The II–V–I, and why three chords are enough
Preparation, tension and rest in three chords; the most frequent sequence in popular music, what makes it work, and how to spot it in any chart.
Take the authentic cadence, dominant to tonic, and put a chord in front of it to prepare the dominant. The chord tradition chose is the second degree, and the result has a name of its own: II–V–I. It is the most frequent sequence in jazz, in bossa nova and in a good part of popular music, and whoever recognises it by ear reads a whole chart in formulas.
Three functions, three chords
The second degree is subdominant: it departs from the tonic without tensing. The fifth degree is dominant: it tenses. The first degree is tonic: it rests. The II–V–I is the whole sentence of tonal harmony — departure, tension, rest — in the fewest chords it fits into.
As seventh chords, the three have fixed qualities, and it is those the ear recognises: minor seventh, dominant, major seventh.
Why it works so well
Two things happen at once, and the strength comes from both together.
The roots fall by fifths: D, G, C. It is the path of the circle of fifths, the bass movement the ear accepts as the most natural, because each chord stands as the dominant of the next.
The upper voices barely move. The seventh of D minor, C, falls a semitone to B, which is the third of G7. The seventh of G, F, falls a semitone to E, which is the third of C major. While the bass leaps, the voices step by semitone, and it is that contrast that makes the sequence sound inevitable.
In any key
The formula is in degrees, so it serves all twelve keys. In F major the II–V–I is G minor, C seventh, F major seventh; in D major it is E minor, A seventh, D major seventh.
Play the three in sequence, each in its key, and notice that the sensation is the same: only the pitch moved. That is why a musician does not memorise "G minor, C7, F major"; they memorise II–V–I and transpose.
In a minor key
The minor II–V–I uses the same degrees with the qualities of the minor key: the second degree becomes half-diminished, the fifth stays dominant, and the first becomes minor.
The fifth degree is major even in a minor key, because it is its leading tone that pulls to the tonic; without it, the dominant does not dominate. It is the same mechanism as the major key with a darker chord to start from.
Spotting it in a chart
Look for a dominant chord and see what comes before and after. If before it there is a minor seventh chord a fourth below, and after it a chord a fourth above, it is a II–V–I, whether or not it is in the song's key. Half the bossa nova charts are chains of II–V–Is, each pointing at a different centre:
E minor and A7 point at D; D minor and G7 point at C. Two II–V–Is in a row, the first of them entirely outside the arrival key, and the ear follows without effort because the formula is the same.
What to take from here
Three chords, three functions, a path of roots by fifths and voices that step by semitone. The II–V–I is the authentic cadence with preparation, and the sequence that repeats most in popular music. Recognising it turns a long chart into a few formulas, and the secondary dominants of the next reading are what happens when the V of a II–V–I points at a degree that is not the first.