Guitar Physics I - Harmonics

A vibrating string has some unusual properties that distinguish it from many other methods of creating measurable pitches or musical notes. One of these is the ability to produce harmonics, which are the natural phenomena of a string vibrating over a certain length but includes some non-vibrating points or nodes that are evenly spaced over the length of the string.

The conventional manner of changing pitches on a string requires us to shorten the string by stopping it at a certain fret. Another way to get a different pitch from a string is to stop it at a point the divides it into a certain number of equal sections. Each of these sections has the non-vibrating nodes as endpoints but the string is still vibrating at all other points.

When you lightly touch a string at the 12th fret, right on top of the fret (not behind where you would press down), you cut the string into 2 equal parts that are both vibrating while the string is stopped at the 12th fret (the node). You could do this with a jump rope tied to a tree that you are spinning. If you spin it faster (twice as fast to be exact), you could make the rope spin in 2 sections and appear to be stopped in the middle.

The 2 vibrating sections of our string are now vibrating twice as fast as the open string would be. This produces a pitch that is an octave higher than the open string. In our music science textbook the open string would be called the fundamental note and the harmonic would be the 1st partial or overtone. The frequency of the 1st overtone is twice that of the fundamental note because we cut the string in half. This doubles the frequency and produces a note 1 octave higher than the fundamental.

A quick recap- the 12th fret is the midpoint of the string. Touching the string there cuts it into 2 halves. This doubles the frequency and produces a harmonic 1 octave above the open string.

There are 2 other places you can cut the string into audible divisions; the 7th fret cuts the string into thirds and the 5th fret cuts the string into quarters. When you cut the string into thirds, you triple the frequency, producing a harmonic 1 octave and a fifth above the fundamental (the 6th string E will become a B- the same pitch s the open 2nd string). When you cut the string into quarters, you quadruple the frequency, producing a harmonic 2 octaves above the fundamental (the 6th string E will become another E- the same pitch as the open 1st string).

The harmonic at the 7th fret cuts the string into three equal parts. This means that the string is stopped at 2 points or nodes. The 19th fret is where this other node would be. You could get the same harmonic by stopping the string at the 19th fret. The same situation applies to the harmonic at the 5th fret. It produces note two octaves higher than the open string and also has nodes at the 12th and 24th frets. Most acoustic guitars don’t have 24 frets but it would be a spot somewhere over the sound hole.

More harmonics can be produced at other frets that divide the string into five, six, seven, or even eight equal parts. Most of these are relatively useless because they will not be loud enough to be heard, although the division of fifths is used occasionally. This harmonic is can be found at either the 4th or 9th fret and produces a pitch two octaves and major third above the open string. The low E string would produce a harmonic that matches the G# on the high E string.

Harmonics can be used very simply and effectively to create an interesting sound. Don’t let the science connection get in the way.