## 11. Diatonic Harmony

Build a triad on every degree of a key and you get seven chords and no others; roman numerals name them by degree rather than by letter, harmonic function sorts them into three jobs, and the order you put them in — ending with a cadence — is what turns a key into music.

Source: https://musictheory.center/course/diatonic-harmony
Level: Intermediate · Harmony · 6 sections
Before this: Keys and Key Signatures, Chords: Triads and Sevenths

### Chords in a Key

https://musictheory.center/course/diatonic-harmony#chords-in-a-key

> Play the first one: seven three-note stacks, each built on the next note up the C major scale, from the bottom to the top. Now play the second: the same seven bottom notes, every stack built the same bright way. One of the two never leaves the key it started in. The other keeps stepping outside it. Which is which — and in the first clip, which of the seven is the odd one out?

**Plays:** Seven in turn, up the scale (C3 E3 G3 D3 F3 A3 B3 C4 D4 E4 F4) · The same seven bottom notes, all made bright (C3 E3 G3 D3 F#3 A3 G#3 B3 F3 C4 D4 C#4 E4 D#4 F#4)

The first of the seven, drawn on the staff: three heads on three consecutive lines, the stack of thirds from Chapter 10. The tool underneath builds the other six the same way and lets you sound any of them on their own, or change the key underneath and watch all seven move. The table lists what comes out in C major. Read the quality column downwards and the order is major, minor, minor, major, major, minor, diminished — three bright, three dark, and one that will not sit still.

| Degree of the scale | Triad | Quality | Notes |
| --- | --- | --- | --- |
| 1st | [C](https://musictheory.center/chord/c-maj) | Major | C3 E3 G3 |
| 2nd | [Dm](https://musictheory.center/chord/d-m) | Minor | D3 F3 A3 |
| 3rd | [Em](https://musictheory.center/chord/e-m) | Minor | E3 G3 B3 |
| 4th | [F](https://musictheory.center/chord/f-maj) | Major | F3 A3 C4 |
| 5th | [G](https://musictheory.center/chord/g-maj) | Major | G3 B3 D4 |
| 6th | [Am](https://musictheory.center/chord/a-m) | Minor | A3 C4 E4 |
| 7th | [Bdim](https://musictheory.center/chord/b-dim) | Diminished | B3 D4 F4 |

**diatonic chord**

**Definition.** A diatonic chord is a chord built only from the notes of the [key](https://musictheory.center/course/keys-and-key-signatures#what-a-key-is): take a degree of the scale, [stack thirds](https://musictheory.center/course/chords#stacking-thirds) on it using nothing but the other degrees, and whatever comes out is what that key gives you on that degree.

Nobody chooses the qualities. Run the stack from the second degree of C major and the only notes available are D, F and A, which is a [minor triad](https://musictheory.center/course/chords#the-four-triads) — not because minor was wanted there, but because F is what the key has between D and A. The seventh degree gives B, D and F, and that is a diminished triad for the same reason. **The key decides, and the composer decides what to do about it.** That is what the second clip demonstrates: three of the seven — the first, fourth and fifth degrees — are already major and come through untouched, and forcing the other four to be major drags every one of them outside the key, so that the sound of leaving arrives on the second stack and keeps returning.

This is also why the word "diatonic" is worth keeping. It divides everything you might play into two piles — chords the key supplies, and chords that come from outside it — and almost all [harmonic analysis](https://musictheory.center/course/advanced-harmony#harmonic-analysis) is a matter of noticing which pile a chord came from. Chapter 14 is about the second pile. This chapter is about the first.

Seven degrees, seven chords, and there are no others: a major key contains exactly three major triads, three minor triads and one diminished triad, in that fixed order up the scale.

**Good to know**

- (Fact) The order of qualities is the same in every major key, because the scale it is derived from has the same shape in every major key. C major gives [C](https://musictheory.center/chord/c-maj) [Dm](https://musictheory.center/chord/d-m) [Em](https://musictheory.center/chord/e-m) [F](https://musictheory.center/chord/f-maj) [G](https://musictheory.center/chord/g-maj) [Am](https://musictheory.center/chord/a-m) [Bdim](https://musictheory.center/chord/b-dim); G major gives [G](https://musictheory.center/chord/g-maj) [Am](https://musictheory.center/chord/a-m) [Bm](https://musictheory.center/chord/b-m) [C](https://musictheory.center/chord/c-maj) [D](https://musictheory.center/chord/d-maj) [Em](https://musictheory.center/chord/e-m) [F♯dim](https://musictheory.center/chord/fsharp-dim). Different letters, the same seven qualities, in the same order — major, minor, minor, major, major, minor, diminished.
- (Convention) "Diatonic" is used in two slightly different ways. Strictly it means "belonging to the seven-note scale in question", which is how this chapter uses it. Loosely it is used to mean "in the key, unaltered", which is the same thing for major and minor keys and gets blurry for [modes](https://musictheory.center/course/modes#what-a-mode-is) and for the minor key's raised seventh degree — a chord most writers are happy to call diatonic even though the scale it comes from is an altered one.
- (Tendency — Western folk, popular and church repertoire; classical music from Bach onward leaves the seven constantly, and jazz treats leaving them as the normal case) Whole repertoires stay inside these seven chords from the first bar to the last. Folk song, hymnody, nursery rhyme, most country, a great deal of rock and the overwhelming majority of chart pop never use anything else, which is why the seven are worth knowing cold before anything chromatic is worth attempting.

**You already know this**

- The four triads from Chapter 10 — major, minor, diminished, augmented — three of which are what a major key produces and one of which it never does — https://musictheory.center/course/chords#the-four-triads
- Scale degrees from Chapter 7, which is what each of the seven chords is built on — https://musictheory.center/course/scales#scale-degrees

**Where this goes**

- Every chord that is not one of these seven has been borrowed from somewhere else, and where it was borrowed from is the whole of chromatic harmony — https://musictheory.center/course/advanced-harmony

**In real music**

- The Beatles — “Let It Be” — not one chord in the whole song comes from outside C major — the verse, the chorus and the solo between them use five of these seven and nothing else
- Bob Dylan — “Blowin’ in the Wind” — the entire song is three of the seven, repeated; listen to the second line of the first verse, where the harmony moves and the melody does not

**Try it on your instrument:** Pick a [major key](https://musictheory.center/course/keys-and-key-signatures#what-a-key-is) you can play. Build a three-note stack on its first degree, then on its second, and so on to the seventh, using only notes from that scale and skipping a note between each pair. Say major, minor or diminished aloud before you play each one, then check yourself with the tool above.

[See the seven chords of any key lit up on the circle, each with its numeral](https://musictheory.center/tools/circle-of-fifths?k=C&lens=chords)

**Check:** One stack, sounded after the seven you heard in C major. Does every note in it belong to that key, or does one of them come from outside it?

- All three belong to C major — The stack built on the second degree of C major is D, F, A — a minor triad, because F natural is what the key has between D and A. This one was a half step brighter in the middle, which is the single change that put it outside the key.
- One note comes from outside **(correct)** — Correct. That was D, F sharp and A. The key gives F natural on that degree, which would make the chord minor; raising it to F sharp brightens the chord and takes it out of C major, because there is no F sharp anywhere in the key.
- Two notes come from outside — Only the middle note was altered. The outer notes, D and A, are both ordinary members of C major; the whole difference was one half step in the middle, which is usually all it takes.

### Roman Numerals

https://musictheory.center/course/diatonic-harmony#roman-numerals

> Play both. Each is three stacks from a single key, taken from the same three degrees of that key and played in the same order. Two of the three stacks are note for note the same in both clips — and each of those two arrives in a different place and does a different job in the second clip from the one it did in the first. Even so, something about the two is plainly the same thing twice. What is it that survives the move?

**Plays:** Three from one key (C3 E3 G3 F3 A3 C4 B3 D4) · The same three from another key (G3 B3 D4 C3 E3 D3 F#3 A3)

The fifth-degree chord of C major with a seventh added — G, B, D and F, four heads on four consecutive lines. Written as a numeral it is V7, and the 7 does the same job it did in Chapter 10: it says the stack was carried one third further. The table gives all seven numerals of a major key, what quality each one carries, and what the same numeral names in two different keys. Read the last two columns across: the numerals never change and the letters change completely.

- **Case carries the quality** — Capitals are major — I, IV, V. Lower case is minor — ii, vi. A small circle is diminished — vii°.
- **A number adds a note to the stack** — V7 is the fifth-degree triad with a seventh on top, G3 B3 D4 F4; ii7 is the second-degree triad with its own, D3 F3 A3 C4.

| Numeral | Degree | Quality | In C major | In G major |
| --- | --- | --- | --- | --- |
| I | 1st | Major | [C](https://musictheory.center/chord/c-maj) | [G](https://musictheory.center/chord/g-maj) |
| ii | 2nd | Minor | [Dm](https://musictheory.center/chord/d-m) | [Am](https://musictheory.center/chord/a-m) |
| iii | 3rd | Minor | [Em](https://musictheory.center/chord/e-m) | [Bm](https://musictheory.center/chord/b-m) |
| IV | 4th | Major | [F](https://musictheory.center/chord/f-maj) | [C](https://musictheory.center/chord/c-maj) |
| V | 5th | Major | [G](https://musictheory.center/chord/g-maj) | [D](https://musictheory.center/chord/d-maj) |
| vi | 6th | Minor | [Am](https://musictheory.center/chord/a-m) | [Em](https://musictheory.center/chord/e-m) |
| vii° | 7th | Diminished | [Bdim](https://musictheory.center/chord/b-dim) | [F♯dim](https://musictheory.center/chord/fsharp-dim) |

**roman numeral**

**Definition.** A roman numeral is a name for a chord that gives its degree in the [key](https://musictheory.center/course/keys-and-key-signatures#what-a-key-is) instead of its letter: I is the chord on the first degree, V the chord on the fifth, and which actual notes those are depends entirely on what key you are in.

It is a shorthand with one purpose — to say what a chord is doing rather than what it is called. [G](https://musictheory.center/chord/g-maj) is a fact about pitch; V is a fact about relationship, and the relationship is what repeats from song to song. The two clips above make the point twice over. They are the same three relationships in two keys, which is why they sound like the same idea moved. And they share two chords outright — [C](https://musictheory.center/chord/c-maj) and [G](https://musictheory.center/chord/g-maj) are in both — yet [C](https://musictheory.center/chord/c-maj) is the home chord of the first clip and the departure of the second, while [G](https://musictheory.center/chord/g-maj) is the tense chord of the first and home in the second. The same three notes, a different job: that difference is what a numeral records and a letter cannot.

The spelling carries the quality, so a numeral is a complete description of the chord. Capital letters are major and lower case is minor, a small raised circle after the numeral means diminished, a plus sign means augmented, and a number after it extends the stack exactly as it did in a [chord symbol](https://musictheory.center/course/chords#reading-chord-symbols): V7 is the fifth-degree chord with a seventh on it. Nothing else has to be written down.

This is the notation the rest of the book runs on. Cadences, progressions, [modulation](https://musictheory.center/course/advanced-harmony#modulation) and everything in Chapter 14 are stated in numerals, because stating them in letters would produce twelve versions of every fact.

**Good to know**

- (Convention) Case is one convention, not the only one. Most classical and popular theory writes I for major and ii for minor and marks the diminished chord with a circle. A substantial tradition — much German theory, a number of North American textbooks and most jazz pedagogy — writes every numeral in capitals and appends a quality instead: II–7 or IIm7 where this book writes ii7, and VII° or VIIdim where it writes vii°. (The slashed circle in VIIø7 is a different chord again — the [half-diminished seventh](https://musictheory.center/course/chords#seventh-chords) of Chapter 10, a diminished triad with an ordinary minor seventh, which is what the seventh degree of a major key actually gives when a fourth note is added.) Both notations say the same thing; the all-capitals form is easier to type and loses the quality at a glance.
- (Convention) A numeral describes a chord in a key, so it is meaningless without one. "V" on its own names nothing at all. That is why analysis always writes the key first — C: I IV V — and why a change of key in the middle of a piece has to be declared before the numerals after it can be read.
- (Fact) The numeral survives [transposition](https://musictheory.center/course/keys-and-key-signatures#transposing) and the letter does not. Move [C](https://musictheory.center/chord/c-maj) [F](https://musictheory.center/chord/f-maj) [G](https://musictheory.center/chord/g-maj) up a whole step and every letter changes to [D](https://musictheory.center/chord/d-maj) [G](https://musictheory.center/chord/g-maj) [A](https://musictheory.center/chord/a-maj); the numerals are I IV V before the move and I IV V after it, because transposing changes the notes and not the degrees they sit on.

**You already know this**

- Transposing from Chapter 8, where every note of a passage moved by the same distance and the passage stayed recognisable — a progression written in numerals has been transposed already — https://musictheory.center/course/keys-and-key-signatures#transposing
- Chord symbols from Chapter 10, which compress a chord into a root and a quality; a numeral compresses it one level further, into a degree and a quality — https://musictheory.center/course/chords#reading-chord-symbols

**Where this goes**

- A numeral with a slash in it — V/V, the dominant of the dominant — is how a chord from outside the key gets named, and the notation extends to cover it without changing — https://musictheory.center/course/advanced-harmony

**In real music**

- The Beatles — “Twist and Shout” — the rising "aah" before the last verse sits over the fifth-degree chord and nothing else; the band is holding V while the voices climb, and the release is the I underneath the next line
- The Troggs — “Wild Thing” — I, IV, V and back to IV, roughly a bar apiece — in A that is A, D, E, D — repeating from the first bar to the last, which makes it short enough to hear the numerals go past in real time

**Try it on your instrument:** Take a song you can already play and write its chords out as numerals: [work out the key](https://musictheory.center/tools/key-finder), count each chord root up from the tonic, and use a capital for major and lower case for minor. Then play the same numerals in a different key, reading from your numerals rather than from the original letters.

[Type numerals and read them as chords in any key — or type chords and read them as numerals](https://musictheory.center/tools/roman-numeral-converter?c=I+IV+V&k=G)

**Check:** The clip plays two chords in C major — the first degree, then the fourth — and then, after a gap, the home chord of G major on its own. Which chord would stand in the same relation to that last one as the second chord did to the first?

- C major **(correct)** — Correct. The move you heard first was C to F, a rise of a fourth, which is I to IV. Make the same move from G — count G, A, B, C — and you land on C, and stacking thirds on it from the notes of G major gives C, E, G. The numeral did not change: IV is IV in every key, and only the letters underneath it moved.
- D major — D is the fifth degree of G major, so D major is V rather than IV — one degree too far. Sing the first two chords of the clip again and then sing the same distance up from G: the note you arrive on is C, not D. Counting one degree too far is the commonest slip when reading numerals in a new key.
- G major — G major is the chord the clip finished on: the key itself, the first degree, numeral I. The answer is the chord that stands a fourth above it, three letters further up the scale, which lands on C.

### Harmonic Function

https://musictheory.center/course/diatonic-harmony#harmonic-function

> Play both. Three stacks each; the first and the last are identical in the two clips, and only the middle one differs. In one clip the middle stack sounds as though it is being pulled backwards and cannot help itself. In the other, the middle stack sounds like a step sideways that could perfectly well have stayed where it was. Which is which?

**Plays:** Home, away, home — the first way (C3 E3 G3 B3 D4) · Home, away, home — the second way (C3 E3 G3 F3 A3 C4)

Two notes: B, then the C a half step above it. That half step is the engine the whole section is about. B is the seventh degree of C major, it sits one half step under the tonic, and any chord containing it inherits the pull — which is why the fifth-degree chord, G, B, D, cannot sit still in this key while the fourth-degree chord, F, A, C, can. The table sorts all seven chords of the key by the job they do.

| Function | Chords in C major | What it does | Where it wants to go |
| --- | --- | --- | --- |
| Tonic | [C](https://musictheory.center/chord/c-maj) · [Am](https://musictheory.center/chord/a-m) · [Em](https://musictheory.center/chord/e-m) | Rests. This is the place the rest of the key is measured against | Nowhere. It is the destination |
| Subdominant | [F](https://musictheory.center/chord/f-maj) · [Dm](https://musictheory.center/chord/d-m) | Departs. Moves away from home without creating tension | On to the dominant, or straight back to the tonic |
| Dominant | [G](https://musictheory.center/chord/g-maj) · [G7](https://musictheory.center/chord/g-7) · [Bdim](https://musictheory.center/chord/b-dim) | Tightens. Every chord here contains the note a half step under the tonic | Home, to the tonic — and the stronger the chord, the harder it insists |

**harmonic function**

**Definition.** Harmonic function is the job a chord does inside its [key](https://musictheory.center/course/keys-and-key-signatures#what-a-key-is) — resting, departing, or creating tension that wants resolving — and in a major key the seven diatonic chords sort into three families according to which of those three jobs they do.

The families are not arbitrary groupings: the chords in one share notes with the chord the family is named after, which is why they can stand in for it. [C](https://musictheory.center/chord/c-maj) shares two of its three notes with [Am](https://musictheory.center/chord/a-m) — C and E — and two with [Em](https://musictheory.center/chord/e-m) — E and G — so either can be used as a resting point in its place, [Am](https://musictheory.center/chord/a-m) being simply the shadier one. The same holds elsewhere: [F](https://musictheory.center/chord/f-maj) and [Dm](https://musictheory.center/chord/d-m) have F and A in common, and [G](https://musictheory.center/chord/g-maj) and [Bdim](https://musictheory.center/chord/b-dim) have B and D.

What separates the dominant family from the other two is one [half step](https://musictheory.center/course/intervals#half-steps-and-whole-steps). The [seventh degree](https://musictheory.center/course/scales#scale-degrees) of the key — B, in C major — sits a half step under the tonic, and the ear treats a half step below a stable note as unfinished business. [G](https://musictheory.center/chord/g-maj) contains it. [G7](https://musictheory.center/chord/g-7) contains it and adds F, which is a half step above the third of the home chord and leans the other way, so the two of them close in on [C](https://musictheory.center/chord/c-maj) from both sides at once. Nothing in [F](https://musictheory.center/chord/f-maj) or [Dm](https://musictheory.center/chord/d-m) does anything of the kind, which is exactly why the second clip above sounds relaxed where the first sounds strained.

Function is the level at which harmony is actually planned. A songwriter does not think "now I need the chord G"; they think "now I need to get home", and the dominant family is what does it.

**Good to know**

- (Fact) The pull is a half step, and you can point at it without any harmony around it. The seventh degree of C major and the tonic are [Minor Second](https://musictheory.center/interval/minor-second) apart — B3 then C4 — and the fifth-degree chord is the ordinary diatonic chord that contains that seventh degree.
- (Tendency — common-practice tonal music: Western classical from roughly 1650 to 1900 and the popular song, film scoring and jazz descended from it. [Modal writing](https://musictheory.center/course/modes#what-a-mode-is), much folk music and a great deal of post-1960s rock use the same chords with no such expectation, as Chapter 9 showed) V pulls to I. A dominant chord sets up an expectation of the tonic so reliably that going anywhere else is heard as a deliberate evasion rather than as a neutral choice — which is what makes the deceptive cadence in the next section possible at all.
- (Convention) The family names are borrowed from the names of scale degrees, and they fit imperfectly. "Predominant" is now the commoner term for the subdominant family in North American textbooks, precisely because [Dm](https://musictheory.center/chord/d-m) does that job as well as [F](https://musictheory.center/chord/f-maj) does while not being the subdominant degree at all. Older British writing keeps "subdominant" for both. The families are the same either way.

**You already know this**

- The leading tone from Chapter 7 — the seventh degree, a half step under the tonic — which is the single note that makes the dominant family behave as it does — https://musictheory.center/course/scales#scale-degrees
- The tonic from Chapter 8, the note everything in a key is heard in relation to; the tonic chord is that note harmonised — https://musictheory.center/course/keys-and-key-signatures#what-a-key-is
- The dominant seventh from Chapter 10, whose narrowed fifth between its third and its seventh is what sharpens the pull — https://musictheory.center/course/chords#seventh-chords

**Where this goes**

- Which way each note of a tense chord has to move when it resolves is a question about individual voices, not about chords, and that is what voice leading studies — https://musictheory.center/course/voice-leading

**In real music**

- The Beatles — “Hey Jude” — the first line goes home, away and home again — the chord under "don’t make it bad" is the dominant, and the release is the moment "take a sad song" lands back on the tonic
- Ben E. King — “Stand By Me” — the bass walks the same four-chord cycle all the way through; the chord in the third bar of each cycle is the tense one, and the whole thing resets the instant it gives way

**Try it on your instrument:** In any [major key](https://musictheory.center/course/keys-and-key-signatures#what-a-key-is) you can play, sound the home chord, then the chord built on the fifth degree, then the home chord again. Do the same with the chord built on the fourth degree in the middle instead. Then stop on the middle chord in each version and try to sing the note that would finish it — the two versions will make your voice do different things.

**Check:** One chord, sounded on its own in C major. Does it sound like somewhere to rest, or like somewhere that wants to move on?

- It wants to move on **(correct)** — Correct. That was G, B, D and F — the fifth-degree chord with a seventh added. It holds the two most restless notes in the key at once: B, a half step under the tonic, and F, a half step above the third of the home chord. Both resolve by a half step when C major follows, which is why the pull is as strong as it is.
- It is a resting place — The resting chord of this key is C, E, G, which contains no half-step pull at all. Play the clip again and try to sing a note that finishes it: the note your voice reaches for is C, and C is precisely what was not playing.
- Neither — it is neutral — Nothing in this key is neutral once the tonic has been established, and this chord is the least neutral of the seven. Compare it with the fourth-degree chord, F, A, C, which does move away from home but arrives somewhere it could comfortably stay.

### Cadences

https://musictheory.center/course/diatonic-harmony#cadences

> Play all four. Each is the end of a phrase in C major and each one stops in a different way. One shuts the door. One settles without having leaned on anything first. One stops in mid-air and waits. One lands somewhere you were not expecting. Before reading anything below, decide which is which — and which of the four you would use to end a piece. The fifth clip runs all four together, a bar each, which is the staff below played as written.

**Plays:** A pair that shuts the door (G3 B3 D4 C3 E3) · A pair that settles without leaning (F3 A3 C4 C3 E3 G3) · Three that stop in mid-air (C3 E3 G3 F3 A3 C4 B3 D4) · A pair that lands somewhere else (G3 B3 D4 A3 C4 E4) · The four endings in a row, as written (G3 B3 D4 C3 E3 F3 A3 C4 E4)

The four endings, one to a bar, in the order you heard them, and the fifth clip above is these four bars played straight through in exactly the values printed. In bar one the bass falls a fifth, from G to C, and arrives. In bar two it falls a fourth, from F to C, and settles — nothing leaned first, so nothing had to give way. Bar three takes three chords rather than two, because what defines it is not what it lands on but that nothing comes after: the bass reaches G and the bar simply ends. Bar four sets out exactly like bar one and then puts A in the bass instead of C, so the last two bass notes are a whole step apart rather than a fifth. That last bass note is the whole of the difference between an ending and a swerve.

| Cadence | Chords | Feels like | Where to hear it |
| --- | --- | --- | --- |
| Authentic | V → I | A full stop. The phrase is finished and the key is confirmed | "Twist and Shout" — the chord the band crashes onto at the very end, arriving from the one a fifth above it |
| Plagal | IV → I | A settling rather than an arrival. Nothing leaned, so nothing had to give way | "Let It Be" — the two chords under the last "let it be" of each chorus, and the amen at the end of a hymn |
| Half | anything → V | A comma. The phrase stops without finishing, and waits | "Happy Birthday to You" — the first "to you", which hangs in the air, against the second, which lands |
| Deceptive | V → vi | A swerve. The approach promises home and the landing is a step higher, and minor | "Don’t Stop Believin’" — the third chord of the piano figure, where the pull of the second chord is answered by a minor chord instead of the tonic. It sits inside a loop rather than at the end of a phrase, so it is the sound rather than a cadence proper |

**cadence**

*also called*: a perfect cadence (British usage, for what North American theory calls an authentic cadence), an imperfect cadence (British usage, for the half cadence), an interrupted cadence (British usage, for the deceptive cadence), the amen cadence (hymn practice, for the plagal cadence, after the two chords sung on "amen")

**Definition.** A cadence is the chord movement a [phrase](https://musictheory.center/course/melody#phrase-antecedent-consequent) ends with — the harmonic punctuation that tells a listener whether the music has stopped, paused, or been diverted at the last moment.

There are four worth knowing and they divide by two questions: does the phrase end on the tonic, and does it lean before it gets there. The authentic cadence, V–I, leans and arrives, and is the strongest ending in tonal music. The plagal cadence, IV–I, arrives without leaning, which is why it sounds like a benediction rather than a conclusion. The half cadence ends on V and does not arrive at all — it is the musical equivalent of a comma, and it is what the first half of an eight-bar tune almost always does. The deceptive cadence, V–vi, leans exactly as the authentic one does and then steps up to the sixth degree instead, so the ear is prepared for an ending and given one more phrase instead.

What makes the difference audible is the bass. In V–I the bass falls a [Perfect Fifth](https://musictheory.center/interval/perfect-fifth), from G to C, which is the strongest root motion in tonal harmony. In IV–I it falls a fourth, from F to C — the same two letters the other way round, and a weaker move, which is part of why the plagal cadence settles rather than concludes. In V–vi it rises a [whole step](https://musictheory.center/course/intervals#half-steps-and-whole-steps), from G to A, and a step is precisely the motion the ear does not read as an arrival, which is why the deceptive cadence works on a first hearing and goes on working on a fiftieth.

Cadences are how music is punctuated at every scale at once: a phrase ends with one, a section ends with a stronger one, and a whole piece ends with the strongest available. Learning to hear them is learning to hear where music is in its own sentence.

**Good to know**

- (Fact) The authentic cadence has a [leading tone](https://musictheory.center/course/scales#scale-degrees) in it and the plagal cadence does not. [G](https://musictheory.center/chord/g-maj) contains B3, a half step under the tonic; [F](https://musictheory.center/chord/f-maj) contains no note that touches the tonic by a half step at all. That single structural difference is the whole reason one sounds decisive and the other sounds settled.
- (Convention) The four names are from Western classical theory and they do not agree across the Atlantic: what this book calls authentic, half and deceptive are called perfect, imperfect and interrupted in most British teaching. Classical theory also grades the authentic cadence further — "perfect authentic" when both chords are in [root position](https://musictheory.center/course/chords#inversions) and the tonic is in the top voice, "imperfect authentic" otherwise — a distinction worth knowing exists and not worth worrying about yet.
- (Tendency — common-practice tonal music and the popular song descended from it; in modal and much contemporary writing a phrase can end anywhere without the ear demanding a continuation) A phrase that ends on the dominant is heard as unfinished, and a listener will wait through a considerable silence for the answering phrase. It is one of the most reliable expectations in the repertoire, and comic timing in music is built out of not satisfying it.

**You already know this**

- The dominant family from earlier in this chapter, whose tension is what three of these four cadences are made from — https://musictheory.center/course/diatonic-harmony#harmonic-function
- The dominant seventh from Chapter 10, which is what the fifth-degree chord usually becomes when a cadence needs to be as strong as possible — https://musictheory.center/course/chords#seventh-chords

**Where this goes**

- Cadences are the joints of musical form: where they fall, and how strong each one is, is what divides a piece into phrases, sections and movements — https://musictheory.center/course/form-structure

**In real music**

- The Beatles — “Let It Be” — the chorus ends on two chords that settle without leaning — listen to the very last "let it be" of a chorus, where the chord before home is the fourth-degree one and nothing pulls
- Journey — “Don’t Stop Believin’” — the third chord of the opening piano figure is the swerve: the second chord pulls towards home and a minor chord takes the landing. Strictly it is a loop turning over rather than a phrase ending, which is exactly why nothing ever stops — but it is the standard classroom example of the sound, because it recurs every two bars for four minutes
- The Beatles — “Twist and Shout” — the final chord of the record arrives from the chord a fifth above it and the band stops dead on it — the plainest full stop in pop

**Try it on your instrument:** In a [major key](https://musictheory.center/course/keys-and-key-signatures#what-a-key-is) you can play, sound the home chord, then the chord on the fifth degree, then the home chord again. Play it a second time ending on the chord built on the sixth degree instead, and a third time stopping on the fifth-degree chord and not playing anything after it. Sing the last note of each version — your voice will want to keep going in two of the three.

**Check:** A four-chord phrase in C major. Listen to how it ends, then name the cadence.

- Authentic — V to I — You heard the dominant, which was there: the third chord is G, B, D, and it leans exactly as an authentic cadence does. But it did not land on I. The bass moves up a step, from G to A, rather than down a fifth to C, and the chord it reaches is minor.
- Plagal — IV to I — A plagal cadence has no leading tone in it. This phrase has one — the B inside the second-to-last chord — and that leading tone is exactly what set up the expectation the ending then refused. A plagal ending never sets the expectation in the first place.
- Half — ending on V — A half cadence ends ON the dominant and stops there. This one moved past it: count the chords again and there are four, with the dominant third and one more after it.
- Deceptive — V to vi **(correct)** — Correct. The dominant resolved to vi instead of I — the bass rose a whole step, from G to A, rather than falling a fifth to C, and the chord it landed on is minor. Everything about the approach promised home; only the last chord broke the promise, which is why it sounds like a phrase that has been extended rather than ended.

**Check:** The fifth-degree chord of C major, on its own. Before you play anything, decide which chord the ear expects to hear next.

- C major — the home chord **(correct)** — Correct. The dominant contains the leading tone, B, which lies a half step under the tonic and resolves onto it; the ear has heard that resolution so many thousand times that it supplies the C for itself. That expectation is what every other option on this list is defined against.
- A minor — the sixth-degree chord — A minor is where the deceptive cadence goes, and it works precisely because it is not what was expected. It shares two notes with C major — C and E — so it is close enough to be a plausible substitute and different enough to register as a swerve.
- F major — the fourth-degree chord — F major after G major reverses the usual order of the families, putting the departure chord after the tension chord. Common-practice classical writing avoids it at a cadence, which is why the ear does not predict it here; blues and rock use it constantly, as the V–IV–I turnaround at the end of a twelve-bar chorus. The hymn-book amen is a different thing again: there the tonic arrives first and the IV–I is tagged on after it.

#### Why the half cadence needs a phrase, not a pair

The other three cadences can be demonstrated with two chords, because what defines them is the relationship between the last two. The half cadence cannot, because what defines it is where it stops rather than what it stops after — the chord before the dominant can be almost anything, and the point is that nothing follows.

That is why the third clip at the top of the section has three chords in it where the other three cadence clips have two. It is also why half cadences are heard in pairs of phrases rather than on their own: the classical [antecedent–consequent period](https://musictheory.center/course/melody#phrase-antecedent-consequent) is a first phrase that ends on the dominant and a second, near-identical phrase that ends on the tonic, and the half cadence is what makes the first one sound like a question. Chapter 13 takes that shape up as a way of building [melodies](https://musictheory.center/course/melody#what-makes-a-melody).

The habit worth forming is to listen for the silence rather than the chord. If a phrase stops and the air still feels tilted, you have heard a half cadence, whatever chord was underneath it.

### Common Progressions

https://musictheory.center/course/diatonic-harmony#common-progressions

> Play all four. Each is a short loop drawn from the seven stacks this chapter started with, and you have heard every one of them many hundreds of times without being told what it was. Two of the four contain exactly the same four sounds in a different order and do not feel remotely alike. Which two are they, and which one of the four ends by leaning hardest back towards its own first sound?

**Plays:** Four, starting at home (C3 E3 G3 B3 D4 A3 C4 E4 F3) · Four, starting in the shade (A3 C4 E4 F3 C3 E3 G3 B3 D4) · Four, and three of them plain (C3 E3 G3 F3 A3 C4 B3 D4) · Three, falling home (D3 F3 A3 G3 B3 D4 C3 E3)

The first loop written out, one chord to a bar: C, G, A minor, F. Look at the bass notes across the four bars — C, G, A, F — and you have the whole of what the loop does, which is why a bass player can carry a song like this on their own. The table gives the four loops, what each one is in C major, and where they have been heard. Every chord in all four is one of the seven from the start of this chapter; nothing here comes from outside the key.

| Numerals | In C major | Where you have heard it |
| --- | --- | --- |
| I–V–vi–IV | [C](https://musictheory.center/chord/c-maj) [G](https://musictheory.center/chord/g-maj) [Am](https://musictheory.center/chord/a-m) [F](https://musictheory.center/chord/f-maj) | "Let It Be", "Don’t Stop Believin’", "Someone Like You" — the four-chord loop of modern pop, which ends on IV and so never quite closes |
| vi–IV–I–V | [Am](https://musictheory.center/chord/a-m) [F](https://musictheory.center/chord/f-maj) [C](https://musictheory.center/chord/c-maj) [G](https://musictheory.center/chord/g-maj) | "Despacito", "Cheap Thrills", "Zombie" — the same four chords rotated to begin on the minor one, which makes it sound darker without changing a note |
| I–IV–V–I | [C](https://musictheory.center/chord/c-maj) [F](https://musictheory.center/chord/f-maj) [G](https://musictheory.center/chord/g-maj) [C](https://musictheory.center/chord/c-maj) | "Twist and Shout", "La Bamba", "Johnny B. Goode" — the three primary chords, and the skeleton of the twelve-bar blues |
| ii–V–I | [Dm](https://musictheory.center/chord/d-m) [G](https://musictheory.center/chord/g-maj) [C](https://musictheory.center/chord/c-maj) | "Autumn Leaves", "All the Things You Are", "Satin Doll" — the cell most jazz standards are assembled from, often several times in one chorus and in several keys |

**chord progression**

**Definition.** A chord progression is an ordered series of chords — most often a short pattern of two to four bars that repeats — and it is what gives a passage of music its harmonic shape, establishing which chord is home, moving away from it, and deciding how and whether to come back.

A progression is not a list. What makes one memorable is the order, because order is what creates expectation: the same four chords starting in a different place are a different progression, as the first and second clips above demonstrate with no change of material whatsoever. [I–V–vi–IV](https://musictheory.center/progression/i-v-vi-iv) sounds bright and unfinished; vi–IV–I–V sounds shadowed and driving. Identical chords, opposite effects, and the only variable is which one arrives first.

Two structural facts do most of the work. The first is where a loop ends: a loop ending on IV or V leaves the ear tilted and hands straight back to the top, which is why pop loops are built that way and why they can repeat for three minutes without fatigue. The second is root motion. A root falling by a fifth is the strongest move in tonal harmony, and [ii–V–I](https://musictheory.center/progression/ii-v-i) is two of them in a row — which is why it is the cell jazz builds out of, and why standards are largely a matter of chaining ii–V–Is through several keys.

The numerals are how progressions get talked about at all. "The four chord song", "the 1564", "a two-five-one" are all names for numeral patterns rather than for chords, because the pattern is what recurs and the key never does.

**Good to know**

- (Fact) Root motion by a falling fifth is the strongest in tonal harmony, and the numerals show it directly: in ii–V–I the roots run D, G, C, each a fifth below the last. Extending the chain backwards gives vi–ii–V–I and then iii–vi–ii–V–I, which is the circle progression, and the pull increases with every link added.
- (Tendency — Anglophone pop, rock, country and EDM from roughly 1990 onward; the same four chords appear throughout earlier repertoire, but as part of longer phrases rather than as an unbroken loop) I–V–vi–IV and its rotations carry an extraordinary share of the chart repertoire, to the point where a comedy act built a career on medleying songs that share them. The reason is structural rather than fashionable: the loop contains three major chords and one minor, covers every note of the scale between them, and never closes.
- (Convention) Progressions are named by their numerals and spoken as numbers: ii–V–I is "a two five one", I–V–vi–IV is "the one five six four" or "the 1564". A name of that kind carries no key at all, which is the point — the same four words describe the loop in every key a band might [transpose](https://musictheory.center/course/keys-and-key-signatures#transposing) it to.

**You already know this**

- Transposing from Chapter 8 — a progression written as numerals has already been transposed into every key at once, which is why bands call these patterns by number — https://musictheory.center/course/keys-and-key-signatures#transposing
- The cadences from earlier in this chapter, one of which is sitting at the end — or in the middle — of every loop in the table — https://musictheory.center/course/diatonic-harmony#cadences

**Where this goes**

- Which inversion each chord of a loop is played in, and how the individual voices move between them, is what separates a good arrangement of these four chords from a clumsy one — https://musictheory.center/course/voice-leading
- A tune is usually written against a progression like these, and which notes of the scale are available at each moment is decided by the chord underneath — https://musictheory.center/course/melody

**In real music**

- Adele — “Someone Like You” — the piano figure cycles the same four chords from the first bar to the last; the third chord of each cycle is the minor one, and it is where the vocal line sags every time
- Cannonball Adderley, "Somethin’ Else" — “Autumn Leaves” — bars 1–3 of the tune are a ii–V–I and bar 4 is the IV; the next four bars answer with a minor ii–V–i in the [relative minor](https://musictheory.center/course/keys-and-key-signatures#relative-and-parallel). The whole standard, written by Joseph Kosma, is built by chaining those two cells
- Ritchie Valens — “La Bamba” — three chords in the same order from the first bar to the last, with no variation at all; everything that happens in the record happens in the rhythm and the voice

**Try it on your instrument:** Play I–V–vi–IV in a [key](https://musictheory.center/course/keys-and-key-signatures#what-a-key-is) you are comfortable in, four beats to a chord, and loop it eight times. Then play the same four chords starting from the vi and loop that eight times. Then take a song you know and find out which of the four patterns in the table it is using, if any.

[Move I–V–vi–IV into the key you play in](https://musictheory.center/tools/chord-transposer?c=C+G+Am+F&to=D)

**Check:** Four chords in C major, played once through. Which of the four patterns from the table was it?

- I–V–vi–IV — The same four chords, and the easiest of the four to confuse this with. I–V–vi–IV starts on the bright home chord and ends on F — which is not an arrival either, but hands back softly rather than leaning. What you heard started dark and ended on the chord that pulls hardest. Play the first and second clips at the top of the section back to back and listen only to the first chord of each.
- vi–IV–I–V **(correct)** — Correct. It began on the minor chord, A minor, and ended on G, the fifth-degree one, which leaves the loop tilted and pulls straight back to the start. These are the same four chords as I–V–vi–IV; only the starting point moved, and that was enough to change which chord sounds like home.
- I–IV–V–I — I–IV–V–I contains no minor chord at all and returns to the chord it began on. This one opened on a minor chord, which is the first thing to listen for, and it did not come back to its starting chord at the end.
- ii–V–I — ii–V–I is three chords, not four, and it lands on the home chord — the most conclusive ending of the four patterns. There were four chords here, and the last of them did not sound like an arrival.

### Harmony in Minor

https://musictheory.center/course/diatonic-harmony#harmony-in-minor

> Play both. Four stacks each, in A minor, ending in the same place, and exactly one note anywhere in the eight is different between the two clips. One of them arrives as though it had been aimed at its last stack from some distance away. The other simply stops there. Which is which, and where in the four is the note that differs? The third clip is the two of them end to end with no gap, which is the four bars of the staff below as printed.

**Plays:** Four, every note inside the scale (A3 C4 E4 D3 F3 E3 G3 B3) · The same four, one note moved (A3 C4 E4 D3 F3 E3 G#3 B3) · All eight stacks, as written (A3 C4 E4 D3 F3 E3 G3 B3 G#3)

The two clips written out, two bars each, which the third clip above plays as one eight-stack run. The first two bars use nothing but the notes of A natural minor, which is why there is not an accidental in sight. The last two bars are identical except for one thing: the sharp printed in front of the G in the second-to-last chord. That sharp is not in the key signature and has to be written every time it appears, which is the clearest sign in any printed minor-key music that the seventh degree has been raised. The table gives the chords a minor key uses most, with the two that exist only when the seventh degree is raised.

| Numeral | Triad in A minor | Quality | Notes | Where it comes from |
| --- | --- | --- | --- | --- |
| i | [Am](https://musictheory.center/chord/a-m) | Minor | A3 C4 E4 | The natural minor scale |
| ii° | [Bdim](https://musictheory.center/chord/b-dim) | Diminished | B3 D4 F4 | The natural minor scale |
| III | [C](https://musictheory.center/chord/c-maj) | Major | C3 E3 G3 | The natural minor scale — and the relative major’s home chord |
| iv | [Dm](https://musictheory.center/chord/d-m) | Minor | D3 F3 A3 | The natural minor scale |
| v | [Em](https://musictheory.center/chord/e-m) | Minor | E3 G3 B3 | The natural minor scale — no leading tone, so no pull |
| V | [E](https://musictheory.center/chord/e-maj) | Major | E3 G♯3 B3 | The harmonic minor scale, which raises G to G♯ |
| VI | [F](https://musictheory.center/chord/f-maj) | Major | F3 A3 C4 | The natural minor scale |
| VII | [G](https://musictheory.center/chord/g-maj) | Major | G3 B3 D4 | The natural minor scale |
| vii° | [G♯dim](https://musictheory.center/chord/gsharp-dim) | Diminished | G♯3 B3 D4 | The harmonic minor scale |

**minor-key harmony**

**Definition.** Minor-key harmony is the set of chords a minor key supplies: the seven triads built on the degrees of its [natural minor scale](https://musictheory.center/course/scales#the-three-minors) — i, ii°, III, iv, v, VI and VII — together with the major V and diminished vii° that appear whenever the scale’s seventh degree is raised.

The seven natural ones are not new. A minor and C major contain the same notes, so they harmonise into the same seven triads; what changes is which chord the ear takes as home, and therefore what each one is called. C major's I is A minor's III, and C major's vi is A minor's i. This is the [relative-key relationship](https://musictheory.center/course/keys-and-key-signatures#relative-and-parallel) from Chapter 8 seen from the harmony side.

One thing is genuinely missing, and it is the important one. The natural minor scale puts a [whole step](https://musictheory.center/course/intervals#half-steps-and-whole-steps) between its seventh degree and its tonic — G up to A in A minor — so the chord on the fifth degree comes out minor, [Em](https://musictheory.center/chord/e-m), with no [leading tone](https://musictheory.center/course/scales#scale-degrees) anywhere in the key. Nothing pulls home. Raise that G to G♯, which is what the [A Harmonic Minor](https://musictheory.center/scale/a-harmonic-minor) does, and [Em](https://musictheory.center/chord/e-m) becomes [E](https://musictheory.center/chord/e-maj): the same root, one note a half step higher, and a leading tone where there was none. That is the entire reason harmonic minor exists, and it is why the second clip above lands where the first merely stops.

So a minor key is a choice rather than a fixed set. Composers move between the two versions freely, often within a single phrase — natural minor for the descending, modal-sounding parts and the raised seventh at the cadence — and a printed [accidental](https://musictheory.center/course/notation#accidentals) on the seventh degree is usually the sign that a cadence is coming.

**Good to know**

- (Fact) One note separates the two versions of the fifth-degree chord. [Em](https://musictheory.center/chord/e-m) is E, G, B and [E](https://musictheory.center/chord/e-maj) is E, G♯, B; G♯ lies a half step under A, so the second chord contains a leading tone and the first does not. Every other chord in the key is untouched by the change.
- (Tendency — common-practice classical, most minor-key jazz and musical theatre, and minor-key pop in the Tin Pan Alley line. Folk, modal rock, film music and a great deal of post-1960s writing keep the natural minor v throughout, which is exactly what makes those repertoires sound modal rather than tonal) The raised seventh, and the major V it produces, is the normal sound of a minor-key cadence: a piece in A minor will spend most of its time in the natural minor and then use E major to come home.
- (Convention) The numerals in a minor key are counted against the natural minor scale, which is why III, VI and VII are written as plain capitals with no flat sign in front of them. A chart that measures the same chords against the parallel major — the common practice in jazz and in a lot of pop writing — writes the same three chords ♭III, ♭VI and ♭VII instead. Both notations describe C major, F major and G major in the key of A minor; they differ only in what they are counting from.

**You already know this**

- The harmonic minor scale from Chapter 7, whose raised seventh degree is the one alteration this whole section turns on — https://musictheory.center/course/scales#the-three-minors
- Relative keys from Chapter 8 — the same seven notes and the same seven chords, with a different one of them treated as home — https://musictheory.center/course/keys-and-key-signatures#relative-and-parallel
- The dominant family from earlier in this chapter, which a minor key has to manufacture rather than simply inherit — https://musictheory.center/course/diatonic-harmony#harmonic-function

**Where this goes**

- Borrowing a chord from the parallel key is the same move the raised seventh makes, generalised — and it is how a major key gets a minor iv and a minor key a major I — https://musictheory.center/course/advanced-harmony

**In real music**

- The Animals — “House of the Rising Sun” — the verse cycles through the minor chords of the key and then, in the second half of each cycle, reaches a major chord on the fifth degree containing a note the key signature does not provide — that is the chord that throws the whole cycle back to the start
- Ray Charles — “Hit the Road Jack” — four chords falling away from home over and over, and the last of the four is the major one with the raised seventh degree in it; it arrives on every second bar, which is why the song never stops turning over
- Bill Evans, "Portrait in Jazz" — “Autumn Leaves” — the second four bars of Kosma’s tune turn to the relative minor, and the chord immediately before the minor home chord is a major one with a raised leading tone in it — the exact moment the song stops sounding like its relative major

**Try it on your instrument:** Play A, C and E together, then D, F and A, then E, G and B, then A, C and E again. Now play the whole thing a second time with G sharp in place of G in the third chord. Then do both versions from a different minor home note, and say which one you would use to end a piece.

[Enter the four chords with the raised seventh and see how the key finder reads them](https://musictheory.center/tools/key-finder?c=Am+Dm+E7+Am)

**Check:** Two four-chord phrases in A minor, one after the other with a gap between them. One of the two contains a note the key signature does not give you: a raised seventh degree, sitting a half step under the home note. Which phrase was it?

- The first phrase — The first phrase kept every note inside the A natural minor scale, so its third chord was E, G, B — minor, with a whole step between its own third and the home note and nothing pulling anywhere. That is the modal-sounding version, and it is what a great deal of folk and rock uses.
- The second phrase **(correct)** — Correct. The second phrase raised G to G sharp in its third chord, turning E, G, B into E, G sharp, B. G sharp is a half step under A, so that chord leans onto the home chord instead of merely arriving next to it — which is why the second phrase sounds aimed and the first sounds like it stopped.
- Both of them — Only one of the two raised anything. The phrases are identical apart from a single note in the third chord of each; play them again and listen to nothing but the chord immediately before the last one.

### Key Takeaways

https://musictheory.center/course/diatonic-harmony#key-takeaways

- A diatonic chord is one built only from the notes of the key, and a seven-note key supplies exactly seven of them.
- Every major key produces the same order of qualities up the scale — major, minor, minor, major, major, minor, diminished — because every major key has the same shape.
- A roman numeral names a chord by its degree in the key rather than by its letter, with capitals for major, lower case for minor and a small circle for diminished.
- Because a numeral names a relationship rather than a pitch, a progression written in numerals is already transposed into every key at once.
- Harmonic function sorts the seven chords into three families: the tonic rests, the subdominant departs, and the dominant creates tension by containing the note a half step under the tonic.
- A cadence is the chord movement a phrase ends with, and the four worth knowing are the authentic V–I, the plagal IV–I, the half cadence ending on V, and the deceptive V–vi.
- A progression is defined by its order and not by its contents: the same four chords starting on a different one of them is a different progression with a different feeling.
- A minor key harmonises into the same seven triads as its relative major, and raising its seventh degree is what converts the minor v into the major V a cadence needs.

### Questions

**What is a chord progression?**

A chord progression is an ordered series of chords, usually a short pattern of two to four bars that repeats. It gives a passage its harmonic shape: which chord is home, which ones move away from it, and which one leads back. I–V–vi–IV and ii–V–I are two of the most used.

**What do roman numerals mean in music?**

They name a chord by its degree in the [key](https://musictheory.center/course/keys-and-key-signatures#what-a-key-is) rather than by its letter, so one numeral works in every key. Capitals are major chords, lower case minor, and a small circle diminished. In C major, I is C, ii is D minor and V is G; in G major [the same numerals give G, A minor and D](https://musictheory.center/tools/chord-transposer).

**What is a cadence?**

A cadence is the chord movement a [phrase](https://musictheory.center/course/melody#phrase-antecedent-consequent) ends with — its harmonic punctuation. An authentic cadence, V–I, is a full stop. A plagal cadence, IV–I, settles without leaning first. A half cadence stops on V, like a comma. A deceptive cadence, V–vi, swerves at the last moment.

**Why is V major in a minor key?**

The [natural minor scale](https://musictheory.center/course/scales#the-three-minors) gives a minor chord on the fifth degree, and it contains no note a [half step](https://musictheory.center/course/intervals#half-steps-and-whole-steps) under the tonic, so nothing pulls home. Raising the scale’s seventh degree — G to G sharp in A minor — turns that chord major and supplies the leading tone a cadence needs.

**What chords are in the key of C major?**

Seven: C, D minor, E minor, F, G, A minor and B diminished, each built by [stacking thirds](https://musictheory.center/course/chords#stacking-thirds) on one [degree of the scale](https://musictheory.center/course/scales#scale-degrees) using only notes from the key. The order of qualities — major, minor, minor, major, major, minor, diminished — is the same in every major key.

**What is the difference between a plagal and an authentic cadence?**

Both end on the tonic chord. An authentic cadence approaches it from V, which contains the [leading tone](https://musictheory.center/course/scales#scale-degrees) a half step below the tonic, so it pulls hard and sounds conclusive. A plagal cadence approaches from IV, which has no leading tone, so it settles gently — the hymn-book amen.

### Other languages

- https://musictheory.center/course/diatonic-harmony/llms.txt
- https://musictheory.center/fr/cours/harmonie-diatonique/llms.txt
- https://musictheory.center/es/curso/armonia-diatonica/llms.txt