Tonal Relationships: Related Keys and Modulation

Every major and minor key has 5 diatonically related keys. To illustrate, I am arbitrarily choosing the keys of A flat major and C sharp minor. For A flat major, the related keys are B flat minor, C minor, D flat major, E flat major and F minor. For C sharp minor, they are E major, F sharp minor, G sharp minor, A major and B major. Any two diatonically related keys either have the same key signature or a key signature with one sharp or flat more or less. Another type of key relationship is known as ‘parallel’, for example, B flat major and B flat minor. But this is not a diatonic relationship.

The 231-measure fugue from the Prelude and Fugue in E minor, BWV 548 is one of Bach’s longest. The formula given above would suggest that this fugue might visit the keys of G major, A minor, B minor, C major and D major. Every one of these keys indeed appears. In addition, however, there is an excursion, during the 113-measure middle section, to the unrelated key of F sharp minor. Bach achieves this goal by progressing from D major - a related key to F sharp minor - just before it. Thus, while E minor and F sharp minor are not closely related, D major is related to both of them.

Arriving at F sharp minor is done quite straightforwardly. It is the way in which Bach gets from F sharp minor back to related tonal areas that is remarkable. In the passage quoted above, measures 136-145, a continuous modulatory excursion takes place. Starting in F sharp minor, there is a motion to A major [related to F sharp minor], on to E minor [related to A minor, the parallel key of A major], G major [related], D minor [related to G minor, the parallel key of G major], F major [related to D minor], and C major [related]. The excerpt shows only upto the onset of G major. Bach has gone from F sharp minor to the remotest key of C major in only 10 measures by way of 5 intervening keys. Then from C major, the home key of E minor returns by way of a simple harmonic sequence.

Similar tonal excursions are found throughout the music of Bach.