We've established that the VII(dim) can be thought of as the result of combining two triads -- Vma + VII(dim) = V7 (the V7 is just a Vma Triad with one extension tone (7) -- which happens to be 'Fa' of the 'Mother Major Scale.') Because this knowledge becomes useful when we begin to study 4-part harmony -- we've made an attempt to include the VII(dim) Triad Function (in the theory). But, while the sound of the VII(dim) is excellent for ear training -- the 'angular' sound of the Diminished Triad is not commonly heard in the context of modern modal harmony. However, the functional root movement (VII in the bass) is absolutely essential in modern modal harmony. Here's how we exclude the VII(dim) triad sound while utilizing the 'VII' Function's root movement:
The Key Center of 'C' Major ('C' Ionian) would look like this:
The G/B is called a 'Slash Chord' -- it is a G Major Triad with the B-note in the bass (it is an 'inversion' of the G triad). [For guitar players - it may help to know that this can be as simple as a two-note chord (G-note with a B-note in the bass -- a minor 6th interval that we all get to know well when we are learning tunes)].
The Key Center of 'A' Minor ('A' Aeolian) would look like this:
The Key Center of 'Eb' Major ('Eb' Ionian) would look like this:
The Key Center of 'C' Minor ('C' Aeolian) would look like this:
The combination of the 'C' Major and 'C' Minor Key Centers looks like this: