Perfect intervals

Most intervals come in major and minor forms. Four do not: the unison, fourth, fifth and octave. These are perfect.

Why they are a separate category

The historical reason is acoustic. The octave, fifth and fourth correspond to the simplest frequency ratios — 2:1, 3:2 and 4:3. Notes in those relationships share many overtones, so they blend into something that sounds like one enriched sound rather than two notes.

Major and minor thirds and sixths are more complex ratios. They sound consonant but coloured; medieval theory called them imperfect consonances and treated them with suspicion for centuries.

The practical consequence for you is a naming rule:

• Perfect intervals can be perfect, augmented or diminished.
• They are never major or minor. "Major fifth" is not a thing.
• Seconds, thirds, sixths and sevenths are major or minor, and never perfect.

The perfect fifth does most of the work

The fifth is the outer interval of every major and minor triad — it is the note that is the same in both, which is why the third alone decides the chord's quality.

It is also the interval the circle of fifths is built from, and the reason neighbouring keys share six of their seven notes.

Violins, violas and cellos tune their strings in perfect fifths. Bass and guitar tune mostly in perfect fourths.

The fourth is the awkward one

The perfect fourth is acoustically simple but contextually unstable. Played above the bass in tonal harmony it tends to want resolution — which is exactly what a suspended fourth chord exploits. Played between upper voices it sounds perfectly consonant.

That is why it is often classed as a conditional consonance rather than a plain one. It is the only interval whose category genuinely depends on where it sits.

Inverting them

Perfect intervals invert to perfect intervals. A fourth inverts to a fifth, a unison to an octave — the numbers add to nine and the quality stays put.