14: The circle of fifths

 

There are twelve notes in the chromatic scale—twelve possible roots from which to build major or minor scales, major or minor chords, and so on. Musicians, therefore, have coopted the 12-hour clock face to create a device known as the circle of fifths.

Recall, for example, that C major is C D E F G A B C, and that the formula for any major scale, if you start from a place we’ll label “0” is [0, 2, 4, 5, 7, 9, 11, 12]—the “2, 2, 1, 2, 2, 2, 1” formula we discussed several articles ago.

A consequence of how the formula is built is that, in order to differ by exactly one note, you must move the new tonic up or down by exactly a perfect fifth. C up a perfect fifth is G, and C down a perfect fifth is F.

C major, again, is C D E F G A B C. G major, similarly, is G A B C D E F# G—differing from C only in terms of the F, which is sharp in G major, but natural in C. Meanwhile, F is F G A Bb C D E F—and so it too differs from C in only one place, regarding the B, which is natural in C but flat in F. This is true of any neighboring scales; they’ll always differ by one note from their immediate neighbors, and where those differences will be is entirely predictable.

The same holds for the minor scale. Because of the way the formula works out, a minor scale will be different by exactly one note from the minor scales rooted a fifth away in either direction.

A minor: A B C D E F G A
E minor: E F# G A B C D E (different from A minor only in terms of F vs. F#)
D minor: D E F G A Bb C D (different from A minor only in terms of B vs. Bb)

Musicians, then, have come to place the keys on the clock face with C major/A minor at the 12 o’clock position and going around in both directions from there: 1-sharp G major/E minor at 1 o’clock and 1-flat F major/D minor at 11 o’clock; 2-sharp D major/B minor at 2 o’clock and 2-flat B-flat major/G minor at 10 o'clock; and so on—until at 6 o'clock, 6-sharp F-sharp major/D-sharp minor and 6-flat G-flat major/E-flat minor overlap.

This clock face, at a glance, gives us a very good overview of which keys are closely related to which other keys. For example, the major key at 12 o’clock (that’s C) is very closely related to the major keys at 11 and 1 o’clock (F at 11 and G at 12), and to the minor key at its own position (which is A minor). The converse of this, however, is that the further you have to travel, the more distantly related any pair of keys is—until you travel diametrically opposite your starting point and you are at as distant a place, literally and musically, as you could possibly be.

Learn the circle of fifths just the same way in school you learned addition facts and times tables—it will become your best friend when you step into the wonderful world of analysis, and even more so when you start writing on your own.




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