Circle of Fifths

Play the top key of a piano. It should be a C. Starting from there, count that key as 1, and count down the white keys to get to 5. That's an F. Do it again, and you'll get a B, an E, an A, a D, a G, and then a C again.

Now build chords on top of this. Just triads, all on the white keys. You should end up with the following sequence: C, F, Bdim, Em, Am, Dm, G, C. This is your basic Circle of Fifths progression.

This has turned out to be a rather popular progression. This is probably in part because it uses the strength of the Authentic Cadence, multiple times in a row—especially if you modify the chords appropriately, you can pretty much produce a chain of overlapping authentic cadences.

The basic progression, in Roman numeral notation is as follows:

major: I, IV, vii°, iii, vi, ii, V, I
minor: i, iv, VII, III, VI, ii°, V, i

For example, in the C major and A minor (the relative major/minor pair with a key signature of 0 sharps or flats), the progressions are as follows:

C major: C, F, Bdim, Em, Am, Dm, G, C
A minor: Am, Dm, G, C, F, Bdim, E, A

The exact chords can be modified, but the sound is still similar. Note that the first four chords of the minor version are the same as the last four chords of the major version; this overlap is often used by composers to modulate between keys or express ambiguity of tonality for various purposes.

The full eight-chord progression (or seven-chord, if you don't count the repeated chord at either end) is pretty prominent when it occurs, but doesn't occur too often. Much more frequent, though, is a half-sized progression consisting of four chords—usually the last four of either progression or the first four of the minor progression (which is the last four of the major one anyway).

The partial version, especially when using the last four chords of the major progression or the first four chords of the minor progression, is closely related to the Humoresque Progression, with the only difference being the second chord. The difference is not that great since the two second-chords share two triad notes anyway.

This progression also has a chromatic form, but this is much less observed because of the tendency of music to stay in one key. Here is the chromatic circle anyway, for reference:

C, F, Bb, Eb, Ab, Db (C#), F# (Gb), B (Cb), E, A, D, G, C

The term "circle of fifths" also refers to a circular diagram shown on the right here. This, however, shows the relationships between the different pairs of keys major and minor and how many sharps or flats they have. To put it in layman's terms, there are twelve different notes in each octave, and each one of them has a major scale (along with a minor scale starting on a different note), and they each have some number of sharps or flats, and the circle diagrams them in an easy-to-reference format. This also shows "enharmonics"—keys that can be spelled in two ways, but (generally) sound the same, because notes like F# and Gb are basically the same.

Note: The notation "m7b5" (i.e. "minor 7th chord, with flatted fifth") is the half-diminished seventh chord. So, "A#m7b5" is the same as A#^ø7. The m7b5 notation is just an artifact of the jazz-originated letter-based chord notation system.

Examples of Circle of Fifths include:

Examples of the full (eight- or seven-chord) progression, or more than half at least:

George Frederic Handel, the Passacaille from the Suite in G minor, HWV 432: It's a theme and variations based on a theme that is EXACTLY this chord progression.
Examples written by Antonio Vivaldi
- The first movement of the Violin Concerto in A minor, Op. 3 #6 (a.k.a. RV 356). This piece is best known for being included in the Suzuki violin method, book 4. You can hear instances of this in the first movement at 0:07, and another at 1:31. It occurs again in the third movement at 6:17 and 8:16.
- The first movement of the Violin Concerto in F minor, Op. 8 #4, a.k.a. "Winter", from The Four Seasons. You can hear one instance of this progression at 1:12, in the first movement.
This passage from the Toccata In D Minor by Johann Sebastian Bach.
Wolfgang Amadeus Mozart, the first movement of the Sonata in F major, K. 332, at 1:16, and again in the recap later
Franz Schubert, Impromptu in Eb major Op. 90 #2, starting at 0:23, and again in the recap at 6:07
Gloria Gaynor, "I Will Survive", and its covers (which is this progression in A minor, repeated)
In Final Fantasy I, the Game Over theme, "Dead Music".
Leon Lai, "Summer Love" (the refrain has the first seven chords, in G minor)
Selah: "You Are My Hiding Place" (like "I Will Survive", the entire song is built on repeated instances of Bm, Em7, A, D, G, Em, F#; so only the sixth chord is altered, into a very similar chord)
The SNES game Demon's Crest, several times in the track "Palace of Decadence"
In the Rockman Dash (i.e. Mega Man Legends) soundtrack, the insert song "Your Wind is Blowing", combines Circle of Fifths with the Humoresque Progression, by changing the second chord in the minor-key sequence to VI—thus producing an instance of the latter within a variation of the former.
Ritsuko Okazaki, "Serenade", insert song from Fruits Basket, two instances in the verse: A7, G#m7, C#m7, F#m7, B7, E (skips the D#dim chord); followed immediately by A#m7b5, D#7, G#m7, C#m, F#m9, B11, E)
Melocure, "Agapé" (in the verses: Em7 A7 Dm7 Gm7 Cm7 F7 Bb M 7; in the bridge: Em7b5, Am7, Dm9, G7, Cm7)

Examples of the half (four-chord) progression:

King Harvest, "Dancing in the Moonlight" (Cm7 Fm7 Bb9 Eb)
Talk Talk, "It's My Life", refrain, right after using the very similar Humoresque Progression
Hidetoshi Sato, the Neon Genesis Evangelion theme song "Cruel Angel's Thesis" (Cm Fm Bb Eb in the refrain, multiple times)
Weezer, "Island in the Sun" (everything that isn't the refrain is Em Am D G in G major)
Melocure, "Agapé" (Gm Cm F Bb in the refrain, repeatedly)
This troper thinks Queen's "Now I'm Here" should count as a circle of fifths progression, even though it's technically A-D-B-E-C sharp-F sharp-E flat (D sharp)-A flat (G sharp).
Aqua's "Barbie Girl" (C#m-F#m-B-E)
Elton John's "Crocodile Rock" chorus (Em-A7-D-G)
The refrain of the opening theme for the English dub of Digimon Frontier.