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Lesson 29 - Everything on harmonics

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Previous page: Lesson 28 - Top Note Chords (voice leading) Next page: Blues Guitar

Lessons of The Week was a series of guitar lessons circulated in "News", in the pre-web days of the Internet. 29 lessons were written before it died out, and I happende to write the first three. They represent a little bit of internet history, as they may have been the first guitar lessons written for the internet.

The lessons were all written in txt format - they were written around the same time as Tim Berners Lee were sitting in Switzerland specifing the first version of html. I have converted them to html, and may have added a few links from the lessons.

Lesson: 29
Title: Everything on harmonics
Level: Beginners ( and the other )
Style: Technique
Instructor: Vincent Pagel

Dear Guitar Lessoners of the Week, today we're going to meditate Steve Portigal's thoughts about harmonics :

"Hey man , it's easier to produce harmonics on the 12th fret than 7th fret, on the 7th than on the 5th and so on. Can you help me ? "

Is it him , his guitar , or both? Well it's not surprising that harms on the lower frets are more difficult to produce. I'll try to give you an initiation , giving you some theoretical reasons first, then I'll give you practical advice to produce them queer notes coming from outer spaces.

Fasten your seatbelts ...for those of you who are really disgusted by maths you can SKIP the theoretical part, but it sometimes can help you to understand the grounds of strings' behavior.

When you play a note, you initiate the vibration of the string with your right hand, and as you perhaps know the physics of vibrating strings tells us that for a given string there exists an infinite ( theoretically ) of vibrating modes:

the first , which is called the fundamental with a frequency F1, and the others, called harmonics whose frequency is an integer multiple of F1:

Fn = n * F1

F1 is the fundamental it is the perceived frequency

F2= 2 * F1 is one octave higher than the fundamental

F3= 3 * F1 is one octave and a half higher => it's a fifth, that is to say that if F1 is a C, F3 is a G on the octave above, that's the reason why when you play a C and a G at the same time it sound very consonant to your ears, because the C already include a G !

F4= 4 * F1 is two octaves higher

F5= 5 * F1 is two octaves plus a third. That is to say for a C , F5 is E, and what do you see in front of your puzzled eyes : C E G is a chord of C major, also called the perfect chord. With F7 you get the B which is a major seventh.

Here is the base of the theory of our music ( consonance ).

REMARK : to transform Frequency into semi-tone intervals ->

log (F/440) * 12 / log 2 = number of semi tones from A (440Hz).

This explain :

      * when you multiply by 2 the frequency, you raise by an octave
           log( 2F / 440)/log2*12 - log(F/440)/log2*12
           = log( 2f/f ) /log2 *12
           = 12 semitones interval = 1 octave
      * F3 = 3 * F1 gives us  log 3/log2 * 12 = 19.01955 
           = 1 octave + 7 semitones 
        So the interval between F3 and F1 is 1 octave and a fifth

So when the string begins to vibrate, its movement is not monochromatic, it's made of the fundamental which is the more energetic, superposed with the succession of its harmonics whose energy goes decreasing like an exponent function. As someone, I forgot the name, replied to me this is due to the initial condition of the string : the shape it has when you release it with your finger or mediator is approximativately a triangle ( the flat corner being made at the position where you pull the string ). And the Fourier transform of such a wave function gives us an exponential repartition. So the sound ( the repartition ) depends on the way you pinch the string, of the resonance with the wood of your guitar an so on (( Note: even on an electric guitar there's resonance with the wood of it's body))) You can notice that if you pinch the string nearly at the 12th fret, the sound is very dull. The reason is that there is nearly no second harmonic

What's the conclusion : when you make a note, your ear perceive only one note, that is to say the most energetic, the fundamental, but in fact there are fainter other notes you don't perceive but you can clearly see on a spectrogram as represented below => when you play one note, you actually play a perfect chord without knowing it !!!!

|       |
|       |       
|       |       |                       
|       |       |       |       -
|       |       |       |       |       |       -       _       _

F1      F2      F3      F4      F5      F6      F7      F8      F9 ...

You can hear harmonics when you play a note and that you let the sound die. When the fundamental has nearly completely damped, then you hear the rest. This is particularly true on an electric guitar with much amplification.

But there is one way to make the harmonics audible at first => if you manage to absorb all the harmonics from F1 ( fundamental ) to Fk, then Fk+1 become audible because all the other frequencies more energetic than it are dead, so Fk+1 becomes the most energetic frequency and is audible ( and as a matter of fact is the new fundamental )!!!!


because the 12th fret is exactly in the middle of the string, and your finger creates an initial condition saying : the middle of the sting is moveless, since the finger prevent it from moving ! So the possible vibration frequencies are multiple by 2 of F1

So if you draw the spectrogram of the sound you get => you see F2 F4 F6 F8 F10 and so on, with energy decreasing. So if you make it on the first string which is E, you will hear a E one octave higher.

ON THE SEVENTH FRET, only multiples of F3 are heard because the 7th fret parts the string in exactly 3 parts : spectrogram shows F3 F6 F9 F12 ..... on the first string it gives you a B

ON THE FIFTH FRET, multiples of F4 cos' the 5th parts the string in 4 equal parts: spectro shows F4 F8 F12 ... you hear a E two octaves higher than the fundamental

ON THE THIRD , multiples of F5 : F5 F10 F15 F20 .... your hear a G sharp


So let's give up with theory, let's speak technic. There is two convenient ways to produce harmonics:

FIRST: you put one of your finger (the thinner side of your little finger) of the left hand on the 12th fret WITHOUT PRESSING AT ALL, and as the same time as you pinch the string you take this finger off. It's not easy to have a good coordination between the pinching and the taking off. If you go off to early the string sound as usual, and if you go off too late the harmonic sounds "poor" and doesn't last long. Just train on the 12th fret to get some beautiful harmonics that sound bright and last for a minute


When your sound is neat, you can train on the 7th, 5th, 3th fret... which is getting harder and harder. First of all the position on the string is not exactly the position of the fret because, as I did not mention earlier, the higher the order of the harmonic is, the more it is getting "untuned". For this reason try to move your finger of the left hand around the position of the fret to FEEL the exact place of the harmonic. E. G. 2 ^ ( 7 / 12 ) = 1.4983071 which indicates the position of the 7th fret. To divide the string in 4 equal parts the rate should have been 1.5, so the position of the third harm is a bit higher than the 7th. For the fifth fret => 2 ^ (5/12) =1.3348399 , to divide the string in three part the rate should have been 1.3333333 so this time the harmonic position is lower than the 5th fret. 2^((4/12) = 1.259921 so to reach the 1.25 rate and get the fourth harmonic you must place your finger between the 3th and the 4th fret.

Something funny, when around the 3th fret the position of successive harmonics becomes closer and closer and is not adjusted at all with frets, and if you simply move a bit your finger, you will change the note by a great interval. But those harmonics near the third fret are very hard to produce and are not usually used. The current range is 12th, 7th and 5th fret (equivalent to 9th).

ANOTHER TECHNIC WHICH IS LESS COMMON: it comes from classical guitar and allows to play ANY NOTE with harmonics. The idea is to make 12th fret harmonic all the time, as they are very easy to make. You place the finger of your left hand on the note you want to play in harmonic (you press the string against the fret as usual), and then you spot the position which is 12 frets higher than this note. You give away your mediator, get your right hand ready because all the difficulty is here ( as i don't know the name of fingers in English let's number fingers beginning from the thumb=0, the finger to show=1, the finger to fuck=2,the finger for rings =3 the finger to clean ones ears=4 ! ).

You stiffen your finger 1 and put it on the fret you have spotted ( 12 frets above the note you are playing with the left hand) this finger doesn't press the string, simply lays on it. Then with you finger 2 you pinch the string and take off your finger 1 swiftly. Is it clear? In fact the whole movement is equivalent to the first method described, the point was that for this first method the string was played without pressing a note with the left hand.

With some training you can play a whole melody in harmonics. The difficulty is that with the finger 1 of the right hand you must follow the moves of the finger of your left hand 12 frets higher, which is not easy at first. But I assure you that you can play some complex, single notes, tune fast enough this way. If someone manage to play chords this way, he'll have to explain how !

IN CONCLUSION I should add that this last method is applied by rockers (without knowing it!) to make strings sound odd : the method is to play with a mediator, and let a part of the thumb protude, so just after the mediator has pinched the string, the flat part of the thumb hit the string very quickly as your right hand is going forth, which absorb the most energetic frequencies, leaving some harmonics. I don't know the reason why but people call it "artificial harmonics".

When you try it first, it's not easy not to completely mute the string. And if you have followed my explanations, you'll understand that you mustn't do that at any position with your right hand : it will be easier if the approximative position where your mediator attack the string is a position where you have spotted harmonics. So try many positions to find a spot , and then when your left hand moves to another note, you'll have to move a bit in the same direction with your mediator by an amount which is usually smaller than the move made by the left hand, as to follow the nodes on the string.


To VINCENT PAGE1 (and the guy who needed the tips)

As I'm not doing a Doctorate in producing Harmonics, this is a rough translation of your thesis on how to produce them.

1. Hold your pick close to the end, with your thumb at roughly the same level as the picking edge. When you pick, the edge of your thumb should touch the string ALMOST simultaneously. Pick at the same speed as usual. Practice on the G string first.


2. Lightly touch the string with a left hand finger, over a fret (eg. fifth). Pick the string (as normal), and simultaneously remove your left hand finger. This works anywhere along the string (as Vincent said y=mx+c) but some places are better than others. Try fourth, fifth, seventh and twelfth frets on the G string to start with.
Yours, a harmonics layman.

After that lesson I hope you can play the Aram Khatchaturian Violin Concerto in Dm with harmonics only ....

Good work and happy Christmas

Vincent Pagel alias alias HTS ( Harmonique Ta Soeur )

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