Remember the first time you played Ex. 1? (You can probably hear these harmonics without even touching your guitar or spinning the intro to Yes’ “Roundabout.”) Presumably, it wasn’t long after this revelatory moment that you discovered similar mysterious tones at both the 7th and 5th frets on each open string. Hopefully, you explored that concept and took it to new and greater heights, but if your command of harmonics begins and ends with these pedestrian natural harmonics, you’re in for an epiphany that would make Pythagoras proud.
For our purposes, harmonics (originally associated with the violin family and called flageolet tones) can be defined as non-vibrating, dead spots, or nodes, which manifest at equal divisions of a vibrating string. Playing a harmonic overtone on the guitar splits the string’s vibrational pattern into equal segments. In addition to extending the upper range of the guitar, harmonics can add a lot of color to your musical palette. Practically speaking, open strings produce “natural” harmonics, while fretted notes yield “artificial” harmonics. The physics behind them are the same. They both follow the same laws of nature and can be sounded in a number of ways. Fade into them with your volume control for soothing, flute-y or voice-like timbres, or pluck them hard for more, ahem, clang, chime, and skronk. Overdrive them and add a touch of compression, and they scream prismatically.
Regardless of how it looks, an open string set into motion vibrates back and forth between its two points of suspension—the nut and the bridge. When you fret a note, you’re simply moving those two points closer together, because your fretting finger is essentially acting as a moveable nut, thus shortening the active length of the string. Ex. 2 illustrates the vibrational path of any plucked open string. All notes—open and fretted—contain varying degrees of harmonics in accordance with nature’s overtone series: 1st harmonic = octave, 2nd harmonic = octave + perfect fifth, 3rd harmonic = two octaves, 4th harmonic = two octaves + major third, 5th harmonic = two octaves + perfect fifth, 6th harmonic = two octaves + minor seventh, 7th harmonic = three octaves, 8th harmonic = two octaves + major ninth (or three octaves + major second), and so on. (Rule of Nature: The harmonic overtone series always follows the same series of intervals relative to its fundamental.)
What we perceive as a standard open or fretted “note,” or fundamental pitch, is actually the sum total of these stacked harmonic overtones. An instrument’s tone, or timbre, is determined by its harmonic content. By their physical or electronic nature, different instruments naturally or synthetically emphasize different harmonics. Guitarists should have no problem accessing the first ten natural harmonics derived from a low, open-E fundamental, as shown in Ex. 3.
The Big Reveal
The epiphany you should soon experience (if you haven’t already) is that the overtone series generates mirror-image natural harmonics on the other side of the 12th fret as well—identical harmonics reside equidistant from the middle of any ringing string. That’s right, folks, harmonics go both ways, as we’ll explore more deeply in the conclusion of this lesson. First, know that it’s difficult to notate exact tab positions for the harmonics (and there are many of them) that are located between frets or—when you’re playing the “mirror” harmonics on the picking-hand side of the 12th fret—those that are located off the fretboard. You’ll have to fish for some harmonics’ positions and assign each a visual landmark.
For the uninitiated: Prepare natural harmonics by lightly placing a fretting-hand finger directly over a desired node on an open string, barely touching the string, and definitely not pressing the string against the fret or fretboard. Pluck the string and quickly remove your fretting hand. The resulting harmonic vibrates the string in equal parts, or “loops.”
The Great Divide
So, why does this touch-and-pluck approach work? Choose any open string and check it out: The first harmonic node divides the string in half, directly above the 12th fret. The string vibrates in two equal parts and the node produces a note one octave higher than the fundamental open string. Ex. 4a shows the node and its vibrational path. (Fact: You can actually see this figure-eight loop pattern strobing by looking across the string in front of a blank, snowy channel on your old-school TV screen!) The second harmonic node divides the string into thirds, segmenting the string directly above the 7th and 19th frets. The string vibrates in three equal loops, and each node produces a note one octave plus a fifth higher than than the fundamental. Ex. 4b shows both nodes and their vibrational path.
The third harmonic node quarters the string, directly above the 5th, 12th, and 24th frets (or virtual 24th fret if you don’t have a two-octave fretboard). The string vibrates in four equal parts, and the nodes at the 5th and 24th frets sound two octaves higher than the fundamental, while the 12th-fret node still sounds one octave higher. Ex. 4c shows the three nodes and their vibrational path. The fourth harmonic divides the string into five equal loops, and can be found directly above the 4th, 9th, 16th and (virtual) 28th frets. The string vibrates in five equal parts and each node sounds two octaves plus a major third higher than the fundamental. Ex. 4d shows the four nodes and their vibrational path.
As we progress through the overtone series, the harmonics divide the string into even smaller increments. The fifth harmonic divides the string into six equal parts, the sixth harmonic divides the string into seven equal parts, and so on. Get the idea? The harmonic nodes sit closer and closer together as you continue to divide the string more times. This makes them increasingly difficult to locate, but, with perseverance, you’ll be able to find many of them and incorporate them into your music. Now, practice finding natural harmonics on each open string. If you haven’t noticed, the overtone series contains all the notes in a major triad (root, 3, and 5) plus the b7 and 9. You can make a lot of music with just those tones. Additionally, every note in the chromatic scale, except A#/Bb, which is not present in any open string’s overtone series, is available as a natural harmonic.
Assuming you’ve already explored the inherent triad and dominant-7th arpeggios on each open string (Tip: Check out Jeff Beck’s “Two Rivers” from Guitar Shop), let’s assemble a few scales and runs using nothing but natural harmonics. Ex. 5 shows a koto-like E pentatonic minor scale—derived entirely from 7th- and 12th-fret harmonics—played from B to E, while Ex. 6 illustrates how to squeeze an entire B minor scale out of the 3rd, 4th, and 5th frets on the bottom four strings. Note the repetitive fingering patterns in each, and be sure to explore the diatonic modal substitutions for both examples. (i.e., try Em harmonic patterns over G major, or Bm patterns of D major, etc.) Ex. 7 is an excerpt from my solo on the Call’s “The Walls Came Down”—as played during recent tours with Todd Rundgren—in which I quote the song’s main riff entirely in natural harmonics.
Bar 1 shows the I-chord riff, which is built from a simple ascending and descending A major scale lick. For the IV chord (D) in bar 2, simply shift bar 1’s riff up one string group. If your guitar has a tremolo system, add some bar manipulation as indicated for extra mojo throughout.
Your Secret Sustain Pedal
Combining natural harmonics with conventional notes [Ex. 8] also offers a lot of interesting musical possibilities. Try playing natural harmonics against static or moving bass notes to create shimmering chordal sounds. Let the notes ring so that the overlapping timbres generate a full, piano- with-sustain-pedal-engaged sound. As an option, try playing the bass notes before adding the harmonics à la Jaco.
Artificial harmonics are found at equal divisions of fretted strings, and they follow the same principles as natural harmonics. The only difference lies in how they are produced. When the fret hand is occupied with its most common duty—fretting a note—a node must be both touched and plucked with the pick hand. To play an artificial harmonic one octave above any fretted note, touch the node 12 frets higher with the pick-hand index finger while picking the string between the node and the bridge with either the thumb or a pick held between the thumb and middle finger. (You can effectively reverse this technique and play “Jaco-style” by using your thumb on the node and plucking behind it with your index finger.) The same divisions apply to both open and fretted strings, so artificial harmonics seven frets above any fretted fundamental sound an octave plus a fifth higher, those played five frets above the fundamental will sound two octaves higher, and so forth. Ex. 9a demonstrates how to extract the first three artificial harmonics from a single C note, while Ex. 9b pulls them from a held Bb/C chord.
Harp On It
Lenny Breau and Chet Atkins were pioneers of harp harmonics, a blend of natural or artificial harmonics with open or fretted notes used to create cascades of chordal color. In Ex. 10, the fretting hand holds a Gm11 voicing (all six strings barred at the 3rd fret) while the pick hand sequences a series of two-string groups, each containing one fretted note and one artificial harmonic. Begin by plucking the D string using a middle-finger (m) upstroke, then play the artificial harmonic at the 15th fret on the low E string. (Use your thumb to pluck the string while your index finger touches the node.) Continue alternating the same two-string pattern across the remaining adjacent string groups, then reverse and descend the same pattern. Once you’ve got it sounding pretty, move everything up a half-step and repeat the entire routine with G#m11, Am11, Bbm11, and so on. When you feel ready, apply the same technique to the chord voicings in Ex. 11, as well as chords of your own design. Just trace each chord’s contour one octave (12 frets) higher up the neck using artificial harmonics, and you’re there!
Tappin’ & Slappin’
Both open and fretted notes can be tapped or slapped to produce brilliant harmonics. Single notes and arpeggios lend themselves to harmonics tapped mallet-style by a pick-hand fingertip, while intervals and full chords can be sounded as harmonic clusters via sideways slaps of a pick-hand finger (typically the index). First, tap and arpeggiate the first harmonic nodes located twelve frets above each fretted note, then repeat the same technique for the remaining Am7, Bm7, and Cmaj7 shapes [Ex. 12]. (Tip: Remove your tapping finger quickly.) You can also try tapping at the second nodes (seven frets higher) and third nodes (five frets higher). Execute each full-chord slap in Ex. 13 with a sharp slap of your flattened index or middle pick-hand finger, then remove it abruptly. This may or may not produce a clear artificial harmonic for every note in the chord, but the approach usually generates enough harmonic content enough to fool most ears. Bottom line? Your aim is critical on single-note taps, while chord slaps just have to be in the ballpark.
Graze the Twine ...
... and make it whine. These immortal words of wisdom from Billy Gibbons have been taken to heart by many players, as pinched harmonics (AKA “pick harmonics”) have become a regular sonic color of most electric guitarists’ tonal palettes. To really take advantage of the wide spectrum of sounds this technique produces, though, you need to be able to manipulate them at will.
In truth, these squeaky partials aren’t actually pinched, but are produced by allowing part of the thumb—usually the flesh near the base of the nail—to graze the string as soon as you pick it. The harmonic you hear is a result of your thumb touching down on a random or intended node. As you move your pick hand up and down the string, different harmonics emerge in accordance with the overtone series. Got it? Now, choke up on your pick so only its tip is exposed and pull the first nine harmonics in the overtone series from the lone C fundamental in Ex. 14. Finally, let’s go back to The Big Reveal: Transpose the same divisions to the open low-E string (i.e., shift Ex. 14’s nodes three frets lower) and check out how these pinched nodes produce a mirror image of those on the fretting-hand side of the 12th fret, as in Ex. 3. Now you’re getting it!
Did You Know …
... that except for A#/Bb, every note in the chromatic scale is available as an open-string natural harmonic? What are you waiting for? Map ’em out and write ’em down!
Learn even more about harmonics and all things guitar in The Guitar Cookbook [Backbeat] by Jesse Gress, available in bookstores and online at jessegress.com.