Most people self-identify as left- or right-brained. Many who consider themselves left-brained, with an affinity for music, often see themselves as humanities-aligned. But the math in music goes further than just counting beats or keeping rhythm. Fractions of octaves, harmonizing intervals and the velocity of string vibration all influence what sounds good to the brain. Music does not discriminate between left- and right-brained individuals, but those who enjoy it may be more mathematically inclined than they think.
Music revolves around the physics of sound. A string’s number of vibrations per second is its frequency. Frequency, measured in hertz, depends on four factors: string length, density, thickness and tension. The shorter a string is, the more vibrations per second it will have, and the higher the note.
That knowledge applies not only to string instruments but also to singers. Middle and Upper School choir teacher Tim Kraak said understanding sound can have positive effects on performers.
“Knowing the physics of sound makes people better musicians because you can understand why your tone sounds the way it does,” Kraak said.
The choral curriculum includes lessons to help students amplify their voices and improve their singing.
The math behind harmonization and octaves lies in division. A musical interval, or octave, is created by doubling the frequency of a vibrating string. Multiplying a frequency by an integer creates different intervals, which can stack on top of one another to form a harmonic series. Scales are made by taking these intervals and bringing them into the same octave.
“Wavelengths line up on top of each other, the neatest wavelengths being the same note, and the next neatest lining up on octaves, and then you keep dividing. Then it starts to get less neat as you go,” Kraak said.
The same principle explains clashing harmonies. Chords that sound bad resemble clashing waves.
“When the wavelengths don’t line up on top of each other, you get interference, and they start to scramble a little bit,” Kraak said.
Junior Aldegundo Brenneman, who recreationally composes music, usually does not think much about the physics behind it. For most people, it is more intuitive to listen to what sounds good.
“I’ll be playing something and eventually I’ll play it enough that it’s memorized,” Brenneman said. “Then I’ll write down the basic melody, maybe one bar, and then I would stack a set melody and write that down.”
Kraak said he often takes a similar approach. While geometric formations can help explain why notes sound the way they do, oftentimes it is easier to realize them by ear.
“The more you compose, the more you can hear ahead of time what you want and find the notes that fit what you’re hearing in your head,” he said.
Music can sound beautiful regardless of whether someone understands the theory behind it. But theory is what enables composers to create grand arrangements that seem almost magical, physics teacher Joe Martin said.
“Physics and math can help you appreciate music in a different way,” Martin said.
While most people listen passively in the car, at the gym or while working, a deeper dive into a melody reveals its mechanics. Martin said implementing math in composition can lead to new musical possibilities.
“You can make sounds that you did not know existed,” he said.
Music is often thought of as unrelated to math, and math’s role in the art form can be overlooked. In reality, music is a natural bridge between STEM and the arts, which are more connected than they may seem.
