LOCATING AND ANNOTATING MODULATION

To find the location of a modulation, it is helpful to compare the diatonic tones of the old and new key and find between them those that are diatonic only in one of the muscal keys. The diatonic and altered tones were explained in chapter Diatonic and altered tones. First, we will explain how to compare keys and then how to locate and annotate a modulation.

Comparing keys

Let us compare, for instance, the diatonic tones of the C major key with the diatonic tones of the G major key. The comparison is shown in the next figure. 

Figure: The comparison of the diatonic tones of the C major key and G major key 

We see that most of the diatonic tones are diatonic in both keys. This is expected because we are comparing two closely related keys. For instance, C is diatonic in both keys. It is shown in black color in both keys. However, some diatonic tones are diatonic only in one of the keys. For instance, F is diatonic only in the C major key thus it is shown in red color in the C major key. F# is diatonic only in the G major key so it is shown in red color in the G major key. The same thing can be seen immediately by comparing only the key signatures of the C major key and G major key. However, we will see that the situation is more complex when we are comparing a minor key. 

When we compare diatonic tones of a minor key, we must include both the ascending and descending sixth and seventh scale degrees. For instance, the next figure shows the comparison of the diatonic tones of the A minor key with the diatonic tones of the D major key. We see that, for instance, D is diatonic in both keys. Also, for instance, G# is diatonic only in the A minor key, while C# is diatonic only in the D major key.

Figure: The comparison of the diatonic tones of the A minor key and D major key 

Locating modulation

The next figure shows a typical modulation and illustrates the method for locating it. The figure is a simplification because it implies that only diatonic tones appear near the location of a modulation. We know that altered tones also appear in tonal music, although typically much less frequently than diatonic tones. In the figure, we see the passage which is diatonic in the old key, the passage which is diatonic in the new key and their intersection which forms a passage that is diatonic in both keys. Also, we see notes which are diatonic only in the old key and notes which are diatonic only in the new key. 

We can find two points in time:

• The first point corresponds to the last occurrence of a note that is a diatonic only in the old key. Let’s call it the exit point. This is the point of exit from the old key. 

• The second point corresponds to the first occurrence of a note that is diatonic only in the new key. Let’s call it the entry point. This is the point of entry in the new key.

Figure: Locating modulation

We know for certain that the old key is present before the exit point and the new key is present after the entry point. The area between the exit and entry point is a kind of border area. Thus, we can position the modulation anywhere between the exit and entry points. We can consider that the ears resist the key change and put the modulation as far as we can i.e. at the entry point. Sometimes we can get a stronger initial chord progression in the new key if we move the modulation a little earlier. For instance, by doing that, we may get P > D > T as the initial chord progression in the new key, instead of D > T (see chapter Harmonic functions).

Annotating modulation

After determining the location of a modulation, we annotate the chords before it in the old key and the chords after it in the new key. The next figure illustrates this.

Figure: Annotating modulation

In the chapters that follow, we shall see many examples of finding exit and entry points.