Overtone vs Harmonic
Overtone and harmonic are two topics discussed under stationary waves in wave mechanics. These two topics play a vital role in fields such as acoustics, Audio engineering and even mechanical engineering. It is very important to have a proper understanding in these concepts in order to excel in such fields. In this article, we are going to discuss what overtone and harmonic are, their similarities, the definitions of overtone and harmonic, and finally the differences between overtone and harmonic.
What is Harmonic?
To understand the concept of harmonic properly, one must first understand the concepts of standing waves and fundamental frequency. Imagine two identical waves travelling in opposite directions; when these two waves meet, (superimpose), the result is called a standing wave. The equation of a wave travelling in the +x direction is y = A sin (ωt – kx), and the equation of a similar wave traveling in the –x direction is y = A sin (ωt + kx). By the principle of superposition, the resultant waveform from overlapping of these two is y = 2A sin (kx) cos (ωt). This is the equation of a standing wave. x being the distance from the origin for a given x value the 2A sin (kx) becomes a constant. Sin (kx) varies between -1 and +1. Therefore, the maximum amplitude of the system is 2A. The fundamental frequency is a property of the system. At the fundamental frequency, the two ends of the systems are not oscillating, and they are known as nodes. The center of the system is oscillating with the maximum amplitude, and it is known as the antinode. A harmonic is any of the integer multiplications of the fundamental frequency. The fundamental frequency (f) is known as the first harmonic, and 2f is known as the second harmonic, and so on. A highly useful application of harmonics is the Fourier analysis. In Fourier analysis, any periodic function can be built using the harmonics of a simple wave such as a sine wave.
What is Overtone?
Overtone is defined as any frequency having a larger value than the fundamental frequency of the system. When an overtone is combined with the fundamental frequency, it is known as a partial. A harmonic is such a partial having an integer multiplication of the fundamental. Such partials are produced in every musical instrument. These partials are the reason why each musical instrument has its distinct sound. If musical instruments created pure harmonics, every one of these instruments would sound exactly the same. In naming the overtones, the second harmonic is named as the first overtone etc.
What is the difference between overtone and harmonic?
• Harmonics are exact integer multiplications of the fundamental frequency, but overtones can take any value above the fundamental frequency.
• The fundamental frequency itself is considered as the first harmonic, but it is not classified as an overtone. Not all overtones are stationary waves. Only the overtones matching the frequencies of the harmonics act as stationary waves. All harmonics are stationary waves.