There are many ways in which math and music go hand-in-hand, and this also holds true for the guitar. When you play guitar, everything from the note played to its tonal quality can be described using mathematics.

As far back as 570 BCE, mathematicians have teased out the secrets to how music is made and why humans like to hear certain guitar chords. Starting with this early study, here are just three ways mathematics and music interact when it comes to the guitar.

### 1. Making an Octave

Pythagoras, an ancient Greek philosopher and mathematician, discovered an interesting relationship between sound and the length of the string producing it. One experiment describes him shortening a string by half and producing a note one octave higher than the original string.

You can try this out by placing your finger on the twelfth fret, which is the halfway point of a guitar string. The note you play will be one octave higher than when you leave the string open.

### 2. Up and Down by Half Steps

A complex formula, known as the wave function, describes how each of the common 12 tones is an octave different from each other. This formula led to the Rule of 18, which is how the space between frets is determined.

In order to go a single half-step, say from C to C#, the length of the string is divided by 18 and that amount is subtracted to get to the next note. While 18 is still used by some manufacturers, advanced computations and technology mean that the more accurate 17.817 can be used, but saying the Rule of 17.817 is too much of a mouthful to change how the standard is stated.

### 3. What’s So Special About Six?

When you first start to take guitar lessons, you’ll most likely use a standard six-string. How this got the be the standard is mostly based on popularity, but there is something important about the tuning of each string.

The lowest string is typically tuned to E, and when you use each of your four fingers, in turn, on the next few frets, you will hear the notes F, F#, G and G#. To continue the chromatic scale, you need to move to the next string, and since all your fingers are currently occupied, you want to leave that string open, which turns it into A.

The four lowest string all follow this pattern to give you E, A, D and G. While continuing the pattern would make the last two strings C and F, the shape of human hands makes B and E easier. As you become more advanced, you may learn other tuning styles that work better for different genres of music.

Mathematics and music work together to make some pretty fine sounding harmony. Advancing technology means this mathematical relationship is finding its way into computers that are learning to write music.

If you’ve just started guitar lessons, maybe when you’re ready to take the stage you’ll be playing a famous piece written by a silicon composer.