The Circle of Fifths is usually used to illustrate the keys associated with key signatures, with increasing numbers of sharps on the right side and increasing numbers of flats on the left. But it also shows us which keys are most closely related, especially if relative major and minor are indicated next to each other. In my personally preferred version of the circle, the major keys are shown on the outside of the circle in uppercase, and the corresponding relative minor keys are on the inside in lowercase.
Chopin’s 24 Preludes (op. 28) are ordered according to the circle of fifths in clockwise order, with each major key followed immediately by its relative minor. Thus each prelude is closely related to its predecessor and successor. Chopin also wrote three other preludes outside of the main set, in C-sharp minor, A-flat major, and E-flat minor (the last of which was unfinished).
The preludes and fugues in each of the two books of Bach’s Well-Tempered Clavier, in contrast to Chopin’s scheme, are ordered chromatically: C major, C minor, C-sharp major, C-sharp minor, and so on. When we plot them out on the Circle of Fifths, we see continual leaps across the circle, with each prelude/fugue in a relatively distant key from its predecessor. When Book I of WTC first appeared in 1722, it must have seemed a true tour de force. Bach was taking full advantage of a new tuning system that approximated modern equal temperament. Under older tuning systems, some keys would have sounded fine, but others would have seemed out of tune and would have usually been avoided. The new “well-tempered” system rendered all 24 keys equally palatable, which was a prerequisite for the flowering of chromatic harmony, not only in the Baroque period but especially in the Romanticism of the nineteenth century and beyond.
Sergei Rachmaninoff also composed 24 preludes that included all the major and minor keys. Here, however, the order of keys is relatively haphazard, although he did tend to place parallel major and minor keys side by side, or in some cases relative major and minor. His most famous prelude, in C-sharp minor, was published early in his life (1892) as part of his Five Morceaux de Fantaisie (op. 3). Another Ten Preludes (op. 23) appeared in 1903, followed by the last Thirteen Preludes (op. 32) in 1910. The very last prelude is in D-flat major, which is the enharmonic parallel major to the C-sharp minor of the earliest prelude, and given certain other resemblances between the two preludes (discussed in my dissertation), it is clear that the key relationship is not coincidental.
My Nine Preludes for Piano Solo are arranged in a spiral key sequence, proceeding alternately four semitones up and then one semitone down. Major and minor modes are alternated, except that the last two preludes are both in major. The resulting sequence — d#-G-f#-Bb-a-Db-c-E-Eb — generates a series of leaps across the Circle of Fifths not unlike those of the Well-Tempered Clavier. When the Nine Preludes are played as a set, each prelude contrasts with its predecessor both in key and in mood. These preludes are somewhat long for the genre, so the whole set runs about 35 minutes, even though only nine keys are included.