Now the question becomes: How does a guitar generate the frequencies shown above? A guitar uses vibrating strings to generate tones. Any string under tension will vibrate at a specific frequency that is controlled by:
- The length of the string
- The amount of tension on the string
- The weight of the string
- The "springiness" of the string's material (a rubber band is a lot "springier" than kite string)
On a guitar, you can see that the different strings have different weights. The first string is like a thread, and the sixth string is wound so that it is much thicker and heavier. The tension on the strings is controlled by the tuning pegs. The length of the open strings, also known as the scale length, is the distance from the nut to the saddle. On most guitars, the scale length ranges from 24 inches to 26 inches. When you press down on a string at a fret you change the length of the string, and therefore its frequency when vibrating.
Photo courtesy Gibson Guitars
The neck of a Gibson SJ200 Vine acoustic guitar
The frets are spaced out so that the proper frequencies are produced when the string is held down at each fret. The magic number to use in positioning frets is 17.817. Let's say that the scale length for a guitar is 26 inches. The first fret should be located (26 / 17.817) 1.46 inches down from the nut, or 24.54 inches from the saddle. The second fret should be (24.54 / 17.817) 1.38 inches down from the first fret, or 23.16 inches from the saddle. The 12th fret should be exactly halfway between the nut and the saddle. The following table shows all of the fret positions and the frequency of each note on the first string (assuming a scale length of 26 inches).