Harmonics on the Guitar

What is the Harmonic Series?

When you play any note on the guitar the sound you hear is a combination of that pitch and other pitches called overtones or harmonics. The pitch you play is known as the fundamental. The specific arrangement of intervals associated with the fundamental and its harmonics is known as the harmonic series. The fundamental pitch is considered the first harmonic. Below is the harmonic series starting with the low E string as the fundamental. Note that each harmonic is numbered. These numbers are used to reference a specific harmonic in the series.

The specific pattern of intervals in the harmonic series applies to every note regardless of pitch. For example, if you start with a fundamental of C, the first harmonic would be a C an octave above that. The next harmonic would be a G an octave and perfect fifth above the fundamental, and so on.

The relative strength of each harmonic decreases the higher a harmonic is in the series, which makes them harder to hear and play as you go up the harmonic series. The fundamental is the strongest harmonic since it is first in the series. Every harmonic after the fundamental is progressively weaker. Harmonics are fairly usable on the guitar until about the seventh or eighth harmonic. Some guitars may be capable of producing usable harmonics one or two harmonics higher, but beyond this, the harmonics are usually too weak to be used in actual music.

Vibration of the String

A string vibrates along its length at multiple frequencies simultaneously. These vibrations occur not only over the entire length of the string, but also by dividing the string into halves, thirds, fourths, fifths, and so on. The points where the string is divided are called nodes. These are locations on the string where it doesn't vibrate. Harmonics occur at each node.

A vibrating string is shown below as a wave to illustrate this concept. In this example, the string is divided into fifths, which means there are four nodes. The lowest point of the wave, where the two lines intersect, is a node.

The vibration of a string shown as a wave with nodes labeled

When a string is divided into several equal parts, each node is the exact same distance from the other nodes that divide the string. The harmonic that occurs at each of these nodes will be the same pitch. For example, the third harmonic occurs as the result of dividing the string into three equal parts. This means that there are two nodes. On an open string, these nodes occur at the seventh and nineteenth frets. The pitch will be the same regardless of whether you play the harmonic at the seventh or nineteenth fret.

The Fundamental

The fundamental is the first harmonic in the series. For example, if you play the open low E string, the fundamental is the same pitch as the E string. The pitch of the fundamental results from the string vibrating over its entire length.

Second Harmonic

The second harmonic is found twelve frets above the fundamental. On the open E string, the second harmonic is at the twelfth fret. The pitch of this harmonic is one octave higher than the fundamental. The node for this harmonic is in the exact center of the string, so the string vibrates in halves as shown below:

Third Harmonic

The third harmonic is found seven and nineteen frets above the fundamental. This harmonic divides the string into thirds. The pitch of this harmonic is an octave and a perfect fifth above the fundamental.

Other Harmonics

There are many harmonics beyond the third harmonic and they all follow the same pattern. Each harmonic beyond the third results from dividing the string by four, then five, and so on. Note that these concepts apply to fretted notes as well.

Harmonics from the Fundamental to the Tenth Harmonic

The following chart includes information on the harmonics up through the tenth harmonic in the series. Details are given on where they occur on the guitar and their intervallic relationship to the fundamental pitch.

Harmonic	Fret(s)	Interval Above Fundamental	Division of String
1	n/a	unison	1
2	12	octave	1/2
3	7, 19	octave + a perfect fifth^[1]	1/3
4	5, 12^[2], 24	two octaves	1/4
5	4, 9, 16, *^[3]	two octaves + major third	1/5
6	3.2^[4], 7th, ^[5], 19th, *	two octaves + perfect 5th	1/6
7	2.8, 5.9, 9.6, 14.8, * (2)	two octaves + minor seventh	1/7
8	2.3, 5, 8.1, 12, 17, 24, *	three octaves	1/8
9	2, 4.5, 7.2, 10.3, 14, 18.8, * (2)	three octaves + major second	1/9
10	1.8, 4, 6.2, 9, ^[5], 16, 20.7, * (2)	three octaves + major third	1/10

1. Harmonics at any interval other than an exact octave (or multiples of an octave) are only an approximation of the actual interval.

2. Fret numbers in red indicate that the node is occupied by (or close to) a harmonic lower in the series, which therefore overrides the higher harmonic. This may be somewhat confusing, but these frets are mentioned so that you can more easily see how each successive harmonic divides the string, creating one additional node as you move up the series.

3. An asterisk indicates a harmonic that occurs between the end of the fretboard and bridge of the guitar. The exact location will depend on the length of the string, which will vary based on the size of the guitar. A number after the asterisk indicates that the harmonic is found in multiple locations on this part of the string.

4. All fret numbers with decimal points are approximations of where the harmonic occurs. For example, the harmonic at 3.2 is roughly two-tenths of the distance between the third and fourth frets. You need to experiment to find the exact location on your guitar.

5. This harmonic is somewhere around the twelfth fret, but is overpowered by the second harmonic in the series.