being simultaneously a 24-chord cycle of triadic transformations and a 14-chord cycle which is transposed in each section. Finally the metric modulations accomplished via the woodblock part represent the infinitesimal numbers in the way that the entire work seems to shift around the woodblock, like moving through a different dimension.