The harmonic is a neat little trick to add some variety to your guitar style. More importantly, the principles behind harmonics are the essence of what makes a stringed instrument work, and learning about them is a valuable addition to a musician's understanding of the guitar.

Harmonics are not uncommon; you've probably heard them. I think the first song I learned with harmonics was "Love Song For A Savior". Harmonics are denoted lots of different ways in tablature: often just by the word "harmonic", other times by various different symbols, depending on the preference of the author of the tab.

How And Where Are Harmonics Played?

To play a harmonic, place a finger of your fretting hand on the biggest string, directly over the 12th fret. ("Directly over" in contrast to "slightly behind" the fret as you would normally do to fret a note.) Press down on the string slightly, but not so much that it touches the fret. While pressing the string, pluck it with your other hand (this works best with a pick or fingernail). As soon as you pluck the string, remove your finger from the string over the 12th fret. Now, even though you're no longer touching the string, you should hear the note that you would normally hear while actually fretting the 12th fret. This is a "harmonic".

But the 12th fret isn't the only harmonic. You can produce harmonics of different "orders" at every point that divides the length of the string into equal parts, as described below:

• 1st order is 1/2, dividing the string into two equal parts. This occurs at the 12th fret.
• 2nd order is 1/3 (and 2/3), dividing the string into three equal parts. This is at the 7th and 19th frets.
• 3rd order is 1/4 (and 3/4. Of course 2/4 is just 1/2), which occurs at the 5th fret and over the sound hole.
• 4th order is 1/5 (2/5, 3/5, 4/5), which occurs at the 4th, 9th and 16th frets and over the sound hole.

And so on. You can find them on your own by just working your way bit by bit down the E bass string. (Note that harmonics above the fourth order don't necessarily occur directly over frets, but usually in between.) However, each higher order is progressively quieter. Because of this, only the first few are often used by guitarists.

Theory Of Harmonics

Before continuing I should point out that the most important harmonic is the zeroth order: the entire string in one equal part not divided at all. Of course, we don't usually think of a plain open string as a "harmonic"; maybe that's why it's the zeroth instead of the first. I refer to the pitch of the zeroth order as the "primary tone".

Of course, the string can be divided into infinitely small parts, so really every point on the string has a harmonic, but most of them are so subtle that they're impossible to play. And besides, your finger is too big compared to the length of guitar string that defines the higher order harmonics. But theoretically, there are an infinite number.

Interestingly, any time you pluck a string, all the harmonics are present. You just don't notice them very much because the higher order ones are so much quieter than the zeroth order. For you mathematicians, I believe the strength of each successive order drops off exponentially. Plus the first order (1/2) is simply an octave above the zeroth (and the 1/4, 1/8, 1/16, etc. harmonics are octaves above that), which means it's really the same note and it blends in.

This is a useful concept of which to be aware as a guitar player. Although all the harmonics are always present, the higher order harmonics become louder and the lower order ones quieter as you pick or strum progressively closer to the bridge. This greatly changes the sound produced by the guitar. For a full, bassy sound, play further from the bridge. For a bright, tinny sound, play close to the bridge.

Another implication of this principle: if you listen closely there's actually a complete major "triad" (an E major chord for the E string) when you pluck a single note on one string. In other words, with a guitar "one note" is not really just one note, although the primary tone (the zeroth order) is much more prominent than the others.

Tuning Issues

If you use an automatic electronic tuner, you may have noticed that at times it will get confused and select the wrong note. The tuner may be picking up the second order harmonic (which is a "perfect fifth" interval above the first order). It might help to tune using the 12th fret harmonic, eliminating interference from the even-order harmonics.

While we're on the subject of tuning and harmonics, I would be remiss to neglect mentioning the harmonics method of tuning. This is the main way I tune. Play a 5th fret harmonic on the low E string (the biggest string), immediately followed by a 7th fret harmonic on the A string. They should be exactly the same pitch. Repeat with the A and D, and again with the D and G. Then the open B string should match the low E string 7th fret harmonic, and the open high E string should match the A string 7th fret harmonic. For alternate tunings there are similar methods. One advantage of this harmonics method is that the strings are open and thus the pitches are accurate. When you fret a string it goes a little sharp.

A further note on tuning: to tune with almost perfect accuracy, listen not to the pitch, but rather to the interference between the two strings. Interference happens when the two strings are close but not exactly the same pitch. It's kind of a vibrato, louder and quieter and louder and quieter. You have to listen very closely, and you won't be able to hear it if there's much extraneous noise. Now as you turn the tuner knob and the two harmonic pitches get closer together, the frequency of the interference "vibrato" slows down, and when it stops completely the strings are in tune. Interference is not always easy to hear, but you can use the above harmonics method whether or not you hear the interference.

Physics of Harmonics

What makes harmonics work? The first order harmonic is really like two separate strings, each one half the length of the actual string. So to the left of the 12th fret the string vibrates, and to the right it vibrates, but in the middle it's still, just like it's still at both ends of the actual string (at the nut and bridge).

So the reason you hear the harmonic when you place your finger at the 12th fret is that you muffle the zeroth order (in fact, you muffle all the even orders, that is, all the ones that divide the string into an odd number of parts: 1/3, 1/5, 1/7, etc.), But you don't muffle the 1st order harmonic. In reality, the first order harmonic you hear isn't louder than when you simply play the open string, it's just much easier to hear when the primary tone is muted.

I love learning and sharing things like this. By learning about harmonics, you don't just pick up a new technique, you actually gain a better understanding of how a guitar works. Harmonics describe the way a string vibrates, and of course the string is the most important part of a guitar. Plus I personally find it really cool how mathematical music is, from rhythm to tones and harmonics.

Practical Tips

Now to expand a bit, harmonics aren't limited to the examples given above. The E bass string is a good place to start because harmonics are easier to play on the bigger strings, but of course they can be played on any string. In fact, with practice it's not difficult to play harmonics simultaneously on two or three or even all 6 strings (in an open tuning for example. see "Silver Sword" by Huckleberry.). In standard tuning, harmonics often appear on the 1st and 2nd strings together (a "perfect fourth") or on the 2nd, 3rd, and 4th strings together (an inverted major triad).

Also, harmonics on open strings, called "natural harmonics", are not the only kind. While fingering a fret normally with the fretting hand, harmonics can be produced by tapping the string with the fingertips of the other hand. The trick is not to remove the finger too fast after tapping, but to let it linger just long enough to mute the unwanted harmonic orders. (Phil Keaggy for example does this a lot.) Tapping works without picking or strumming the fretted string, but another method is to first pick the string, and then quickly touch or "pinch" for the harmonic.

Now go play!

T-rev 3/1/2001

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