Chromatic chords

A piece in C major can pass through an F sharp, an A flat, a D flat, and still be in C major. Those notes from outside the scale arrive inside chords, and many of those chords have a name, a function and a set destination. Secondary dominants are the best-known case. This topic is about the others.

What they share is motion by semitone. A chromatic note is almost always a note that wants to go to its neighbour, and the chord that holds it exists to take it there.

The secondary leading-tone chord

Just as a secondary dominant prepares a degree other than the tonic, so does the chord built on that degree's leading tone. Any chord except the tonic can be preceded by a triad or seventh chord built on its leading tone (Blatter 2007, part 3, art. 10).

In C major the leading tone of G, the dominant, is F sharp. The diminished seventh chord on F sharp leads to the dominant:

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F sharp rises to G, E flat falls to D, and the other voices move by step. If the leading-tone chord is a triad it will be diminished; if it is a seventh chord it may be half-diminished or fully diminished. In analysis it is named after the degree it points to, like a secondary dominant: vii°7 of V (Blatter 2007, part 3, art. 10).

The secondary supertonic

The supertonic usually leads to the dominant. The secondary supertonic does the same one level up: it does not lead to the temporary tonic but to its dominant. In practice it prepares a secondary dominant (Blatter 2007, part 3, art. 10). In C major, A minor can act as the supertonic of G and come before D seventh, the dominant of G:

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Taken from a major key, the secondary supertonic is a minor triad or a minor seventh chord; taken from a minor key, a diminished triad or a half-diminished seventh (Blatter 2007, part 3, art. 10).

The passing augmented triad

The augmented triad is the least used of the four. One common role for it is as an altered tonic in a major key, between the tonic and the subdominant (Blatter 2007, part 3, art. 11). The fifth rises a semitone and keeps rising:

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G, G sharp, A: the tonic's fifth becomes a chromatic passing note to the third of the fourth degree. Since tonic to subdominant is the same relationship as dominant to tonic, the same shape works from V to I, with the augmented triad on the dominant in between (Blatter 2007, part 3, art. 11).

The Neapolitan sixth

The Neapolitan sixth is a major triad built on the lowered second degree. In C its root is D flat, its third F and its fifth A flat (Blatter 2007, part 3, art. 11). Since A flat is the sixth degree of the minor scale, the chord probably arose in the minor mode, but it is found equally in both (Blatter 2007, part 3, art. 11).

It resolves, directly or eventually, to the dominant. The most characteristic path is for the root, D flat, to fall to the leading tone, B, by a diminished third (Blatter 2007, part 3, art. 11). In C minor:

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The name "sixth" comes from its traditional form being the first inversion, with the third, F, in the bass. For over two centuries composers have also used it in root position and second inversion, and the name has stuck (Blatter 2007, part 3, art. 11).

The lowered second degree has another name too, the Phrygian second. In the Phrygian mode the minor second between the final and the note above it does, coming down, the job the leading tone does going up in the major and minor scales (Blatter 2007, part 3, art. 11).

The augmented sixth chords

In the minor mode, the fourth degree in first inversion often moves to the dominant. To smooth the way, composers took to raising the root of the fourth degree. The raised note forms an augmented sixth with the bass, and the chord became so attractive that it ended up replacing the original, first in minor and later in major too (Blatter 2007, part 3, art. 11).

With added notes, the chord came in three versions, which resolve to the dominant (Blatter 2007, part 3, art. 11):

Name	Notes in C	Resolves to
Italian sixth	A flat, C, F sharp	V
French sixth	A flat, C, D, F sharp	V
German sixth	A flat, C, E flat, F sharp	V

All three share the same hallmark: the augmented sixth, A flat to F sharp, opens outwards to the octave, and that octave is G, the root of the next chord and the dominant of the key (Blatter 2007, part 3, art. 11). The Italian and French sixths, in C major:

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It is the same gesture the altered chords topic showed through the inverted diminished third: two notes moving apart by semitone towards the same note.

On the keyboard the German sixth sounds exactly like a dominant seventh: A flat, C, E flat, F sharp is the sound of A flat seventh. That is why it serves as a modulation formula, treated as the dominant of another key (Blatter 2007, part 3, art. 11). And going straight to the dominant it produces parallel fifths between the bass and the E flat, which is why it often passes first through the tonic in second inversion.

The augmented six, doubly augmented four

The German sixth has a close relative. In C major the E flat is spelled D sharp: A flat, C, D sharp, F sharp. The sound is the same, but the destination changes. This chord does not go to the dominant; it goes to the major tonic in second inversion (Blatter 2007, part 3, art. 11):

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D sharp rises to E, F sharp to G, A flat falls to G. The augmented sixth still opens to the octave on G, but G is now the bass of the tonic six-four, which then moves on to the dominant.

Names without a homeland

Blatter is keen to say that the names of these chords have no logical justification. The Neapolitan sixth has nothing to do with Naples, and the Italian, French and German sixths are not associated with composers from those countries. The terminology seems to be largely an American phenomenon, and most European languages do not use these names at all (Blatter 2007, part 3, art. 11).

He offers a few memory aids: the French sixth holds notes of a whole-tone scale, associated with the French impressionists; the German sixth sounds like a dominant seventh; the Italian sixth has only three different notes (Blatter 2007, part 3, art. 11).

What comes next

Chromatic chords are the edge of traditional functional harmony: chords full of outside notes, and still with a clear destination. From here the next step is modulation, where the harmony changes its tonic for good.