# Fourth and fifth ## Overview

Audio: fourth and fifth (0:08)

fourth and fifth plays Pythagorean fourths and fifths on a piano. The fourth and fifth figure shows the score consists of the following:

• Bar 1 contains an interval of a perfect fifth, DA.
• Bar 2 contains an interval of a perfect fourth, DG.
• Bars 3-4 contain a melody made from the intervals of unison, octave, fourth and fifth.

The perfect fifth is the most important interval after unison and the octave.

A Pythagorean perfect fifth is constructed by splitting the difference between an octave, 2:1, and unison, 1:1, to produce a new frequency ratio, 3:2, which is an interval of a perfect fifth.

The perfect fourth is the inverse of a perfect fifth. To calculate its frequency ratio, take the ratio of the perfect fifth, 3:2, invert it to get 2:3, and double it to get 4:3.

Pythagorean tuning has now produced four intervals: unison, octave, perfect fifth and perfect fourth with frequency ratios 1:1, 2:1, 3:2 and 4:3 respectively.

The intervals of unison, fourth, fifth and octave are classed as perfect intervals, although the word, perfect, is often dropped in practice and the term implied. Perfect means just that: these intervals sound perfect. This is a perceptual issue and means that the sound of these intervals is deemed the most consonant of all possible sounds. Their frequency ratios are combinations of the simple numbers 1, 2, 3 and 4 and cannot be made more simple. Furthermore, an inverted perfect interval always results in another perfect interval.

The intervals of unison, fourth, fifth and octave enable you to construct all sorts of interesting melodies. They are probably the most commonly used intervals in music.