The Three Functions - Tonic, Subdominant, Dominant

The previous unit established that a key contains seven diatonic chords and showed how to write them as Roman numerals.

The immediate practical problem is that seven options is too many to choose between. Sitting down to write, there is nothing telling you which chord should come next.

Classical harmony solved this by collapsing the seven into three roles. Those roles are called functions.

Three groups, defined by distance from home

The three functions are distinguished by their relationship to the tonic chord.

Function	Symbol	Role
Tonic	T	stable, able to end a phrase. Both the starting point and the destination
Subdominant	SD	moves away from the tonic. Continues either to the dominant or back home
Dominant	D	the least stable. Pulls strongly toward the tonic

The seven chords of C major distribute like this.

Three tonics, two subdominants, two dominants. The allocation is not arbitrary.

Why the dominant pulls toward the tonic

Start with V. What makes a chord dominant comes down to two notes.

The first is the leading tone. The third of V (G–B–D) is B, a half step below the tonic C. Half-step adjacency generates a very strong pull, so B wants to move to C.

The second is the tritone. Add a minor 7th to V to get V7 (G–B–D–F).

B to F is a diminished 5th, the six-half-step tritone. That interval is unstable and resolves by expanding outward or contracting inward. Here B rises to C and F falls to E, landing on the tonic triad.

Leading tone plus tritone: a chord holding both of those is a dominant. Which is exactly why vii° on the seventh degree (B–D–F) is also classed as dominant — it is V7 minus its root, retaining both B and F.

Check

Why is vii° (B–D–F) classified as a dominant?

Because it is a diminished triadBecause it contains the tonic noteBecause it contains the leading tone and the tritoneBecause its root is the seventh degree

Check answer

The subdominant is the one that leaves

Consider IV (F–A–C). It still contains the tonic note C, so it has not left entirely, but it introduces F, which the tonic chord does not have. That F is what produces the sense of having stepped away from home.

ii (D–F–A) shares two notes, F and A, with IV. That is why ii operates as a subdominant in the same way.

Substitutes are chords that share two notes

As those cases show, functional classification is decided by shared notes. A triad has only three notes, so sharing two of them makes the character nearly the same.

Original chord	Substitute	Shared notes
I (C–E–G)	iii (E–G–B)	E, G
I (C–E–G)	vi (A–C–E)	C, E
IV (F–A–C)	ii (D–F–A)	F, A
V (G–B–D)	vii° (B–D–F)	B, D

This table is the entire explanation for why seven chords fit into three functions. It is not something to memorize — writing out the chord tones derives it.

The functions have a preferred direction

There is a natural order to the three.

T → SD → D → T

Leave home, move away through the subdominant, build tension on the dominant, return. That is the basic cycle.

Going D → SD instead releases the tension you just built without resolving it, which feels slack. It is not forbidden, but classical harmony avoids it.

Reordering the functions

▶T→SD→D→T▶T→D→SD→T

Check: The first is the basic T→SD→D→T, and it arrives properly. The second swaps D and SD. Listen at the third chord (F) for the sense of tension being let go rather than resolved. All four chords are identical in both; only the order differs.

C – F – G – C. A proper return

Note that this prohibition on D → SD does not apply to popular music. In rock and blues, progressions like C – G – F – C are standard. The rules of classical harmony are conventions within that style, not laws of music in general — worth internalizing from the outset.

Check

How is the progression I – vi – IV – V written in terms of function?

T – SD – SD – DT – D – SD – TT – T – D – SDT – T – SD – D

Check answer

The same framework operates in minor

In minor keys the diatonic chords are built from harmonic minor, with the seventh degree raised. In C minor that gives:

Degree	i	ii°	III+	iv	V	VI	vii°
Chord	Cm	Ddim	E♭aug	Fm	G	A♭	Bdim
Function	T	SD	T	SD	D	T	D

The entry to notice is that V is a major triad, G. Left as natural minor the seventh degree would be B♭, the chord on the fifth degree would be Gm, and there would be no leading tone. Raising the seventh to B creates the leading tone and lets the chord function as a dominant.

Raising the seventh degree in minor exists precisely to create this dominant function. The reason for harmonic minor, introduced back in Unit 2, connects here.

Thinking in functions lets you design progressions

Once functions are available, the way you write changes.

• decide the next role rather than the next chord
• once the role is fixed, any chord carrying that function will do
• the choice changes the coloring without breaking the structure

Having committed to “T → SD → D → T,” whether the SD is IV or ii is entirely open. IV is the plain choice; ii is a slightly softer one.

▶ See the seven chords color-coded by function The card colors are the functions. Tap through them in order and listen for how chords sharing a color also share a character Diatonic Chord Reference →

The next lesson takes up how a functional sequence comes to an end. The standard closing formulas are called cadences, and they act as the punctuation of a phrase.