May 24th, 2019
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10/31/2007 - Symphony Event Explores Tech Edge

Music, mathematics, and technology all came together at the Spokane Symphony’s “Symphony on the Edge.” Held at the Big Easy Concert House on Friday, October 5, Morihiko Nakahara conducted a program featuring definitely avant-garde music. Starting with a concerto featuring John Marshall on electric cello, to the program’s end – a premier of Parallels, a composition by EWU faculty member Don Goodwin -- the music was exciting and eclectic. In a program featuring modern works by mostly living composers, Dr. Jonathan Middleton’s Reciprocal Refractions was easily the most ‘high tech’. Middleton, D.M.A., is an Assistant Professor of Theory and Composition at Eastern Washington University (EWU). He is also the pioneer in the development of EWU’s new music informatics program.

As part of his work at EWU, Middleton created the “Music Algorithms Project”. An algorithm is a formula or set of steps for solving a particular problem. To be an algorithm, a set of rules must be unambiguous and have a clear stopping point. In mathematics, computing, linguistics, music, and related disciplines, an algorithm is a finite list of well-defined instructions for accomplishing some task that, given an initial state, starts at the beginning, proceeds through the middle, and when it gets to the end, stops. Inventing elegant algorithms -- algorithms that are simple and require the fewest steps possible -- is one of the principal challenges in computer programming. A simple example of an algorithm is a recipe for baking a cake. Although algorithms are designed to solve problems, composers have adopted them as models for creating music. This method for composing music is called algorithmic composition.

While working on the music algorithms project, Middleton became interested in Fibonacci numbers. Fibonacci numbers were named after Leonardo of Pisa, also known as Fibonacci, in 1202, although they had been described earlier in India. Fibonacci numbers and the Fibonacci sequence are good examples of "how mathematics is connected to seemingly unrelated things."

Fibonacci himself posed the first example problem while calculating a simplified model of rabbit population growth. His prediction became known as the Fibonacci Sequence -- 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ... Each term in the Fibonacci sequence is called a Fibonacci number. Each Fibonacci number is obtained by adding the two previous Fibonacci numbers together. Some items in nature that are connected to the Fibonacci numbers are: the growth of buds on trees, the pinecone's rows, the sandollar, the starfish, the petals on various flowers such as the cosmos, iris, buttercup, daisy, and the sunflower, and the appendages and chambers on many fruits and vegetables such as the lemon, apple, chili, and the artichoke.

Using his music algorithm Web site and supporting software, Middleton created his composition using the Fibonacci sequence as the source data and produced audible music. He then placed the Fibonacci theme in an orchestral arrangement, using additional music software for the production of the orchestral score used at the performance.

To try your own hand at producing music using algorithmic composition, visit the music algorithm Web site at

Billie Moreland
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