The ii–V–I progression: a practical introduction

What the numbers mean

Roman numerals name chords by the scale step they are built on. In C major:

ii is built on D: Dm7 (D F A C), a minor seventh chord.
V is built on G: G7 (G B D F), a dominant seventh.
I is built on C: Cmaj7 (C E G B), home.

So ii–V–I in C is Dm7 → G7 → Cmaj7. Written in numerals it is the same in every key, which is why jazz musicians think in numerals: in F it is Gm7 → C7 → Fmaj7, in B♭ it is Cm7 → F7 → B♭maj7. The Infinite Lounge engine stores every form this way, relative to the key, and picks the key per tune from F, B♭, E♭, C, G, A♭, D and D♭.

Why it sounds so smooth: rootless voicings

A jazz pianist’s left hand rarely plays these chords from the root up. The bass has the root, so the left hand plays a four-note rootless voicing in one of two shapes:

Type A: 3rd, 5th, 7th, 9th from the bottom up.
Type B: 7th, 9th, 3rd, 5th.

On dominant chords the 13th takes the place of the 5th (the 5th carries the least information). Then, between neighbouring chords, the pianist picks whichever shape and octave moves the fingers least. Do that through a ii–V–I and something neat happens: type A and type B alternate on their own. Here is what the engine’s rule picks:

Key	ii	V	I
C	Dm7 (type A) F3 A3 C4 E4	G7 (type B) F3 A3 B3 E4	Cmaj7 (type A) E3 G3 B3 D4
F	Gm7 (type B) F3 A3 B♭3 D4	C7 (type A) E3 A3 B♭3 D4	Fmaj7 (type B) E3 G3 A3 C4

Look at the C row. From Dm7 to G7 only one note moves, C down to B. From G7 to Cmaj7, three notes step down and one stays put. The hand hardly moves, and the ear hears three lines gliding rather than three blocks. That “hand doesn’t move” quality is most of what makes a ii–V–I sound like jazz.

Where it turns up

Once you know the shape, you hear it everywhere. In the forms the engine plays:

Jazz blues (12 bars): a ii–V into the IV chord in bar four, ii–V in bars nine and ten, and a ii–V turnaround in bar twelve leading back to the top.
32-bar AABA: each A section opens I–vi | ii–V | iii–VI | ii–V and closes on another ii–V, with the VI7 and other dominants acting as V of the next chord. The bridge is a chain of dominants (III7, VI7, II7, V7), each resolving like a V into the next.
16 bars of descending ii–Vs: a ii–V–I, then the same move a whole step lower, and again, before returning home.
Ballad AABA: slow ii–Vs one chord per bar, plus a backdoor variant in the bridge, iv minor to ♭VII7 (in C: Fm7 → B♭7) landing on I.

Colouring the V

The V chord is where the tension is, so it is where players add colour:

♭9 (G7♭9) and altered dominants (♭9, ♯9, ♯11, ♭13): darker, tighter.
Lydian dominant (7♯11): bright, but unresolved.
Upper-structure triads: a triad played on top of the dominant’s shell. Allowing only tensions that work over a dominant (no natural 11th, no major 7th), the triads that survive over C7 are D, E♭, G♭, A♭ and A.
Tritone substitution: replacing V7 with the dominant a tritone away (in C, D♭7 for G7).

Questions

What is a ii–V–I in C?

Dm7 → G7 → Cmaj7.

What is a ii–V–I in F?

Gm7 → C7 → Fmaj7.

What are type A and type B rootless voicings?

Type A stacks 3-5-7-9 from the bottom; type B stacks 7-9-3-5. On dominant chords the 13th replaces the 5th. Through a ii–V–I the two alternate naturally.