Non-Diatonic Chords

Strict diatonic note and chord selection provides a gigantic amount of possibility for song-writing and solo'ing; however, it still places us inside a box that we occasionally want to escape. Non-diatonic chords allow us to do so. For any key, the possibilities for non-diatonic chords are huge. We limit ourselves to a few popular examples listed below. These fall under one of a few categories.

Tonicizations use diatonic chords from other keys to temporarily alter the tonic center of the harmony.
Borrowed chords use diatonic chords from other keys with the same tonic note.
Chromatic chords cover all remaining cases. They maintain the tonic note but are non-diatonic to all the standard parallel keys/modes. They borrow from the chromatic scale, which allows any possible chord to be formed.

PreReqs

Tonicizations

A Tonicization is the use of a chord to briefly change the tonic note, and thus the harmony used to create and resolve tension. It shifts the gravity from the prior tonic note to the new one, but so briefly that we don't lose the pull of the prior tonic.

Difference from Modulation

The only real difference between a modulation and a tonicization is length. A tonicization may last a single chord or measure, very briefly changing the tonic note, and usually for the purpose of further creating and resolving tension against the original tonic note. A modulation lasts longer (although it may be as brief as about 2 measures) and often creates and resolves tension in the new key numerous times before, if ever, returning to the original key.

Notation

The "/" indicates that the chord is borrowed. The bottom or right side of the slash is the key that is being borrowed from, in relation to the current tonic note. The left or top side of the slash indicates which chord from that scale is being used. V/V means the fifth diatonic major chord of the major key whose root is the fifth diatonic note of the current key.

In the key of C Major, the V/V chord is V/G Major (V of G Major), or D major.

Secondary Dominant

also called borrowed dominant

The most common borrowed chord is the V (or V⁷) of V chord, commonly notated as V/V or V⁷/V. Basically, if we think of the current key's V chord as a I chord, it is the V chord above that. So for the key of C Major, V is G major. In the key of G Major, V is D major. Thus, in the key of C Major, V/V is D major. Notice, the diatonic chord in the key of C Major with a root note of D is actually D minor, making the V/V D major chord a non-diatonic chord. Similarly, in the key of A Harmonic Minor, V is E major, so V/V is B major. The diatonic chord would be B diminished.

Function

It is essentially a dominant function chord whose function is to resolve to the dominant chord of the current key, the same way the V chord normally resolves to I. That chord then resolves to the actual I or i chord. So the entire progression would be V/V - V - I.

The overall effect is to extend the dominant-tonic resolution over a three chord change. It helps create a little extra tension, making the final resolution that much stronger.

Examples

In C Major, the progression would be D - G - C. D is borrowed, as Dm is the diatonic chord. The raised F♯ that makes it a major chord also gives it the dominant function to resolve a half step to G, as part of the G chord.

If the D Major chord did not resolve to G Major, demonstrating its dominant functionality, we might alternatively analyze this as a II or borrowed major from some other key.

In the key of G Major, V/V would be an A Major chord. Let's look at both keys:


	V/V	V	I or i
C Major	D	G	C
G Major	A	D	G
A Harm. Minor	B	E	Am

Notice that both of the first two progressions feature D - G. In G Major, it's V - I. In C Major, it's V/V - V. G Major is built on the fifth note of C Major; it is the V key. In both progressions they contain the same basic dominant-resolution feel, yet by occurring at different parts of the V/V - V - I progression, they serve somewhat different functions. In the first example of C Major, it does not fully resolve to the actual I chord, getting us only halfway there; whereas in G Major, it completes the progression by landing on the true tonic chord.

The A Harmonic Minor example illustrates that the technique works equally well for a minor tonality, when using the harmonic minor variation to get the major V chord.

Other Secondary Harmonies

Another common secondary chord is V/ii (or V⁷/ii). This functions very similarly to V/V - it is a dominant function chord that resolves to the diatonic ii chord from the original key. But rather than proceed directly to the tonic chord from there, it continues along the circle progression to return to tonic:

        V/ii - ii - V - I
C Maj.  A      Dm   G   C
G Maj.  E      Am   D   G

For the key of C Major, V/ii - ii is the same as V - i in the key of D Harmonic Minor.

Borrowed Chords

Chords can also be borrowed from the parallel major/minor of the current key.

Borrowing from Minor

When using a major key, chords can be borrowed from either the parallel natural or harmonic minor keys:

	ii°	♭III	iv	♭VI	♭VII	vii°⁷
C Major	D dim	E♭	Fm	A♭	B♭	B°⁷
G Major	A dim	B♭	Dm	E♭	F♭	F°⁷
Borrowed From	Nat/ Hrm	Nat	Nat/ Hrm	Nat/ Hrm	Nat	Hrm

These are the most often borrowed chords, and they usually resolve to the tonic chord, although the progressions below are also common.

I - ♭VII - ♭VI - ♭VII
I - ♭VII - IV

Picardy Third

A Picardy Third refers to using the I (major) chord instead of i (minor) in a minor key (or mode with a minor tonic chord). As such it briefly borrows the consonance and resolution that the I chord creates, without actually modulating into a major key. It is used in place of the i chord on resolving cadences, not in passing i chords in the middle or beginning of a progression.

Natural Minor:
Am   Dm   Em   A
i    iv   v    I

Harmonic Minor:
Am   Dm   E    A
i    iv   V    I

Chromatic Chords

Chromatic Chords are non-diatonic chords that do not fit into the secondary or borrowed categories mentioned above. While they can take many varieties, the types explained below are the most common (and "musical").

Augmented Sixth Chords

Augmented Sixth Chords are named for the augmented 6th interval they contain. An A6 is enharmonically equivalent to a m7 interval; however, it is spelled as an A6 here for its relation to the surrounding key and its harmonic usage. The A6 occurs between the m6 and A4 notes of the key. The chords take a sub-dominant harmonic function, and when resolving to v or V, the m6 resolves down a half-step while the A4 resolves up a half-step to form an octave of the P5 of the key's tonic note.

If that was confusing hopefully this example helps: In C Major, an augmented sixth chord will feature A♭ and F♯ (the distance from A♭ to F♯ is 11 semitones or an A6 interval). To move to the dominant or V chord (G), A♭ descends to G and F♯ ascends to G, increasing the distance to 13 semitones or 1 octave.

There are 3 variations of the augmented sixth:

Italian Sixth

The Italian 6th (It+6 or It6) features the m6, U, and A4 notes from the current key. In other words, it is comprised of root, M3, and A6. In C Major, it consists of (A♭ C F♯).

R    M3    A6
 -M3-  -tt-
 ----A6----

If the chord contained the P5 of the root, it would be enharmonically equivalent to a dominant 7th chord, built upon the ♭VI note of the scale. Yet it does not function harmonically as such. Its M3 does not function as a leading tone, and it does not resolve to the ♭II chord. Rather the M3 moves down a half-step to become the leading tone for the V chord or up a whole step to be the 5th of the V or v chord. In 4-part writing, the M3 is doubled and each resolves in contrary directions to form the 3rd and 5th of the V chord, while the R and A6 move contrary to both become the root of the V.

   C      AbIt+6 G      C
E--0-------------3------0---
B--1------1------3------1---
G--0------1------0------0---
D--2------4------0------2---
A--3------3------2------3---
E---------4------3----------

French Sixth

The French 6th (Fr+6 or Fr⁴₃) has the same notes as the Italian 6th, plus the M2 note above the key's tonic (m6 U M2 A4). In C Major, that's (A♭ C D F♯).

R    M3    A4    A6
 -M3-  -M2-  -M3-
       ----tt----
 ----A4----
 -------A6-------

All these notes are found in the whole tone scale, giving it a somewhat atonal kind of feel; however, it still retains its sub-dominant harmonic function within the context of a progression.

   C      AbFr+6 G      C
E--0-------------3------0---
B--1------3------3------1---
G--0-------------0------0---
D--2------4------0------2---
A--3------3------2------3---
E---------4------3----------

German Sixth

The German 6th (Gr+6 or Gr⁶₅) similarly takes the Italian and adds a note, but here the note is the m3 above the key's tonic note (m6 U m3 A4). In C Major, that's (A♭ C E♭ F♯).

R    M3    P5    A6
 -M3-  -m3-  -M3-
       ----tt----
 ----P5----
 -------A6-------

The German 6th is enharmonically equivalent to a dominant 7th chord. The difference is its usage, functioning as a sub-dominant for the given key rather than the dominant for the ♭II key. The added P5 here makes for difficult voice leading, often requiring to move it before or to resort to inverting the subsequent dominant chord.

   C      AbGr+6 G      C
E--0------2------3------0---
B--1------1------3------1---
G--0------1------0------0---
D--2------1------0------2---
A--3------3------2------3---
E---------4------3----------

Neapolitan Chord

A Neapolitan Chord is a major chord using the m2 of the scale as its root (♭II). It is typically voiced in first inversion, creating a 6th interval between the bass note (3rd) and high note (root) in its triad formulation. Thus, it is often called the Neapolitan 6th, notated as ♭II⁶ or N⁶.

Harmonically, it functions as a sub-dominant and can be substituted for ii or IV (or iv in a minor key).

In C Major, D♭ is the Neapolitan chord. In first inversion, it is spelled (F A♭ D♭). F is (F A C). Thus, the Neapolitan 6th features the same notes as the IV chord, but the 3rd (A) is lowered a half step, while the 5th (C) is raised a half-step. In C Minor, the iv chord is (F A♭ C), differing from the N⁶ by just 1 half step and lies similarly close to the ii° chord (D F A♭), another sub-dominant functioning chord.

Db 1st Inv. (N6 of C Major/Minor)
||i|-|-|-|
||)|m|-|-|
||i|-|-|-|
||)|-|r|-|
||)|-|-|p|
||i|-|-|-|

C    Db/F    G      C
I    N6      V      I

Bb 1st Inv. (N6 of A Major/Minor)
||i|-|-|-|
||-|-|r|-|
||-|-|m|-|
o|-|-|-|-|
||-|-|-|-|
||-|-|-|-|

Am   Bb/D    Em     Am
i    N6      v      i

Other Uses

The non-inverted Neapolitan chord can easily be used to modulate to a major key a half step below the current key by using the original key's I chord as the destination key's N chord.

    C    F     C    Gb   Cb
C:  I    IV    I
Cb:            N    V    I

If a m7 is added to the N chord, it can serve as a secondary dominant to the original key's ♯IV or ♭V. For example, in C Major, the N chord is (D♭ F A♭). The m7 is C♭ or B. This is the dominant 7th chord of the F♯ or G♭ Major keys.

Chromatic Mediants

As we saw earlier, the mediant chord is a third above the tonic and the submediant is a third below. Depending on the key, this could be a minor or major third.

Chromatic Mediants are non-diatonic mediant or submediant chords for the given key. This is done by using the mediant/submediant of the parallel minor/major key, using the parallel chord (changing the quality of the chord from major to minor or vice versa), or both.

	Mediant				Submediant
	Diatonic	Parallel Key	Parallel Chord	Parallel Key + Chord	Diatonic	Parallel Key	Parallel Chord	Parallel Key + Chord
Major Key	iii	♭III	III	♭iii	vi	♭VI	VI	♭vi
Minor Key	III	♯iii	iii	♯III	VI	♯vi	vi	♯VI
C Major	Em	E♭	E	E♭m	Am	A♭	A	A♭m
A Minor	C	C♯m	Cm	C♯	F	F♯m	Fm	F♯

You may notice that some of these chords could be considered secondary chords for other tonalities (for example VI is enharmonically equivalent to V/ii). However, they are used differently. Most commonly they progress to and from the tonic or as part of a modulation to another key.

The mediant relationship between chords is a quite harmonic one, and it's possible to use any combination of mediant chords in succession. We will lose the tonality of the original key by doing so. This prevents a complete resolution and might fail to produce closure for a progression, but makes for a very interesting journey. For example, let's move in mediants and try to return to our tonic:

I   III  #v    I
C   E    G#m   C (= B#)

E is a parallel chord mediant of C. G♯m is the diatonic mediant of E. B♯ is the parallel chord mediant of G♯. B♯ is also enharmonically equivalent to C, so we have circled back to the original tonic.

Homework

Know what a tonicization is and its harmonic function.
Practice the above examples of tonicizations.
Write your own progressions that make use of tonicizations.
Know what borrowed chords are and how they can be used in terms of harmonic function.
Practice the above examples of borrowed chords.
Write your own progressions that make use of borrowed chords.
Know what an augmented 6th chord is and its harmonic function.
Know the Italian, French, and German variations.
Practice the above examples of augmented 6th chords.
Write your own progressions that make use of augmented 6th chords.
Know what the Neapolitan 6th chord is its harmonic function.
Practice the above examples of Neapolitan 6th chord progressions.
Write your own progressions that make use of the Neapolitan 6th chord.
Know what chromatic mediants are and how they fit into chord progressions.
Practice the above examples of chromatic mediants.
Write your own progressions that make use of chromatic mediants.

Q & A

Related Lessons

Music Theory - Diatonic Chord Progressions

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