Comparison, in cents, of intervals at or near a major third
In classical music from Western culture, a third is a musical interval encompassing three staff positions (see Interval number for more details), and the major third (Play (help·)) is a third spanning four semitones. Along with the minor third, the major third is one of two commonly occurring thirds. It is qualified as major because it is the larger of the two: the major third spans four semitones, the minor third three. For example, the interval from C to E is a major third, as the note E lies four semitones above C, and there are three staff positions from C to E. Diminished and augmented thirds span the same number of staff positions, but consist of a different number of semitones (two and five).
The major third may be derived from the harmonic series as the interval between the fourth and fifth harmonics. The major scale is so named because of the presence of this interval between its tonic and mediant (1st and 3rd) scale degrees. The major chord also takes its name from the presence of this interval built on the chord's root (provided that the interval of a perfect fifth from the root is also present or implied).
A major third in just intonation corresponds to a pitch ratio of 5:4 (play (help·)) (fifth harmonic in relation to the fourth) or 386.31 cents; in equal temperament, a major third is equal to four semitones, a ratio of 21/3:1 (about 1.2599) or 400 cents, 13.69 cents wider than the 5:4 ratio. The older concept of a ditone (two 9:8 major seconds) made a dissonantly wide major third with the ratio 81:64 (play (help·)). The septimal major third is 9:7, the undecimal major third is 14:11, and the tridecimal major third is 13:10.
In equal temperament three major thirds in a row are equal to an octave (for example, A♭ to C, C to E, and E to G♯; G♯ and A♭ represent the same note). This is sometimes called the "circle of thirds". In just intonation, however, three 5:4 major thirds are less than an octave. For example, three 5:4 major thirds from C is B♯ (C to E to G♯ to B♯). The difference between this just-tuned B♯ and C, like that between G♯ and A♭, is called a diesis, about 41 cents.
A diminished fourth is enharmonically equivalent to a major third (that is, it spans the same number of semitones). For example, B–D♯ is a major third; but if the same pitches are spelled B and E♭, the interval is instead a diminished fourth. B–E♭ occurs in the C harmonic minor scale.