V - I is a common progression that represents the sound of tension to resolution.
In the key of D Major, the I chord is D Major, and the V chord is A Dominant 7.

Since V represents tension, it is common to substitute out-of-key tonalities over this for greater suspense.
Here we're going to use the Diminished 7 chord to open up some new possibilities.

If we raise the root of our naturally occuring V chord by a half step, we get a Diminished 7 chord (as shown below).

Here's A7 (V of D Major) and its related Diminished 7 chord A#º7

Notice that the Diminished 7 chord is perfectly symmetrical,
each note seperated by minor 3rds.

Because of this, when we do inversions of a Diminished 7 chord, the shape does not change.
We could label these inversions as root position Diminished 7 chords from a new root.
In this case we have A#º7, C#º7, Eº7, and Gº7.
This is our new family of Diminished chords for that original V chord.

The next step is to use each of these Diminished 7 chords to find new Dominiant 7 V chords.
To do this, we use reverse logic....

We raised the root of our original Dominant 7 chord to get to the Diminished 7 chords.
Now, we lower the root of each Diminished 7 chord to access our family of related Dominant 7 chords.

A#º7, C#º7, Eº7, and Gº7 become A7, C7, D#7, and F#7.

We can use these new Dominant 7 V chords to resolve back to D Major, or its relative minor, B minor.
Relative to the original resolution chord of D Major, these new V chords land on the bII, III, V, and bV.

We can also use these as a bridge to an unrelated key.
Using any of these chords, we can apply the reverse logic to go to one of four related resolution keys.
We'll take a look at this next.

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This quiz generates a key center to practice finding all of its related Diminished V chords, and related Dominant 7 chords.

1. Using the randomly generated key center as your I chord, find its naturally occurring V chord.
2. Raise the root of that V chord to superimpose a Diminished 7 chord over the V.
3. Lower each note of this Diminished 7 chord one at a time to get your new family of Dominiant 7 chords.

Click the button below to randomly generate a new key center.

Generate New Key