Functional Harmony

Functional harmony is a system of understanding and organising chords in relation to a scale, i.e. the key of melody. This contains two parts:

1. Explain the role of the chords built from the scale.
2. Explore the combinations of these chords in progressions.

We are going to cover them scale by scale, grouped by modes. The scope will be limited to heptatonic (7-note) scales, where the chords are typically based on every other notes (like 1st, 3rd, 5th, 7th) of the scale. These harmony patterns form the basics of Western music.

The chords can be triads (3-note chords) or seventh chords (4-note chords). Apart from them, we are also going to discuss the variations (like sus2, sus4, add9) and extensions (like 9th, 11st, 13rd) of these chords.

1 Church Modes (Diatonic Modes)

Chord	C Ionian (Natural Major)	D Dorian	E Phrygian	F Lydian	G Mixolydian	A Aeolian (Natural Minor)	B Locrian
C, Cmaj7	$1$, $1_{\mathrm{\Delta }7}$ (tonic)	$\mathrm{♭}7$, $\mathrm{♭}{7}_{\mathrm{\Delta }7}$ (subtonic)	$\mathrm{♭}6$, $\mathrm{♭}{6}_{\mathrm{\Delta }7}$ (submediant)	$1$, $1_{\mathrm{\Delta }7}$ (tonic)	$4$, $4_{\mathrm{\Delta }7}$ (subdominant)	$\mathrm{♭}3$, $\mathrm{♭}{3}_{\mathrm{\Delta }7}$ (mediant)	$\mathrm{♭}2$, $\mathrm{♭}{2}_{\mathrm{\Delta }7}$ (Phrygian color)
Dm, Dm7	$2_{-}$, $2_{-7}$ (supertonic)	$1_{-}$, $1_{-7}$ (tonic)	$\mathrm{♭}{7}_{-}$, $\mathrm{♭}{7}_{-7}$ (subtonic)	$2_{-}$, $2_{-7}$ (supertonic)	$5_{-}$, $5_{-7}$ (minor dominant)	$4_{-}$, $4_{-7}$ (subdominant)	$1_{\circ }$, $1_{ø7}$ (tonic dim)
Em, Em7	$3_{-}$, $3_{-7}$ (mediant)	$2_{-}$, $2_{-7}$ (supertonic)	$1_{-}$, $1_{-7}$ (tonic)	$3_{-}$, $3_{-7}$ (mediant)	$6_{-}$, $6_{-7}$ (submediant)	$5_{-}$, $5_{-7}$ (minor dominant)	$2_{-}$, $2_{-7}$ (supertonic)
F, Fmaj7	$4$, $4_{\mathrm{\Delta }7}$ (subdominant)	$\mathrm{♭}3$, $\mathrm{♭}{3}_{\mathrm{\Delta }7}$ (modal color)	$\mathrm{♭}2$, $\mathrm{♭}{2}_{\mathrm{\Delta }7}$ (Phrygian)	$\mathrm{♯}4$, $\mathrm{♯}{4}_{\mathrm{\Delta }7}$ (Lydian color)	$\mathrm{♭}7$, $\mathrm{♭}{7}_7$ (subtonic)	$6$, $6_{\mathrm{\Delta }7}$ (submediant)	$\mathrm{♭}5$, $\mathrm{♭}{5}_7$ (diminished)
G, G7	$5$, $5_7$ (dominant)	$4$, $4_7$ (subdominant)	$\mathrm{♭}3$, $\mathrm{♭}{3}_7$ (mediant)	$5$, $5_7$ (dominant)	$1$, $1_{\mathrm{\Delta }7}$ (tonic)	$7$, $7_7$ (subtonic)	$\mathrm{♭}6$, $\mathrm{♭}{6}_7$ (modal color)
Am, Am7	$6_{-}$, $6_{-7}$ (submediant)	$5_{-}$, $5_{-7}$ (minor dominant)	$4_{-}$, $4_{-7}$ (subdominant)	$6_{-}$, $6_{-7}$ (submediant)	$2_{-}$, $2_{-7}$ (supertonic)	$1_{-}$, $1_{-7}$ (tonic)	$\mathrm{♭}7$, $\mathrm{♭}{7}_7$ (subtonic)
Bdim, Bø7	$7_{\circ }$, $7_{ø7}$ (leading tone)	$6_{\circ }$, $6_{ø7}$ (diminished)	$5_{\circ }$, $5_{ø7}$ (dim dominant)	$7_{\circ }$, $7_{ø7}$ (leading tone)	$3_{\circ }$, $3_{ø7}$ (diminished)	$2_{\circ }$, $2_{ø7}$ (supertonic dim)	$1_{\circ }$, $1_{ø7}$ (tonic dim)

1.1 Natural Major (Ionian)

Diatonic Chords

Number	Chord (Key of C)	Function	Role
$1$, $1_{\mathrm{\Delta }7}$	C, Cmaj7	Tonic	Home chord, most stable, feeling of rest
$2_{-}$, $2_{-7}$	Dm, Dm7	Supertonic	Pre-dominant (leads to dominant)
$3_{-}$, $3_{-7}$	Em, Em7	Mediant	Weak pre-dominant
$4$, $4_{\mathrm{\Delta }7}$	F, Fmaj7	Subdominant	Pre-dominant (leads to dominant) or back to tonic (plagal cadence)
$5$, $5_7$	G, G7	Dominant	Tension, wants to resolve to tonic (perfect cadence)
$6_{-}$, $6_{-7}$	Am, Am7	Submediant	Relative minor, can substitute tonic sometimes
$7_{\circ }$, $7_{ø7}$	Bdim, Bø7	Subtonic (leading-tone)	Very unstable, leads to tonic (acts like dominant)

Chord Progressions

Three-Chord Progression (Natural Major)

The three chord progression (in natural major) is a simple progression using only $1$,$4$,$5$ chords. It’s typically in $1$-$4$-$5$-$1$ order, but not always.

It is largely used in major key simple music like folk music, nursery rhymes, and country music. There is a famous saying: “country music is three chords and the truth.” showing that the simplicity of this progression can be very effective and heart-touching.

Canon Progression (Natural Major)

1.2 Natural Minor (Aeolian)

Diatonic Chords

Number	Chord (Key of A)	Chord (Key of C)	Function	Role
$1_{-}$, $1_{-7}$	Am, Am7	Cm, Cm7	Tonic	Home chord, most stable, feeling of rest
$2_{\circ }$, $2_{ø7}$	Bdim, Bø7	Ddim, Dø7	Supertonic	Pre-dominant (lead to dominant)
$\mathrm{♭}3$, $\mathrm{♭}{3}_{\mathrm{\Delta }7}$	C, Cmaj7	Eb, Ebmaj7	Mediant	Relative major, can substitute tonic sometimes
$4_{-}$, $4_{-7}$	Dm, Dm7	Fm, Fm7	Subdominant	Pre-dominant (lead to dominant) or back to tonic
$5_{-}$, $5_{-7}$	Em, Em7	Gm, Gm7	Dominant (modal)	Weak tension, can resolve to tonic$
$\mathrm{♭}6$, $\mathrm{♭}{6}_{\mathrm{\Delta }7}$	F, Fmaj7	Ab, Abmaj7	Submediant
$\mathrm{♭}7$, $\mathrm{♭}{7}_7$	G, G7	Bb, Bb7	Subtonic	Leads to tonic (not strong resolution)

Chord Progressions

Three-Chord Progression (Natural Minor)

The three chord progression (in natural major) is a simple progression using only $1_{-}$, $4_{-}$, $5_{-}$ chords. It’s typically in $1_{-}$, $4_{-}$, $5_{-}$, $1_{-}$ order, but not always.

It is largely used in minor key simple music like Chinese / mongolian folk music.

Andalusian Cadence

Canon Progression (Natural Minor)

Sensitive Female Progression

The progression $1_{-}$, $\mathrm{♭}6$, $\mathrm{♭}3$, $\mathrm{♭}7$ (alternatively $6_{-}$, $4$, $1$, $5$ in natural major) try to cover as many major chords in the diatonic as possible to make the natural minor less depressing.

2 Harmonic Minor Modes

2.1 Harmonic Minor (Aeolian ♮7)

Diatonic Chords

Number	Chord (Key of A)	Chord (Key of C)	Function	Role
$1_{-}$, $1_{-\mathrm{\Delta }7}$	Am, Ammaj7	Cm, Cmmaj7	Tonic	Home chord, most stable, feeling of rest
$2_{\circ }$, $2_{ø7}$	Bdim, Bø7	Ddim, Dø7	Supertonic	Pre-dominant (lead to dominant)
$\mathrm{♭}{3}_{+}$, $\mathrm{♭}{3}_{+\mathrm{\Delta }7}$	Caug, Caugmaj7	Ebaug, Ebaugmaj7	Mediant	Relative major, can substitute tonic sometimes
$4_{-}$, $4_{-7}$	Dm, Dm7	Fm, Fm7	Subdominant	Pre-dominant (lead to dominant) or back to tonic
$5$, $5_7$	E, E7	G, G7	Dominant (modal)	Weak tension, can resolve to tonic$
$\mathrm{♭}6$, $\mathrm{♭}{6}_{\mathrm{\Delta }7}$	F, Fmaj7	Ab, Abmaj7	Submediant
$7_{\circ }$, $7_{\circ 7}$	Gdim, Gdim7	Bbdim, Bbdim7	Subtonic	Leads to tonic (not strong resolution)

Three-Chord Progression (Harmonic Minor)

The three chord progression (in harmonic minor) is a simple progression using only $1_{-}$,$4_{-}$,$5$ chords. It’s typically in $1_{-}$-$4_{-}$-$5$-$1_{-}$ order, but not always.

It is largely used in harmonic minor key simple music like slavic folk music.