# The brilliant harmonics on the guitar: what they are and how to produce them

Suppose you have read the articles on harmonic sounds and equable temperament. In that case, you will certainly have understood that, since the guitar is a kind of hexachord, it is, in principle, possible to produce higher-order harmonics by vibrating the string “around” specific points without pressing on the fret (which would produce a vibrant timbral sound). This article will show which harmonics are most easily generated and how to produce them.

### A brief review of higher-order harmonics

For those who have not, I recommend reading the above article, which explains harmonic sounds and their contribution to the timbre of an instrument. Considering a monochord, we can call a fixed point during vibration a “node.” Of course, we will always have two fundamental nodes corresponding to the extremes T1 and T2, but we will not consider them as they are constant in each scenario.

If we vibrate the whole string, we will produce a sound whose frequency is inversely proportional to the length and a function of the string’s tension and elastic parameters. Consider, then, a length L and produce the first sound, which, for convenience of discussion, we will call C(1) (of course, all reasoning applies to any note), where the number in parentheses indicates the octave. The result is shown in the figure:

At this point, we can proceed with a method similar to that adopted by Pythagoras in defining his diatonic scale. That is, we will introduce additional knots, which, on the guitar, will be produced by a slight touch of the finger at the height of the fret rod.

#### Harmonic on the upper octave (first)

The first step is to halve the length L (remember that in the Pythagorean procedure, we always proceed by integer ratios, which is not perfectly exact in the guitar case because of equable temperament. However, since these are minimal variations and we have to use the fingertip, which is a very imprecise “tool,” we can safely refer to Pythagorean ratios). If we halve the length, we get the same fundamental note, one octave higher, so C(2):

Having introduced node A, the induced vibration will have a frequency precisely double that of the fundamental, so in the case of the guitar, we will have, for example, on the first string an E(1) and at the 12th fret a harmonic E(2). Allow me to digress briefly: E(1) is obtained by making the string sound open-ended and thus producing a “timbral” sound rich in harmonics (including the first one, i.e., E(2)).

In contrast, the sound of harmonics is extremely “poor” since they consist of sine waves. It is admittedly true that our harmonics are imperfect (i.e., unlike those generated by an electronic synthesizer). Still, their distinctiveness is precisely their almost untethered nature from the specific instrument. It is as if, at some point, external sounds are superimposed and are enhanced precisely by their relationship to the corresponding timbres produced by the guitar.

#### Harmonic on the fifth after the upper octave (second)

Proceeding with the subdivision into whole parts, we arrive at the fundamental interval for the Pythagorean diatonic scale: the interval corresponding to the ratio of 3/2. In that case, the rope will have two knots, A and B:

In this case, the sound produced will be a fifth above C(2), so G(2). This interval is called a “fifth” because of the diatonic scale construction method and is partly explained in the article on equable temperament mentioned above. On the guitar, the division of the string into 3 equal parts occurs at the 7th fret, so with standard tuning, we will have:

1. E(1) to blank → B(2) to the 7th key
2. B(1) to blank → F#(2) to the seventh key
3. G(1) in the gap → D(2) in the seventh fret
4. D(1) to blank → A(2) to the seventh fret
5. A(1) at no load → E(2) at the 7th fret
6. As 1

#### Harmonics greater than one second on the guitar

Continuing the subdivision process, we will have:

• 4 parts: in that case, the ratio is 2/4, thus double that of 1/2, so we will again have the fundamental two octaves higher, that is, in our example, C(3). On the guitar, this occurs at the first nodal point at the fifth fret. We will see the other nodal points when we talk about octave harmonics.
• 5 parts: the ratio of 5/4 corresponds to a major third above the second octave, so taking Do(1) as the reference, it will be E(3). On the guitar, this subdivision is achieved at the first nodal point on the IV fret and the second nodal point at the IX fret.
• 6 parts: similar to the 4-part division, the 6/4 ratio is reducible to 3/2, so it will be the fifth after the second octave, thus G(3). On the guitar, this occurs at the III frets, where you will get the same notes shown in the table above but an octave higher.

The succession starting from C(1) is:

C(1) → C(2) → G(2) → C(3) → E(3) → G(3) → B♭(3) → C(4) → D(4) → E(4) → F(4) → G(4) → …

With decreasing amplitude and consequent audibility. In addition, equable temperament makes the nodal point less and less precise, so the use of such harmonics is practically nil.

#### Example of simple harmonics

In the following video, I show the generation of simple harmonics at the 12th, 7th, and 5th frets. I avoided keys IV and III because, as explained in the article on harmonic sounds, the volume tends to decrease, and many classical guitars produce very “dull” sounds. I invite the reader to try freely and evaluate the quality and usability of the sounds. I would also like to point out that the musical literature requiring such harmonics is scarce, if not completely nonexistent.

In the following picture, I show how the finger of the left hand should touch the string:

After placing the finger of the left hand, the string will be plucked with free touch (or sometimes even leaning), and immediately, the finger of the left hand will come off the string to avoid damping.

### Octaved harmonics

On the guitar, the 12th fret defines a “watershed,” dividing the string into precisely two equal parts. So far, the harmonics we have seen were all located at the top of the keyboard and were, therefore, based on a string length equal to ½L + d, where d corresponds to the stretch between the reference key and the 12th. Of course, harmonic sounds can also be obtained using the second part of the string, thus moving an octave forward.

Unfortunately, the fingerboard of a classical guitar has an average of 19 frets (some models have more frets at the first string). Therefore, the only harmonics a bar indicates are those at the 16th and 19th frets. Looking at the guitar symmetrically, it can be seen that the 16th fret corresponds to the IV. Therefore, always considering C(1) as the starting note, the harmonic will be the fourth above the octave, E(4).

Similarly, the 19th fret is the second nodal point of the 3-part division, producing a fifth above the octave, or G(3) if we start from C(1). Other octavate nodal points exist, but they correspond to parts not covered by the keyboard. Specifically, on a “standard” guitar, a nodal point should always be located in the center of the soundhole and corresponds to the third point of the 4-part string division so that it will produce the same fundamental note two octaves higher (e.g., C(1) → C(3)).

The other points (a little before, a little after the hole) are pretty troublesome to locate and memorize, so I will avoid discussion here (also because, frankly, they are used very little).

### Artificial harmonics

With a little gimmick, producing harmonics one octave higher on every note on the keyboard is possible. The method is quite simple but requires some practice. The basic principle is the harmonic at the 12th fret, which is when the length of the string is halved. By pressing any key (suppose we call it T), the new length will be L’ < L, and since the keys follow the progression of notes, the division in half of the L’ string will occur at the T + 12 key.

For example, if I wanted to produce a harmonic on the F of the first string, the nodal point would be at the 13th fret, and so would every other note. Therefore, the method of producing artificial harmonics is based on pressing the reference note (this time, you have to press it down, not touch the key) as if you were to play it regularly and then place your right hand as shown in the figure below:

In the first case, the index finger stands over the T + 12 fret rod, and the ring finger plucks the string. The index finger comes off quickly when the sound is produced to avoid damping. Similarly occurs with the thumb and forefinger, however, I tend to advise against the latter method for several reasons. While the index and ring fingers are almost similar in length, the thumb is generally shorter; therefore, this solution forces one to tilt the right hand and pinch with a very arched index finger.

However, I urge readers to try both solutions and choose the most agreeable one. The main difficulty of this method stems from the need for perfect independence of the two hands (i.e., the left hand must move without any visual guidance) and the speed of finding the key after XII where to perform the harmonic. The advice is to start by playing the chromatic scale in the first position, then reversing the motion (4-3-2-1 on each string), and, finally, make jumps between strings. You can tackle pieces such as M. Llobet’s “El testament d’Amelia,” which extensively uses artificial harmonics when you have mastered this.

#### Example of artificial harmonics

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