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Chromatic Harmony

An oil painting showing a scene from a rowing competition on a river. In the foreground, two men are in an long rowboat, having just manuevered around a stake planted in the riverbed. The two men are wearing dark blue bandanas on their heads, the colors of which match the flag atop the stake. In the middleground, another team of rowers, wearing bright red bandanas, are approaching their stake. In the background, a large riverboat and smaller ship are anchored near a wooded shore under a cloud-filled sky, densely populated with spectators. Other than the bandanas and flags, the colors of the painting are all grays, greens and browns.

The Biglin Brothers Turning the Stake, an oil painting by American painter Thomas Eakins. Like chromatic notes in an otherwise diatonic tonality, the rich blues and reds of the bandanas and flags provide a notable juxtaposition to the muted earthtones of the rest of the painting.

(The Cleveland Museum of Art | Public Domain)

When music is written using a particular scale or key, the notes in that scale will be used much more often than other notes. When notes outside of the scale are used, they bring a certain sound and interest to the music, much like a swatch of rich color in a painting which primarily uses muted hues.

Diatonicism and Chromaticism

In tonal music, notes that are drawn from the current key are considered diatonic, and other notes are considered chromatic. In general, when a key signature is being used, chromatic notes can be identified by the use of an accidental.

A short melody in E flat major which includes a B natural. — Figure 1: In this melody, all the notes are diatonic except for the B natural, which requires an accidental.

However, there are some exceptions to this rule. For example, in a minor key, the raised leading-tone is considered a diatonic note, even though it is traditionally indicated with an accidental. Similarly, music written in a mode might use accidentals for notes that deviate from the nearest major or minor key.

A short melody in G mixolydian which uses a key signature of one sharp and an accidental to show F natural. — Figure 2: The F natural in this melody is chromatic to the key of G major, but is diatonic in the key of G mixolydian.

Similarly, chords which use only the notes in the current key are diatonic. The most commonly used diatonic chords are shown in Figure 3.

A list of all the diatonic triads, diatonic seventh chords and extended harmonies, illustrated in both C major and A minor. — Figure 3: The most commonly used diatonic chords, shown in C major and in A minor.

If a chord contains at least one note that is not in the key, we consider it to be a chromatic chord. Most chromatic chords in the Common Practice Period can be grouped into three categories: borrowed chords, secondary dominants, and augmented sixth chords.

Borrowed Chords

Borrowed chords are chords which are drawn from a parallel mode. The most common examples of borrowed chords are chords in a major key which are drawn from the parallel minor.

The supertonic triad, supertonic half-diminished seventh chord, mediant triad, subdominant triad, submediant triad and leading-tone fully diminished seventh chord shown in basic form in C minor, and the supertonic diminished triad, supertonic half-diminished seventh chord, major mediant triad built on E flat, minor subdominant triad, major submediant triad built on A flat and leading-tone fully diminished seventh chord shown in basic form in C major, with the necessary accidentals. — Figure 4: Diatonic chords in C minor are used in C major as borrowed chords.

Two of these chords, bIII and bVI, are built on roots that are not in the key signature. These are sometimes called altered root chords, and are written with an accidental to the left of the roman numeral to show the alteration.

Borrowed chords can typically be used anywhere their diatonic counterparts would fit. For example, in the verse of Hallelujah, Leonard Cohen moves from the I chord to the diatonic vi chord and back.

Measures two and three of Leonard Cohen’s `Hallelujah,`` with the lyrics `Now I've heard there was a secret chord that David played and it pleased the Lord.` Harmonic analysis in C major shows a tonic chord on beat one of each 4/4 measure, and a submediant chord on beat three of each measure. — Figure 5: Measures 2-3 of Hallelujah by Canadian songwriter Leonard Cohen.

In Horn of Plenty from the soundtrack of The Hunger Games, James Newton Howard uses this same progression but substitutes the bVI chord, giving the piece an anthemic aura.

Measures one and two of a piano reduction of James Newton Howard’s "Horn of Plenty." Harmonic analysis in B major shows a tonic chord on beats one and three of each 3/2 measure, and a lowered submediant (flat six) chord on beat two of each measure. — Figure 6: Measures 1-2 of Horn of Plenty by American composer James Newton Howard.

The Neapolitan Chord

Another frequently used altered root chord is a major triad on the lowered supertonic. While this could be analyzed as bII, it is commonly called the Neapolitan chord, and is notated with the symbol N. Like its diatonic counterpart, ii, the Neapolitan chord is frequently used before a dominant chord.

Measures seventeen through twenty of a piano reduction of `Our Lips Are Sealed` by The Go-Go's, encompassing the phrase `Doesn’t matter anyway in the jealous games people play, hey.` Harmonic analysis in D flat major shows one chord on each downbeat: E major as the lowered submediant (flat six) triad, D flat major as the subdominant triad, A major as the Neapolitan triad, and E flat major as the dominant triad. — Figure 7: Measures 17-20 of Our Lips Our Sealed by American pop/rock group The Go-Go's. Enharmonic respellings are used to simplify the lead sheet; in Ab, bVI is built on Fb and the Neapolitan chord is built on Bbb.

Though it has a similar sound due to use of lowered scale degrees, the Neapolitan chord is not generally considered a borrowed chord because the b2 scale degree is not present in minor. Thus is it commonly found in both major and minor contexts.

In music of the Baroque, Classical and Romantic eras, the Neapolitan chord was almost always used in first inversion.

Measures nineteen through twenty-three of `Ferne` by Fanny Mendelssohn Hensel. The piece is in G minor, and in this excerpt the lyrics `warum ertodtest mich?` are accompanied in the piano with the following chords: a tonic triad in first inversion, a Neapolitan chord in first inversion, a dominant seventh of four in second inversion, a subdominant triad in first inversion, and a dominant seventh. — Figure 8: Measures 19-23 of Ferne, Op. 9, No. 2, by German composer Fanny Mendelssohn Hensel. In this excerpt, the Neapolitan chord is used in first inversion. (The following chord, V43/iv, is a secondary dominant chord, discussed below.)

Secondary Dominants

Composers will often tonicize chords by approaching them with a dominant function chord — a V or viio — from the key where the targeted chord would serve as tonic. For example, in C major, the ii chord — a D minor triad — can be preceded by an A major triad, the chord that serves as V in the key of D.

These chords, called secondary dominants, tonicizations, or applied chords, are labeled using two roman numerals separated by a slash. The first roman numeral shows how the chord would be analyzed in the related key. The second roman numeral shows how that key relates to the current key.

Thus, in the key of C major, an A major triad would be called V/ii (spoken as "five of two"), since A major is V of D, and D is ii in the key of C major.

An A major in two different context. Shown in the key of D major, the A major is analyzed as a dominant chord. Shown in C major, the same chord requires an accidental — C sharp — and is analyzed as the dominant of two. — Figure 9: When in the context of D major, the A major chord is analyzed as V. In the context of C major, the same chord requires an accidental and is analyzed as V/ii — the dominant triad of D, which is the second scale degree in C major.

Secondary dominants usually resolve to the chord following the slash, or in other words, the diatonic chord that would be tonic in the related key.

Figure 10: Measures 13-16 of Umbrella by Barbadian singer Rihanna, illustrating a secondary dominant resolving to the submediant.

Any type of dominant function chord — V, V7, viio, viiø7, and viio7 — can be used. They may tonicize any diatonic chord except the leading-tone (which is too unstable to tonicize).

Melody and chords of measures seven and eight of the main theme from Super Mario Sixty-Four by Koji Kondo. The piece is in C major and four-four time, and the chords, which change every two beats, are a tonic triad, followed by a dominant seventh of four in first inversion, followed by a subdominant triad, and finally a leading-tone triad of five. — Figure 11: Measures 7-8 of the main theme from Super Mario 64, by Koji Kondo.

It is possible to even tonicize altered roots, as in a V/bVI or a V/N.

Augmented Sixth Chords

Augmented Sixth chords are created when an octave interval comprised of two 5s (usually in a I64 or V chord) is approached by half-steps in contrary motion.

An interval containing A flat four and F sharp five, resolving out to an octave of G four and G five. The first interval is analyzed as an augmented sixth and the second as a perfect octave. — Figure 12: The interval which resolves outward by half-steps to an octave is an augmented sixth.

Adding 1 to this interval results in the Italian augmented sixth. From there, 2 can be added to create the French augmented sixth, or b3 can be used to build the German augmented sixth.

The three augmented sixth chords in basic position. The Italian augmented sixth, built with A flat four, C five, and F sharp five, analyzed with the symbol I T. The French augmented sixth, built with A flat four, C five, D five, and F sharp five, analyzed with the symbol F R. The German augmented sixth, built with A flat four, C five, E flat five, and F sharp five, analyzed with the symbol G E R. — Figure 13: The three augmented sixth chords.

Because of the augmented sixth interval, which inverts to a diminished third, these chords do not fit into tertial harmony. As a result, they are not considered to have a root, and are not analyzed for position or inversion.

Augmented sixth chords are not often found popular music; they are most commonly associated with the Classical and Romantic eras.

Measures thirty through thirty-three of the third movement of Beethoven’s Sonata Opus thirteen, commonly known as Sonata Pathetique. This passage is in e flat minor, and the chord progression is as follows: in measure thirty, a tonic first inversion triad on beat one and a dominant seventh in first inversion on beat three. In measure thirty one, a tonic triad on beat one and a dominant triad on beat three. Measure thirty-two is an Italian augmented sixth, which includes a suspension on B flat which moves to the chord tone of A natural. In Measure thirty-three, a dominant triad on beat two (after only B flat two and B flat five on beat one) and a cadential six-four chord on beat three. — Figure 14: Measures 30–33 of the third movement of Sonata, Op. 13 Pathétique by German composer Ludwig van Beethoven.

Enharmonic Modulation

Chromatic chords can be used to create common chord modulations which allow access to harmonically distant keys.

Measures forty-five through forty-eight of a piano reduction of Romance in G for Violin and Orchestra, Opus 39 by Samuel Coleridge-Taylor. The excerpt begins in B major. In measure forty-five, beat one has a fully diminished leading-tone seventh in third inversion on beat one and a tonic triad in second inversion on beat three. In measure forty-six, beat one has a fully diminished leading-tone seventh in second inversion on beat one, and on beat three a tonic triad in first inversion becomes the Neapolitan chord in first inversion in B flat major. Measure forty-seven changes to a key signature of B flat major, and has a tonic triad in second inversion for the whole measure. In measure forty-eight has a dominant triad of five on beat one, a dominant triad on beat two, and a tonic triad on beat three. — Figure 15: Measures 45–48 of Romance in G for Violin and Orchestra, Op. 39 by English composer Samuel Coleridge-Taylor.

In common chord modulations, the chord type does not change; in Figure 15, for example, the pivot chord's role in the key changes but it is a major triad in both keys. Enharmonic modulations occur when the pivot chord's type or inversion changes as a result of enharmonic respelling.

One example of this is uses the fully diminished seventh chord, which divides the octave into four equally-spaced intervals. This allows any note in the chord to be interpreted as the root.

Another type of enharmonic modulation takes advantage of the fact that the German augmented sixth chord can be respelled as a dominant seventh chord.

In either case, to modulate, a composer can reassign the root of the chord in order to shift toward a new key center. In his Nocturne, Op. 9, No. 1, Frédéric Chopin uses both types of enharmonic modulation in the space of three measures to move from Db major to D major and back.