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"Six and one of half a dozen
Black guitars and plastic blues.
Hide behind a wall of nothing
Nothing said and nothing new.
Four chords that made a million."
I-V-vi-IV. There's just something about these four chords that makes for a catchy tune in western pop music, transcending the boundaries of genre, and work in a song with any mood or tempo. This particular ordering of them, the "pop-punk progression" as The Other Wiki calls it, was spawned as a variant of the Doo Wop Progression, and has been particularly popular from the 1990s to the present day. Actually Older Than They Think - this progression is already known in the Baroque music. Pachelbel's Canon is a variant of this progression, known as Pachelbel's Canon Progression.
The Roman numerals above represent a sequence of four chords. If you don't know Roman analysis, check out this video — Porcupine Tree, "Four Chords That Made A Million"
 , or play these chords on a piano: C major, G major, A minor, F major. Repeat if desired. If this progression loops back to I, this effectively produces a Plagal Cadence. Very often, this progression is used as an ostinato—a repeated pattern that occurs throughout a song (or a part of it).
In a major key, this progression is I V vi IV. If we play them in a different order, vi IV I V, (A minor, F major, C major, G major)the progression sounds to be in the relative minor key (the key whose home note starts on the sixth note of its relative major key), in which case we notate it as i VI III VII. This version is sometimes called the "sensitive-female chord progression."
All of these progressions can be and are played with fifth or "power" chords; these are not major or minor chords (they don't possess the "third" which determines whether a chord is major or minor), but people's ears will pick up on the sound they're "expecting" to hear and fill in the blanks mentally so the progression sounds right.
Note, as always, that Tropes Are Tools: while it has proven to be an irresistible progression, a band who relies on it for too many of their songs runs the risk of being regarded as unimaginative and dull.
It's become a recent theme of music oriented comedy to make fun of this trope.
See its predecessor from the 30's to mid 60's, the Twelve Bar Blues.
Related chord progressions:
Examples of I V vi IV (the major key version):
Examples of i VI III VII (the minor key version):
Other chord progressions containing the four chords
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