In her course Physics 1204: Physics of Music, Prof. Kathy Selby, physics, explains the mathematical relationships that help determine why some musical tunes are enjoyable and others are perceived as unpleasant.
“The amazing thing about our ears is that they take logarithms of the frequency ratios,” Selby said. Sound waves enter the ear and are transformed into pitch. Every pitch has a certain frequency, and each frequency belongs to a specific logarithm.
Some people are more sensitive to pitch than others. Those with a good ear for intonations, or variations in pitch, are more precise at interpreting the logarithms, according to Selby. Essentially, their ears follow a strict mathematical formula.
Physics can also help explain the qualities of music that people most readily identify with, such as volume and appeal. While volume depends on the sound wave’s strength – the stronger the sound wave, the louder a person perceives it– one’s affinity for a sound depends on its frequency.
Musical appeal relies on the human hearing system’s interpretation of frequency. Inside the ear, there is a thin, hair-covered tissue called the basilar membrane. The basilar membrane has a two part job: vibrate in response to sound waves entering the ear, and sort out the frequencies within those sound waves.
The vibration of hair cells on the basilar membrane triggers a nerve impulse that goes to the brain. The impulse signals the vibration’s location on the basilar membrane. This identifies the frequency of the wave because different notes excite different hairs on the basilar membrane.
A pair of clean sounding notes do not excite the same hair cells on the basilar membrane. But when two frequencies’ regions overlap, a person perceives a sort of grittiness or roughness in sound. For example, octaves are perceived as enjoyable, but adjacent notes on the piano keyboard sound ugly.
Though the course is primarily physics based, Selby compares music from different cultures, drawing attention to how music’s pleasing quality is socialized. In the U.S., the major scale is interpreted as being happier than the minor scale according to Selby. However, this is purely a Western connotation, she said as the minor scale is not sad in Irish music.
“To Western ears they say it sounds mournful; this is a music of a people who suffered. But Irish people don’t perceive it that way; they say, ‘what a happy tune’,” said Selby. Although cultural relationships between different tunes vary, the pleasantry of sound comes down to a mathematical ratio, Selby said.
“I think students, especially musicians, come away with a much wider angle view of what music is and how they relate to it after taking my course,” she said.