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That is, a song or other vocal or instrumental piece can be in the key of C major or A minor, but a song or some other piece cannot be in the key of B diminished or F augmented (although songs or other pieces might include these triads within the triad progression, typically in a temporary, passing role). Three of these four kinds of triads are ...
The hallmark that distinguishes major keys from minor is whether the third scale degree is major or minor. Major and minor keys are based on the corresponding scales, and the tonic triad of those keys consist of the corresponding chords; however, a major key can encompass minor chords based on other roots, and vice versa.
A diminished triad can be viewed as a minor triad in which the perfect fifth has been substituted with a diminished fifth (6 semitones). In this case, the augmented triad can be named major triad sharp five, or major triad augmented fifth (M ♯ 5, M +5, maj aug5).
A major triad has a major third (M3) on the bottom, a minor third (m3) on top, and a perfect fifth (P5) between the outer notes. In harmonic analysis and on lead sheets, a C major chord can be notated as C, CM, CΔ, or Cmaj. A major triad is represented by the integer notation {0, 4, 7}.
In some fake books and lead sheets, all triads may be represented by upper case numerals, followed by a symbol to indicate if it is not a major chord (e.g. "m" for minor or "ø" for half-diminished or "7" for a seventh chord). An upper case numeral that is not followed by a symbol is understood as a major chord.
A minor triad has a minor third (m3) on the bottom, a major third (M3) on top, and a perfect fifth (P5) between the outer notes. In harmonic analysis and on lead sheets, a C minor chord can be notated as Cm, C−, Cmin, or simply the lowercase "c". A minor triad is represented by the integer notation {0, 3, 7}.
Minor major seventh chord. A minor major seventh chord, or minor/major seventh chord (also known as the Hitchcock Chord) is a seventh chord composed of a root, minor third, perfect fifth, and major seventh (1, ♭ 3, 5, and 7). It can be viewed as a minor triad with an additional major seventh.
But this rule not only applies to major or minor chords, but also to seventh chords. For example, in the key in E minor, the tonic chord (E, G, B) becomes an E minor seventh chord (E, G, B, D), if the fourth note (D) is added to the triad. This applies to all other chords in the scale.