A vibrating string - without the body or amplification - has very little effect on the air around it and creates very little sound. For an electric guitar, vibrations are transferred primarily to electronic pick-ups rather than to an acoustical wooden body. Electrons within the guitar's pick-ups vibrate, thus creating a weak vibrating electrical current. With amplification, this is magnified into a stronger current that is used to power the speakers. The speakers vibrate the air surrounding it - thus creating sound.
The point of this basic description of sound as vibrations is that by playing musical instruments we are ultimately learning to control vibrations. This is also a basis for understanding how different sounds can be combined in different ways. Prior to delving into topics such as scales, chords, etc., it seems appropriate to discuss some basic aspects of harmonics - which relates to the tendency of things to vibrate.
Normally when a guitar string is played in the open position it vibrates as one wave that runs the full length of the string (from the guitar's nut to bridge). The length of the string is controlled by pressing the string against specific frets. Harmonic vibration of the string is achieved by lightly touching the string, rather than pressing it against a fret (see below). This allows the string to vibrate on both sides of the finger/fret position. Aside from the vibration that runs from the fret position to the bridge, there is the added vibration that runs from the fret position to the nut of the guitar.
Full length vibration (from guitar's nut to bridge)
String played by pressing string against the 12th fret.
Harmonic played by lightly touching the string at the 12th fret position.
What is interesting is that by playing the harmonic on the 12th fret position, we are getting the string to vibrate an octave higher than the original note (full length of the string). The string length has been divided in half and is now vibrating twice as fast. Another way of thinking of an octave interval is that it is a second note that is vibration twice as fast as the first.
By playing the harmonic on the 5th fret position (see below), we can get the string to vibrate as four separate waves. These vibrations are four times as fast and they generate a note that is two octaves higher than the original note (full length of the string). Notice that aside from the wave node that is created at the 5th fret by pressing lightly against the string, two additional nodes are created automatically on the longer portion of the string - thus dividing the strings vibrations into four equal parts.
Harmonics at 12th fret position (1/2 string length), and at 5th fret (1/4 string length).
The harmonic played at the 7th fret position (1/3 sting length) gives us something that is quite different (shown below). This gives us an additional note that is actually the 5th note in the major key of original note (full length of the string). As an example: if we establish that the full length of the string is tuned to the note C, and by playing the harmonic at the 7th fret, the resulting note would be G. This interval from C to G could also be described as from Do to Sol (as in Do-Re-Mi...).
Harmonics at 12th fret position (1/2 length), and at 7th fret position (1/3 string length).
If we also look at the harmonic at the 4th fret position (shown below) yet another note, E, is added. The string is vibrating as five equal waves and yields the 3rd note in the major key of the original note. This interval from C to E is a major third and could also be described as from Do to Mi.
Harmonics at 5th fret position, and at 4th fret position (1/5 string length).
Even thought it becomes impractical to play harmonics of higher divisions - they are there. Though we have already introduced the intervals of a fifth (C to G) and of a major third (C to E) it may be helpful to look at some of the additional notes that are built into the natural tendencies of physical vibrations.
| Full length | with string tuned to C |
| 1/2 length = | one octave higher (C) |
| 1/3 length = | one octave plus fifth higher (G) |
| 1/4 length = | two octaves higher (C) |
| 1/5 length = | two octaves plus major 3rd higher (E) |
| 1/6 length = | two octaves plus 5th (G) |
| 1/7 length = | two plus a minor 7th (Bb) |
| 1/8 length = | three octaves (C) |
| 1/9 length = | three octaves plus whole step (D) |
| 1/10 length = | three octaves plus major third (E) |
| etc... |
It is enlightening to notice that there are physical reasons certain intervals harmonize so well. The mathematical simplicity of their vibrations helps explain why certain sounds work well together. This is why an octave is an octave. This is why the 1st and the 5th notes of major scale sound so well when played together. This is why the interval to a major 3rd also harmonizes well. This also validates the intervals involved with a triadic major chord (such as C, E, and G note vibrations shown below).
Three harmonic vibrations represents notes in a triadic major chord:
They are vibrating at 1/4, 1/5, and 1/6 lengths which yields the notes C, E, and G.
~~~CODA
As a final thought, it could be noted that this understanding of harmonics can help explain the basis for why an octave is divided equally into a chromatic scale of twelve notes. This though relies on a bit of an adjustment for the tuning of each interval between the twelve tones. The half-step notes found with piano keys and frets on a guitar are considered "twelve-tone equal temperament" tuned notes - which in essence means some allowance is made for these intervals to be harmonically slightly out of tune. Centuries ago, and maybe still today, this was highly debated. The advantage with equal temperament is that an instrument can then be played in any key desired. The disadvantage though is that for pureness of harmonies, certain intervals will be ever so slightly out of tune. The science and math for how things vibrate does seem to direct things towards dividing an octave into twelve equal parts, though technically this only happen when a slight adjustment away from being harmonically pure is made....
Maybe a topic for a later post?
~~~
