Harmonic Convergence

A small bit of advice: Whenever possible, you should try to number an engineer, mathematician or pure (as opposed to social) scientist among your circle of close friends. You cannot ever underestimate the value of knowing someone who can explain basic scientific principles to you in a way that even you can understand.

Take the guitar in general, for example. I can play it. I can explain to you the musc theory that makes up the chords or takes some of the mystery out of the fretboard, but I cannot give you a reason for why the guitar works. Okay, I can – but it would be something like this: “You pluck the string and then there’s this sound…”

Or specifically take a guitar’s harmonics. This is another aspect of the guitar that I enjoy to the point of overusing, but don’t ask me to explain any of the scientific principles involved in creating a harmonic. I have friends who could, even if they’d never held a guitar before in their lives, tell me where the harmonics on a guitar would be simply (and boy is that the wrong word) by means of mathematical formulas.

Today we’ll take a look at harmonics and hopefully answer all the questions that I’ve gotten about them through the emails in the last two months. And we’ll need two disclaimers! Here’s the first (which I’m sure so all know by heart by now, so let’s all sing together!):

These files are the author’s own work and represents his interpretation of these songs. They are intended solely for private study, scholarship or research.

Our second disclaimer is of a more personal nature:

Any attempt by this author to scientifically explain something should be taken with a grain of salt. If you are truly interested in the physics of sound, please consult either someone who knows what he or she is talking about or a good textbook. And please forgive him because his heart’s in the right place.

Natural Born Harmonics

Most people are familiar with guitar harmonics, even if they’ve never played any themselves. Just mention the beginning of Roundabout by Yes or From The Beginning by Emerson, Lake and Palmer and you’re sure to get an understanding nod. But what exactly are harmonics?

Well, I’m going to let someone else explain this. The following is taken from The Guitar Handbook by Ralph Denyer:

“Harmonics are an important part of every note. Every time a guitar string is struck it vibrates in a complex pattern, and the sound it generates is composed of several elements. The basic building block of the sound is the fundamental. This is the loudest element we hear and the one by which we identify the pitch of the note. It is the sound generated by the string vibrating in a single loop along its entire length. At the same time, the string produces a series of harmonics, overtones or upper partials. These are simply tones with frequencies that are multiples of the frequency of the fundamental, and they are generated by the string also vibrating simultaneously in shorter loops. They begin one octave above the fundamental and then rise in pitch in specific intervals – the fifth, the next octave, the following third, and so on.

All musical instruments produce notes that consist of a fundamental and a number of harmonics. Together, these components of each note are known as its harmonic series, and, in this context, the fundamental is referred to as the first harmonic. The balance or blend of the fundamental and harmonics in relation to each other determines the “tone” of the instrument. In effect, the harmonic series therefore forms a unique “audio fingerprint.” No two guitars – however similar – have exactly the same tone because they do not produce the same balance of harmonics.”

That was a bit to get through, huh? But when you think about it, it’s not all that hard. Just like colors are made of other colors, or molecules are made up of individual atoms (and let’s not get into what atoms are made up of – we can’t have a small enough “basic unit” these days, can we?), so, too is sound. What we perceive as one tone is actually a composite of many.

Let’s think about the fundamental for a moment. Strike the open E string (low or high, I don’t care) and listen. The tone that you hear, the E note, is the fundamental. But along with that fundamental, as we’ve read, are other tones – harmonics. Even though they are part of the entire tone of the open E string, they are being “drowned out,” if you will by the fundamental. Lurking somewhere in that fundamental E tone (if we are to believe what we’ve read), are harmonics composed not only of other, higher E notes, but also B (fifth) and G sharp (thirds) notes as well.

Fortunately for us, the guitar (as is the case with most stringed instruments), has some unexpected built-in luxuries. There are spots where you are able to “deaden” the fundamental while “exciting” a specific harmonic overtone. In other words, playing the string in a certain way at one of these certain spots allows you to play a harmonic without sounding the fundamental. Depending on where on the fretboard you do this determines which harmonic you will get.

And before we move on any further, another quick word. As noted earlier different guitars produce different balances of harmonics. Lots of things come into play here – the type of guitar it is, the wood of which it’s made (body and neck), how old the guitar is, the brand of strings you use – anything and everything can effect the harmonic series of your guitar. Trust me on this. I have talked with some of my “more learned” friends and I can assure you of two things: First, they know what they’re talking about. Second, even though they’ve painstakingly talked me through this process, you do not want to sit through any attempt I might make to relay this to you. Let’s just say that I can get you started. You will have to play around and experiment a bit in order to hone your skills. But isn’t that what this is all about?

The easiest place for anyone to learn how to use harmonics is on the twelfth fret. My advice to you here is the same that it has been throughout all my columns – start simple and work your way to the harder stuff. Let’s begin with one string, the high E (first) string. Place the tip of your index finger (of whichever hand you use to fret the chords – in other words, not your strumming hand) very lightly on the twelfth fret. And when I say on the twelfth fret, I mean on it, not behind it as if you were playing a note. When you pick the string with your strumming hand, you will hear a muted high pitched tone. So far so good.

The real trick to this is to pull your finger away from the fret immediately after you pick the string. Watching people do this, you will swear that they are striking the string and pulling away at the same time but this is not the case. And you don’t have to be overly dramatic about it, either! If you’re a fraction of a centimeter off the string, you’re off the string. When you do this the “muted high pitched tone” we heard earlier will ring out loud and clear. This is the “twelfth fret” harmonic. And if you’ve never done this before, please feel free to say, “Wow! That was cool! And easy!”

Keep experimenting on the twelfth fret. Use the B string. Then all the strings one by one. Try using your middle finger or your ring finger. When you feel confident, then try using the length of your finger (as if you were going to form a barre chord on the fret) instead of the tip and try to do two or more strings at once. Be sure to try to do it with each of your fingers. This is one of those things that you can fool around with at anytime. Are you watching TV or waiting for something to download? Hey, pick up your guitar and work on producing your harmonics.

After working on the twelfth fret, the next easiest places to play harmonics are on the seventh fret and on the fifth fret. Again, depending on your guitar, they might not be right on the fret but they should be so close that if you lived in Florida you’d be running the risk of a recount.

Oh yes, you’ll also notice that the harmonics on these frets sound different from the ones on the twelfth fret.

And Just What Are These Notes?

Remember our first definition of harmonics, all the way back at the beginning of this column?

These are simply tones with frequencies that are multiples of the frequency of the fundamental, and they are generated by the string also vibrating simultaneously in shorter loops. They begin one octave above the fundamental and then rise in pitch in specific intervals – the fifth, the next octave, the following third, and so on.

The harmonic at the twelfth fret is one octave above the pitch of the open string. So if you’re playing the twelfth string harmonic of the D string then you are playing a note one octave above the open D string. By the way, this is how you can tell whether your guitar’s intonation is correct – the twelfth string harmonic should exactly match the note played by normally fretting the twelfth string.

The thing that fascinates me about the above definition is that the naturally occurring harmonics of an instrument actually end up forming a major chord. This makes me wonder if there has always been some sort of, I don’t know, subliminal force at work in our study of music theory. If basic physics dictates how a string will vibrate (and even though we might not consciously register anything beyond the fundamental, we do hear the overtones), then maybe it is science and not environment that has dictated what is and what isn’t dissonant. I know, the things I’ll think about…

The harmonics at the seventh fret are an octave and a fifth above the open string. The harmonics at the fifth fret are two octaves above.

Here is a fretboard map that will hopefully help you. A Harmonics over a fret indicates where the harmonics are found and on that fret I have given you the notes that correspond to that particular harmonic:

Harmonics fretboard map

If you don’t like this, then here is all you have to remember:

  • The harmonics on the 12th fret are one octave above the open string.
  • The harmonics on the 7th and 19th frets are one octave and one fifth above the open string.
  • The harmonics on the 5th fret are two octaves above the open string.
  • The harmonics on the 4th, 9th and 16th frets are two octave and one major third above the open string.
  • The harmonic on the 3rd fret – and actually it is halfway between the third and fourth frets, not on the fret at all – are two octaves and one fifth above the open string.

Concerning that “third and a half fret” harmonic, this is an example of how guitars will differ radically from one another. On many guitars, it is impossible to play this. With some guitars it’s simply a matter of “tweaking.” On my old Yamaha acoustic, for example, the “third and a half” is actually very playable, but it’s really more of a “third and an eighth.” This is why it is always so important to become intimately familiar with what your particular guitar is capable of.

And some guitarists just seem to have the knack or the touch when it comes to this technique. There are indeed a number of guitarists who seem to be wizards at producing harmonics. But this fretboard map shows you the places where you are going to find them on your guitar. As The Guitar Handbook goes on to say:

“In theory, it is possible to go on producing higher and higher harmonics. In practice, you can only go so far before they become impossible to hear.”

So Now That I Know Where They Are, What Can I Do With Them?

Oh, you’re going to hate me, but this is another one of those cases where knowing a bit about theory (specifically what notes make up which chords) can really spice up your playing. But again, let’s start out easy and just look at the notes that make up the harmonics on the twelfth and seventh frets:

Harmonics on 7th and 12th frets

So how hard is it to come up with a use for any of this? Well, in one of those easy two chord songs we’ve been looking at over on the Songs For Beginners page, For What It’s Worth, Stephen Stills, Neil Young and friends incorporate a single note harmonic into the strumming of the song. For many people, it’s what makes the song worth playing:

For What It's Worth

Playing the E note with the E chord is a no-brainer, but what about the B note with the A major chord? Now if you’d been paying any attention at all last week, you’d be saying, “The B makes it an A add 9 which creates both the illusion of a sustained tone (the B is a holdover from the E major, is it not?) as well as a tension over the A which doesn’t release until we’re back at the E major again.” This is certainly one way to help sustain some interest in what would otherwise be a routine two chord song (and yes, that pun was intended. Sorry!).

What else can we do? Looking closely at either fret, we can see whole chords in there! The first three strings on either fret makes a minor chord. E, G and B are the notes that compose E minor, while B, D and F# are the notes used to form a B minor chord. If we look at the second, third and fourth strings, we’ll find major chords – G (G, B and D) on the twelth fret and D (D, F# and A) on the seventh. If you use the first four strings, then you can have either an Em7 (E, G, B and D) or a G6 (same note, obviously).

Different people use “harmonic chords” in different styles, sometimes as full block chords and somtimes in more of a classical, arpeggio style. Here are three that you might recognize (I’ll be willing to settle for one out of three…):

Daisy Jane
Perpetual Change
Barracuda line 1
Barracuda line 2

I enjoy using harmonics when I find myself in a jam with three or four guitarist and consequently need to find a “space” of some sort to call my own. They can serve as accents to chords or strumming patterns, as we’ve seen, but with a little thought (or inspiration), you can also use them as melodic fills. Especially when you are playing music that involves a lot of G, Em, D and/or Bm chords. If you’re ever playing the Moody Blues’ Nights in White Satin, for example, and nobody thought to bring a flute, then step up and be the flute yourself:

Nights in White Satin

One other thing that I’m sure that some of you have already realized – if you change the open strings for any reason, you will also change your available harmonic notes. In Over My Head by Fleetwood Mac, Lindsay Buckingham uses a guitar tuned to open D in order to get those gorgeous harmonic fills (which are simply rapidly arpeggiated D, A and D chords):

Over My Head

Using a capo will likewise alter the harmonics, not only of the available notes, but where you find them. If your capo is on three, for instance, your “twelth fret” harmonics are now actually on the fifteenth, which will give you the following notes:

Harmonics with capo on 3

As I’ve been telling you, what you get out of something will always depend on what you decide to put into it. Like most things about the guitar, natural harmonics can add a lot of interesting aspects to your own style of play.

Making Your Own

If I haven’t already given you enough to think about, then consider that you can also create “artificial” harmonics. No lie. We’ve covered this in brief in Picking Your Poison, but it could probably stand a retelling.

There are a couple of ways of going about making artificial harmonics. The way most electric guitarists will be familiar with involves the subtle use of the pick. Fret a note, any note you please, as normal. Now you want to be holding the pick in such a manner that when you strike the string, you also catch your thumb on the string with the same stroke. This results in the creation of the harmonic which is an octave above the fretted note. You can vary the harmonic series by playing around with how much of your thumb (and when) you manage to connect to the string as well as by fiddling around with the various tone settings on your guitar, amp or effects. Solos from ZZ Top songs are peppered with this style of playing.

Most people are not aware that you can do this on an acoustic guitar as well. As I said in the earlier article, “It simply takes a little more practice.”

If you don’t use a pick, don’t despair. You merely use the same idea but with different “tools.” Simply try to strike the string with the thumb (instead of the pick) and catch a bit of your thumbnail (instead of the thumb) when you make the stroke. This also takes a bit of practice.

These is also another method which is very interesting, albeit harder. Essentially what you want to do is recreate making a natural harmonic in a decidedly artificial manner. Let’s try a Bb for example. Finger a Bb note on your G string (this will be on the third fret). Now with your strumming hand, place your index finger very lightly on the fifteenth fret of the G string. Do you see where we’re going with this? The fifteenth fret is twelve frets above the third. So instead of using one hand to strike the string and on to finger the harmonic, we’re going to use our strumming hand to perform both functions. While the index finger of the strumming hand rests lightly on the G string’s fifteenth fret, pluck the G string with your thumb and take your finger from the fret in the same motion. Voila! Instant harmonic. I strongly suspect that this technique, often used by classical guitarists, led to the “tapping” techniques used by many electric guitarists. Maybe not, but it’s just another one of those things that I wonder about…

Well, I hope that this has answered most of the questions concerning harmonics that have been sent my way of late. If not, and as always, please feel free to write in any questions I may not have covered. Of course, all questions, comments, concerns or topics you’d like to see covered in future columns are welcome. Always. You can either drop off a note at the Guitar Forums or email me directly at [email protected].

Until next week…