DIATONIC COMMON CHORD MODULATIONS

Diatonic common chord modulation is common chord modulation in which the annotated common chord is a diatonic chord in both the old and new keys. Such a common chord is called a diatonic common chord.

Diatonic common chords

To better understand what diatonic common chords are and how they can be found between any two keys, we shall find all the diatonic common chords between the C major key and G major key. They can be used in diatonic common chord modulations from the C major key to G major key or vice versa. The procedure is the same for any chosen par of keys.

First, we shall write down all the diatonic triad chords in the C major key and then in the G major key. We shall mark those of them that are common to both the keys. After that, we shall do the same for the diatonic seventh chords. The marked triad and seventh chords are diatonic common chords between the C major key and G major key. They are shown in red in the following two figures.

Figure: The diatonic common triad chords between the C major and G major keys are marked in red

Figure: The diatonic common seventh chords between the C major and G major keys are marked in red

We can conclude that all the diatonic chords from the C major key which do not contain the note name F and all the diatonic chords from the G major key which do not contain the note name F# are common. The reason is that the C major key and G major key are closely related keys and differ only in the note names F and F#. Thus, the result is 4 diatonic common triad chords and 3 diatonic common seventh chords. 

Closely related keys have more diatonic common chords than more distant keys. For instance, the C major key and D major key have 2 diatonic common triad chords and 1 diatonic common seventh chord. This can be easily seen from the preceding two figures if we add a sharp to all note names C in the second row. The C major key and A major key have no common diatonic chords.

Finding diatonic common chord

Usually, diatonic common chords occur between the exit and entry points. However, they can occur even before the exit point and after the entry point. The exit and entry point were explained in chapter Locating and annotating modulation. However, we are interested only in finding and annotating the common chord at the location of modulation.

The next figure shows an example of finding and annotating diatonic common chord. It shows the beginning of Bach’s Two-part Invention No. 8 in F major. This composition starts in the F major key. As we have already said in chapter Key of composition, a composition written in a certain key almost always begins in it.

Figure: Finding and annotating diatonic common chords

It is easy to see that from the seventh measure until the last shown measure, the note B is persistently used instead of Bb. This indicates a possible modulation from the F major key to its closely related C major key. Why? If we compare the diatonic tones of the F major key and the C major key, we see that they differ precisely in the note names Bb and B. This is shown in the same figure. The same thing can be seen immediately by comparing only the key signatures.

Also, we can easily see where the exit and entry points are. To find the exit point, we must search for the last occurrence of Bb. To find the entry point, we must search for the first occurrence of B. In the figure, they are marked in blue. Before the exit point, harmony is annotated in the F major key. After the entry point, harmony is annotated in the C major key.

The beginning of measure 6 is chosen for the location of the modulation and the common chord is annotated there. This is a diatonic common chord because it is a diatonic chord in both the old and new keys. 

Again, we see P > D > T as the initial chord progression in the new key. This is a convenient way to modulate to a new key, but as we shall see, it is by no means the rule. 

Examples of diatonic common chord modulation

In this chapter we shall examine a few more examples of diatonic common chord modulation.

First example:

The next figure shows the measures eight to eleven from Bach’s Two-part invention No. 13 in A minor. This is an example of the diatonic common chord modulation from the C major key to its closely related E minor key. 

The diatonic tones of the C major key and E minor key are also shown in the figure. We see that they differ in the note names F, F#, C# and D#. 

To find the exit point, we must search for the last occurrence of F. To find the entry point, we must search for the first occurrence of any of the note names F#, C# and D#. In the figure, the entry and exit points are marked in blue. Before the exit point, harmony is annotated in the C major key. After the entry point, harmony is annotated in the C major key.

The beginning of measure 9 is chosen for the location of the modulation and the common chord is annotated there. This is a diatonic common chord because it is a diatonic chord in both the old and new keys.  

Figure: The diatonic common chord modulation in Bach's Two-part Invention No. 13 in A minor

Second example:

The next figure shows the beginning of Bach’s Prelude No. 21 in Bb major from Well-Tempered Clavier, book I. It contains two diatonic common chord modulations. The first one is from the Bb major key to its closely related D minor key. The second one returns from the D minor key back to the Bb major key.

The diatonic tones of the Bb major key and the D minor key are also shown in the figure. They differ in the note names Eb, E, B and C#.

To find the exit point for the first modulation, we must search for the last occurrence of Eb. To find the entry point, we must search for the first occurrence of any of the note names E, B and C#. The exit and entry points occur in measures 2 and 3 and are marked in blue in the figure. 

The beginning of measure 3 is chosen for the location of the modulation and the common chord is annotated there. This is a diatonic common chord because it is a diatonic chord in both the old and new keys.  

To find the exit point for the second modulation, we must search for the last occurrence of any of the note names E, B and C#. To find the entry point, we must search for the first occurrence of Eb. The exit and entry points occur in measure 4 and 5 and are marked in blue.

The beginning of measure 5 is chosen for the location of the modulation and the common chord is annotated there. This is a diatonic common chord because it is a diatonic chord in both the old and new keys.

Figure: Two diatonic common chord modulations in Bach's Prelude No. 21 in Bb major from Well-Tempered Clavier, book I

To find the entry point for the second modulation, we must search for the first occurrence of Eb. To find the exit point, we must search for the last occurrence of any of the note names E, B and C#. The exit and entry points occur in the fourth and fifth measure and are marked in blue. There are four diatonic common chords here, all of them occurring between the exit and the entry point, where only note names common to both keys exist.

Third example:

The next figure shows the beginning of Bach’s Two-part Invention No. 13 in A minor. We see the modulation from the A minor key to its relative key, the C major key. 

The diatonic tones of the A minor key and the C major key are also shown in the figure. They differ in the note names F# and G#. However, both F# and G# are diatonic tones of only the A minor key and there are no notes that are diatonic tones of only the C major key. This means we can find only the exit point and we cannot find the entry point. To find the exit point, we must search for the last occurrence of the note names F# or G#. The exit point is marked in blue in the figure. How to find the place where the new key should be annotated? This example illustrates an easy solution which is available when the passage from the old key is repeated in the new key (a melodic, harmonic or any kind of repetition is helpful). We see the chord progression consisting of harmonies on the first and the fifth scale degrees in the A minor key, which is later repeated in the C major key. The beginning of this repetition was chosen as the convenient place from where the new key begins.

Figure: The modulation to the relative key from Bach's Two-part Invention No. 13 in A minor