Re: Inversions of 7o and 5+, etc

On 27 Mar, 02:07, "Tom K." <tkor...@[EMAIL PROTECTED]
> wrote:
> "Alain Naigeon" <anaig...@[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 =A0But... 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.=


Right idea, execution slightly off. Here's a corrected version:

Min. 2 forms the chromatic scale - 1 semitone, 12 possibilities (12 /
1 =3D 12)
Maj. 2 forms the whole-tone scale - 2 semitones, 6 possibilities -
(12 / 2 =3D 6)
Min. 3/Aug. 2 forms the o7 - 3 semitones, 4 possibilities - (12 / 3 =3D
4)
Maj. 3 forms the Aug. triad - 4 semitones, 3 possibilities - (12 / 4 =3D
3)
Aug. 4/Dim.5 forms the tritone - 6 semitones, 2 possibilities - (12 /
6 =3D 2)
Octave - 12 semitones, 1 possibility (12 / 12 =3D 1)