Phyllotaxis

The word phyllotaxis means “leaf arrangement” in Greek.  It describes the phenomenon that plants seem to grow in patterns that make for the most efficient use of space.  As a plant grows, the number of “turns” made before a new leaf or petal appears is called the phyllotactic ratio, and common ratios include 1/2, 2/5, 3/8—all ratios involving numbers from the Fibonacci sequence.  On a sunflower head, the eye is drawn to clockwise and counterclockwise spirals, and there are usually 34 going one way and 55 going the other way—also Fibonacci numbers!  This phenomenon can be recreated by generating successive points on a spiral that are separated by 137.5 degrees—the “Golden Angle” or 360°/Φ.

Phyllotaxis makes extensive use of the Fibonacci numbers, the Golden Ratio, and the Golden Angle.  The piece is separated into four sections, all of which have a golden relationship with the succeeding sections in terms of elapsed time.  The pitch material of each section is derived from various methods related to Fibonacci numbers, Lucas numbers, and the Golden Angle. Through these compositional processes, I hope to capture some of the intrinsic beauty of natural objects like the pinecone, the pineapple, and the rose.

Phyllotaxis was composed for Kimberlee Goodman with the partial support of the Otterbein Faculty Development Committee. The electronic sound is derived from earlier recordings of the flute part and from live processing of the flute, both of which are controlled from a Max patch.