Nature's Way: The Miracle of Natural Harmonics

Imagine this in your mind’s ear: You pick up a guitar and lay a finger on the low E string directly above the 12th fret, making contact but not depressing the string, deftly pluck it and immediately remove your finger to produce a bell-toned E natural harmonic, and then, while letting it ring, do the same thing using a raking action to pick the top three strings low-to-high (G, B, and E).
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Imagine this in your mind’s ear: You pick up a guitar and lay a finger on the low E string directly above the 12th fret, making contact but not depressing the string, deftly pluck it and immediately remove your finger to produce a bell-toned E natural harmonic, and then, while letting it ring, do the same thing using a raking action to pick the top three strings low-to-high (G, B, and E).
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Imagine this in your mind’s ear: You pick up a guitar and lay a finger on the low E string directly above the 12th fret, making contact but not depressing the string, deftly pluck it and immediately remove your finger to produce a bell-toned E natural harmonic, and then, while letting it ring, do the same thing using a raking action to pick the top three strings low-to-high (G, B, and E). Hear that? (Of course, you could actually play it, but the “mind’s ear” is a powerful thing.) It’s the E minor chord in natural harmonics that kicks off a classic prog-rock song.

Okay, so you’ve been there/done that. But if you haven’t dabbled in harmonics much beyond the “Roundabout” intro—maybe you’ve discovered they also exist at the 7th and 5th frets, used them to tune up, or perhaps elicited a few Buchanan/Gibbons-style squeals and squawks—you may have wondered what’s really going on here. In a word, physics.

GOOD VIBRATIONS

A plucked open string vibrates in a continuous loop between its two points of suspension—the nut and the bridge. Conventional fretting shortens the string length, hence raising the pitch in half-step increments as you travel up the fretboard. What many don’t realize is that when we play any note, open or fretted, we hear what is called a fundamental pitch, one whose tonal characteristics are shaped by its inherent harmonic overtones. The harmonic overtone series is omnipresent in nature and is contained in varying degrees (though not always audibly) in every sound we hear, both musical and otherwise. It’s called a “series” because its order of ascending intervals always follows the same sequence regardless of the fundamental. Why? It’s all about division.

DIVIDE & CONQUER

Simply put, natural harmonics on the guitar are dead spots, or nodes, that occur at equal divisions of any open string, and they always follow the same order: The first harmonic divides a string in half, the second into three equal parts, the third into four equal parts, the fourth into five equal parts, and so on. Though this study is limited to natural harmonics played on the fretboard on or below the 12th fret, it’s important to realize that a mirror image of the following node divisions also occurs between the 12th fret and the bridge. In other words, you can produce the overtone series in either direction, but you’ll eventually run out of handy fret markings and have to go “fishing” for them when venturing above the fretboard.

Ex. 1a lays out the overtone series up to the 11th harmonic using an open-A fundamental. The first harmonic node divides the string in half at the 12th fret and produces a harmonic one octave above the fundamental. Moving towards the nut, the rest of the overtone series occurs as follows:

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Second harmonic = 7th fret, third harmonic = 5th fret, fourth harmonic = 4th fret, fifth harmonic = slightly above the 3rd fret (notated in TAB as “3+”), sixth harmonic = slightly below the 3rd fret (notated in TAB as “3-”), seventh harmonic = between the 2nd and 3rd frets, eighth harmonic = slightly above the 2nd fret (notated in TAB as “2+”), ninth harmonic = slightly below the 2nd fret (notated in TAB as “2-”), tenth harmonic = between the 1st and 2nd frets, and eleventh harmonic = between the 1st and 2nd frets.

The intervals produced by these ascending harmonics always follow the same order in relation to the fundamental:

Octave (first harmonic); octave + fifth (second); two octaves (third); two octaves + major third (fourth); two octaves + fifth (fifth); two octaves + flatted seventh (sixth); three octaves (seventh); three octaves + major second (eighth); three octaves + major third (ninth); three octaves + flatted fifth (tenth); and three octaves + fifth (11th).

Get to know them because here’s the good news: When we change the fundamental to the open D and E strings (Examples 1b and 1c), all of the exact same node divisions and order of intervals still apply. Your D.I.Y. project is to similarly map out the natural harmonics on the remaining three strings and memorize where they live—each one has a permanent address. (Tip: Once you include the G string, you’ll have access to natural harmonics for every note of the chromatic scale.)

TEAR DOWN THAT WALL

When you combine natural harmonics across several adjacent strings, organized patterns emerge and can be employed to play melodies. For instance, the simple root-2-3-4- 3-2-root melody in A (A-B-C#-D-C#-B-A) in Ex. 2a can be played entirely using harmonics on the bottom three strings between the third and fifth frets, as shown in Ex. 2b. Check it out: We use the third harmonic on the fifth-string/5th-fret to sound the opening and closing A’s, the “3+” node (fifth harmonic) on the sixth string for the B’s, the fourth-fret node (fourth harmonic) on the fifth string for the C#’s, and the third node (third harmonic) on the fourth string for the lone D. This creates a nice, tidy diagonal-shaped pattern that is easy to memorize.

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Ex. 3a superimposes the same harmonics over a partially syncopated rhythmic motif resulting in something very similar to how I played my solo in the Call’s “The Walls Came Down” on past Todd Rundgren tours. Ex. 3b illustrates the same figure transposed to D, the IV chord. Note how the patterns are identical, albeit on a different string set. However, when we go to create the V-chord (E) version of the line, we run out of low strings and can’t use the same pattern— that would only work on a 7-string sporting a low-B string—so we adapt it using octave-higher F#’s (fourth node on the fourth string/4th fret) as shown in Ex. 3c. Put ’em all together as follows and you’ve got yourself a 16-bar solo played entirely in natural harmonics: Ex. 3a (2x); Ex. 3b (1x); Ex. 3a (1x); Ex. 3c (1x); Ex. 3b (1x); and Ex. 3a (2x). Pretty cool, huh? And the fun doesn’t stop there.

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MINOR ELEGANCE

Ex. 4a reveals how an entire B minor scale (or Aeolian mode) lurks within the third and fifth frets on the bottom four strings. If you know your harmony and theory, you’ll suss that Bm(7) is the relative minor VI chord in the key of D major, which means the scale can be modally adapted to fit any chord diatonic to that key—D(maj7), Em(7), F#m(7), G(maj7), A(7), Bm(7), or C#dim/C#m7b5. For instance, re-designating the root of the same pattern to an added A harmonic (third node on the fifth string/5th fret) yields the blues-approved A Mixolydian mode notated in Ex. 4b, and preceding that scale with a G harmonic (first node on the third string/12th fret) results in Ex. 4c’s G Lydian mode, perfect for creating altered Gmaj7b5(#11) melodies. (Tip: Try playing all three examples in a row.)

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This pattern’s potential really opens up when you start applying intervallic and melodic sequences that utilize all six strings. Ex. 5a recasts our B minor scale as an ascending sequence of diatonic third intervals, while Examples 5b, 5c, and 5d respectively follow suit with sequenced fourths, fifths, and sixths. For descending sequences, just play each one backwards. Ex. 6’s descending four-note melodic sequence is also easily reversible. Your D.I.Y. project is to do the same with two-, three-, five-, and six-note melodic sequences.

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HARMONIC PENTATONICS

Shifting gears to our beloved E pentatonic minor scale (relative to G pentatonic major), Ex. 7 shows you how to descend and ascend the scale using only 12th- and 7th-fret harmonics on all six strings. Finally, Ex. 8 turns the previous pattern into a descending fournote E-pentatonic-minor/G-pentatonic-major melodic sequence, which should encourage you to explore two-, three-, five-, and six-note sequences on your own.

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EPILOGUE

When you fret any string, all of the same harmonic node divisions apply to the shortened string length, only in different locations—you just have to play them differently by tapping, choking up on the pick, or using Chet Atkins/Lenny Breaustyle artificial harmonics (all of which can also be used to play natural harmonics), but that’s another story. Happy hunting!

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