Seventh chords · Music theory
The dominant seventh, its resolution and inversions, and the leading-tone and diminished sevenths.
What a seventh chord is
If another 3rd is added on top of a triad, the result is a four-note chord: the root, the 3rd, the 5th and the 7th. Because the 7th is a dissonance, these chords sound tense and ask to resolve.
The most important one is built on degree V, the dominant seventh: in C major, G–B–D–F.
They are named by their triad and the quality of their 7th, measured from the root: G–B–D–F is a major triad with a minor 7th. Those two facts define it.
From ornament to chord
The 7th began as an ornamental note: a passing dissonance over a triad that gave impetus toward the next one. In time the ear grew used to it and it came to be considered part of the chord.
The dominant seventh was the first to be used regularly. The other sevenths went on being treated as dissonances to prepare and resolve, until the 19th century, and still more jazz, used them with great freedom.