Inversions of diminished and augmented chords

[riddlereader]

Given a specific diminished 7th chord, how do you determine whether it
is in root position or an inversion? Ditto for augmented chord.

In my (probably oversimplified) view, the first inversion of a C dim 7
would be an Eb dim 7; and the second inversion would be a Gb dim 7.


So I can't tell the difference between an Eb dim 7 in root position,
vs a C dim 7 in first inversion. However, the chord drill on
https://forum.emusictheory.com  makes a distinction.


I have the same problem with augmented chords. I don't see a
difference between C aug in first inversion vs E aug in root position,
but the chord drill makes a distinction.


I'd be grateful if anyone can explain.


Thanks,


Ed

[counterpoint]

Given a specific diminished 7th chord, how do you determine whether it
is in root position or an inversion? Ditto for augmented chord.

In my (probably oversimplified) view, the first inversion of a C dim 7
would be an Eb dim 7; and the second inversion would be a Gb dim 7.

Yes, that's right from the view which keys to press. But you have to know, that diminished 7th chords are chords of 5 notes, where the root note is left out.

So the C dim 7 could be

a Ab major triad with added 7th (Gb) and 9th (Bbb) (but the Ab is not played!) => C Eb Gb Bbb

or

a B major triad with added 7th (A) and 9th (C) (but the B is not played) => C D# F# A

or

a D major triad with added 7th (C) and 9th (Eb) (but the D is not played) => C Eb F# A

or

a F major triad with added 7th (Eb) and 9th (Gb) (but the F is not played) => C Eb Gb A


So you have to look how the chord is notated, then you can find out, which is the real root note of the chord.

[riddlereader]

Thank you very much for your quick response.

So I understand that any diminished 7th chord can be seen as a dominant flat ninth, without the root. And if you see a diminished 7th chord by itself, you can interpret it as a dominant flat ninth with implied root a half step below one of the notes in the diminished chord. And the spelling gives you the information you need to identify which of the four possible roots of the dominant flat ninth chord is implied.
 
Which note then is considered the “root” of a stand-alone diminished chord? From your example, if you see the following, with no other context:

C Eb Gb Bbb,
C D# F# A,
C Eb F# A,
C Eb Gb A,

then which one would you say is in root position? Which is in first inversion, etc?

I should mention that my reason for asking is that I was using the chord drill at
https://www.emusictheory.com, where there is no context, and the only clue seems to be which spelling is used (e.g., Eb or D#).

Thanks again,

Ed

[counterpoint]

Thank you very much for your quick response.

So I understand that any diminished 7th chord can be seen as a dominant flat ninth, without the root. And if you see a diminished 7th chord by itself, you can interpret it as a dominant flat ninth with implied root a half step below one of the notes in the diminished chord. And the spelling gives you the information you need to identify which of the four possible roots of the dominant flat ninth chord is implied.

Great, you understand that perfectly well!

Which note then is considered the “root” of a stand-alone diminished chord? From your example, if you see the following, with no other context:

C Eb Gb Bbb,
C D# F# A,
C Eb F# A,
C Eb Gb A,

then which one would you say is in root position? Which is in first inversion, etc?

Oh yes, that's the big question!

In the previous example: look, if there's anywhere an augmented second. Example 2: C D#, Example 3 Eb F#, Example 4 Gb A
Then the upper note of the augm 2nd is the (major!) third of the chord you're searching 

[thalberg]

Interesing, Counterpoint!  Here's a little historical trivia:

Arnold Schoenberg used to have a name for diminished seventh chords and augmented triads -- he called them "vagrant chords."  Vagrant means homeless.  He called them by this name because you cannot determine their inversion by hearing them--you need to see them on the page.  Just from hearing them, they could be any inversion, and therefore belong to any of several keys.  They were like skeleton keys used to unlock various tonal regions.  So they belonged really to no key--they were homeless.

Schoenberg also did say they were the top four voices of a ninth chord, much like counterpoint explained.

When composers want to be ambiguous about where they are going, they often use diminished sevenths or augmented chords.  Both are great for modulations.

[mattgreenecomposer]

Well I've never heard it explained that way counterpoint...but what ever works!

In order to tell a diminished chords inversion it's necessary to look at its function and where it is headed (what chord or chords come next.)  But if counterpoints explination worked for you than go with that.

I don't use fully diminished 7th chords that much frankly in my music b/c  I think they sound kinda cheesy but the half diminished chord which is easily distinguishable I use much more frequently.
Its very commonly used as in ii V i in a minor key for example.

[counterpoint]

Well I've never heard it explained that way counterpoint...but what ever works!

How would you explain it?

[thalberg]

Yes, Matt, you can find Counterpoint's explanation in Schoenberg's Theory of Harmony.