The information on this page is must have for guitar players, eventually. Again it helps to make sense of the theory later on but we're still looking at they why rather than the how.
In mathematics a harmonic series is a series of fractions 1/2, 1/3, 1/4, 1/5 .....In music the harmonic series is the sequence of notes produced when you divide a wavelength by the same ratios. When you play harmonics on your guitar (see the video) you can hear thes harmonic series in action..
Divide the string in 2 and you get a note exactly one octave higher than that of the open string note. I'd encourage you to stop and think about this for a moment. Simply by playing a string and then dividing it in half and playing it again we get two notes with such a close relationship to each other that they function in exactly the same way harmonically. If you're tuned GDG or any 151 tuning, play the top and bottom notes and listen to how similar they are. This is not an accident, it's fundamentally simple mathematics.
Now play the harmonic on the 7th fret, this time you've divided the string into 3 equal lengths. The note now is the 5th note in the scale, sometimes called the dominant. We would all know by now that this is the same note as the middle string in our 151 tuning, play all three and hear how close they sound harmonically.
Remember that when you play an open string you also get a number of standing waves, the strongest with wavelengths, 1/2 and 1/3 of the fundamental. We now know that these vibrations produce the 1st and 5th notes in the scale and together give us a very stable harmony. It is little wonder that we tune our guitars this way.
If we keep dividing the string according to the harmonic series the vibrations become so weak that they are very difficult to hear. Divide the string in 4 and play the harmonic at the 5th fret. This note is an octave higher again than that at the 12th fret which you would expect because its wavelength is half the length again.
Divide the string in 5 and play the harmonic at the 4th fret and you'll get the major 3rd note. Now we have the 1, the 3 and the 5, the three notes in our major chord, another very stable harmomic structure.
Divide the note in 6 and we get the dominant again, divide it in 7 and the next note is the flattened 7th note, the final note in our 7th chord although by now it is extremely weak.
Take Home
We can interupt the vibration of a string to only play particular harmonics and this gives us clues to what notes work well together.
the video lesson
In this video I demonstrate how the three notes in a major chord can all be played as harmonics on the open string. This gives us some very important clues about which notes work well together harmonically.
Download the video here.
Learning the fretboard
See if you can play the harmonics on the 12th (G), 7th (D), 5th (G) and maybe even the 4th fret (B). Then find these notes elsewhere on the guitar, there'll be one on each string.
To do this play each note open and then each note on the 12th fret. These 8 pitches will be replicated at other points on the neck, it's your job to find them. There's some more information on this task in the FaceBook group if you're keen.