Graph showing the harmonic frequency spectrum

Harmonics and Overtones

Harmonics and overtones are terms used a lot by audio engineers and musicians. We will explore what they are and why they are important.

Sound moves in waves. In our article on Loudness, we talked about different frequencies. If we use tone generator and set it to 440hz we get an “A4” note. 440hz means there are 440 sound waves per second. This sound frequency is what we call A. If you play the “A4” created by the tone generator and compare it to an “A4” played on a different instrument like a piano or guitar they all sound different. This article isn’t going to explore all of the reasons they sound different, but one of the reasons is how they produce harmonics and overtones.

Before we explore harmonics, let’s talk octaves. As we said earlier, and “A4” is 440hz. The octave above “A4” is “A5” and it’s double the frequency at 880hz. “A6” is 1760hz, and so on. Same principle is applied to lower Octaves. An “A3” is 220hz, “A2” is 110hz, “A1” is 55hz, and “A0” is 27.5 hz. Since the limit of human hearing is 20hz, we can’t hear an “A-1”, but it would be 13.75hz if we could.

When you play an A4 on an instrument, you get not only that frequency, but the instrument also produces a series of harmonics. These harmonics are a mixture of upper and lower octaves, as well as other frequencies. Relative 5th’s, 4th’s, etc.. How many and what frequencies will vary depending on the instrument. As humans we can’t consciously hear each of these harmonics. We perceive them as part of the “fullness” of the instrument. If we played the note through a spectral analyzer we could see them.

The website Another Producer has a handy Overtones & Harmonics Calculator that we can use to see all of the harmonics produced by our “A4”. As we said earlier, we cant consciously hear these harmonics but they add to the tone and character of the instrument. Generally speaking, the higher the frequency, the quieter it is.

1st440 HzA 4: 440.000 Hz0
2nd880 HzA 5: 880.000 Hz0Octave
3rd1320 HzE 6: 1318.510 Hz-1.965th
4th1760 HzA 6: 1760.000 Hz0Octave
5th2200 HzC#/Db 7: 2217.461 Hz13.69Major 3rd
6th2640 HzE 7: 2637.020 Hz-1.965th
7th3080 HzG 7: 3135.963 Hz31.17Dominant 7th
8th3520 HzA 7: 3520.000 Hz0Octave
9th3960 HzB 7: 3951.066 Hz-3.912nd
10th4400 HzC#/Db 8: 4434.922 Hz13.69Major 3rd
11th4840 HzD#/Eb 8: 4978.032 Hz48.68Major 4th
12th5280 HzE 8: 5274.041 Hz-1.955th
13th5720 HzF 8: 5587.652 Hz-40.53Flat 6th
14th6160 HzG 8: 6271.927 Hz31.17Dominant 7th
15th6600 HzG#/Ab 8: 6644.875 Hz11.73Major 7th
16th7040 HzA 8: 7040.000 Hz0Octave

That’s a lot of sound from just 1 note. Next month, we will explore how these come in to play and how the relate to distortion and saturation.

The image used on this article is used by permission of Wikipedia.

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