Diminished VII degree that resolves to tonic.

In the Prelude in C major, Bach shows us the use of the chord as:

• Secondary diminished seventh auxiliary of the second degree (measures 12 to 13).
• VII degree of a major key (14 to 15).

More interesting is his use in the Chromatic Fantasy. In the following example, we see:

1. A pedal tone of D (primary key of the work) in the lowest voice.
2. A melodic line on the upper voice.
3. A series of diminished seventh chords (in red in the example) descending chromatically between the pedal and the melodic line. This series of diminished sevenths is interrupted briefly on the last beat of the second measure (D minor chord) and on the last beat of the next-to-last measure (G minor):

How do we explain these diminished seventh chords? Let's start from this series of fifths that includes dominant sevenths of the twelve keys:

Let's replace each dominant chord with the corresponding diminished seventh chord (G major's VII degree, F# diminished replaces G major's V degree):

If we arrange the movement of the voices so that each voice moves to the nearest note (the F# of the first chord would move to F natural), we will obtain the chords used by Bach:

The harmonic progression used by Bach is a cycle of fifths that takes us through the twelve keys.

One of the notes of the diminished seventh chord is the fundamental of the chord with which it links.

In the following example, Schubert links an A-flat major chord with a B diminished seventh chord. The common note is the A flat:

Here a dominant F chord goes to a B diminished seventh chord. The common note is the F:

In measure 46 of the above passage, Schubert transforms the B diminished seventh (B-D-F-Ab) into the vii degree of F# minor (E#-G#-B-D) to modulate from B-flat major to F# minor.

One of the chord's notes resolves by descending semitone.

In this passage, Bach resolves a C# chord diminished to A minor. If we add the missing seventh (B-flat), we see that it is a B-flat descending by a semitone to A. The progression is repeated using a B diminished and a G minor chord:

Note: You can see another example in the Chromatic Fantasy passage discussed in the previous topic on the minor chords interrupting the chromatic series of diminished sevenths.

Chopin uses practically the same chords in his Prelude in E minor but adds the minor seventh to the A chord:

Finally an example of Jobim using the same chords: