If you have studied any discipline acoustics radio signal technology, or electronic engineering, you may remember covering the topic of harmonic frequencies. It is an integral part of how music is heard and perceived. Harmonic frequency is one component that helps us pinpoint the unique quality of sound produced by different instruments, even when they play the same note.

Definition of harmonic frequency

The frequency of a harmonic is a regular and repeating multiple of the original wave pattern, known as the fundamental frequency. If the main wave is set to 500 hertz it experiences the first harmonic frequency at 1000 hertz or doubles the fundamental frequency. The second harmonic frequency is 1500 Hz, which is three times the fundamental frequency, and the third harmonic frequency is 2000 Hz, which is four times the fundamental frequency, and so on.

Grid screen showing two sinusoids.  One has a larger amplitude than the other.

High-frequency sinusoids on the oscilloscope screen.
Clive Streeter/Getty Images

In another example, the first harmonic of the 750 hertz fundamental 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 number of nodes and antinodes.

Effects of harmonic frequency

Guitar Vibrato

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

Almost all musical instruments produce a characteristic standing wave pattern that contains both fundamental and harmonic frequencies. The precise composition of these frequencies allows the human ear to distinguish differences between two vocalists singing notes in unison at the same level of pitch (frequency) and loudness (amplitude). We also know that a guitar sounds like a guitar, not like an oboe, trumpet, piano, or drum. Otherwise everyone and everyone will sound the same. Experienced musicians can instinctively tune instruments by listening and comparing harmonic frequencies between tunings.

Harmonics vs. Overtones

The term «overtones» is often used in discussions regarding harmonic frequencies. While similar — the second harmonic is the first overtone, the third harmonic is the second overtone, etc. — the two terms are actually separate and unique. Overtones contribute to the overall quality or timbre of the instrumental sound.

Harmonic frequency distortion in speakers

The presenters are tasked with providing an accurate, harmonious representation of the instruments they design. To quantify the difference between audio input and speaker output, each speaker is assigned specification for total harmonic distortion (THD) — The lower the score, the better the speaker will sound. For example, a THD of 0.05 means that 0.05 percent of the sound coming out of the speaker is distorted or dirty.

Acoustic system Monoprice 10565 - Satellite speakers - Photo - Front and back view

Monoprice 10565 5.1-channel speaker system — satellite speaker — front and rear view.
Photo © Robert Silva — Licensed About.com

THD matters to home buyers because they can use the THD rating listed for a speaker to gauge the sound quality they can expect 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 another.

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

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