Fifth

The strongest consonance after the octave

Two tones sound the more fused, the simpler the ratio of their frequencies. At 3:2 the common pattern of both waves repeats after every two and three vibrations respectively, a very short period that the ear perceives as one sound. The fifth therefore sounds powerful and open. Because it lacks the third that would give it a major or minor colour, it feels empty. C–G is neither cheerful nor sad.

On the guitar the fifth sits seven frets above the note you fret. The seventh fret is also the place of the third partial: if you touch the string lightly above the 7th fret, the fifth above the octave sounds as a harmonic.

Fifths in everyday music

A power chord consists only of root and fifth, for example A5 of A and E. Leaving out the third allows heavy distortion without the sound turning muddy, and fits over major and minor melodies alike because it does not commit itself. In medieval organum two voices ran parallel in fifths and fourths; thirds were then counted as dissonances. The third partial of the harmonic series lies a fifth above the octave (a twelfth): if you play a fifth, you only double what sounds along in every tone anyway.

Stacking fifths

If you go up a fifth from C again and again, the series C, G, D, A, E, B, F♯, C♯, G♯, D♯, A♯, E♯, B♯ arises. On the circle of fifths this has become a circle, and every step adds exactly one sharp or flat to the key signature. Twelve pure fifths, however, miss seven octaves by the Pythagorean comma, 23.46 cents. In equal temperament the fifth is therefore 2 cents too low, which nobody hears. Why that is so is explained in the article Equal, meantone, just: why your piano is slightly out of tune.

Common mistakes

• Mixing up fifth and fourth: Seven instead of five semitones, and a different direction of tension.
• Hearing the fifth as a major chord: Without a third it has no colour.
• Thinking all fifths are equally pure: On the piano no fifth is exactly pure.