Behavior of a String

Here we see the fundamental with the 1/2, 1/3, and 1/4 partials overlaid.
Here we see the 1/2, 1/3, and 1/4 partials overlaid.

In order to make a tone, a string must be somewhat elastic and be under tension. When a string is struck it vibrates back and forth until it runs out of energy and returns to its resting position. If too much tension is applied to a string it will break.

There are several factors that affect the behavior of a string. The four most obvious factors are diameter of the string, weight of the string, the tension of the string, and the length of the string. If we have two strings that have the same diameter, weight, and tension, but differ in length we will find that the shorter string produces a higher pitch. It is easy to test this out with the banjo. Just compare the pitch of any string played open with the pitch of the same string played with a finger placed on any fret. The higher up the neck the string is fretted, the shorter the active length of the string becomes, and the higher the pitch of the note that results when the string is struck.

The tone that we hear the most prominently from a string is called the fundamental. A vibrating string simultaneously makes other sounds called partials that vibrate in harmony with the fundamental. It is easy to find, play, and hear the partials that occur when the string is divided in halves, thirds, and fourths on the banjo. We can do this with a technique called chiming.

  1. Find the 12th fret.
  2. Lay a finger very lightly on any of the full length strings. Hover that finger directly over the 12th fret. Do not push down on the string. Just lay your finger on it very lightly so that you are barely touching the string.
  3. Strike the string gently with the pick or fingertip of the other hand. You should hear a very clear chime like tone.

In the case of the partial we can hear at the 12th fret, the tone matches the tone we would hear if we push down the string onto the 12th fret and strike it. Not all partials match the note that results from fretting the string at the same position. The partial at the 12th fret is the octave of the fundamental. The 12th fret is located exactly half way between the nut and the bridge. Another partial can be found at the 5th fret. The distance between the nut and the 5th fret is ΒΌ the length of the string. Yet another partial can be found at the 7th fret. The distance between the nut and the 7th fret is 1/3 the length of the string. These three partials are the easiest to demonstrate with the chiming technique. In addition to these partials there are many others that are active whenever a string vibrates. The chiming technique we explored here can come in handy when tuning the banjo.

Here we see the fundamental vibration of a string.
Here we see the fundamental vibration of a string.
The one half partial.
The one half partial.
The one third partial.
The one third partial.
The one fourth partial.
The one fourth partial.

Leave a Reply

This site uses Akismet to reduce spam. Learn how your comment data is processed.