8,720
edits
Changes
m
* I - {{f}}VII - {{f}}VI - {{f}}VII * I - {{f}}VII - IV
D{{b}} Db 1st Inv. (N{{6}} N6 of C Major/Minor)
B{{b}} Bb 1st Inv. (N{{6}} N6 of A Major/Minor)
===== Other Uses =====
C{{f}}Cb: N V I
→Secondary Dominant
{{Top-Level Crumbs|1}}
{{Lesson Crumbs|3}}
{{Advanced Lesson Crumbs|3}}
===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.
<small>''also called '''borrowed dominant'''''</small>
The most common borrowed chord is the V (or V7V{{7}}) of V chord, commonly notated as ''V/V'' or ''V7V{{7}}/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====
=== Other Secondary Harmonies ===
Another common secondary chord is V/ii (or V7V{{7}}/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
These are the most often borrowed chords, and they usually resolve to the tonic chord, although the progressions below are also common.
=== Picardy Third ===
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{{b}} C F{{s}}).
If the chord contained the P5 of the root, it would be enharmonically equivalent to a dominant 7th chord, built upon the {{f}}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 {{f}}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 Fr<sup>4</sup><sub>3</sub>) 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{{f}} C D F{{s}}).
R M3 A4 A6
-M3- -M2- -M3-
----tt----
----A4----
All these notes are found in the [[Exotic Scales#Whole Tone|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 Gr<sup>6</sup><sub>5</sub>) 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{{f}} C E{{f}} F{{s}}).
R M3 P5 A6
-M3- -m3- -M3-
----tt----
----P5----
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 {{b}}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 ===
In C Major, D{{b}} is the Neapolitan chord. In first inversion, it is spelled (F A{{f}} D{{f}}). 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{{f}} C), differing from the N{{6}} by just 1 half step and lies similarly close to the ii{{dim}} chord (D F A{{f}}), another sub-dominant functioning chord.
||i|-|-|-|
||)|m|-|-|
||i|-|-|-|
C D{{f}}Db/F G C I N{{6}} N6 V I
||i|-|-|-|
||-|-|r|-|
||-|-|-|-|
Am B{{f}}Bb/D Em Am i N{{6}} N6 v i
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 G{{f}} Gb C{{f}}Cb
C: I IV I
If a m7 is added to the N chord, it can serve as a secondary dominant to the original key's {{s}}IV or {{b}}V. For example, in C Major, the N chord is (D{{f}} F A{{f}}). The m7 is C{{b}} or B. This is the dominant 7th chord of the F{{s}} or G{{b}} Major keys.
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 bvi #v I
C E G#m C (= B#)
== 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 ==