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.
| HARMONIC | FREQUENCY | CLOSEST NOTE | OFFSET IN CENTS | Relationship |
|---|---|---|---|---|
| 1st | 440 Hz | A 4: 440.000 Hz | 0 | |
| 2nd | 880 Hz | A 5: 880.000 Hz | 0 | Octave |
| 3rd | 1320 Hz | E 6: 1318.510 Hz | -1.96 | 5th |
| 4th | 1760 Hz | A 6: 1760.000 Hz | 0 | Octave |
| 5th | 2200 Hz | C#/Db 7: 2217.461 Hz | 13.69 | Major 3rd |
| 6th | 2640 Hz | E 7: 2637.020 Hz | -1.96 | 5th |
| 7th | 3080 Hz | G 7: 3135.963 Hz | 31.17 | Dominant 7th |
| 8th | 3520 Hz | A 7: 3520.000 Hz | 0 | Octave |
| 9th | 3960 Hz | B 7: 3951.066 Hz | -3.91 | 2nd |
| 10th | 4400 Hz | C#/Db 8: 4434.922 Hz | 13.69 | Major 3rd |
| 11th | 4840 Hz | D#/Eb 8: 4978.032 Hz | 48.68 | Major 4th |
| 12th | 5280 Hz | E 8: 5274.041 Hz | -1.95 | 5th |
| 13th | 5720 Hz | F 8: 5587.652 Hz | -40.53 | Flat 6th |
| 14th | 6160 Hz | G 8: 6271.927 Hz | 31.17 | Dominant 7th |
| 15th | 6600 Hz | G#/Ab 8: 6644.875 Hz | 11.73 | Major 7th |
| 16th | 7040 Hz | A 8: 7040.000 Hz | 0 | Octave |
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.
Alex Weeks is the Logistics and Operations Manager at Upstage Productions. Alex is also an experienced audio engineer and music producer. You can check out Alex’s band Thru The Haze.
