# fully-diminished chord for chromatic modulation

I was reading up on modulation to distantly-related keys.

Fully-diminished chord is used for modulation to chromatic keys, because the root is changeable.

And then I encountered this picture.

If the root is changeable, shouldn't the 2nd inversion of fully-diminished chord in m.135 be written in 3rd inversion?

Is this typo or a convention?

• That is third inversion. Or are you referring to the figures? Commented Jun 12 at 6:55
• 4 over 3 is second inversion. 4 over 2 is third inversion, isn't it?
– Sean
Commented Jun 12 at 9:53
• Where does the chord analysis come from? Online? Your teacher? Commented Jun 12 at 10:58
• I see. You’re asking about the figures, not the written chords. Commented Jun 12 at 13:55
• online, free book. site name is "MILNE library" and the book title is "Fundamentals, Functions, and Form". I find it is good book.
– Sean
Commented Jun 13 at 2:16

It is indeed an error, likely due to copy and paste. It's also the first time I've seen the diminished circle being used to denote an augmented fourth.

The diminished chord, by the way, is a triad, usually found in first inversion in the common practice period. These are diminished seventh chords.

As an inversion of vii°7 of G minor, the correct spelling is F♯, A, C, E♭. With C in the bass, that is second inversion, so the figure should be 4/3. The spelling with D♯ is for vii°7 of E minor: D♯, F♯, A, C. With C in the bass that is third inversion, as you note, and the figure should be 4/2: augmented second, augmented fourth, and major sixth.

• I think you meant E minor for the D# spelling. Ironic typo. Commented Jun 12 at 13:56
• @Aaron yes, thanks. Commented Jun 13 at 12:43

@phoog's answer clarifies much of the confusion with regard to the figured bass analysis, but this may be helpful to know going forward...

Any fully-diminished seventh chord can be used to modulate to eight different keys. It's easiest to visualize with a piano keyboard.

This chord could act like vii of Db, since C is a minor second below Db. But if we inverted the chord, we find that the same is true for every inversion. This gives us four possible tonics.

• C is the vii of Db
• D# is the vii of E
• F# is the vii of G
• A is the vii of Bb

Further, each of these tonics could be either a major or minor key. So this one chord could be used to bring us to Db major, C# minor, E major, E minor, G major, G minor, Bb major, or Bb minor. The exact spelling of the accidentals would change slightly but you get the idea.