Harmonics, Partials and Overtones are generated by almost all instruments and help to define it’s timbre. A pure sine wave generated by a computer would not have these harmonics, flutes have very few, and guitar strings have a few more, many percussion instruments have so many partials that their pitch is difficult or impossible to discern.

The harmonics we’re interested in are multiples of the fundamental frequency of the non-dampened string. Those with frequencies that are not multiples of the fundamental frequency, are called partials.

We’ll start with a Fundamental Frequency of A2 = 110Hz which is the open A string in A440 12 Tone Equal Temperament Tuning. See the [Tuning Standards] page for more details.
*Note: C4 is Middle C although some computer software counts from zero and labels middle C as C3.

fundamental
Fundamental.

The open 5th String is an A2 or 110Hz.

1st harmonic
1st Harmonic

110Hz + 110Hz = 220Hz which sounds an Octave or A3
110 / 220 = 1/2 so the node is at 1/2 way point or fret 12.

2nd harmonic
2nd Harmonic

220Hz + 110Hz = 330Hz which sounds a 5th or E4
110 / 330 = 1/3 so the nodes are at the 1/3 points or frets 7 and 19.

3rd harmonic
3rd Harmonic

330Hz + 110Hz = 440Hz which sounds another Octave or A4
110 / 440 = 1/4 so the nodes are at the 1/4 points or frets 5 and 24.

4th harmonic
4th Harmonic

440Hz + 110Hz = 550Hz which sounds just flat of a Major 3rd or just flat of C#5 which is 554.37Hz in A440.
110 / 550 = 1/5 so the nodes are at the 1/5 points or near frets 4, 9 and 16.

The fact that the first 4 harmonics are all octaves, 5ths and a near Major 3rd reinforces the power of Power Chords and the stability of Major Triads.

The series keeps going and includes another 5th, a minor 7th, another octave, a 2nd, etc, and are easy enough to map out by continuing the math above and using a ruler to find the 1/6, 1/7, 1/8 points etc., however, the higher harmonics become very difficult to sound and are very low in volume, so are of little practical use to us.

Technique

If you lightly touch a finger to a string at a node, pluck it and i quickly remove your finger from the node, you can hear a bell like harmonic sound. Your finger has dampened all harmonics that do not have a node at that point.

The easiest one to sound is the first harmonic, whose node is at the 12th fret as indicated above, because the 12th fret is the 1/2 way point of the string. This first harmonic is an octave above the fundamental frequency.

Although it is difficult to sound harmonics above the fourth harmonic, the more interesting case is where we adjust the length of the string by fretting at say the 3rd fret with your fretting hand, and then find the 1/2 way node at the 15th fret (3 frets above the 12th fret) with your picking hand. Lightly touch the string at the 15th fret with your first finger, and pluck it with the pick between your thumb and 2nd finger.  In this way, we can easily play melody lines in this harmonic bell timbre.

What other ways have you found to use Harmonics?

Join the discussion and let us know.

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