Re: Inversions of 7o and 5+, etc

"Alain Naigeon" <anaigeon@[EMAIL PROTECTED]
> wrote in message 
news:47eae637$0$13930$426a74cc@[EMAIL PROTECTED]
> 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)
>

It's the 2,3,4 and 6 semitone intervals which form symmetrical structures.

Maj. 2 forms the whole-tone scale - 6 tones, 2 possibilities - 6x2=12
Min. 3/Aug. 2 forms the o7 - 4 tones, 3 possibilities - 4x3=12
Maj. 3 forms the Aug. triad - 3 tones, 4 possibilities - 3x4=12
Aug. 4/Dim.5 forms the tritone - 2 tones, 6 possibilities - 2x6=12

The P4, having 5 semitones isn't a factor of 12.

Tom K.