Harmonics and sound

What are harmonics?

When we talk about sound or music, we hear the word "harmonics" many times. Actually this word is related to music harmony. If we want to understand what harmonics are, first we need to understand that sound is based on vibrations. That is, sound originates with a vibrating object and then, this vibration gets to our ears though the air. After that, our eardrum also vibrates and then our inner ear generates an electric signal (bioelectric signal). Then, this signal travels through our nervous system to our brain, where it's interpreted as sound.

Fig. 1. Vibrations in the air forming waves.

Vibrations have an oscillation frequency which tells us how fast this vibration is. For example, a heavy object vibrates slower than a light object. The heavy object vibrates at a low frequency and the light object vibrates at a high frequency. We use Herz (Hz) or cycles per second to measure that frequency. Generally speaking, the human ear can sense vibrations between 20 Hz and 20,000 Hz (20 kHz).

To have a better idea of these vibrations let's think about a hummingbird. This bird can flap its wings at around 50 times per second. So this movement generates 50 Hz vibrations which we can perceive as a very low "hum".

Fig. 2. A hummingbird flapping generates 50 Hz vibrations.

On the other hand, a mosquito flaps its wings so much faster: around 600 times per second! That's why the mosquito generates a 600 Hz vibration that we perceive as a higher pitched sound... and a really annoying one!

Multiple simultaneous vibrations

We find vibrations in nature all the time, but this vibrations are not constant nor simple. Almost every sound we hear is made of different frequencies occurring at the same time. For example, when we pluck a guitar string, the string will vibrate at different frequencies at the same time. Yet, there will be a predominant frequency which usually sounds louder. We can see that in this slow motion video:

The lowest frequency of vibration is called fundamental frequency. The other frequencies of vibration are called overtones. When these overtones are multiple frequencies of the fundamental, then we call them harmonics, phew! Let's see an example to make this clearer.

The heaviest string of a guitar has a fundamental frequency of around 80 Hz (E note). The other vibrating frequencies (overtones) in that string are:

• 160 Hz
• 240 Hz
• 320 Hz
• 400 Hz
• 480 Hz
• etc.

All these overtones are multiples of 80 Hz, hence they are called harmonics. Harmonics usually have different intensities, some of them are louder than others. This depends on many factors, like the string material, playing style or technique and point on the string where the string is plucked. In the next figure, we can see the harmonic spectrum of an A string. The peaks represent the different harmonics, each with different amplitude.

Fig. 3. Spectrum of a string with fundamental frequency at 55 Hz (note A).

A very interesting fact is that strings produce all these harmonics in a natural way. This is why the most popular musical instruments are based on strings, like the guitar, piano or violin. Anyway, there are other vibrating systems which are also very good for generating harmonics, like the pipes or bars.

The amount and intensity of harmonics determine the timbre of a sound. Harmonics are also fundamental to perceive a sound as pleasant or unpleasant. This is applied when composing, arranging and performing music, and even while mixing or mastering audio!