Major third
The major third spans four semitones with a just ratio of 5:4, the bright imperfect consonance that gives major chords their sound.
From C
- Size
- 4 semitones
- Abbreviation
- M3
- Just ratio
- 5:4 (386.31 cents)
- Equal-tempered
- 400 cents (+13.69 from just)
- Inversion
- Minor sixth
What it sounds like
The major third is an imperfect consonance, the brighter of the two thirds. Its just ratio, 5:4, is simple, so the two notes blend warmly and sound settled. Melodically it is an open leap that sounds cheerful, and it is one of the most common intervals in tonal melody. Harmonically it is the third of every major triad, where it gives the chord its brightness. Equal temperament makes it about 14 cents wider than the just version, a difference that singers and string players often correct by ear.
How to recognise it by ear
The first two notes of 'When the Saints Go Marching In' rise by a major third, from C to E. Without that tune, sing C up to E in C major and listen for the open, settled sound of the bottom two notes of a major chord. Practice: sing C up to E, then C up to E♭, and hold each until the difference in brightness is clear before naming it. The minor third sits one semitone lower and sounds darker, so comparing the two is the most reliable test.
Theory
The major third inverts to the minor sixth: the lower note moves up an octave, the semitones total twelve, and the quality changes from major to minor. Major triads stack a major third on the root and a minor third above it, and dominant seventh and major seventh chords also contain a major third above the root. Within the major scale, the major third spans degrees 1 to 3, 4 to 6 and 5 to 7. Its just ratio, 5:4, measures 386.31 cents. The equal-tempered major third is 400 cents, so the just size is 13.69 cents narrower.
The major third above every note
Spelled by letter name, so the interval’s number is always right: a major third above E♭ is not the same spelling as above D♯.
| From | To | Hear it |
|---|---|---|
On the piano
Further reading
- Reading Intervals at Sight: Generic and SpecificFundamentals · 6 min
- Just Intonation, Beating and Why Intervals Sound in TuneTuning & Temperament · 8 min
- Equal Temperament: What It Costs and What It BuysTuning & Temperament · 8 min
Questions
Why do singers tune the major third lower than equal temperament?
A singer or string player adjusts pitch by ear, so the third can settle at the just 5:4 ratio rather than the equal-tempered 400 cents. That places it about 14 cents narrower, which blends more cleanly with the fifth. A keyboard in equal temperament cannot make the adjustment, so its major thirds sit wider.
Is a major third always four semitones?
In equal temperament, yes. The name, though, depends on the letters as well as the distance. C to E is a major third, while C to F♭ spans the same four semitones and is a diminished fourth. Just tuning gives the major third a size of 5:4, so the semitone count is not the whole definition.
Why is the major third built into the harmonic series?
The fourth and fifth partials of any fundamental form a major third, with a ratio of 5:4. Those partials are among the first few that a sung or played note produces, so the interval has a natural sound. Equal temperament shifts its size slightly, but the underlying relationship remains.