Chromatic Harmony

A chromatic chord is a chord containing at least one note the key does not supply — one of the five pitches the key signature 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.

A secondary dominant is a dominant seventh chord — or the major triad inside one — built a fifth above a chord of the key other than the tonic, and used to make that chord sound, for a moment, like home. (also called applied dominant, much North American theory teaching, where the chord is described as applied to its target)

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.

A borrowed chord is a chord taken from the parallel key or mode — 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. (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)

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♭4Play and A♭4Play in the first, B♭4Play 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.

Modulation is a change of key 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. (also called key change, ordinary speech and most popular-music writing)

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, 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. 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.

The Neapolitan chord is a major triad built on the lowered second degree of a key — D♭ major in C minor — used as a predominant and played, almost without exception, with its third in the bass. (also called Neapolitan sixth, classical analysis, for the first-inversion form the chord nearly always takes; written N6 or ♭II6)

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 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.

Harmonic analysis is the practice of reading a passage as a sequence of chords in a key: naming each chord by its position in that key, accounting for every note the key does not supply, and marking where the phrases end. (also called roman numeral analysis, classroom teaching, where the activity is named after the notation it is written down in)

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.