# Tonal Harmony - Chromatic

## borrowed chords

- a few harmonies from the parallel minor or major (with the same tonic)are borrowed
- using the same scale degree
- similar notes, same function

### major borrow minor

Examples
- $\text{ii}^6$ in C (FAD) -> corresponding degree 2 triad in c minor is $\text{ii}^{\circ 6}$ (FbAD)
- ${\text{vii}^{\circ}}_3^4$ has notes FbABD
- [sound](https://en.wikipedia.org/wiki/Borrowed_chord)


[sound](https://www.youtube.com/watch?v=5C2WdcY1EWs&t=73s)

[sound](https://www.youtube.com/watch?v=VSvCQRbJLhQ&t=85s)

- [sound](https://www.youtube.com/watch?v=hgwcde9qiKc)
- $\text{ii}$ in C is DFAC, $\text{ii}^{\varnothing7}$ is DFbAC

the borrowed chord use the same voice leading as if in minor

frequently borrowed

- $♭\text{VI}$: major triad rooted at lowered $\hat{6}$
- $♭\text{III}$: major triad rooted at lowered $\hat{3}$
- $♭\text{VII}$: major triad rooted at lowered $\hat{7}$


borrowed chords using subtonic $\hat{7}$ (leading tone in minor key) is uncommon

### minor borrow major

- modal mixture in minor
- [sound](https://www.youtube.com/watch?v=JbVzn9xz9Pg&t=17s)


- in minor borrowed chord rarely used in isolation
- chords on raised degrees are not considered borrowed

<img src="https://hackmd.io/_uploads/SkInZHjA6.png" width="550"/>


picardy third is considered borrowed

<img src="https://hackmd.io/_uploads/BJZu7Si0T.png" width="500"/>

## Neopolitan 6th

- major chord on lowered $\hat{2}$, called $♭\text{II}$ （major: ↓re-fa-↓la）(minor:↓si-re-fa )
- usually in first inversion $♭\text{II}^6$, also known as $\text{N}^6$
- appears mostly in minor keys in place of $\text{ii}^{\circ 6}$


- **subdominant** (like $\text{ii}^{\circ 6}$)
- leads to dominants

examples

- $♭\text{II}^6-\text{V}$

<img src="https://hackmd.io/_uploads/ryRzLHiRT.png" width="500"/>

- $♭\text{II}^6-\text{V}^7$
- [sound](https://www.youtube.com/watch?v=naalwlNH7Vo&t=11s)

<img src="https://hackmd.io/_uploads/SJRMIHoR6.png" width="600"/>

- $♭\text{II}^6-$ cad.$_4^6-\text{V}^7$
- [sound](https://www.youtube.com/watch?v=0UhnfWzOCMo&t=33s)


- $♭\text{II}^6-\text{vii}^{\circ 7}/\text{V}-\text{V}$ (#D#FAC is the $\text{vii}^{\circ 7}$ in e minor)
- [sound](https://www.youtube.com/watch?v=WXguaYfAxKU&t=32s)

<img src="https://hackmd.io/_uploads/ByyX3HiRT.png" width="550"/>

### voice leading
- in minor, **root** and **fifth** of b$\text{II}$ are tendency tones; do not double the tendency tones (can double the third, which is the **bass** of $\text{N}^6$)
- in minor, lowered $\hat{2}$ move a whole note (**melodic diminished third**) **down** to the **leading tone** $\hat{7}$

<img src="https://hackmd.io/_uploads/H1xhYvo0a.png" width="550"/>

<img src="https://hackmd.io/_uploads/Bkj7hDs06.png" width="400"/>

- [sound](https://www.youtube.com/watch?v=SqbzZEZA_Z8&t=9s)

## Augmented 6th
- major 6th plus semitone (10-semitone interval)
- $\hat{1}-$ lower note interval: minor 6th
- $\hat{1}-$ higher note interval: augmented 4th
- both are tendency tones (in both major and minor)
- major: ↓la - ↑fa
- resolve to $\hat{5}-\hat{5}$ octave (sol-sol)
- minor: fa - ↑re
- resolve to $\hat{5}-\hat{5}$ octave (mi-mi)
- leads to **V**



you might need to use double sharp or double flat

### italian/french/german
- differs by **what's added** in between the lowest and highest notes
- italian: $\hat{1}$ (doubled)
- major: ↓la-do-↑fa
- minor: fa-la-↑re
- french: $\hat{1},\hat{2}$
- major: ↓la-do-re-↑fa
- minor: fa-la-si-↑re
- german: $\hat{1}$, minor $\hat{3}$ (in major is lowered $\hat{3}$, in minor is just $\hat{3}$)
- major: ↓la-do-↓mi-↑fa
- minor: fa-la-do-↑re
- enharmonically equivalent to a dominant seventh chord (both major and minor)
- all notes are a semitone higher than the $\text{V}^7$
- when sol-si-re-fa dominant seventh is replaced as ↓re-fa-↓la-si, which is a dominant seventh with a root that is a tritone apart from the original root, it's called **tritone substitution**
- all notes are a semitone highr than $\text{I}^7$


how to notate

in major keys you may occasionally write $\text{Ger}^{+6}$ in two different ways

### progressions
[more examples](https://musictheory.pugetsound.edu/mt21c/ExamplesWithAugmentedSixthChords.html)

$\text{It}^{+6}/\text{Fr}^{+6}-\text{V}$

$\text{It}^{+6}/\text{Fr}^{+6}-\text{V}_{4-3}^{6-5}$

[$\text{It}^{+6}/\text{Fr}^{+6}-\text{V} \text{ sound in minor}$](https://musescore.com/user/32728834/scores/6221757/embed)


[sound](https://musescore.com/user/27638568/scores/5001870/embed)


[sound](https://www.youtube.com/watch?v=qbmAfCklg5M&t=946)

[sound](https://www.youtube.com/watch?v=WuqE3T-pEW4&t=34s)

$\text{Ger}^{+6}-\text{V}$ is bad because of the parallel 5th; needs cadential $_4^6$
$\text{Ger}^{+6}-\text{V}_{4-3}^{6-5}$
$\text{Ger}^{+6}-\text{V}\underset{\text{4-3}}{\overset{\text{8-7}}{\Tiny{\text{6-5}}}}$


[sound](https://www.youtube.com/watch?v=y0YO31EKGGU&t=239s)

[sound](https://www.youtube.com/watch?v=7a47CkWxjoQ&t=59s)

### preceding chord

any harmony that may precede $\text{V}$

- tonic
- [sound](https://www.youtube.com/watch?v=ANTk-mX-G4Q&t=17s)


- $\text{VI}/\text{IV}^6$
- [sound](https://www.youtube.com/watch?v=kj3ok01A7KU&t=1076s)


[sound](https://www.youtube.com/watch?v=0XKuUW9TaX0&t=5s)

<img src="https://hackmd.io/_uploads/SyUHSni06.png" width="550"/>
### as embellishment of $\text{V}$

[sound](https://www.youtube.com/watch?v=xM-yPjalK5Y&t=365s)


## other altered chords

unlike borrowed chords, use notes that are not found in the parallel major or minor key

### $\text{VI}♯$

major triad formed by submediant triad raising the third (la-#do-mi)


### $\text{III}♯$
major triad with raised third rooted at $\hat{3}$ (mi-#sol-si)

[sound](https://www.youtube.com/watch?v=8QT7ITv9Ecs&t=378s)


[sound](https://www.youtube.com/watch?v=-GCbUSMhO3M&t=33s)

### $\text{V}$ with raised fifth

- $\text{V}^{+}$
- $\text{V}_{+5}^{\phantom{+}7}$


<img src="https://hackmd.io/_uploads/SkktC3oAT.png" width="450"/>


$\text{V}^7$ (or inversions) can also be altered with **lowered fifth**

<img src="https://hackmd.io/_uploads/S17J1pjCT.png" width="500"/>

### $♭\text{II}$ in root position

- **subdominant**
- (neopolitan 6th is the first inversion)
- usually only appears in minor key, but may also **appear as borrowed chord** in major key

[sound](https://www.youtube.com/watch?v=XeX4X_1_lo0&t=55s)
<img src="https://hackmd.io/_uploads/BkdtypsRT.png" width="600"/>

[sound](https://www.youtube.com/watch?v=65Zb3JxOgyk&t=15s)

### aug 6th with other bass

using raised $\hat{4}$
- $\text{Ger}^{+6}$ with raised $\hat{4}$ as bass (an inversion of $\text{Ger}^{+6}$) is called "German diminished third chord"


[sound](https://www.youtube.com/watch?v=ejUG_nAEQKM&t=43s)

<img src="https://hackmd.io/_uploads/SJYvb6iAa.png" width="400"/>

### common-tone chromatic chord
[more](https://viva.pressbooks.pub/openmusictheory/chapter/common-tone-chords/)

the shared tone (common-tone) is usually sustained


<img src="https://hackmd.io/_uploads/HyFSS6sC6.png" width="400"/>

#### common tone $^{\circ 7}$

#D#FAC: a **fully diminished** chord

<img src="https://hackmd.io/_uploads/r1miipjAa.png" width="250"/>

- often built when the root of a triad is sustained while the **third** and **fifth** are decorated by chromatic neighbors.
- can also result from passing tones (note other than bass is sustained)

[sound](https://www.youtube.com/watch?v=bKnNHEtMjUc)

[sound](https://www.youtube.com/watch?v=Y_rBqNSsVPY)

[sound](https://www.youtube.com/watch?v=RvM6uF9k2bM&t=13s)

## Chromatic Modulation

Modulation to distant keys (differ by more than one accidental)

### pivot chords involving mixture

When modulating to distant keys
- the pivot chord is often diatonic to only one of the keys
- the pivot chord is a chromatic borrowed chord on the other key


[sound](https://www.youtube.com/watch?v=YrkZFNyQkCM&t=5s)

[sound](https://www.youtube.com/watch?v=uaPV0-6Klvo&t=14s)

### common tone modulation

the last chord before the modulation shares just one tone with the first chord after the modulation, so that only a single tone serves as a pivot.

[sound](https://www.youtube.com/watch?v=q6eO3groGwA&t=58s)

### enharmonic modulation

any diminished 7th function as four $\text{vii}^{\circ 7}$ in four different minor keys and their parallel majors


German augmented 6th chords could also be enharmonically re-interpreted as dominant 7th. This could be done in both direction.

<img src="https://hackmd.io/_uploads/HkZpRL4tA.png" width="400"/>


- $\text{Ger}^{+6}$ -> dominant 7th
- [sound](https://www.youtube.com/watch?v=P79Ol_3hlJw&t=190s)


- dominant 7th -> $\text{Ger}^{+6}$
- [sound](https://www.youtube.com/watch?v=P79Ol_3hlJw&t=171s)


### other modulation

- abrupt change
- [sound](https://www.youtube.com/watch?v=6O6Nme3fw5k&t=1842s)


modulate to $♯\text{III}, ♯\text{VI}$


- modulate to $♭\text{III}, ♭\text{VI}$
- tonic not in the origial key


- successive modulation: modulate back to the original key
- [sound](https://www.youtube.com/watch?v=mnVAvlukpsM&t=29s)