Perfect intervals

What it means

Unison, fourth, fifth, and octave are called perfect. These four intervals do not occur in major and minor forms — unlike the second, third, sixth, and seventh — but only in one shape, which, when altered, is called augmented or diminished. The reason lies in their simple frequency ratios: 1:1, 4:3, 3:2, and 2:1. They appear low down in the harmonic series and therefore merge especially strongly.

Musical use

In part-writing theory, the unison, fifth, and octave count as perfect consonances with the corresponding consequences: parallel motion in them is forbidden, because it loses the independence of the voices. The fourth occupies a special position — consonant between upper voices, treated as dissonant above the bass.

Historically this group was for a long time the entire stock of fully valid combined sounds. The early polyphony of organum knows only the octave, fifth, and fourth; the third became established only in the fourteenth and fifteenth centuries and fundamentally changed the sound of European music.

Upon inversion, perfect intervals remain perfect: the fourth becomes the fifth, the unison becomes the octave. If one of them is expanded by a semitone, it is called augmented; if narrowed, diminished — the diminished fifth and the augmented fourth are the best-known cases.

Perfect intervals are called so because they occur only in one normal form and not, like thirds or sixths, in major and minor forms. They can become augmented or diminished. In the harmonic series they arise between the first four partials. Their simple frequency ratios explain why they have counted as especially pleasant-sounding since antiquity.

Performance practice

Tune in this order: octaves first, then fifths, only then thirds — the perfect intervals give the most reliable reference points, because their beats are most clearly audible. Take them without vibrato when checking. And use them in ear training as anchors from which the other intervals can be derived.