Going around in circles—the phrase implies the frustration of not getting anywhere fast. But in music, circles offer magical, never-ending pathways of harmony and bliss. Last time we looked at the circle of 4ths and circle of 5ths. Harmonies, melodies, and bass lines often move in patterns that reflect the circle of 4ths (or 5ths, depending on the direction around the circle).
This month, let’s contemplate a graphic diagram of the circle of 4ths and 5ths (see Fig. 1). In his seminal theory textbook Elementary Training for Musicians [1949, Schott], composer Paul Hindemith explains the concept: “If we arrange all the major scales, starting with C, progressing accordingly to the number of their sharps in one direction and of their flats in the other, we see that they follow each other at the distance of a 5th and a 4th respectively.”
Much of the confusion about the circle arises because an interval of a perfect 4th (abbreviated P4), when inverted, becomes an interval of a perfect 5th (P5): The interval between the notes G up to C is a 4th (P4), but the interval going down from G to C is a 5th (P5). Going around the circle of 5ths means moving up in intervals of 5ths, whereas moving through the circle of 4ths means moving up in intervals of 4ths.
A lot of information is packed into the circle diagram. At the top, the key of C major indicates no sharps, no flats. Moving left (counterclockwise), a flat is added for each new key signature, the next major keys being F, Bb, Eb, and Ab. This is the circle of 4ths.
Three same-sounding flat and sharp keys cohabitate in the circle’s swamp bottom: The key of Db major (five flats) is sonically duplicated by the key of C# major (seven sharps); Gb major (six flats) sounds the same as F# major (six sharps); and Cb major (seven flats) contains the same pitches as B major (five sharps). Moving further through the circle in counterclockwise motion, sharps are removed with each new major key: E, A, D, G, before finally arriving back to C.
Look at Example 1 to review how to build an interval of a 4th (P4). Many standard songs use harmony moving in intervals of 4ths: “All the Things You Are,” “Autumn Leaves,” and “All of Me” all contain passages of root motion up in 4th intervals. Even the ubiquitous IIm–V7–I progression (for example, Dm7 to G7 to Cmaj7) is a series of chords with roots moving up in 4th intervals. Root movements in the circle of 4ths sound stable and familiar.
Example 2 shows a simple pattern moving up through the circle of 4ths. Note that I did not write a new key signature every bar; instead, I chose to use accidentals when necessary on each note. Extra credit: Transcribe the 13-bar exercise to a separate sheet of manuscript paper, writing the key signature for each new measure. This will cement the concept of the circle of 4ths progression in the theory side of your brain.
Example 3 shows the construction of the perfect 5th (P5) interval. The P5 interval spans a distance of seven half-steps, whereas the P4 covers five half-steps. Harmonic progressions moving in the circle of 5ths, which sound brighter, are less common that those moving in the circle of 4ths. Jimi Hendrix’s “Hey Joe” [Are You Experienced, 1967, Polydor], with Noel Redding on bass, offers a satisfying example of the circle of 5ths in action. Hendrix moves partially through the circle using the chords Bb, F, C, G, D. Example 4 shows a simple pattern moving up through the circle of 5ths.
Remember, the key of C major contains no sharps and no flats. Moving clockwise (to the right) through the circle of 5ths, a sharp is added for each new key, the next major keys being G, D, A, and E. As you know from the circle of 4ths, several key signatures share common pitches: B major (five sharps) and Cb major (seven flats), F# major (six sharps) and Gb major (six flats), and C# major (seven sharps) and Db major (five flats). Moving further through the circle of 5ths in clockwise motion, more flats are removed with each new major key: Ab, Eb, Bb, F before finally arriving back to C.
Keep digging into this special spiral and you’ll uncover many useful theoretical relationships. I’ve indicated the relative minor keys in lowercase letters inside the circle. A relative minor shares the same key signature (the same number of sharps or flats) with the corresponding major key signature, for example: C major and A minor, E major and C# minor, Ab major and F minor. Next time, we’ll explore minor chords around the circle.
Circles make the bass world go round! Check out John’s new video lesson series, The Upright Bass Handbook, at truefire.com and johngoldsby.com.