V7 to I
The dominant seven chord, or V7, typically resolves to I. It naturally gravitates to the I chord for several logical reasons.
1. The interval of a fifth is special because of its cyclic nature. The perfect 5th (perfect 4th) is the only interval which cycles through the entire chromatic scale (excluding the m2). This is represented very clearly in the circle of fifths (see Diatonic & Non-Diatonic).
2. The V7 chord, aside from having a naturally strong gravity to I, also shares a common tone with the I chord. For example, in C Major, the root of the 5th chord, G, is also the fifth of the one chord, C-E-G.
3. The tri-tone (Aug4 or Dim5th) contained within the V7 chord is a highly unstable interval. In the V7 chord, G7, the tri-tone is B and F (the 3rd and 7th of the chord). When resolving this interval, the closest and most stable resolution is for the 3rd of the V7 chord to resolve upward to the root of the I chord and for the 7th of the V7 chord to resolve downward to the 3rd of the I chord.
