What Is Harmonic Frequency? You May Already Know the Answer

Harmonics help you distinguish between different musical instruments

Green sound waves coming out of a guitar

antonioiacobelli / Getty Images

If you have studied any discipline of acoustics, radio signal technology, or electronic engineering, you might remember covering the topic of harmonic frequency. It is an integral part of how music is heard and perceived. The harmonic frequency is one component that helps us accurately determine the unique quality of sound made by different instruments, even when they are playing the same note.

Definition of Harmonic Frequency

A harmonic frequency is a regular and repeating multiple of an original wave pattern, known as a fundamental frequency. If the fundamental wave is set at 500 hertz, it experiences a first harmonic frequency at 1000 hertz, or double the fundamental frequency. The second harmonic frequency occurs at 1500 hertz, which is triple the fundamental frequency, and the third harmonic frequency is 2000 hertz, which is quadruple the fundamental frequency, and so on. 

A screen with a coordinate grid, showing two sine waves. One has a large amplitude compared to the other.
High frequency sine waves on oscilloscope screen. Clive Streeter / Getty Images

In another example, the first harmonic of the fundamental frequency 750 hertz is 1500 hertz, and the second harmonic of 750 hertz is 2250 hertz. All harmonics are periodic at the fundamental frequency and can be broken down into a series of nodes and antinodes.

Effects of Harmonic Frequency

Guitar Vibrato
Guitar Vibrato. © 2014 by David Patterson. All rights reserved.

Almost all musical instruments produce a characteristic standing wave pattern that contains both fundamental and harmonic frequencies. The exact composition of these frequencies allows the human ear to discern the differences between two vocalists singing notes in unison at the same pitch (frequency) and volume (amplitude) level. This is also how we know that a guitar sounds like a guitar and not an oboe or a trumpet or a piano or a drum. Otherwise, everyone and everything would sound the same. Skilled musicians can instinctively tune instruments by listening to and comparing harmonic frequencies between adjustments.

Harmonics vs. Overtones

The term "overtones" is often used in discussions relating to harmonic frequencies. Although similar — the second harmonic is the first overtone, the third harmonic is the second overtone, and so on — the two terms are in fact separate and unique. Overtones contribute to the overall quality or timbre of the instrumental sound.

Harmonic Frequency Distortion in Speakers

Speakers are tasked with delivering accurate harmonic representations of the instruments they project. To quantify the difference between the incoming sounds and the output of speakers, a specification for Total Harmonic Distortion (THD) is assigned to each speaker — the lower the score, the better the speaker's delivery of sound. For example, a THD of 0.05 means that 0.05 percent of the sound coming from the speaker is distorted or contaminated.

Monoprice 10565 Speaker System - Satellite Speaker - Photo - Front and Rear Views
Monoprice 10565 5.1 Channel Speaker System - Satellite Speaker - Front and Rear View Photo. Photo © Robert Silva - Licensed to About.com

THD matters to home buyers because they are able to use the THD score listed for a speaker to evaluate the sound quality they can expect to get from that speaker. Realistically, the differences in harmonics are small, and most people probably won't notice a half a percent difference in THD from one speaker to the next.

However, when the harmonic frequency is distorted by even 1 percent, instruments in a recording sound unnatural, so it is wise to stay away from speakers at the high end of the THD scale.