|OGDEN, Utah – Shawn Fowers isn’t looking to replace Mozart or
Beethoven with a mathematical formula, but he hopes that his recently
completed math project might be a source of inspiration for future
Fowers, who graduated last year from Weber State University with a bachelor’s degree in mathematics and minors in physics and music, has developed a process that uses modular arithmetic to create melodies from any sequence of numbers.
Over the span of six months, Fowers worked with WSU assistant mathematics professor Mihail Cocos to turn a sequence of prime numbers into music. The methodology and results of that project are now available for all to see on YouTube.com. The pair hopes to publish a paper about the project.
For Fowers, a trombone player, and Cocos, a jazz guitarist, the project offered an opportunity to combine their love of math and music.
At the start Fowers assigned a numeric value to every note in the chromatic scale. Then he developed some parameters, such as deciding to use prime numbers as the basis for the music. The next step was to select a musical mode or scale. He opted for a major key of seven notes, then divided each prime number in the sequence by eight. The remainder generated from each calculation (a value one through seven), was then used to assign a melodic note to each specific number.
The next step was to create a harmonic note, again derived by using modular arithmetic and based on a harmonic interval of six. Fowers took the melodic note’s value and subtracted the harmonic interval (a value one through six) to find the harmonic note.
“It translated so well that I had a spread sheet where I put in a new modular value and the notes in the scale and it would recalculate the melody and harmony,” Fowers said. “That allowed me to experiment with different modes and keys. The blues one sounded musically interesting, so I expanded on my idea using that key.”
Adding rhythm to the piece proved more challenging. When he introduced quarter, eighth and sixteenth notes, the results were uneven. “In that scenario, the results were so bad I deleted all traces of it,” Fowers said.
Eventually he opted to simplify the parameters and used only quarter and eighth notes, again relying on modular arithmetic and spreadsheets.
“The rhythms we came up with required some human interpretation. I added a little more conclusion to what the spreadsheets produced so they were more pleasant to listen to. Casual listeners are used to hearing items that end in a regular number of beats,” Fowers said.
|“Our method is good for generating melodic and harmonic notes;
others might find a better way to assign things rhythmically,” he said.
Fowers said this approach isn’t the only way to interpret numbers into music. “All sorts of variation could come from this method. It’s a new tool, a new method for experimenting musicians to come up with ideas and find engaging new melodies.”
The lifelong Ogden resident is mulling graduate school offers from Utah State University and USC, but he’s not sure he’ll expand on this concept in graduate school.“I’d like to be a math teacher and I’ve actually thought about the reverse of this project, using music to help teach math,” Fowers said. “Taking music and applying it to math might make it more enjoyable for students to learn the concepts, and music would help make it stick in their head.”
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