The dominant seventh · Seventh chords · Music theory
It is a major triad with a minor 7th above the root. It is the same chord in a major key and in its parallel minor, because the leading tone is used in…
The dominant seventh
It is a major triad with a minor 7th above the root. It is the same chord in a major key and in its parallel minor, because the leading tone is used in minor: the V⁷ of C major and that of C minor are both G–B–D–F.
Two of its notes tend to move. The leading tone (its 3rd) rises to the tonic and the 7th falls by step to the 3rd of the tonic chord. Together they form a tritone (B–F), which resolves on arriving at I.
Why it asks to resolve
Piston explains it through its two dissonant intervals: the diminished 5th between the 3rd and the 7th, and the minor 7th between the root and the 7th. Harmonically, both seek a consonant interval; melodically, the notes move where they tend, and on arrival the tension disappears.
In practice: the diminished 5th closes into a 3rd, with the leading tone rising and the 7th falling. The minor 7th resolves into a 6th if only the upper voice falls, or better into a 3rd if the root also leaps to the tonic. That is why a complete V⁷ usually goes to a I without a 5th, with the root tripled.