Perfect fourths and fifths

A perfect fifth is seven half steps, and flipping it upside down gives a perfect fourth of five half steps.

The open, hollow sound

Fourths and fifths are called perfect intervals. A perfect fourth spans five half steps, for example C up to F. A perfect fifth spans seven, for example C up to G. Played together, a fifth sounds open and steady, with none of the colour that a third adds. That steadiness is why violin, viola and cello strings are tuned a fifth apart, and why guitarists play "power chords" of just a root and a fifth.

Every white-key fourth and fifth is perfect, except one pair

The white-key rule is even simpler than for thirds. All white-key fourths are perfect except F up to B, which is six half steps: an augmented fourth. All white-key fifths are perfect except B up to F, also six half steps: a diminished fifth. Both are nicknamed the tritone, because six half steps are three whole steps. The tritone splits the octave exactly in half and has a restless sound. So if you see a fourth or fifth on white keys, check only whether it is F and B; if not, it is perfect.

Inversion: a fourth is an upside-down fifth

Take C up to G, a fifth, and move the C up an octave. Now G is at the bottom and C at the top: G up to C, a fourth. This flip is called inversion. The sizes of an interval and its inversion always add up to nine (5 + 4), and their half steps add up to twelve (7 + 5), because together they fill one octave. Perfect intervals invert to perfect intervals. Major intervals invert to minor ones: a major third (4) becomes a minor sixth (8).

Fourths and fifths also organise instruments and keys. Guitar strings are tuned mostly in fourths: E, A, D and G are each a fourth apart, then G to B is a major third, and B to the top E is a fourth again. Fifths organise the keys themselves. Moving up a fifth from C to G to D adds one sharp each time, so G major has one sharp and D major two. That chain of fifths, called the circle of fifths, is the backbone of the scales and keys course.

Famous fourths and fifths

The hymn "Amazing Grace" (words published by John Newton in 1779, sung to the tune "New Britain" since 1835) opens with a rising fourth on "A-ma-", from D up to G in the key of G. The Bridal Chorus from Wagner's opera Lohengrin, known in English as "Here Comes the Bride", and the Scottish song "Auld Lang Syne" also begin with a rising fourth. For the fifth, the clearest example is "Twinkle, Twinkle, Little Star": C, C, then up to G on the second "twinkle".