How mathematics relates to music
"There is geometry in the humming of the strings, there is music in the spacing of the spheres." — Pythagoras.
Disclaimer: I am neither a musician nor a mathematician, though I did take piano lessons as a child and passed calculus I in college.
We hear often about the studies that show learning about music helps improve academic performance. Immediately, we think of math, right? Whole notes, half notes and quarter notes, time signatures, measures of music — we see the connections between music notation and understanding fractions. Also, mathematics and music composition both rely on patterns. But that’s only the beginning.
The many connections between mathematics and music are both ancient and cutting edge. Many of the ancient philosophers considered music a branch of mathematics, and modern-day researchers are finding applications for these connections.
When people hear the term mathematics, they first think of numbers, but the most innovative research doesn’t involve numbers, it’s more about geometry and symmetry, according to Alan Parks, mathematics professor at Lawrence University.
In the 500s B.C., the ancient philosopher and mathematician, Pythagoras (remember his a2 + b2 = c2 theorem from geometry?) discovered that the music coming from his lyre resulted from vibrations of the strings that had mathematically proportional lengths.
Pythagoras, having concluded that vibration is related to pitch, applied that knowledge to the motion of planets and noted that their sounds vary according to their rates of motion. He called this the “harmony of the spheres.”
Today, Princeton University music professor Dmitri Tymoczko’s book “A Geometry of Music” is breaking new ground in the analysis of music through mathematics. His 2006 article The Geometry of Musical Chords was the first music-theory article published in the 130-year history of Science magazine, according to his biography.
These geometric studies look at harmonies as they move from note to note in a composition. For example, are there patterns, ratios or formulas that can be observed geometrically?
Parks also cited the study of symmetry as a geometric application to music. He said to think of a square as a very symmetrical figure. If you have a square piece of cardboard, you can turn it or flip it and it’s still the same shape. The study of symmetry can be applied to the study of music — for understanding musical structures, analyzing compositions and comparing genres.
For example, a deeper study of the genre of jazz music might show similarities in the geometric structures of compositions. Such studies might also allow for more specific classifications of music, especially when trying to define a genre.
But did the classical composers think that deeply about their works? Many of them did. Wolfgang Amadeus Mozart and Johann Sebastian Bach often thought in terms of symmetry and number theory when composing music in the 1700’s.
STEM (science, technology, engineering and mathematics) fields of study are cited as the gateway to 21st century careers, but adding “art” to create STEAM may be even more innovative. In 2006, the Society for Mathematics and Computation in Music was founded for those scientists and musicians working in these interdisciplinary fields.
The next time I hear the name Pythagoras, I’ll think about more than the length of the hypotenuse of a triangle.
Linda Drezdzon is the development director for the Fox Valley Symphony Orchestra, a member of the Fox Arts Network. FAN is a grassroots arts organization made up of nonprofit arts groups serving the Fox Cities and surrounding communities with a goal of encouraging trial in all art forms. Email foxartsnetwork@gmail.com.
VOICES OF THE ARTS
A community columnist from the Fox Valley arts community writes on issues, trends and observations from the arts world each Monday in Life. Today’s columnist is Linda Drezdzon, development director of the Fox Valley Symphony Orchestra.