The musical chord is a harmonic structure, a set of three or more intervals. Two notes sounding simultaneously make an interval so a chord consists of at least three different notes. Any three-tone chord is called a triad. The three tones of a triad are a root, a third and a fifth. The root is the main chord tone. It is the note on which the triad was built. The third determines the quality of a chord, so does the fifth.
The function of a triad depends on the scale degree on which it was built. So the triad built on tonic will represent the tonic function. If the root of the triad is dominant it will represent the dominant function etc.
There are four quality types of triads. They are major, minor, diminished and augmented. Musical chords also vary by their stability.
The major chord is the strongest and most stable because of the major third and the perfect fifth.
C + M3 + P5 = Cmaj.
The minor chord is quite stable because of the perfect fifth. However, the minor third is less stable interval than the major third.
A + m3 + P5 = Amin.
The diminished and the augmented chords are weak and unstable because of their fifths. Instead, of perfect consonances they are dissonant: diminished fifth and augmented fifth.
B + m3 + d5 = Bo.
G + M3 + A5 = G+.
If you add another third above a fifth of a triad you will get a seventh chord. Seventh chords also have several quality types which are determined by their seventh.
Here are some of the most useful of them: dominant (it is the most commonly used seventh chord), minor, diminished and half-diminished.
The dominant seventh chord includes a major third, a perfect fifth, and a minor seventh: G + M3 + P5 + m7 = G7.
The minor seventh chord includes a minor third, a perfect fifth, and a minor seventh: D + m3 + P5 + m7 = Dmin7.
The half-diminished seventh chord includes a minor third, a diminished fifth, and a minor seventh: B + m3 + d5 + m7 = Bø7.
The diminished seventh chord includes a minor third, a diminished fifth, and a diminished seventh: G♯ + m3 + d5 + d7 = G♯o7.
In the harmonic analysis, chords are marked by Roman numerals to distinguish on which scale degree the chord was built. Capital Roman numerals symbolize major chords. Lowercase Roman numerals symbolize minor chords. Lowercase Roman numerals with o - diminished chords. Capital Roman numerals with + - augmented chords. Roman numerals with 7 - seventh chords.