Take a note, played by a string or wind instrument, or sung by the human voice. Put it into an analyzer and see what frequencies it contains. Let's say that the note is the A two octaves below Middle C.
The note that you hear subjectively has a frequency of 110 Hz. But there are also other frequency components...
Are you starting to see a pattern? Yes, all of these frequencies are integer multiples of the fundamental 110 Hz and we call them all, including the fundamental, harmonics. This sequence of harmonics is called the harmonic series.
(As a quick aside, I prefer to think of this as the harmonic series of string and wind instruments, which are effectively one-dimensional sound sources. A two-dimensional source such as the head of a drum will have a more complex sequence of overtones, and a three-dimensional source such as a bell even more so, and these extra frequencies would not be considered to be in the harmonic series, unless coincidentally.)
So why don't we hear all the frequencies separately? Why do we hear just one note? Well, I'll have to direct you to your nearest consultant in auditory neuroscience for the latest on that one, but we can accept that we do hear just one note, and thank goodness for that or music would be nothing more than a jumble.
The harmonic series is also important in audio, aside from music.
When you plug your electric guitar into an amplifier or distortion pedal, or when you insert a 'warmth' plug-in into a track in your DAW, you are adding harmonics to the original signal.
So if you started with a simple sound such as a sine wave, which only has a fundamental frequency and no additional harmonics, then the amplifier or warmth plug-in would add harmonics in the harmonic series, just as above.
What then if we could separate out the notes of the harmonic series? This might help us understand it better.
Well I have an example, which I heard by accident and which prompted this article.
It's from BBC Radio 3, the series is called The Listening Service, and the episode is The French Horn Unwound, all of which I recommend for further investigation (some links will only be available to BBC licence holders, and only temporarily). In this episode Anneke Scott demonstrates a natural horn that has no modern valves.
Because the length of the natural horn is fixed with no valves, different notes are played by varying the tension of the player's lips. The player can relax their lips to produce the instrument's lowest note, then progressively tighten them to produce each of the notes of the harmonic series going upwards in frequency. You want to hear..?
That's a fascinating sound, both in terms of the pitches played and the timbre of the instrument. You may have noticed that not all of the notes sound in tune. This isn't the fault of the instrument or the player, it's the fault of the harmonic series itself! This causes all kinds of ramifications in music, but at the same time adds interest and texture to the musical sounds we hear.
I'm not suggesting that you take up the French horn and learn to play it (you might probably want a good modern one, then take ten years or more of tuition and practice to learn how to sound decent), but I do suggest that you consider that when you use a guitar amplifier, distortion pedal or warmth/harmonic generation plug-in, then these are the sounds, in terms of frequencies, that you are adding to your music.
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