Generally speaking, a major chord is any chord which has a major third above its root, as opposed to a minor chord which has a minor third. More specifically, it is the three-note chord made up of a major third and perfect fifth above the root - if the root of the chord is C, the chord will consist of the notes C, E and G. This is also known as a major triad.
The minor chord resembles the major chord except that it has a minor third with a major third on top, while a major chord has a major third with a minor third on top. They both contain fifths because two pitches a major and minor third apart are a fifth apart.
A major chord in just intonation is tuned to the frequency ratio 6:5:4, while in equal temperament it has 3 semitones between the third and fifth, 4 between the root and third, and 7 between the root and fifth. It is represented by the integer notation 0,4,7. In equal temperament, the fifth is only two cents narrower than the just perfect fifth, but the major third is noticeably different at 13.686 wider.
The majortriad consists of the first, third and fifth notes of a major scale, for example in C, these would be C, E and G. Thus C, E, G is a C majortriad.
The interval from C to E is a major third (two tones), and from E to G a minor third (one and a half tones).
Triads of the Welsh bards, poetical histories, in which the facts recorded are grouped by threes, three things or circumstances of a kind being mentioned together.
Like triads, the names of other notes of the seventh are derived from their interval above the root: the third and the fifth and the seventh.
Seventh chords built upon augmented triads are extremely rare, as are minor triads with a major seventh and major or minor triads with diminished sevenths.
In this method, the roman numeral is upper case for major (and augmented chords), lower case for minor, and lower case plus the small superscript "o" for diminished triads.