Sound Engineering Explained, 2nd Edition

2  Hearing and the nature of sound

Part 2

Pitch

We said earlier that the frequency ratio between two adjacent semitones was approximately 6%. In scientific (but not necessarily musical) terms, the exact number is

¹²2 (the twelfth root of 2)

This is the number which, multiplied by itself 12 times, equals 2 and is 1.0594631. A pitch change of one semitone is therefore equivalent to a frequency change of 5.94631%. (Six per cent is a good enough approximation for most purposes!)

The reasoning behind the mathematics is that there are 12 equal semitone ‘intervals’ in an octave, which itself is a frequency ratio of 2:1. Each step must therefore be 12 ...