Inversions of 7o and 5+, etc

Each position of the diminished seventh chord sounds the same
as the root position, and can be rewritten by enharmony (thus
allowing modulations)
I remember having read that this is "because this chord is made of
equal" intervals - all minor thirds.

Recently, it made me think about a chord made of identical major
thirds, for instance C E G#...
First, it turns out that we can't build a seventh, since B# is C !
(Indeed I should have guessed that an augmented 7th would
 give an octave ;-) )

Then :
E G# C is the same as E G# B#, and sounds like the root position.
G# B# E is the same as G# B# D## obviously the same kind
of chord once again, but this time built on G#.

Up to this point I was still thinking that the argument "... because
made of equal intervals" was a sensible one.

But, but..., after all, why would the third be the only interval we
would be allowed to have a look at ?
Thus I took fourths, for instance, and I failed to find anything
special with the inversions of such "chords" made of fourths !

Now my question isn't about these fourth chords, it's about
the real reason to these miracles for chords B D F bA
and C E G# ; since the reason given (equal intervals) is wrong
because there is at least one counter example, what can be the
*real* reason ?
I more or less see that enharmonies are possible with chords
made of fifths and equal (minor/major) thirds, but not with
those made of fourths : it's quite obvious that starting from
C F bB and considering F bB C we can't cheat enough
with the C to re-build a fourth :-o  But... why, then, are thirds
behaving in such a special and miraculous way, why only the
thirds?
(ok you might find another interval having this property, but
 what I'm looking for is a general explanation why some have
it, and some don't)

-- 

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Alain Naigeon - anaigeon@[EMAIL PROTECTED]
 - Oberhoffen/Moder, France