### Introduction

This section actually belongs to Music, Scales and Tuning and Constructing Scales in this same folder, however I intend to re-organise those 2 pages in the near future to make them more coherent.

I just need to build on one particular result we obtained, namely that to decrease the pitch by half a step, we need to increase the string length by

.

This sort of makes sense intuitively: The 2 in the formula stems from the fact that the octave is halfway the string, and the 12 notes lie within the one octave. So we regard the whole string as 2 units. The 12th root accounts for the fact that we need to multiply something with itself 12 times to get 2. This means that lowering a tone equals to multiplying the present length by 12√2, and raising a tone equals to dividing the present length by 12√2. As I said, this only makes sense intuitively, read the above mentioned pages if you want the mathematics.

We will discuss 2 methods to construct a fretboard, both of which are build upon the above finding.