Play middle C on a violin, then on a flute, then have someone hum it. All three vibrate at the same fundamental frequency – approximately 262 Hz. All three are technically “the same note.” And yet you could easily pick each one out blindfolded in half a second…how is that? Read on to learn about overtones and harmonics that make a sound distinguishable.
When a violin string, a column of air in a flute, or vocal cords start vibrating, they don’t produce a single pure tone, but rather a whole family of tones simultaneously. We perceive the lowest frequency in the series as the pitch; however, along with this “fundamental” frequency there is also a stack of overtones, or harmonics, above it and they typically occur at whole-number multiples of the fundamental. Play a 100 Hz note, for example, and the instrument will also generate energy at 200 Hz, 300 Hz, 400 Hz, on and on up the ladder, all layered on top of each other.
What makes one instrument sound different from another isn’t the fundamental frequency – the middle C pitch in our example – it’s the relative loudness of the fundamental frequency and each of its overtones. This combination of harmonics is called timbre, and it’s what gives each instrument its unique sound – the reason a trumpet sounds bright and brassy while a flute sounds soft and breathy even when both are playing the exact same pitch.
The exact timbre of an instrument comes down to physics and geometry. Strings, for example, vibrate along their whole length in a dense pattern of overlapping modes, producing a rich, full harmonic series. Air columns behave differently depending on whether they’re open at both ends, like a flute, or closed at one end, like a trumpet. A closed-end design suppresses even-numbered harmonics, which can give these instruments a more hollow sound.
Other types of instruments, particularly struck instruments like drums and xylophones, don’t follow the simple whole-number harmonic pattern. The degree to which their overtones depart from whole number multiples of the fundamental frequencies is also known as “inharmonicity,” and it’s why percussion can sound more like a thud or a clang than a musical pitch.
Beyond musical instruments, any sound can be broken down into its constituent parts. In the early 1800s, Joseph Fourier showed that any periodic waveform, no matter how complex, can be broken down into a sum of simple periodic sine waves at different amplitudes, frequencies, and phases. His appropriately named Fourier Transform is still used today as a method of evaluating complex sounds to determine the different frequencies of which they’re composed. While musical notes have an organized ladder of overtones, many common sounds contain a much more chaotic mixture of frequencies with no clear harmonic pattern, which is why they lack a strong discernable pitch.
So next time you hear a dripping faucet, a whirring fan, or passing car, don’t think of it as an annoyance, listen to it closely as every sound is a rich symphony of frequencies!