Harmonic Minor and Augmented Chords
As noted in the last lesson, the dominant-function chords in natural minor do not contain the note a M7 above the root (ie half-step below), also known as the leading tone. This makes them less tense or distant than dominant-function chords in a major key. And thus the dominant - tonic progression has less resolution in natural minor than major.
The harmonic minor scale seeks to remedy this by using the same notes as the natural minor scale, but sharping the 7th note to get the leading tone.
A harmonic minor key is typically marked with the shorthand "hm" after the tonic note name. For example, "C" is C Major, "Am" is A Minor (natural), and "Ahm" is A Harmonic Minor.
Contents
PreReqs
A Harmonic Minor
A Harmonic Minor is composed of A - B - C - D - E - F - G♯ - A.
Open Position
E---------------------------------------------- B---------------------------------------------- G-------------------1--2--1-------------------- D----------0--2--3-----------3--2--0----------- A-0--2--3-----------------------------3--2--0-- E---------------------------------------------- A B C D E F G# A G# F E D C B A
E-------------------------------------------0--1--4-/5-- B----------------------------------0--1--3-------------- G----------------------------1--2----------------------- D-------------------0--2--3----------------------------- A----------0--2--3-------------------------------------- E-0--1--4----------------------------------------------- E F G# A B C D E F G# A B C D E F G# A
Changes to whole-half Pattern
By changing one of the notes, we change the whole-half sequence of the notes in the scale. We now have:
w h w w h (w+h) h A B C D E F G# A or w h w w h + h A B C D E F G# A
That (w+h) is 1 whole step + 1 half step, or 3 half-steps, or 1.5 whole steps (marked as "+" in whole-half patterns) . And the scale itself now contains 3 half steps instead of 2. Such 1.5 step jumps in a scale and numerous half-steps are more commonly associated with Eastern-sounding music. When you play the scale, it should be quite apparent.
Some composers value the scale simply for that Eastern sound. Think of Kirk Hammet's solos in Metallica's Wherever I May Roam.
However, the classical usage was more focused on its impact on harmony (hence harmonic minor)...
Changes to Diatonic Chords
The sharped 7th impacts the 3 dominant-function chords of natural minor: III, v, and VII. This does not change their harmonic function - they still function as dominant chords "wanting" to resolve to tonic. However, it does change the relative tension they create and the strength of their resolution to tonic, as the leading tone to tonic movement is a stronger resolution.
| Natural Minor | Harmonic Minor | Raised note in chord |
What Happened? |
|---|---|---|---|
| III | III+ | 5th | Raising the 5th of a major chord makes it augmented |
| v | V | 3rd | Raising the 3rd of a minor chord makes it major |
| VII | vii° | root | Raising the root of a major chord makes it diminished |
Here's the full list of diatonic chords:
| Chord in A Harmonic Minor |
Harmonic Name |
Harmonic Function |
|---|---|---|
| Am | i | Tonic |
| Bdim | ii° | Pre-Dominant |
| C+ | III+ | Dominant/Tonic |
| Dm | iv | Pre-Dominant |
| E | V | Dominant |
| F | VI | Tonic/Pre-dominant |
| G#dim | vii° | Dominant |
Sample Progressions
Let's revisit the progressions from natural minor, adjusting the chords where necessary...
Am Dm/A E Am i iv V i E--0------1------0------0-- B--1------3------0------1-- G--2------2------1------2-- D--2------0------2------2-- A--0------0------2------0-- E----------------0---------
Am C+ F Bdim C+ F Bdim E Am i III+ VI iio III+ VI iio V i E-0-------------|-0----1---1------|-0----1---1----0-|-0---------- B-1-------------|-1----1---3------|-1----1---3----0-|-1---------- G-2-------------|-1----2---x------|-1----2---x----1-|-2---------- D-2-------------|-2----3---3------|-2----3---3----2-|-2---------- A-0-------------|-3--------2------|-3--------2----2-|-0---------- E---------------|-----------------|---------------0-|------------
Quite an impact, yes? You can definitely hear the increased tension of the dominant chord and stronger resolution to tonic. Notice the 3rd string - between III+ - VI and V - I, we see the G♯ on the first fret move a half-step up to A.
Augmented Chord
Whoa? What's that III+ (C+) chord? This is an augmented chord.
An augmented chord consists of a root note, its major 3rd, and its augmented 5th. The augmented fifth is the same distance as two major 3rds, so the chord consists of 2 major thirds and one augmented 5th (and their inverses). While the major 3rds are quite harmonic, the augmented 5th is a bit less so - more similar to a minor 3rd. But the real kicker is that we're missing the perfect 5th, which is the most harmonic interval. Thus, the chord sounds quite weird and unsettling, but not as dissonant as a diminished chord.
Also, the distance from the augmented 5th to the octave is another major 3rd. Thus, the augmented chord looks like a bunch of stacked M3 intervals. This is demonstrated on a single string:
-M3- -M3- -M3- --0----4----8----12-- R 3 5 R
Or as a chord on the bottom 4 strings:
G----------------0- D-----------1------ A------2----------- E-3---------------- R 3 5 R
Here are some fingering charts:
| Open Pos. | 1st Inv. | 2nd Inv. |
|---|---|---|
E o|-|-|-|-| C ||i|-|-|-| G# ||i|-|-|-| E ||-|m|-|-| C ||-|-|r|-| E o|-|-|-|-| |
||-|-|-|-|-|
||-|-|-|-|-|
G# ||i|-|-|-|-|
E ||-|m|-|-|-|
C ||-|-|r|-|-|
G# ||-|-|-|p|-|
|
E o|-|-|-|-|
C ||r|-|-|-|
G# ||m|-|-|-|
E ||-|p|-|-|
||-|-|-|-|
||-|-|-|-|
|
Although I call the last 2 examples inversions, they are identical to other root position augmented chords. The distance between each note and those above and below it is always a M3.
C+ C+/E C+/G# or C+ E+ G#+ E---------0--------- E---------0--------- B---1-----1--------- B---1-----1--------- G---1-----1-----1--- G---1-----1-----1--- D---2-----2-----2--- D---2-----2-----2--- A---3-----------3--- A---3-----------3--- E---------------4--- E---------------4---
Instead of saying C+/E (C+ 1st inversion), we could just as easily call that a E+ (E G♯ B♯) - C and B♯ are enharmonic. Similarly, C+/G♯ is the same pitches as G♯+ (G♯ B♯ D
), D = E.
| C+ | E+ 2nd Inv. | G♯+ 1st Inv. | |
|---|---|---|---|
| Note 1 | C | B♯ | B♯ |
| Note 2 | E | E | D
|
| Note 3 | G♯ | G♯ | G♯ |
Enharmonic Notes and Harmonic Function
Two notes are enharmonic if they have the same pitch but are spelled differently. For instance, B♯ and C are enharmonic, as are D and E. It seems simplest to always use the least amount of sharps and flats possible, changing notes to their enharmonic equivalents. This is a good approach where harmonic function is obvious and doing so would not be controversial, which is most of modern popular music. However, in classical music, the note name often implies more than just a pitch, but a function.
In the above example, the E+ and G+ chords are not diatonic to the key of Am. Writing them as such instead of as inversions of C+ could be construed as a modulation into a different key, and that the E+ or G+ chords were not the III+ chord of A Harmonic minor and will function differently.
Homework
- Know that the harmonic minor scale uses the same notes as the natural minor scale, but with a raised 7th (M7).
- Know that the harmonic minor scale uses the same notes as the major scale, but with a flatted 3rd and 6th.
- Know that the harmonic minor scale consists of the whole-half pattern w-h-w-w-h-+-h.
- Practice the Ahm scale in open position, both one octave and all notes.
- Know that the diatonic chords of the harmonic minor scale are i, ii°, III+, iv, V, VI, vii°.
- Know that the diatonic dominant-function chords of the harmonic minor scale contain the leading tone (M7), which makes their dominant - tonic resolution stronger than natural minor.
- Practice the chord progressions above, listening for the minor tonality with the strengthened dominant-tonic resolutions due to the raised 7th.
- Know that an augmented chord consists of a root note and the M3 and A5 above.
- Know that augmented chords consist entirely of M3 intervals between its member notes, including the augmented 5th to the octave.
- Practice the augmented chord shapes above.
- Know what enharmonic notes are and why their different spellings can suggest different harmonic functions.