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We'll look at the guitar in particular, but the same general principles apply to all string instruments.
Tuning a guitar means setting the fundamental frequency of each string to a particular value. Standard tuning has the six strings covering two octaves:
| String | Note |
|---|---|
| Bottom (lightest) | E |
| Second | B |
| Third | G |
| Fourth | D |
| Fifth | A |
| Sixth | E |
The fundamental frequency is given by f = v/λ, where the wavelength is determined by the length of the string and v is given by:
| v | = | ( |
|
) | ½ |
All the strings are under approximately the same tension and they're all the same length. The lighter the string the faster the wave speed and the higher the frequency. Tuning a given string to a precise frequency is done by adjusting its tension.
Pressing down on a particular string shortens its length. This decreases the wavelength, which increases the frequency. On a guitar the correct length for every note on the scale is marked with metal bars called frets. Moving your finger from one fret to the next changes the frequency by one note, which is a factor of 21/12. To increase the frequency by this factor the length must be multiplied by a factor of 2-1/12 = 0.944, which is why the frets gradually get closer together as you move away from the neck of the guitar.