## 14. Chromatic Harmony

Chromatic harmony is what a piece does when it reaches past the seven notes of its key: a dominant borrowed from somewhere else and aimed at one of its own chords, a chord lifted from the parallel minor, a move to a new key altogether, or one of the handful of specialised chords that exist to push hard at the dominant.

Source: https://musictheory.center/course/advanced-harmony
Level: Advanced · Harmony · 6 sections
Before this: Diatonic Harmony, Voice Leading

### Leaving the Key

https://musictheory.center/course/advanced-harmony#leaving-the-key

> Play the first one: four chords in C major, and every note in every one of them comes from the same seven notes. Now play the second: the same four chords with a fifth one pushed in among them, and one note in that fifth chord is not among the seven. Play both twice. What does that one foreign note do to the chord that arrives after it?

**Plays:** Four chords, all from one scale (C3 C4 E4 G4 F2 A3 F4 G2 B3 D4) · The same four with a fifth pushed in (C3 C4 E4 G4 Bb3 F2 A3 F4 G2 B3 D4)

The chord from outside, drawn on its own: four note heads in one stack, and a flat printed in front of one of them. That printed flat is the whole subject of this chapter. Nothing in the key signature accounts for it, so it has to be written in as an accidental wherever it first appears in a bar — which is why a score full of chromatic harmony looks busy long before you have played a bar of it. The table below names the three ordinary ways a note like that gets into a piece, and the rest of the chapter takes one of them per section.

- **A key supplies seven notes and leaves five out** — C major supplies C, D, E, F, G, A and B. The five it leaves out are the notes a chromatic chord reaches for, and the second clip reaches for one of them: B♭3.
- **One foreign note is enough** — The second clip adds one chord, and that chord is the first one with a single note moved — C4 down a whole step to B♭3, which makes [C7](https://musictheory.center/chord/c-7) out of [C](https://musictheory.center/chord/c-maj). Nothing else in the clip changes.

| Door out of the key | What it brings in | Example in C major | Taken up in |
| --- | --- | --- | --- |
| A dominant aimed elsewhere | A dominant seventh chord built on the fifth degree of a chord other than the home chord, which makes that other chord sound briefly like home | [C7](https://musictheory.center/chord/c-7) pulling on to [F](https://musictheory.center/chord/f-maj), which brings B♭3 in | Section 2 |
| A chord from the parallel key | A chord taken from the key with the same tonic and a different key signature, which darkens the colour without moving the centre | [Fm](https://musictheory.center/chord/f-m) in place of [F](https://musictheory.center/chord/f-maj), which brings A♭3 in | Section 3 |
| A new key | A new tonic altogether, after which the foreign note is ordinary and the old home chord is merely one chord among seven | [D7](https://musictheory.center/chord/d-7) and then [G](https://musictheory.center/chord/g-maj), after which F♯4 needs no excuse | Section 4 |

**chromatic chord**

**Definition.** A chromatic chord is a chord containing at least one note the [key](https://musictheory.center/course/keys-and-key-signatures#what-a-key-is) does not supply — one of the five pitches the [key signature](https://musictheory.center/course/keys-and-key-signatures#why-key-signatures-exist) leaves out — in a passage that is still heard as being in that key.

The arithmetic behind the definition is small and worth stating. There are twelve notes in an octave and a key claims seven of them; the other five are available, unused, and a half step away from something. A chord that uses one of them is chromatic. A chord that uses none is diatonic, which is the word Chapter 11 spent itself on. Nothing more than that separates the two, and the difference is audible in the two clips above the instant the second one reaches its second chord.

What a chromatic chord is **for** is almost always the same thing: a half step. The five leftover notes each sit a half step from a note of the key, and a half step is the strongest pull a single line can have. Put a foreign note a half step below a note of the next chord and the ear hears the next chord coming before it arrives. Put one a half step above, and it leans down instead. **A chromatic chord is a tendency tone with a chord built underneath it**, and the three doors in the table are three answers to the question of which chord to build.

None of this is a departure from the key. A passage can use every one of the five leftover notes and still end where it began, still be measured against the same tonic, still be in C major. That is the difference between chromatic harmony and the music of the twentieth century that abandoned keys altogether: here the key is the thing all the colour is measured against, and without it none of the colour would register.

**Good to know**

- (Fact) Every note outside a key is a half step from a note inside it. B♭3 sits a half step below B4’s pitch class and a half step above A4’s, and the same is true of all five leftover notes in every key. That is a fact about the twelve-note division of the octave and not about any style: the pull those half steps exert is learned, but the distances are not.
- (Convention) Chromatic chords are labelled by extending the [roman numerals](https://musictheory.center/course/diatonic-harmony#roman-numerals) rather than by replacing them. An accidental in front of the numeral alters its root, so bVI and bVII are major chords on lowered degrees; a slash after it names a target, so V7/V is the dominant seventh of the dominant; and four chords that fit neither pattern comfortably carry names borrowed from places instead — Neapolitan, Italian, French, German.
- (Tendency — tonal Western repertoire from the Baroque onward and the popular music descended from it, which is where a tonic is stable enough for a departure from it to register. In modal and loop-based writing there is often no tonic firm enough for the distinction to mean anything) A single chromatic chord colours a key rather than leaving it. One foreign chord in a phrase is heard as decoration of the key it sits in; three or four in a row, ending in a [cadence](https://musictheory.center/course/diatonic-harmony#cadences) somewhere else, are heard as a move to a new key. There is no fixed number at which the switch happens, and composers exploit the ambiguity deliberately.

**You already know this**

- A key from Chapter 8 — the seven notes a passage measures itself against, and the tonic it keeps returning to — which is what a chromatic chord steps outside of without abandoning — https://musictheory.center/course/keys-and-key-signatures#what-a-key-is
- Diatonic chords from Chapter 11 — the seven chords a key builds out of its own notes and nothing else — which is the complete list this chapter begins adding to — https://musictheory.center/course/diatonic-harmony#chords-in-a-key

**Where this goes**

- Jazz reharmonisation is chromatic harmony applied systematically — substituting a chord from outside the key for almost any chord inside it — and it starts from exactly the three doors this section names — https://musictheory.center/course/contemporary

**In real music**

- The Beatles — “Let It Be” — the verse and the chorus use nothing but chords built from the notes of one key, so play it beside anything else cited in this chapter and the contrast is the chapter’s subject
- Frédéric Chopin — “Prelude in E minor, Op. 28 No. 4” — the left hand changes chord by moving one inner note down a half step at a time, so most of the chords under the melody contain a note the key does not supply

**Try it on your instrument:** Play a major chord on your instrument and then the chord a fourth above it. Now go back and, before you move, add to the first chord the note a whole step below its own root — one finger on a keyboard, usually one string on a guitar. Play that four-note chord and then the chord a fourth above it again. Say out loud whether the note you added belongs to the scale you started from, and which way it moved when the second chord arrived.

**Check:** Five chords in a row. Four of them are built only from the seven notes of C major, and one is not. Which one was the outsider?

- The second chord **(correct)** — Correct. The second chord sounded C3, B♭3, E4 and G4, and B♭ is not one of the seven notes of C major. It is the only foreign note anywhere in the clip. The chord it makes is a C7 — the chord you heard first with one of its notes lowered a whole step — and that B♭ falls a half step on to the A3 of the chord that follows.
- The first chord — The first chord was C3, C4, E4 and G4: a plain C major triad, every note of it inside the key. It is also the chord the clip ends on, which is what makes the key audible in the first place and what gives the outsider something to be outside of.
- The fourth chord — The fourth chord was G2, B3, D4 and G4 — G major, built from the fifth, seventh and second degrees of C major. All three notes are inside the key. It is the ordinary dominant, and Chapter 11 spent a section on it precisely because nothing in it is foreign.
- All five were built from the same seven notes — One of them was not. Play the first clip at the top of the section, which really is built from seven notes only, and then this one: the extra chord lowers a C to a B♭, and B♭ is one of the five notes C major leaves out.

### Secondary Dominants

https://musictheory.center/course/advanced-harmony#secondary-dominants

> Play the first: three chords, ending at home. Now play the second: the same three with one more chord in front of them. That extra chord is not in the key, and it is pointing at the chord immediately after it rather than at home. Play the third, which does the same thing to a different target. In each case, work out which chord the newcomer is pointing at — and see whether you could have named it before it arrived.

**Plays:** Three chords, ending at home (D3 A3 D4 F4 G2 B3 G4 C3 C4 E4) · The same three with one chord in front (A2 G3 C#4 E4 D3 A3 D4 F4 G2 B3 G4 C3 C4) · One more in front, aimed elsewhere (D3 F#4 A4 C5 G2 D4 G4 B4 C3 C4 E4)

The two notes that do the work, and where they go. The first pair is an F sharp and the C above it, six half steps apart — the sharpest dissonance a dominant seventh contains, and the one that decides where the chord goes. The second pair is the note a half step above the first and the note a half step below the second: a G underneath and a B on top, four half steps apart, a major third. Both notes moved the smallest distance there is, towards each other, and between them they supply two of the three notes of the chord that arrives. That mechanism is not tied to any one key, which is the whole reason a dominant seventh can be aimed at any chord you like. The table lists the five targets a major key offers.

| Numeral | The chord in C major | What it brings from outside the key | Where it goes |
| --- | --- | --- | --- |
| V7/ii | [A7](https://musictheory.center/chord/a-7) | C♯4 | [Dm](https://musictheory.center/chord/d-m), the minor chord on the second degree |
| V7/iii | [B7](https://musictheory.center/chord/b-7) | D♯4 and F♯4 | [Em](https://musictheory.center/chord/e-m), the minor chord on the third degree |
| V7/IV | [C7](https://musictheory.center/chord/c-7) | B♭3 | [F](https://musictheory.center/chord/f-maj), the major chord on the fourth degree |
| V7/V | [D7](https://musictheory.center/chord/d-7) | F♯4 | [G](https://musictheory.center/chord/g-maj), the major chord on the fifth degree |
| V7/vi | [E7](https://musictheory.center/chord/e-7) | G♯4 | [Am](https://musictheory.center/chord/a-m), the minor chord on the sixth degree |

**secondary dominant**

*also called*: applied dominant (much North American theory teaching, where the chord is described as applied to its target)

**Definition.** A secondary dominant is a [dominant seventh chord](https://musictheory.center/course/chords#seventh-chords) — or the major triad inside one — built a fifth above a chord of the key other than the [tonic](https://musictheory.center/course/scales#scale-degrees), and used to make that chord sound, for a moment, like home.

The whole device is one chord shape moved around. Chapter 11 established what a dominant seventh does to the chord a fifth below it: it contains a tritone, the two notes of that tritone each sit a half step from a note of the target, and the ear hears the target coming. Nothing in that argument mentions the tonic. So take the shape, build it a fifth above some other chord of the key, and the same pull appears — aimed somewhere else. The technical word for what it does to the target is **tonicization**: the target is treated as a temporary tonic and then abandoned, without the key ever actually changing.

A major key offers five usable targets, and the table has all of them. The one chord left over, the diminished triad on the seventh degree, is the exception: it is too unstable to be tonicized, so the dominant that would point at it has no work to do. The commonest of the five by a wide margin are the dominant of the dominant and the dominant of the sixth-degree chord, and after them the dominant of the fourth degree, which is the one the previous section used — it is the home chord with one more note stacked on top, and in a voicing that already doubles the tonic a single finger moving a whole step is enough to produce it.

A related chord does the same job with a different colour. Instead of a dominant seventh a fifth above the target, build a diminished seventh a half step **below** it: three of its four notes lie a half step from notes of the target, so the pull is harder and the resolution more abrupt. These are the secondary leading-tone chords, written vii°7 of the same target, and they are used interchangeably with secondary dominants throughout nineteenth-century music and in jazz.

**Good to know**

- (Fact) A dominant seventh contains a [Tritone](https://musictheory.center/interval/tritone) between its third and its seventh, and both notes of that tritone lie a half step from a note of the chord a fifth below. In [D7](https://musictheory.center/chord/d-7) the pair is F♯4 and the C5 above it, six half steps; move the lower up a half step to G4 and the upper down a half step to B4 and you have two of the three notes of [G](https://musictheory.center/chord/g-maj), four half steps apart. The distances are the same in every key, which is exactly why the shape can be transplanted.
- (Convention) The slash in V7/V is read "of", not "over": it names the chord the dominant is aimed at. A slash in a [chord symbol](https://musictheory.center/course/chords#reading-chord-symbols) names something else entirely — in C/E the letter after the slash is the lowest note — so the same mark means two unrelated things in the two notations, and which one you are reading is decided by whether what precedes it is a numeral or a letter.
- (Tendency — tonal repertoire: common-practice classical music, ragtime and jazz standards, and popular song descended from them. Modal and loop-based writing uses the same chords as colours with no obligation to resolve at all) A secondary dominant is followed by its target. That is what makes the label worth using: a chord is only called the dominant of something if the something turns up. Composers break the expectation on purpose — a chain of dominants in which each one resolves to the next dominant rather than to a triad is the ordinary sound of ragtime and of the first bars of a great many jazz standards — but the deception only works because the default is so reliable.

**You already know this**

- The dominant seventh from Chapter 10 — a major triad with a minor seventh stacked on top of it — which is the only chord shape this section uses, moved to five different roots — https://musictheory.center/course/chords#seventh-chords
- Harmonic function from Chapter 11 — the dominant family, whose pull comes from the two notes inside it that sit a half step from the chord it points at — which is that same pull aimed at a new target — https://musictheory.center/course/diatonic-harmony#harmonic-function

**Where this goes**

- A chain of dominants in which each one resolves to the next is the backbone of ragtime and of a large part of the jazz standard repertoire, and substituting other chords into that chain is where jazz reharmonisation begins — https://musictheory.center/course/contemporary

**In real music**

- The Beatles — “Something” — the third chord of the verse is the home chord with one note added a whole step below its root; the chord that follows is the one that added note is pulling towards, and the whole opening is that single descent harmonised
- Ben Bernie, Maceo Pinkard and Kenneth Casey — “Sweet Georgia Brown” — the first three chords are all dominant sevenths, each one aimed at the next, and the home chord does not arrive until the fourth of them — the clearest chain of the kind in the standard repertoire

**Try it on your instrument:** In a [key](https://musictheory.center/course/keys-and-key-signatures#what-a-key-is) you can play, find the minor chord on its second degree and play it. Now build a dominant seventh on the note a fifth above that chord’s root and play that first instead, then the minor chord after it: one note in the seventh will be outside your key, and you should be able to name it. Do the same for the chord on the fifth degree and for the chord on the sixth degree, and write down the foreign note each time.

**Check:** A home chord in C major, then a chord that is not in the key, and then nothing. Predict the chord that would come next.

- The minor chord built on the third note of the key **(correct)** — Correct. The second chord sounded B2, A3, D♯4 and F♯4 — a B7. Its D♯ sits a half step below E and its A sits a step above G, and E, G and B are the notes of the E minor chord. B7 stands to E minor exactly as G7 stands to C major, which is the second row of the table.
- Back to the home chord — Going straight back home is possible but it wastes the chord. Nothing in B7 points at C: the D♯ leans up to E and the F♯ sits a step above it, and neither of them has anything to do with C. Play the clip again and sing what your voice wants after the second chord — it will not be the note you started on.
- The minor chord built on the sixth note of the key — The dominant seventh of the sixth-degree chord is E7, built on E with a G♯ in it. This one is built on B and contains a D♯, one letter further round, and its target is a fifth higher: the chord on the third degree, not the sixth.
- The major chord built on the fifth note of the key — The major chord on the fifth degree is the target of D7, which is the third clip at the top of this section. The chord in this clip is built on B rather than on D, and its D♯ is a half step below E rather than a half step below G.

### Borrowed Chords and Modal Interchange

https://musictheory.center/course/advanced-harmony#borrowed-chords-and-modal-interchange

> Play the first: three chords, a pause, then the same three again with one note of the middle chord lowered by a half step. Find the note. Now play the second: home, then two chords that belong to no part of C major at all, then home again — and notice how completely unsurprising the two strangers are. Then play the third, which brings in two more of the same kind. What do all the newcomers have in common, and which way did every altered note move?

**Plays:** Three chords, then the same three darkened (C3 C4 E4 G4 F2 A3 F4 Ab3) · Home, two chords from nowhere, home again (C3 C4 E4 G4 Ab2 Eb4 Ab4 Bb2 D4 F4 Bb4) · Two more of the same kind (C3 C4 E4 G4 Eb3 Bb3 Eb4 D3 Ab3 D4 F4 G2 B3)

The altered chord from the first clip, drawn on its own: four note heads, with a flat printed in front of the second one up from the bottom. Compare it with the picture in the first section of this chapter and the difference is instructive — there the printed accidental raised the pull of the chord, and here it lowers its colour. Every chord in the table below is the same trick: one, two or three notes of the key replaced by the notes the key of the same name and the opposite quality would have supplied. The last column says which those are.

- **Parallel keys share a tonic and differ by three notes** — C major supplies E4, A4 and B4; C minor supplies E♭4, A♭4 and B♭4 in their places. The other four notes — C, D, F and G — are the same in both, which is why the tonic never moves.
- **Relative keys are the other pairing, and are no use here** — C major and A minor share all seven notes and have different tonics, so nothing can be borrowed between them: every chord of one is already a chord of the other. Borrowing needs the pairing that keeps the tonic and changes the notes.

| Borrowing | In C major | Where it comes from | The note or notes that change |
| --- | --- | --- | --- |
| iv, the minor chord on the fourth degree | [Fm](https://musictheory.center/chord/f-m) | C minor, and equally the Aeolian and Phrygian modes on C | A4 lowered to A♭4 |
| ♭VI, the major chord on the lowered sixth degree | [A♭](https://musictheory.center/chord/aflat-maj) | C minor | A4 lowered to A♭4, and E4 to E♭4 |
| ♭VII, the major chord on the lowered seventh degree | [B♭](https://musictheory.center/chord/bflat-maj) | C minor, and equally the Mixolydian mode on C | B4 lowered to B♭4 |
| ♭III, the major chord on the lowered third degree | [E♭](https://musictheory.center/chord/eflat-maj) | C minor | E4 lowered to E♭4, and B4 to B♭4 |
| ii°, the diminished chord on the second degree | [Ddim](https://musictheory.center/chord/d-dim) | C minor | A4 lowered to A♭4 |

**borrowed chord**

*also called*: modal interchange (jazz and popular-music writing, which describes the move as interchange between parallel modes), mixture (older classical analysis, which speaks of modal mixture between the parallel major and minor)

**Definition.** A borrowed chord is a chord taken from the [parallel key](https://musictheory.center/course/keys-and-key-signatures#relative-and-parallel) or [mode](https://musictheory.center/course/modes#what-a-mode-is) — the one built on the same tonic with a different set of notes — and used inside a passage that otherwise stays in the original key.

The mechanism depends on a fact Chapter 8 established and this section puts to work: C major and C minor are two different keys with the same tonic. They share four notes and differ in three, and because the tonic is one of the four, nothing about borrowing a chord moves the centre. You take the chord you want, replace whichever of its notes the other key spells differently, and put it back. The home chord is still home; only the light on it has changed.

Five borrowings account for most of what you will meet, and the table has them. **The minor fourth-degree chord is the commonest single chromatic chord in popular music**, and it is at its most effective immediately after its major version — the same chord twice, the second time with one note lowered, which is what the replay beside the character-note link below plays. The pair of major chords on the lowered sixth and lowered seventh degrees are the other famous case: played in succession into the home chord they make an ending that a century of film scoring, video-game music and stadium rock has leaned on. They work for a different reason from the minor fourth-degree chord: each is a plain major triad rooted on a lowered degree of the parallel minor, and between them they import all three of the notes that separate C minor from C major — E♭4 and A♭4 in the first, B♭4 in the second — while their roots climb A♭–B♭–C straight into the tonic.

It is worth being exact about what this is not. Borrowing does not change the key, so nothing here is a modulation; and the borrowed chord is not aimed at anything, so nothing here is a secondary dominant either. **The altered notes fall rather than rise**, which is the single most useful diagnostic in the whole chapter: a raised note that pushes upward into the next chord is almost always the previous section’s device, and a lowered note that darkens the chord it belongs to is almost always this one.

**Good to know**

- (Fact) C major and C minor share a tonic and differ in exactly three notes. E4, A4 and B4 in the major are E♭4, A♭4 and B♭4 in the minor; C, D, F and G are common to both. Every chord in the table is built using at least one of those three replacements, and no chord that uses none of them can be a borrowing.
- (Convention) The flat sign in bVI and bVII lowers the root the numeral is built on, not a note inside the chord: bVI is a major triad whose root is the lowered sixth degree, and the numeral is upper case because that triad is major. A numeral with no [accidental](https://musictheory.center/course/notation#accidentals) always means the chord the key itself supplies, so plain VI in C major would be a chord on A and ♭VI is a chord on A♭.
- (Tendency — popular song, film and game scoring since roughly the middle of the twentieth century, and a long line of nineteenth-century precedent before it. In music that is genuinely modal rather than tonal the category dissolves: there is no home key for the chord to have been borrowed into) A borrowed chord is heard as a change of colour rather than a change of place, and almost always resolves into the key it was borrowed into rather than pulling towards a new one. That is why a phrase can take one and carry on as though nothing happened, and why the same chord repeated often enough stops sounding borrowed at all and simply becomes part of the vocabulary of the song.

**You already know this**

- Relative and parallel keys from Chapter 8 — C major and C minor share a tonic and differ by three notes, while C major and A minor share all seven and differ in their tonic — and it is the first pairing that this section borrows from — https://musictheory.center/course/keys-and-key-signatures#relative-and-parallel
- Character notes from Chapter 9 — the one altered degree that tells two modes apart — which is exactly what a borrowed chord imports, one chord at a time instead of for a whole passage — https://musictheory.center/course/modes#character-notes

**Where this goes**

- Treating every chord of a key as replaceable by its parallel-mode equivalent is a standard jazz and contemporary songwriting move, and it turns the five borrowings here into a whole second set of chords for any key — https://musictheory.center/course/contemporary

**In real music**

- Radiohead — “Creep” — the fourth chord of the four-chord loop is the third chord with a single note lowered by a half step; it arrives at the end of every line and it is the sound the record is remembered for
- Lynyrd Skynyrd — “Sweet Home Alabama” — read the three-chord loop in D major and the middle chord is a major chord on the lowered seventh degree — the third row of the table, repeated for the length of the song

**Try it on your instrument:** In a [major key](https://musictheory.center/course/keys-and-key-signatures#what-a-key-is) you can play, play the chord on the fourth degree, then lower its middle note by a half step and play it again, going home from each. Then find the major chord a whole step below your home chord, and the major chord a whole step below that one, and play the two of them into home. Write down, for each of the three chords, which note of your key had to be altered and which way it moved.

[Enter the progression with its borrowed chord and see it read against the key](https://musictheory.center/tools/key-finder?c=C+F+Fm+C)

**Check:** Three chords. The middle one is built on the fourth degree of the key. Was it the major chord the key supplies, or the minor one?

- The minor chord on the fourth degree **(correct)** — Correct. The middle chord sounded F2, A♭3, C4 and F4. The key supplies an A, not an A♭, so that one lowered note is the borrowing — the commonest of all five in the table, and the same chord the first clip at the top of the section darkens into.
- The major chord on the fourth degree — The major chord on the fourth degree would have had an A in it rather than an A♭, and it is the version the key itself supplies. Play the first clip above, which gives you both in succession: the difference is one note moving down by the smallest distance there is, and it changes the whole colour of the chord.
- A dominant seventh on the fourth degree — A dominant seventh has four different notes: a major triad with a seventh on top. This chord had three — F, A♭ and C, with the F sounded twice — and its third is lowered rather than its seventh added. Nothing in it points anywhere; it darkens the chord it stands in place of.
- A diminished chord on the fourth degree — A diminished triad needs its fifth lowered as well as its third. This one keeps its C, a perfect fifth above the F, so only the middle note has moved. The diminished chord in this section is the one on the second degree, the last row of the table, and it appears in the third clip at the top rather than here.

### Modulation

https://musictheory.center/course/advanced-harmony#modulation

> Play the first: five chords, beginning at home in C major. Play the second: five chords, also beginning at home, and also containing one chord from outside the seven. Both of them wander; only one of them comes back. Then play the third, which states four chords and then states the same four again from a starting note one half step higher. Ask yourself, of each clip, whether the note you would hum at the end is the note you would have hummed at the start.

**Plays:** Five chords that do not come back (C3 C4 E4 G4 F2 A3 F4 A2 A4 D3 F#4 C5 G2 D4 B4) · Five chords that do (C3 C4 E4 G4 A2 G3 C#4 D3 A3 D4 F4 G2 B3) · Four chords, then the same four higher (C3 C4 E4 G4 F2 A3 F4 G2 B3 D4 Db3 Db4 Ab4 Gb2 Bb3 Gb4 Ab2 Eb4)

The third chord of the first clip, drawn on its own: four note heads and not an accidental in sight. Nothing in the picture says which key it belongs to, and that is precisely what makes it useful. It is the chord on the sixth degree of the key the clip starts in and the chord on the second degree of the key the clip ends in, and a listener hearing it has no way of telling which reading is meant until the chord after it arrives. A chord that can be read two ways is a hinge, and the table gives the four standard ways of getting from one key to another, of which hinging on a shared chord is the smoothest.

| Method | How the join is made | How it sounds |
| --- | --- | --- |
| Pivot chord | One chord belonging to both keys is played as a chord of the old key and then treated as a chord of the new one — [Am](https://musictheory.center/chord/a-m) is the sixth-degree chord of C major and the second-degree chord of G major | Seamless. Most listeners cannot say afterwards where the change happened, only that it did |
| Direct | The new key simply begins, with no preparation at all, almost always at the start of a phrase. The third clip above restates its four chords a half step higher | Abrupt and unmistakable, which is the point. A half step upward is the standard last-chorus lift in popular song |
| Common tone | One note is repeated across the join while the harmony around it is rebuilt in the new key | Suspended. The repeated note is the only fixed point the listener has while the ground moves underneath it |
| Sequential | A phrase is restated from a new starting note, and the restatement itself establishes the new key | Driving. This is how a development section climbs through three or four keys without ever seeming to stop |

**modulation**

*also called*: key change (ordinary speech and most popular-music writing)

**Definition.** Modulation is a change of [key](https://musictheory.center/course/keys-and-key-signatures#what-a-key-is) inside a single piece: the music stops measuring itself against one tonic and begins measuring itself against another, so that a note which was foreign becomes ordinary and the chord which was home becomes merely one chord among seven.

The distinction that matters most is between this and what the second section of this chapter did. A secondary dominant points at a chord, that chord arrives, and the passage carries on in the key it was already in — the second clip above does exactly that and ends where it began. A modulation does not come back. Both use chords from outside the key and the chords themselves can be identical; **what separates them is how long the new centre lasts and whether a cadence confirms it.** There is a real grey area in the middle, and analysts argue about individual passages constantly.

How the join is made is the other half of the subject, and the table lists the four standard methods. The pivot chord is the classical default and the smoothest: find a chord the two keys have in common, play it, and then treat it as belonging to the new key rather than the old. It works best between **closely related keys** — the neighbours on the [circle of fifths](https://musictheory.center/course/keys-and-key-signatures#the-circle-of-fifths), which differ from each other by a single note and therefore share four of their seven chords. C major and G major differ only in that G has an F sharp; four of the seven chords pivot between them, including the tonic of each.

A modulation is not believed until something confirms it, and what confirms it is a [cadence](https://musictheory.center/course/diatonic-harmony#cadences). The first clip above introduces the foreign note in its fourth chord and lands on the new home chord in its fifth, and it is that landing, not the foreign note, that makes the passage end somewhere other than where it started. Take the last chord away and the passage is merely a question; the chapter’s entire distinction between visiting and moving is carried by whether the phrase ends in the new place.

**Good to know**

- (Fact) Two keys a fifth apart differ by exactly one note. C major and G major share six of their seven notes; the seventh is F4 in C and F♯4 in G. Three of C major’s seven triads contain that F — ii, IV and vii° — so the other four are chords of both keys at once: [C](https://musictheory.center/chord/c-maj), [Em](https://musictheory.center/chord/e-m), [G](https://musictheory.center/chord/g-maj) and [Am](https://musictheory.center/chord/a-m). Any of those four can serve as a pivot.
- (Convention) A pivot chord is marked with a bracket carrying two readings: the chord is numbered once in the old key and again underneath in the new one, and everything after the bracket is numbered in the new key. Nothing in the music decides where the bracket goes. It is the analyst’s decision about where the listener’s allegiance switched, and two analysts frequently place it on two different chords in the same passage.
- (Tendency — common-practice classical music and the popular song descended from it, where cadences are frequent and unambiguous. A great deal of modal, ambient and loop-based music shifts its centre without ever cadencing at all, and film scoring routinely moves between keys on a single held note) A modulation is not heard as one until a cadence in the new key confirms it. Until then the same chords read as a tonicization of one degree of the old key, and a composer who introduces the foreign notes and then withdraws them has produced a colouring rather than a move. The cadence is the evidence; the accidentals are only the argument.

**You already know this**

- The circle of fifths from Chapter 8, whose immediate neighbours are the closely related keys — the ones a single note apart, which is what makes them the easy destinations for a pivot — https://musictheory.center/course/keys-and-key-signatures#the-circle-of-fifths
- Cadences from Chapter 11 — the chord pairs that end phrases — which are the evidence a listener actually accepts that a new key has arrived rather than merely been visited — https://musictheory.center/course/diatonic-harmony#cadences

**Where this goes**

- Which keys a piece visits, in what order, and where it comes home is one of the largest-scale decisions in composition — sonata form is very largely an argument about exactly that — https://musictheory.center/course/form-structure

**In real music**

- The Beatles — “Penny Lane” — the verse and the chorus are in two different keys and the join is made at the phrase boundary with no preparation at all; listen for the moment the trumpet-led chorus arrives and the whole harmonic floor has shifted
- Beyoncé — “Love on Top” — the last two minutes repeat the chorus four times, each one a half step above the last — the second row of the table, used four times in a row and audible to anyone

**Try it on your instrument:** Play a four-chord phrase in a key you know, ending at home. Then find a chord that belongs both to your key and to the key a fifth above it — the minor chord on your sixth degree will do — play it, follow it with the [dominant seventh](https://musictheory.center/course/chords#seventh-chords) of that higher key, and end on the higher key’s home chord. Then play your original phrase again and simply restart it a half step higher with no preparation. Say which of the two joins a listener would be able to point at.

[Compare the two keys on the circle: the chords they share are your pivots](https://musictheory.center/tools/circle-of-fifths?k=C&lens=compare&vs=G)

**Check:** The first four chords of the first clip at the top of this section. In the clip a fifth chord follows immediately. Predict which chord it is.

- The major chord built on the fifth note of the starting key **(correct)** — Correct. The fourth chord sounded D3, F♯4, A4 and C5 — a D7 — and its F♯ is the single note that separates the starting key from the key a fifth above it. A D7 is the dominant seventh of G, so G major follows, and arriving there is what leaves the passage in a different key from the one it opened in.
- Back to the home chord of the starting key — Coming home is what the second clip at the top of the section does: there the chord from outside the key is followed by two more that lead back, and the phrase ends where it began. Nothing in this fourth chord points back at C — its F♯ is a half step below G, not a member of the home chord.
- The major chord built on the second note of the starting key — That is very nearly the chord you have just heard. The fourth chord already is a D with an F♯ and an A in it, plus a C on top; the C is there precisely so that the chord cannot rest on itself and has to push on to something else.
- The minor chord built on the sixth note of the starting key — The A minor chord was the third of the four, and it is the hinge: the chord on the sixth degree of the key the clip starts in and the chord on the second degree of the key it ends in. By the time the fourth chord arrives it has already done its work, and the passage does not go back to it.

### The Neapolitan and Augmented Sixths

https://musictheory.center/course/advanced-harmony#the-neapolitan-and-augmented-sixths

> Play the first two. Five chords each, in C minor, and exactly one note anywhere differs between them: in the second clip a single note of the middle chord has been lowered by a half step. Play them back to back until you can name it. Then play the third: three chords you have not heard before, each one followed by the same arrival. Listen to the lowest note and the highest note of each of those three, and to what those two do the moment the arrival comes.

**Plays:** Five chords in C minor (C3 C4 Eb4 G4 F3 F4 Ab4 Ab3 D4 G3 B3) · The same five with one note lowered (C3 C4 Eb4 G4 F3 F4 Ab4 Ab3 Db4 G3 B3 D4) · Three chords, each pulling at the same place (Ab3 C4 F#4 G3 B3 D4 G4 Eb4)

The outer two notes of the third of the three unfamiliar chords in the third clip — the description is true of all three — and where they go. In the first bar, an A flat below middle C and an F sharp above it: ten half steps apart, written as a sixth because of the letters and sounding exactly like a seventh. In the second bar the lower note has fallen a half step and the upper has risen a half step, and both have landed on a G — the same letter, twelve half steps apart. A sixth has opened into an octave, and neither note travelled further than the smallest distance in the system. The table gives the three chords that are built around that interval and says what each one adds.

- **The Neapolitan chord is a major triad on the lowered second degree** — In C minor that is [D♭](https://musictheory.center/chord/dflat-maj) — the notes D♭4, F3 and A♭3 — and it is nearly always played with F3 at the bottom, which is what the 6 in its two labels records.
- **An augmented sixth is a sixth widened by a half step** — A♭3 up to F4 is a major sixth, nine half steps. Raise the upper note to F♯4 and the letters still say sixth while the distance is ten — the same distance as a minor seventh, spelled differently to record where the two notes are going.

| Chord | Scale degrees | Notes in C minor | What distinguishes it |
| --- | --- | --- | --- |
| Italian sixth | Lowered sixth, first, raised fourth | A♭3, C4, F♯4 | Three notes only, and the leanest of the three: nothing in it but the augmented sixth and the note between them |
| French sixth | Lowered sixth, first, second, raised fourth | A♭3, C4, D4, F♯4 | Adds the second degree, which puts a whole step inside the chord and makes it the most astringent of the three |
| German sixth | Lowered sixth, first, lowered third, raised fourth | A♭3, C4, E♭4, F♯4 | Adds the lowered third degree. It is the richest and by far the commonest, and its four notes are the same four a dominant seventh on the lowered sixth degree would contain |

**Neapolitan chord**

*also called*: Neapolitan sixth (classical analysis, for the first-inversion form the chord nearly always takes; written N6 or ♭II6)

**Definition.** The Neapolitan chord is a [major triad](https://musictheory.center/course/chords#the-four-triads) built on the lowered second degree of a key — D♭ major in C minor — used as a [predominant](https://musictheory.center/course/diatonic-harmony#harmonic-function) and played, almost without exception, with its third in the bass.

What it is doing there becomes obvious the moment you compare the two clips above. The ordinary predominant in a minor key is the diminished chord on the second degree, and putting its third in the bass gives you F, A♭ and D. Lower the D a half step to D♭ and the chord becomes a plain major triad, the bass note has not moved, and you have gained a note that sits a half step *above* the tonic, where the key’s own second degree sits a whole step above it. That half step above the tonic is the [Phrygian](https://musictheory.center/course/modes#the-seven-modes) colour, and it is the whole reason the chord sounds the way it does: grave, a little archaic, and very much darker than the chord it replaced.

**Augmented sixth chords** attack the same job from the other side. There are three of them and they share three properties: all are predominants, all resolve to the dominant, and all contain the interval they are named after — the lowered sixth degree at the bottom and the raised fourth degree at the top, ten half steps apart and spelled as a sixth. That spelling is not pedantry. The lower note is going down a half step and the upper is going up a half step, and when they arrive they are an octave apart on the root of the dominant. A sixth expanding to an octave is what the notation describes; a seventh contracting to a fifth would be something else entirely.

The three differ only in what is put between those two outer notes. The Italian adds nothing but the tonic; the French adds the second degree as well; the German adds the lowered third degree, which makes its four notes identical to a dominant seventh built on the lowered sixth degree. That identity is not a coincidence a reader should file away — it is a door. The same four pitches can be spelled one way and resolved outward to the dominant, or spelled the other way and resolved down a half step like any dominant seventh, and a composer who spells them one way and resolves them the other has changed key in a single chord.

**Good to know**

- (Fact) The augmented sixth expands by half steps to an octave. A♭3 and F♯4 are ten half steps apart; the lower falls a half step to G3, the upper rises a half step to G4, and the two arrive twelve half steps apart on the same letter. Both notes travel the smallest distance the system contains, in opposite directions, which is what the sixth spelling records.
- (Convention) The national names mean nothing. Italian, French and German sixths are not Italian, French or German in origin or in use; the labels were attached by nineteenth-century English-language writers and survived because they are short. Other traditions number them instead — It+6, Fr+6, Ger+6, or a figured-bass number after a plus sign — and a good deal of modern teaching drops the names, calls all three augmented sixth chords, and lists the notes.
- (Constraint — common-practice classical writing from roughly Corelli to Wagner, which is where both chords were codified and where the exercises that teach them are set. Later practice takes the same pitch collections and does what it likes with them: a German sixth is spelled and used as a dominant seventh a half step above its target throughout jazz, where it is called the tritone substitute and resolves downward rather than outward) An augmented sixth chord resolves to the dominant, and the two notes forming the sixth resolve outward by half step to an octave on the dominant’s root. The Neapolitan is under the same obligation: it goes to the dominant, sometimes by way of the tonic chord with the dominant already in the bass, and it does not go home directly.

**You already know this**

- Interval quality from Chapter 5 — the rule that the letters decide the number and only then does the distance decide the quality — which is why A♭3 up to F♯4 is an augmented sixth and not the minor seventh it sounds like — https://musictheory.center/course/intervals#number-and-quality
- Minor-key harmony from Chapter 11 — the raised seventh degree that gives a minor key a major dominant to cadence on — which is the chord both of this section’s devices are built to push at — https://musictheory.center/course/diatonic-harmony#harmony-in-minor

**Where this goes**

- The German sixth read as a dominant seventh a half step above its target is the tritone substitute, one of the first reharmonisation moves any jazz musician learns, and the enharmonic trick in this section is exactly where it comes from — https://musictheory.center/course/contemporary

**In real music**

- Ludwig van Beethoven — “Piano Sonata No. 14 in C♯ minor, first movement” — near the end of the movement the harmony lands on a major chord built a half step above the home note and sits on it before the final cadence — the Neapolitan, in the most cited place it appears

**Try it on your instrument:** On your instrument, play A♭ below middle C, the C above it, and the F♯ above that, all together. Hold them and listen to the outer two. Now move the A♭ down a half step and the F♯ up a half step, keeping the C where it is, and play the result: say out loud what the outer two notes have become. Then do the same starting from A♭, C, E♭ and F♯. Finally play F, A♭ and D together, lower the D a half step, and play that into the chord on G.

**Check:** Two chords. Listen to the lowest note and the highest note of the first one, and to where each of them goes when the second chord arrives.

- The lowest note fell a half step and the highest rose a half step **(correct)** — Correct. The outer notes of the first chord were an A♭ below middle C and the F♯ above it; in the second chord they are a G and the G an octave above it. The lower fell a half step and the upper rose a half step, so ten half steps became twelve. All three of the chords in the third clip at the top of this section do exactly this, and it is what the interval is named for.
- The two notes moved towards each other — Towards each other is what the two notes of a dominant seventh do: in the D7 of the second section of this chapter the F♯ rises to a G and the C above it falls to a B, so the gap between them narrows from six half steps to four — a major third. Here the gap widened instead, from a sixth to an octave, which is the opposite motion and the reason this chord has a separate name.
- Both notes moved in the same direction by the same distance — Two notes moving the same way by the same distance keep the gap between them fixed, so the second chord would have been exactly as wide at its edges as the first. Play the pair again and compare the widths: the second chord is noticeably the wider of the two, because one note went down while the other went up.
- Neither of the two outer notes moved — Neither outer note stayed, and nor did anything else. The chord that arrives has the same letter top and bottom — a G in both places — and not one of its four notes was in the chord before it. The A♭ fell and the F♯ rose, and the C and the E♭ between them both stepped down a half step as well.

### Harmonic Analysis

https://musictheory.center/course/advanced-harmony#harmonic-analysis

> Play both. Eight chords each, one to a bar, in the same key at the same speed, and six of the eight are identical between the two. The other two are the point: in the first clip they each contain a note the key does not supply, and the two do different jobs. One of them pushes hard at the chord after it; the other darkens the chord it stands in place of. Play the pair twice and see whether you can hear which does which before you read anything below.

**Plays:** Eight chords, one to a bar (C3 C4 E4 G4 A2 A4 D3 F#4 C5 G2 B3 D4 F2 Ab3 F4) · The same eight, nothing from outside (C3 C4 E4 G4 A2 A4 D3 A3 D4 F4 G2 B3 F2)

There is nothing to draw here, because the object of this section is a procedure rather than a sound. The table is that procedure. It is written in the order it has to be done in: the key first, because every label after it is relative to the key; then the chords the key itself supplies, because they are free; then the notes left over, which is a much shorter list than it looks; then one decision per leftover note; and the cadences last, because a cadence is what tells you whether a chromatic passage was a visit or a move. Run it on the first clip above and it takes about a minute.

| Step | What you do | What it leaves you with |
| --- | --- | --- |
| 1. Find the key | Read the key signature, then look at the first chord, the last chord and the bass note under the strongest ending. A key signature names two keys, a major one and its relative minor, and only the music decides which of the two is in force | A tonic, which every label after this is measured against |
| 2. Number what is diatonic | Put a roman numeral under every chord built only from notes the key supplies: upper case for major, lower case for minor, a small circle for diminished, a number for any note added above the triad | A skeleton with gaps in it, and usually fewer gaps than you expected |
| 3. List what is left over | For each chord you could not number, write down which of its notes the key does not supply. Almost always this is one note, occasionally two | A very short list of accidentals, each attached to a chord |
| 4. Decide which door each one came through | A raised note sitting a half step below the root of the next chord means a dominant aimed at that chord. A lowered note matching what the parallel minor would supply means a chord borrowed from it. Several in a row, ending in a cadence somewhere else, mean the key itself has changed | A numeral for every chord in the passage, with no gaps left |
| 5. Mark the cadences | Find where the phrases end and name each ending: dominant to tonic, dominant stopped on, dominant to the sixth-degree chord, fourth-degree chord to tonic | The punctuation, which is what turns a list of chords into a reading of the music |

**harmonic analysis**

*also called*: roman numeral analysis (classroom teaching, where the activity is named after the notation it is written down in)

**Definition.** Harmonic analysis is the practice of reading a passage as a sequence of chords in a [key](https://musictheory.center/course/keys-and-key-signatures#what-a-key-is): naming each chord by its position in that key, accounting for every note the key does not supply, and marking where the phrases end.

The order in the table is not arbitrary, and getting it wrong is the commonest way for an analysis to go astray. Every numeral is relative to a key, so the key has to be settled first — and it is settled by the endings, not by the opening, because a piece can begin anywhere and can only finish somewhere convincing. Once the key is fixed, the diatonic chords label themselves and take no thought at all. What is left is a handful of chords with one foreign note each, and that is where the work is.

For each of those the question is the one this whole chapter has been answering, and it has three ordinary answers. **Is the foreign note raised, and does it sit a half step below the root or the third of the chord that follows?** Then the chord is a dominant aimed at that chord. **Is the foreign note lowered, and is it what the parallel minor would have supplied?** Then the chord is borrowed. **Are there several in a row, and does the passage cadence somewhere other than where it started?** Then the key has changed, and everything after the pivot should be renumbered. The first clip above contains one of the first kind in its third bar and one of the second kind in its sixth.

One caution is worth more than any amount of technique. An analysis is a reading, not a measurement: two competent analysts will disagree about where a pivot falls, about whether a passage modulated or only visited, and about whether a chord is a genuine harmony or three notes that happen to coincide on the way between two others. The test of a reading is not whether it is correct but whether it accounts for what you hear. A numeral that explains nothing is worth less than an honest question mark.

**Good to know**

- (Convention) [Roman numerals](https://musictheory.center/course/diatonic-harmony#roman-numerals) describe position and [chord symbols](https://musictheory.center/course/chords#reading-chord-symbols) describe content, and the two answer different questions. V7 means "the dominant seventh of this key" — true of [G7](https://musictheory.center/chord/g-7) in C major and of [D7](https://musictheory.center/chord/d-7) in G major. G7 means "G, B, D and F", true wherever it appears and in no key in particular. An analysis of anything chromatic usually needs both, because the numeral says what the chord is doing and the symbol says what it is.
- (Convention) More than one analytical system exists and they are not rivals. Roman numerals give function inside a key. Lead-sheet symbols give exact content and are what a player actually reads. Schenkerian analysis discards most of the chords and asks which few of them carry the structure of a whole movement. The same passage can be described by all three at once, and choosing between them is choosing what you want to find out.
- (Tendency — common-practice classical music and the popular song descended from it, where the three categories of this chapter cover the great majority of chromatic chords. Post-tonal music, modal jazz and loop-based production regularly produce chords that none of the three explains, and forcing a numeral on to those explains nothing at all) When a chord will not fit the key, its foreign note resolves by a half step, and the direction it moves names the door it came through: a raised note rises into the chord after it and you are looking at a dominant aimed somewhere, while a lowered note falls and you are usually looking at something borrowed. Checking the direction takes a second and settles most cases before any numeral is written.

**You already know this**

- Roman numerals from Chapter 11 — upper case for major, lower case for minor, a number for an added note — which is the notation an analysis is written in and which this chapter has been extending rather than replacing — https://musictheory.center/course/diatonic-harmony#roman-numerals
- Non-chord tones from Chapter 12 — notes that belong to no chord and are merely passing between two that do — which have to be set aside before step 2, because mistaking one for a chord member invents chromatic harmony that is not there — https://musictheory.center/course/voice-leading#non-chord-tones

**Where this goes**

- Chord-scale theory asks a different question of the same chords — not what each one is doing in the key, but which scale a player should improvise over it — and it takes the numerals produced here as its input — https://musictheory.center/course/contemporary
- Analysing a whole song from a recording is this procedure run at length, and it is the one skill that turns everything in the course into something you can use on music you did not write — https://musictheory.center/course/applications

**In real music**

- J. S. Bach — “Prelude in C major, BWV 846” — every bar is a single chord broken into an arpeggio and nothing else, so the piece is an analysis exercise printed out: name the chord of each bar and the entire harmonic scheme is in front of you
- Joseph Kosma — “Autumn Leaves” — the first eight bars run a [two-five-one](https://musictheory.center/progression/ii-v-i) into one key and then the same three-chord figure into another; hearing exactly where the second one takes over is the whole of step 4

**Lesson:** https://musictheory.center/lessons/negative-harmony

**Try it on your instrument:** Take eight bars of a song you can already play and write the five steps out on paper: the key, a roman numeral under every chord the key supplies, the foreign note under every chord it does not, a decision for each of those notes, and a name for the ending. Then play the eight bars and check the reading against what you hear. Where the reading and your ear disagree, trust your ear and look again.

[Find the key of your eight bars and read every chord as a numeral](https://musictheory.center/tools/key-finder?c=C+A7+Dm+G7+C)

**Check:** Eight chords, one to a bar. One of them is a minor chord standing where the key supplies a major one. Which bar was it in?

- The sixth bar **(correct)** — Correct. Bar six sounded F2, A♭3, C4 and F4 — an F minor chord, where C major supplies F, A and C. The A♭ is the foreign note, it is lowered rather than raised, and lowering it is the commonest single borrowing in popular music. Bars five and eight are both the home chord, which makes the darkening easy to place once you know to listen for it.
- The second bar — Bar two was a minor chord, and it is the tempting answer — but A, C and E are all notes of C major, so it is simply the ordinary chord on the sixth degree and nothing has been borrowed. The question is never whether a chord is minor; it is whether the key supplies its notes.
- The third bar — Bar three did contain a note from outside the key, the F♯ of a D7 — but that chord is major with a seventh added, not minor, and its foreign note is raised rather than lowered. It is the other kind of chromatic chord in this passage, and it pushes forward into bar four instead of darkening bar three.
- The seventh bar — Bar seven was G2, B3, D4 and F4: a dominant seventh, major with a note added on top, and every one of those notes is in C major. It is the chord that closes the passage on to the last bar, and there is nothing borrowed about it at all.

### Key Takeaways

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

- A chromatic chord is one containing at least one note the key does not supply, and a passage can use several of them without ever leaving the key.
- There are three ordinary doors out of a key: a dominant aimed at a chord other than the tonic, a chord borrowed from the parallel key, and a modulation to a new key altogether.
- A secondary dominant is a dominant seventh built a fifth above a chord of the key other than the tonic, written V of that chord, and a major key offers five usable ones.
- The pull of any dominant seventh comes from the tritone inside it, whose two notes each lie a half step from a note of the chord it points at, which is why the shape can be aimed anywhere.
- A borrowed chord comes from the key of the same name and the opposite quality, so the tonic never moves and the effect is a change of colour rather than of place.
- The altered note of a secondary dominant is raised and rises; the altered note of a borrowed chord is lowered and falls, and that single test settles most chromatic chords at sight.
- Modulation changes the key the whole passage is measured against, and a listener does not accept it until a cadence in the new key confirms it.
- A pivot chord modulation hinges on a chord that belongs to both keys, while a direct modulation simply starts the new key at a phrase boundary with no preparation at all.
- The Neapolitan chord is a major triad on the lowered second degree, normally with its third in the bass, and it leads to the dominant.
- All three augmented sixth chords contain the same interval between the lowered sixth and raised fourth degrees, and it expands outward by half steps to an octave on the dominant.
- Harmonic analysis is a procedure rather than a talent: find the key, number what is diatonic, list what is not, decide which door each chromatic chord came through, and mark the cadences.

### Questions

**What is a secondary dominant?**

A secondary dominant is a [dominant seventh chord](https://musictheory.center/course/chords#seventh-chords) built a fifth above a chord of the key other than the tonic, used to make that chord sound briefly like home. C major offers five: A7 pointing at D minor, B7 at E minor, C7 at F, D7 at G and E7 at A minor.

**What is a borrowed chord?**

A borrowed chord is a chord taken from the [parallel key](https://musictheory.center/course/keys-and-key-signatures#relative-and-parallel) — the one with the same tonic and a different set of notes — used inside a passage that stays in the original key. In a major key the commonest are the minor chord on the fourth degree and the major chords on the lowered sixth and seventh degrees.

**What is the difference between modulation and tonicization?**

Both bring in chords from outside the [key](https://musictheory.center/course/keys-and-key-signatures#what-a-key-is). A tonicization points at one chord for a moment and the music carries on where it was; a modulation changes the key the whole passage is measured against, and is not believed until a [cadence](https://musictheory.center/course/diatonic-harmony#cadences) confirms it. Duration and a cadence separate them, not the chords themselves.

**What is a Neapolitan chord?**

A Neapolitan chord is a [major triad](https://musictheory.center/course/chords#the-four-triads) built on the lowered second degree of a key, which is D♭ major in C minor. It is nearly always played with its third in the bass, which is why it is written N6 or ♭II6, and it functions as a [predominant](https://musictheory.center/course/diatonic-harmony#harmonic-function) leading to the dominant.

**What is an augmented sixth chord?**

An augmented sixth chord is a [predominant](https://musictheory.center/course/diatonic-harmony#harmonic-function) containing an augmented sixth — ten [half steps](https://musictheory.center/course/intervals#half-steps-and-whole-steps), spelled as a sixth — between the lowered sixth degree and the raised fourth. Those two notes expand outward by half step to an octave on the dominant. Three forms exist, called Italian, French and German, differing only in what sits between them.

**How do you analyse a chromatic chord?**

Find the [key](https://musictheory.center/course/keys-and-key-signatures#what-a-key-is) first, [number every chord the key supplies](https://musictheory.center/tools/chord-transposer), then list the notes it does not. A raised note a half step below the next chord’s root means a dominant aimed at that chord; a lowered note matching the parallel minor means a borrowed chord; several in a row ending in a new [cadence](https://musictheory.center/course/diatonic-harmony#cadences) mean the key has changed.

### Other languages

- https://musictheory.center/course/advanced-harmony/llms.txt
- https://musictheory.center/fr/cours/harmonie-avancee/llms.txt
- https://musictheory.center/es/curso/armonia-avanzada/llms.txt