Re: Inversions of 7o and 5+, etc

On Mar 26, 7:07 pm, "Alain Naigeon" <anaig...@[EMAIL PROTECTED]
> wrote:
> 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.

Keep that thought!

> 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 ?

SHORT ANSWER
I think that this may be more what you are looking for:

The equality of the intervals of the 3rds is a mathematical exercise,
but does not address why they are special in a musical sense, but do
provide the reason that they are capable of this special thing that
they do.

Their symmetrical construction allows them to be present in more than
one key. Each of the 3 dim7 chords occur in three different keys. Each
Augmented chord does exist in 4 different keys and the interval of the
tritone simultaneously exists in 2 different keys. THIS is the thing
that makes them special.

The B D F Ab chord, for example, can be the leading tone of C, Eb, Gb
and A (and other enharmonic  tones) thus as it is a common chord to
these 4 keys, it allows for the direction of the tonality to go in
either of these 4 directions by keeping its inherent function in the
original key and  assuming the same function in one of the other
keys.

The other chords, major, minor can exist in more than one key as well.
but they do not have such a characteristic and unique function as the
dim7 chord The dim7 chord is also an incomplete dominant chord and
thus will have a stronger tendency to resolve (it does contain 2
tritiones!) and this is what makes it such a force. It acts as a 1st
class chord (a dominant function chord) for 4 keys. It is the only
arrangement of tones in our system that does that.
LJS