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.
>
> 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)
>
> --
>
> Fran=E7ais     *=3D=3D>     "Musique renaissance"     <=3D=3D*    
English=

>                midi - facsimiles - ligatures -
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> Alain Naigeon - anaig...@[EMAIL PROTECTED]
 - Oberhoffen/Moder, France

Mostly because we use tertian harmony. We build our chords in thirds.
our scale is divided into 12 parts. when you have the 3 half steps in
the 4 minor thirds and they form a circle. there are 3 and only 3
different chords of this type (called the diminished seventh) but it
has 8 different possible names for each different chord. lower any one
of the tones a half step and you have created a dominant chord and
this will send you to a choice of 4 different keys for each of the
three chords.

There are 4 half steps in the major thirds. They circle after the 3rd
note. There are only 4 different chords of this type (augmented
chords) but they have different enharmonic names as well. So each
chord can be common to 3 different keys.

The only other interval that this works with is the tritone. It is 6
steps and it circles after 2 so it can only be in two keys. There are
only 6 different tritones and thus it can imply the dominant chord in
two different keys. (That is the basis of the TriToneSub.

There are no other intervals that divide evenly in to our 12 tones
that we use in our music so that is why these are the only ones that
will work like that. 3 4 and 6 (the number of half steps in the
intervals) are the only number (except 1 and 12) that can go into 12
evenly.
LJS