Symmetry Of Diminished 7 Chords
One very important thing about diminished 7 chords is that they are symmetrical in nature, meaning that their structure repeats at regular intervals.
This symmetry arises from the equal spacing of minor thirds within the chord.
A diminished 7 chord is constructed by stacking three minor thirds on top of each other.
Let's take an example to illustrate this. Consider the diminished 7 chord built on C:
1. Start with C.
2. Add a minor third above C, which gives you E♭.
3. Add another minor third above E♭, which gives you G♭.
4. Finally, add one more minor third above G♭, which gives you B♭♭.
Because of the symmetry, you obtain three other diminished chord starting on each note of the C diminished 7 chord that are E♭dim7, G♭dim7 and B♭♭dim7 (Adim7 if you prefer).
In other words, each note of a diminished 7 chord is a root note.