Musical intervals

What it's for

An interval is the distance between two notes. Recognizing it (major third, perfect fifth, tritone…) is essential for harmony, singing and composition.

How it works

The distance is measured in semitones: from C to G there are 7 semitones, i.e. a perfect fifth. The tool measures the interval going up from the first note to the second.

Why an interval has two names at once

The name of an interval is made of two pieces answering two different questions. The number (second, third, fifth) counts how many letters apart the notes are, including the starting one: from C to E there are three letters, so it is a third. The quality (major, minor, perfect, augmented, diminished) says how many semitones actually sit inside those letters.

That is why C to E flat is a minor third and C to D sharp, which on the instrument is the same sound, is an augmented second: the same number of semitones, different names, because the letters involved differ. The distinction looks academic until you read a score, where the name tells you what that interval is for.

How they are recognised by ear

The method that works is associating each interval with the opening of a song you know by heart. The perfect fourth is the start of the Wedding March, the perfect fifth the Star Wars theme and the opening of Twinkle Twinkle, the major sixth the opening of My Way, the octave the first two notes of Over the Rainbow.

One precaution is needed, though: descending intervals are not recognised with the same references as ascending ones, and have to be practised separately. It is the commonest mistake of self-taught students, and the reason people end up recognising a sixth perfectly going up and getting it wrong every time going down.

The tritone, the interval that splits the octave in half

Three whole tones exactly, that is six semitones: it is the only interval sitting precisely at the middle of the octave, and for that reason the only one that stays itself when inverted. In the Middle Ages its harshness earned it the nickname diabolus in musica, and for centuries it was taught as something to avoid.

In modern music it is instead one of the fundamental building blocks: it lives inside every dominant seventh chord, between the third and the seventh, and it is precisely its instability that creates the tension asking to resolve. Without the tritone there would be neither the blues nor almost any final cadence.

Inversion, and the rule of nine

Turning an interval over, that is moving the lower note an octave up, gives its inversion: the third becomes a sixth, the fourth a fifth, the second a seventh. The two numbers always add up to nine, and that is the quickest way to work it out in your head.

The quality swaps for its opposite: major becomes minor, augmented becomes diminished, and perfect stays perfect. That is why the fourth and the fifth are both «perfect»: each is the inversion of the other, and in Western music they are the two most stable intervals after the octave.

Nearby tools

The notes that form a scale are in Musical scales, those of a chord in Chord notes. The families of keys are in Circle of fifths, and the frequencies in Note to frequency.