Harmonics (lesson)

Harmonics

Natural harmonics, pinch harmonics, artificial harmonics, tapped harmonics - what are they? What is a harmonic anyway? Lets see ...

What is a Harmonic?

First, what is a harmonic? Well a mathematically perfect string on a guitar would vibrate all the way from the nut or whichever fret you have chosen to the bridge, all as a single unit, meaning that if you slowed it down, you would see the middle of the string moving the most and bowing out and back in hundreds of times a second, like this:

This is an illustration of a string vibrating at its fundamental frequency and the string has non moving parts or nodes at each end. The fundamental frequency is the frequency that we usually associate with that open string - for instance, E for the 1st string. But guitar strings are pretty complex things. In addition to the fundamental, it is possible for the string to vibrate in a more complex way, such that you get a situation where the string is separated into 2 or more parts which vibrate separately, with additional nodes - in this case, if you slowed the string down, you would see nodes at various points on the string, and the string vibrating from those still points up to the nut or fret, and down to the bridge, like this:

In the picture above, we have an extra node and 2 separate portions of the string are vibrating - this is an example of the 2nd harmonic, so called because there are 2 separate parts to the string. In this case, the 2 parts of the string each are half the length, so vibrate at twice the frequency, and a string vibrating in the manner shown above would sound an octave higher than the string in the first diagram.

We can take this several steps further and talk about 3rd, 4th, 5th, 6th, 7th and higher harmonics. As we divide the string into ever smaller units, we get higher frequencies that conform to the ratios in which the string is divided. The higher harmonics are often called partials or overtones - a partial is generally related to the fundamental frequency in some fixed way, whereas an overtone needn't be.

In order for a harmonic to be present on a string, it has to be divided into exact fractions of the length of the whole string. You can't have two and a half nodes for example - that just isn't stable and wouldn't happen on a string in real life, so we are restricted to the exact fractions we have described.

The harmonics and some of their musical attributes look like this:

Owing to construction of the guitar and the way it is tuned, some of the higher order harmonics aren't exact matches for the notes I have stated, but they are a reasonably close match - the ones with asterisks are significantly adrift from the stated pitches.

So far we have been talking about mathematically pure harmonics - the situation on a real guitar is a little more complicated. What actually happens in real life is that a plucked string will be a complex mixture of the fundamental and multiple harmonics all playing at the same time. The fundamental will be loudest but depending on various features of the instrument, various harmonics will also play. This is actually true of any instrument, including other stringed instruments, woodwind and brass instruments. In fact it is the mixture of overtones and they way they are reinforced that gives each instrument its characteristic tone. If you played just the fundamental from an oboe next to a fundamental from a guitar of the same frequency, they would sound pretty similar, because both are basically a single sine wave. Of course there are many other things that make an instrument sound unique such as the various resonances it possesses, the way the note is driven be it through plucking or blowing, and additional noises such as breath or pick noise, but the basic musical signals are similar.

So our string is a mixture of the fundamental and various ever higher harmonics - in theory they go on forever, but in practical terms as they become higher they also become quieter and tail off quickly. This means the waveform the guitar string creates is actually incredibly complex.

What does creating a harmonic mean in guitar playing terms?

In playing terms, as we mentioned above, there are many different types of harmonic techniques, and they are used to get different sounds or effects from the guitar. I'll explain the different types and techniques for playing them a little later, but first I'd like to take some time to explain what we are doing when playing a harmonic.

At this stage I want to point out that there is a difference between the technique of "harmonics", and the individual harmonics themselves - the first is a generic term to describe guitar techniques that manipulate the harmonic content of a note, the second refers to the actual harmonics that make up that mix. We tend to use them interchangeably, but be aware that they are talking about different things. From this point, I'll put quotation marks around the word harmonic when I am referring to technique rather than the harmonics themselves. Actually a better term for "harmonics" would be something like "harmonic selection" - lets see why.

In fact, it all comes down to the nodes. When you are plucking an open string, there are only 2 nodes that are unmovable - the bridge and the nut. This means that all possible combinations of harmonics - 2nd, 3rd, 4th etc are free to sound out, because there is nothing preventing them from forming their characteristic nodes anywhere on the string. The various techniques to create a "harmonic" involve forcing nodes to be in a specific place along the string. Now, think about that - if we force a node in the middle of the string, at the 12th fret we are immediately preventing or filtering out any of the other harmonics that do not have a node there. So, for instance, the fundamental can no longer exist, as it does not have a node at the 12th fret. The 2nd harmonic does, so it will be alive and well. The 3rd harmonic? No, it only has nodes at the 7th and 19th frets. What about the 4th harmonic? In the table above I gave the 5th and 24th frets, but it also has a node at the 12th fret, so it can exist. Carry on working through, and you will find that all of the even harmonics have nodes at the 12th fret.

So, forcing a node at the 12th fret will give us a note that has a 2nd harmonic, 4th harmonic, 6th harmonic, 8th harmonic and so on - all the even harmonics in fact. So that note will sound very different to an open string because its harmonic structure is different - it is harmonically a much purer note than a regular open string. In fact, checking the table above, we can see that the strongest note will be the 2nd harmonic, which is an octave above the fundamental, but there will also be a flavor of the 4th harmonic which is an octave above that, and the 6th harmonic which is an octave and a 5th above the fundamental.

Lets take another example, and play a "harmonic" at the 7th fret. This will of course give us a 3rd harmonic which sounds out at an octave plus a 5th above the fundamental. What other harmonics are compatible? The answer is, at least for the lower harmonics, anything that is a multiple of 3, so the 6th harmonic will also figure (the 6th harmonic is 2 octaves and almost a minor 3rd above the fundamental). So the sound we get will be mostly the 3rd harmonic, which is an octave and a 5th above the fundamental, with a smaller amount of the 6th harmonic (Octave + minor 3rd) added. When you start to look at the mixture of notes we are getting it starts to become clear why we get higher notes, and strange mixtures of sounds.

So another way to look at this is that when we play a "harmonic", we are using a technique that forces the string to vibrate in a way that includes certain harmonics and forbids others. It is this different mix of harmonics that causes the sometimes weird effects that "harmonics" give us.

Another thing to note about "harmonics" is that to a large extent it doesn't matter where you set the node up - you will get the same effect. For a 2nd harmonic there is just one possibility - the 12th fret, but in general, the number of positions you can get a particular harmonic effect is the same as the number of nodes on the string, and they should all sound the same, as long as you are careful that the node you pick doesn't also allow a lower harmonic. For instance, we can play 4th harmonics at frets 5 and 24. The 12th fret is also a valid node for the 4th harmonic, but it also allows the 2nd harmonic which dominates.

As we'll see later, whammy bar harmonics use nodes clustered up near the nut, whereas pinch harmonics work near the bridge - in fact both techniques are generating a very similar harmonic series, they are just using different techniques and different nodes to set them up.

How Do We Perceive Harmonics?

Our ears fool us - this happens in music more than anywhere else. Our brain is equipped to figure out single notes pretty well, but play more than a couple, and the brain starts to perceive them as a whole, merging the individual notes into an overall sound or timbre. This is especially true of musical tones such as guitar string notes. Remember all of those harmonics? With the right analysis, a computer can listen to a note and figure out all of the harmonics in it, but we can't do that - we just hear a single note, and in pitch terms we perceive it as being identical to the fundamental. This is a little more than the fact that the fundamental is loudest; we still perceive that note even if it isn't present in the signal - this is a psychoacoustic consequence of the way our brains are wired, and is something that music producers use to good effect to make us believe we are hearing bass notes that are not present because small speakers cannot reproduce them - they just use an effects unit to add in the appropriate harmonics (which are higher so the speakers can reproduce them) and our brain is fooled into thinking there is some low bass in there that really isn't present.

OK, enough theory, lets look at some actual harmonic techniques.

Natural Harmonic

All of the techniques I mentioned in the introduction achieve the same thing - they create a modified harmonic series, but they differ in the way you create it. In all of these, some knowledge of what you are trying to achieve in terms of the different harmonics you are setting up is helpful. You can't create a "harmonic" anywhere on the string, it has to be at a node for a particular harmonic series, and the exact mixture of harmonics you select by this choice controls the effect you get.

"Natural Harmonics" are probably the easiest to create, the technique is used with an open string. With the right hand you would pluck the string with your pick as usual, and at the same time gently touch your left finger to the string at the appropriate point then immediately remove it. Your left finger forces the string to stay still in that place, creating a node, whilst the rest of it vibrates. The quicker you remove your finger, the clearer the "harmonic " would be. Where you place your left finger is of course all important for "natural harmonics" - it has to match the exact placement of the node of the harmonic series you want to create. There are strong "natural harmonics" on the following frets:

In most cases your finger needs to be above the the fret, not the gap in between them as you can see in the diagram. The 9th fret "harmonic" is pretty hard to get, the others should be easy with a little practice, with the 12th fret being the absolute easiest and best place to start.

Artificial Harmonic

"Natural harmonics" are created on open strings, which limits the notes we can easily get. "Artificial harmonics" take this a step further and open up a lot more possibilities, although they are a lot harder to play. The principle is simple however - we are just shortening the string by fretting it somewhere. This means that for instance a 2nd harmonic although still consisting of 2 equal notes split in the middle would sound higher because we have shortened the string by fretting it. It also means that we have to move the point that we create the node up by half the distance we have moved up the fretboard (so that we are still hitting the exact center of the part of the string that is free to move). Since we figure the positioning of the nodes as a division of the part of the string that is able to vibrate, all of the nodes will be closer together, and will move on the string slightly. To actually execute the "harmonic", since your left hand is busy fretting the string, you must place a finger from your right hand on the appropriate spot, and use another finger on the same hand to actually pluck the string - this is fairly hard to do and requires a lot of practice. When practicing "artificial harmonics", the exact same rules apply, just remember that you have to adjust for the amount you have moved up the neck. Using Artificial harmonics it is possible to play entire complex melodies, but if you are moving your fret hand up the string even to play successive notes, you also need to change the place you are creating the "harmonic" to match.

The 2 techniques mentioned above are equally at home on a classical or electric guitar, but now we get to the really good stuff - the rest are really only usable on an electric guitar.

Pinch Harmonic

The "pinch harmonic" is the archetypal guitar scream - you know the one where the lead guitarist is ripping into the solo and suddenly plays one or more notes that just scream and sound amazing. What he is doing is playing "pinch harmonics". The principles remain the same but this time all of the action is at the pick hand. What the guitarist is doing here is picking a note as normal, but also letting his thumb brush up against the note just after he picks it. The thumb is setting up the node of the "harmonic" and forcing the strings to vibrate with the desired harmonic series. If you crank the gain and treble up, when you have the technique right you will almost always get a screaming harmonic of some sort. As with other harmonics you need to fine tune the exact position you are using to hit the sweet spot, and you can even switch between different harmonic types in between notes (an old ZZ Top trick). Since Pinch Harmonics are executed near the bridge, we are selecting from the higher harmonics, so we get high notes - some of the higher harmonics include dissonant components, contributing to the scream. There are many other possibilities within a small space - we get more because the guitar is artificially sensitive to the higher order harmonics as be have upped the gain a lot. As I said earlier, these harmonics are present in the note anyway but at such low volumes that hey are not normally heard.

Tap Harmonic

A "Tap Harmonic" is similar to an "Artificial Harmonic", the difference is that instead of separately touching and plucking the string, the "tap harmonic" uses a single action - a tap, to do both. To do this you need to tap the string lightly so that it very briefly hits the fret underneath it and very quickly remove your finger. The tap sets the string vibrating and at the same time creates the node in the correct place - so of course you need to actually tap the string at the exact place required to set up the "harmonic" you want.

Whammy Bar Harmonics

Finally, the "Whammy Bar Harmonic" is similar to the "tap harmonic", the difference being that usually when playing these you are selecting very high order harmonics, and there is no fret beneath the exact spot you need to hit, so you need to use a whipping action to set the string vibrating and deaden it in the exact spot to set up the desired node. For this reason, "whammy harmonics" are about the most difficult "harmonic" technique I am aware of. A good place to do this is on the G string between the 2nd and 3rd frets - there are 3 or 4 different harmonic series there depending on the exact position you whip. Before you whip, push your whammy bar down, and after the tap release it and add some vibrato - with this technique you can get some crazy screams.

Pickups, Treble & Gain

A final word on some of the electric guitar related "harmonic" techniques. There is a myth that some guitars are good for "harmonics" others aren't ... well in terms of actually creating "harmonics", all guitars are exactly equal. If you turn off your amp and play your electric without any volume, you can actually hear natural harmonics. If you are good a pinch harmonics you will hear those too.

Where guitar and amp combos differ is in how good a job they do of picking up and amplifying the harmonics. Since a lot of harmonics are low in volume, hot pickups and a lot of gain on the amp improve the loudness of the signal, making the "harmonics" clearer. Since a lot of harmonics are quite high frequencies, your pickups need a good treble response - and this varies between guitars. Finally, your pickup is looking at one very narrow portion of the string, and if you had the ability to move it whilst playing a "harmonic" you would pick up different proportions of the different harmonics in the signal. This means that different harmonics will sound different on different guitars depending on the exact pickup placement - you can check this by changing which pickup you use whilst playing harmonics - you may find that one is better than the other.

So, crank up the gain and treble, play with your pickups, but don't blame the guitar if you can't play harmonics!