Instrumentation:

2 Flutes (2nd dbl. Piccolo)
2 Oboes (2nd dbl. English Horn)
2 Clarinets in Bb
2 Bassoons (2nd dbl. Contrabassoon)

4 Horns in F
3 Trumpets in Bb
2 Trombones
Bass Trombone
Tuba

Timpani
Percussion 1: Glockenspiel, Chimes, Bass Drum, Crash Cymbals
Percussion 2: Crotales, Vibraphone, Gong, Sus. Cymbal

Harp

Violin I
Violin II
Viola
Violoncello
Contrabass

Duration: 7:15

Fractals are self-similar subsets of points in space, appearing identical at all levels of magnification. These phenomena occur both theoretically (in mathematics) and in concrete form in the natural world. This piece is my second experiment utilizing the relationship between mathematics, nature, and music; I herein employ fractals and fractal relationships to create flow and continuity.

The base unit from which I derived most of the musical elements is the introductory melody—it appears in some form in nearly every section of the piece. The music that occurs later on, while different on the surface, uses the same material as the beginning; it merely appears at a different fractal magnification. Some of the methods I employed to represent this difference in level are changes in registration, harmony, rhythm, and tempo. There is also a connection between the melodic contour of the melody and the registral contour of the entire piece, and other similar inter- level connections exist. The fractal magnification can be seen as a movement toward a central point, and this is the source of the title of the piece: Convergence.

As related to fractals, this convergence is unachievable. No matter how many times one magnifies a fractal, it will always appear the same, and will continue to do so indefinitely. Music itself may seem incompatible with this concept; one can magnify a piece to a section, to a melody, to notes, rhythms, and eventually down to single pulses of air or dots on a page, and each of these levels will appear different. The goal of this piece, therefore, is not to create a literal fractal—it is to evoke fractal-like qualities in the music and to demonstrate the relationship of such concepts to compositional ideas which have existed for hundreds of years.

March 2021 - Buffalo, NY