Intervals

An interval is the distance between two pitches. In Western music we count intervals by the number of letter-name steps from the lower to the upper note, inclusive: C to E spans three letter names (C, D, E) and so is a third; C to G spans five letter names and is a fifth.

The numerical name fixes the diatonic size; a quality label — perfect, major, minor, augmented, diminished — fixes the chromatic size. Both labels matter: a third on the page can be major or minor, and the difference of a single semitone changes the whole feel of the chord built on it.

Intervals are the atoms of harmony and melody. Every chord is a stack of intervals. Every melodic step is an interval. The capacity to hear an interval and name it on the spot — minor sixth, perfect fourth, tritone — is the central skill of aural training, and it is the bedrock of memorising music, transcribing it, improvising over it, and analysing it. Without ear-trained intervals, written theory remains abstract; with them, it becomes a description of what you already hear.

Four intervals are called perfect: the unison, the fourth, the fifth, and the octave. They are perfect because they are acoustically the most consonant, sharing the simplest frequency ratios (1:1, 4:3, 3:2, 2:1), and because their major and minor forms have historically been treated as a single category rather than as two qualities. A perfect fifth is always seven semitones; a perfect fourth is always five.

The remaining diatonic intervals — seconds, thirds, sixths, sevenths — come in major and minor versions. A major third spans four semitones (C to E); a minor third spans three (C to E-flat). A major sixth spans nine semitones; a minor sixth spans eight. A major seventh spans eleven; a minor seventh ten.

Switching between major and minor is always the difference of a single semitone, and in tonal music the two qualities carry the difference between bright and dark, joyful and melancholy.

Semitones:  0   1   2   3   4   5   6   7   8   9   10   11   12
Quality:    P1  m2  M2  m3  M3  P4  ♭5  P5  m6  M6  m7   M7   P8
            unison      thirds     fourth tritone fifth  sixths  sevenths  octave

Widening a perfect or major interval by a semitone produces an augmented interval. Narrowing a perfect or minor interval by a semitone produces a diminished interval. C to F-sharp is an augmented fourth; C to G-flat is a diminished fifth. They sound the same on a piano but spell differently on the page, and resolve in opposite directions: the augmented fourth typically expands outwards to a sixth, the diminished fifth typically contracts inwards to a third.

The augmented fourth and diminished fifth are both names for the tritone, the most unstable interval in tonal music. It bisects the octave exactly. Mediaeval theorists called it diabolus in musica — the devil in music — because of the difficulty of singing it cleanly and the strong sense of needing resolution it produces.

Resolved cleanly inside a dominant seventh chord, the tritone is the engine of every authentic cadence; loose in a melody it remains the most striking interval the ear can hear.

Invert any interval — move the lower note up an octave, or the upper note down an octave — and the two sizes always sum to nine. A third inverts to a sixth; a fourth to a fifth; a second to a seventh. Quality flips too: major becomes minor, augmented becomes diminished, perfect stays perfect.

This sum-to-nine rule is one of the most useful pieces of theory: knowing that an interval and its inversion behave in mirrored ways simplifies voice leading and aural identification alike.

• 2nd ↔ 7th — quality flips (major ↔ minor).
• 3rd ↔ 6th — quality flips.
• 4th ↔ 5th — both perfect; quality stays.
• Octave ↔ unison — both perfect.

Intervals larger than an octave are called compound. A ninth is an octave plus a second, an eleventh an octave plus a fourth, a thirteenth an octave plus a sixth. In voicing chords, a compound interval often sounds more open and less crowded than its simple equivalent, which is why jazz voicings stack ninths, elevenths, and thirteenths above the root. The same C-E-G triad voiced widely as C–G–E (an octave higher) sounds bigger and more luminous than the closed C-E-G fist.

Most musicians learn to identify intervals by associating each one with a familiar tune. The opening leap of Twinkle Twinkle is a perfect fifth. The first two notes of Here Comes the Bride are a perfect fourth. The Star Wars theme opens with a perfect fifth then a major third. The opening of Maria from West Side Story is a tritone resolving to a perfect fifth. With twelve such anchors the entire interval set becomes immediately recognisable.

Melodic intervals (one note then the next) are easier to identify than harmonic intervals (both notes sounding together). Train both. Aim to name an interval inside one second of hearing it; that is the speed at which composers and improvisers are working in real time. Aural training apps and simple piano drills get you there inside a few months.

A melodic interval moves through time: one note, then the next. A harmonic interval is two notes sounding together. The same C and G can be either, depending on whether they are played in succession or together. In practice the rules of voice leading govern harmonic intervals (no consecutive perfect fifths between voices, for example), while the rules of melodic shape govern melodic intervals (avoid a tritone leap unless followed by a step in the opposite direction).