Theory On Tap Lesson 9, Minor Chords by: Grant D. Green In the last lesson we looked at the various minor scales. Now, let's pull out the box of flats and head for the triads and seventh chords. Each of the minor scales has some triads in common, and some triads peculiar to the specific scale. We'll look at them one by one.
	I. The Natural Minor Chords You'll recall from the previous lesson that the natural minor scale is like the major scale, but with the 3rd, 6th, and 7th lowered. In the key of A minor, the scale is
	A B C D E F G A \ / \ / \ / \ / \ / \ / \ / w h w w h w w (where w= whole step and h= half step)
	A. The triads The root triad (i) in minor is composed of a root, a minor third, and a perfect fifth. You can also view it as a major third on top of a minor third (remember that the major triad is a minor third on top of a major third).
	For example, in F minor (four flats):
	F Ab C \ / \ / m3 M3 (m3= minor third, M3= major third)
	The root triad is *always* a minor triad in a minor key: you could say that this is what *defines* the key as minor. Each of the minor key scales provides a minor root triad, because all of the minor key scales have a lowered (minor) third. In the key of A minor (to keep it simple), the triads are as follows:
	i: A, C, E (minor) ii: B, D, F (diminished, aka dim or o) III: C, E, G (major) iv: D, F, A (minor) v: E, G, B (minor) VI: F, A, C (major) vii: G, B, D (major)
	Notice that some of the triads are indicated with lower case characters: it is traditional to indicate minor (and diminished) triads in lower case, and major in upper case. More importantly, notice that the v chord (the dominant V) is now minor. As was pointed out in part 1 of this lesson, having a minor chord for the dominant just doesn't work as well. This is why you're not very likely to see a "pure" natural minor harmonic progression.
	Now, let's play a few, just to see what they sound like. The abbreviations used are as follows:
	R : root m3 : minor third, 3 half steps up M3 : major third, 2 whole steps up d5 : diminished fifth, half step below perfect fifth 5 : perfect fifth a5 : augmented fifth, half step above perfect fifth m7 : minor seventh, whole step below root M7 : major seventh, half step below root
	minor triad (i, iv, v in natural minor): |---|---|---|---|---|---| |---|---|m3-|---|---|---| |---|---|---|---|---|---| |---|---|---|---|-5-|---| |---|---|-R-|---|---|---| ========================== |---|---|---|---|---|---| |---|-R-|---|---|---|---| |---|-5-|---|---|---|---| |---|---|m3-|---|---|---| |---|---|---|---|---|---|
	diminished triad (ii in natural minor): |---|---|---|---|---|---| |---|---|---|m3-|---|---| |---|---|---|---|---|---| |---|---|---|---|d5-|---| |---|---|---|-R-|---|---| ========================= |---|---|---|---|---|---| |---|---|-R-|---|---|---| |---|d5-|---|---|---|---| |---|---|---|m3-|---|---| |---|---|---|---|---|---|
	major (III, VI, VII in natural minor): |---|---|---|---|---|M3-|---|---| |---|---|---|---|---|---|---|---| |---|---|---|---|---|---|-5-|---| |---|---|---|---|-R-|---|---|---| |---|---|---|---|---|---|---|---| ================================= |---|---|---|---|---|---|---|---| |---|---|---|---|---|---|---|---| |---|-R-|---|---|---|---|---|---| |---|-5-|---|---|---|---|---|---| |---|---|---|M3-|---|---|---|---|
	C. The Seventh Chords If we look at the seventh chords:
	i A, C, E G (minor 7, or min7, or -7) ii B, D, F, A (half diminished 7, or min7b5) III C, E, G, B (major 7, or Maj7) iv D, F, A, C (minor 7, or -7) v E, G, B, D (minor 7, or -7) VI F, A, C, E (major 7, or Maj7) VII G, B, D, F (dominant 7, or 7)
	we see that the v is still a minor 7 chord. There *is* a dominant 7 (the VII7), but this is really the V7 of C, and would not resolve correctly to A minor. OK, so what do they sound like?
	the ii7, a half-diminished 7 (min7b5): |---|---|---|---|---|---| |---|---|---|m3-|---|---| |---|---|---|-7-|---|---| |---|---|---|---|d5-|---| |---|---|---|-R-|---|---| ========================= |---|---|---|---|---|---| |---|---|-R-|---|---|---| |---|d5-|---|---|---|---| |---|---|---|m3-|---|---| |---|---|---|-7-|---|---|
	the iv7, your typical minor 7 (m7 or -7): |---|---|---|---|---|---| |---|---|m3-|---|---|---| |---|---|-7-|---|---|---| |---|---|---|---|(5)|---| |---|---|-R-|---|---|---| ========================= |---|---|---|---|---|---| |---|-R-|---|---|---|---| |---|(5)|---|---|---|---| |---|---|m3-|---|---|---| |---|---|-7-|---|---|---|
	the V7, dominant seventh (7): |---|---|---|---|---|---| |---|---|---|---|-7-|---| |---|---|---|M3-|---|---| |---|---|---|---|-R-|---| |---|---|---|---|(5)|---| ========================= |---|---|---|(R)|---|---| |---|---|---|---|---|---| |---|-R-|---|---|---|---| |---|---|---|---|-7-|---| |---|---|---|M3-|---|---|
	the VI7, a Maj7: |---|---|---|---|---|---| |---|---|---|---|M7-|---| |---|---|M3-|---|---|---| |---|---|---|-R-|---|---| |---|---|---|(5)|---|---| ========================= |---|---|-R-|---|---|---| |---|---|---|---|---|---| |---|---|---|---|---|---| |---|---|---|---|M7-|---| |---|---|-M3|---|---|---|
	II. The Harmonic Minor The harmonic minor differs from the natural minor in that the seventh note is raised, restoring the leading tone found in major keys:
	A B C D E F G# A \ / \ / \ / \ / \ / \ / \ / w h w w h w+ h (where w+ is an augmented second)
	A. The triads Since the harmonic minor has the raised seventh, all of the triads that contain the seventh get altered (at least as compared with the natural minor triads). The triads affected are the III, V, and VII triads.
	Again in the key of A minor, the harmonic minor triads are as follows:
	i A, C, E (minor) ii B, D, F (diminished, aka dim or o) III C, E, G# (augmented, aka aug or +) iv D, F, A (minor) V E, G#, B (major) VI F, A, C (major) vii G#, B, D (diminished)
	Notice that the V triad is now major. Its that raised G# that makes the V triad major when it would otherwise be minor in the natural minor. This also preserves the strong cadence that results in a V-I progression (or V-i in minor keys): in classical voice leading (which we may revisit later on), the third of V (which is the leading tone) always resolves to the root of I (or i). The III chord has been stretched (augmented), by increasing the interval between its root and fifth (the 3 and 7 of the scale). In contrast, the vii chord is now compressed (diminished), by decreasing the interval between its root and fifth (the 7 and 4 of the scale).

	C E G# G# B D \ / \ / \ / \ / M3 M3 m3 m3
	The aug chord is built on a stack of two major thirds, while the dim chord is a stack of two minor thirds. Now, between major, minor, augmented, and diminished triads, we have every possible combination of major and minor thirds (taken in pairs).

	The augmented triad is the only new chord here, so let's hear how it sounds:
	augmented (iii in harmonic minor): |---|---|---|---|---|---| |---|---|---|---|---|---| |---|a5-|---|---|---|---| |---|---|M3-|---|---|---| |---|---|---|-R-|---|---| ========================= |---|---|---|---|---|---| |---|---|-R-|---|---|---| |---|---|---|a5-|---|---| |---|---|---|---|M3-|---| |---|---|---|---|---|---|
	B. The Seventh Chords If we look at the seventh chords:
	i: A, C, E G# (minor-Maj7) ii: B, D, F, A (half diminished 7, or min7b5) III: C, E, G#, B (augmented 7, or aug7, or +7) iv: D, F, A, C (minor 7, or -7) V: E, G#, B, D (dominant 7, or 7) VI: F, A, C, E (major 7, or Maj7) vii: G#, B, D, F (diminished 7, or dim7, or o7)
	we see that the dominant seventh (V7) chord is preserved unchanged as well. The V7 resolves to I (or i) with the leading tone (G#) resolving to A, and the seventh (D) resolving to the third of i, or C. When you take it apart, you can hear the seventh of V7 as a suspension that naturally resolves to the third of the root triad (its even easier to hear with the major progres- sions). The third and the seventh provide nearly all the energy and motion contained in the V7 chord: that's why you can omit the fifth of a dominant seventh chord without changing the character of the chord. Note: DON'T leave out the fifth in a diminished or augmented chord. That's where ALL of the character for those chords comes from.
	We've now added the minor-Maj7, the full diminished 7 (dim7) and an augmented 7 (+7), so let's have a listen:
	First, the i7, a minor-Major7 (min-Maj7: rare!): |---|---|---|---|---|---| |---|---|m3-|---|---|---| |---|---|---|-7-|---|---| |---|---|---|---|-5-|---| |---|---|-R-|---|---|---| ========================= |---|---|---|---|---|---| |---|-R-|---|---|---|---| |---|---|---|---|---|---| |---|---|m3-|---|---|---| |---|---|---|-7-|---|---|
	vii7, a diminished 7 (dim7, o7): |---|---|---|---|---|---|---| |---|---|d5-|---|---|---|---| |---|-R-|---|---|---|---|---| |---|---|---|m7-|---|---|---| |---|---|m3-|---|---|---|---| ============================= |---|---|---|---|---|---|---| |---|---|---|---|d5-|---|---| |---|---|---|-R-|---|---|---| |---|---|---|---|---|m7-|---| |---|---|---|---|m3-|---|---| BTW, in "o7", the "o" is supposed to be a small circle, not the letter "o."
	the iii7 augmented7 (+7): |---|---|---|---|---|---|---| |---|---|---|M3-|---|---|---| |---|---|---|-7-|---|---|---| |---|---|---|---|---|a5-|---| |---|---|-R-|---|---|---|---| ============================== |---|---|---|---|---|---|---| |---|-R-|---|---|---|---|---| |---|---|a5-|---|---|---|---| |---|---|---|M3-|---|---|---| |---|---|---|-7-|---|---|---|
	III. The Melodic Minor Just to review, the melodic minor scale has a raised sixth and seventh when ascending, and is the same as the natural minor when descending.
	A B C D E F# G# A G F E D C B A \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / w h w w w w h w w h w w h w |----ascending------------->|----------descending------->
	A. The Triads We essentially covered the descending melodic minor at the same time we covered the natural minor, so we'll concentrate on the ascending form here. The triads affect by raising the sixth scale note are the II, IV, and VI:
	i: A, C, E (minor) ii: B, D, F# (minor) III: C, E, G# (augmented, aug or +) IV: D, F#, A (major) V: E, G#, B (major) vi: F#, A, C (diminished) vii: G#, B, D (diminished)
	We haven't changed the most important chords, V and I, but we've converted II from diminished to minor, IV from minor to major, and VI from major to diminished. No new types of chord, just minors and majors in different places.
	B. The Seventh Chords If we look at the seventh chords:
	i: A, C, E, G# (minor-Maj7) ii: B, D, F#, A (minor 7, min7) III: C, E, G#, B (augmented 7, aug7, or +7) IV: D, F#, A, C (dominant 7, 7) V: E, G#, B, D (dominant 7, 7) vi: F#, A, C, E (half diminished 7, min7b5) vii: G#, B, D, F (diminished 7, dim7, or o7)
	we see that we've picked up a second dominant 7 chord (the IV), and a half- diminished for VI. We've already covered these chords as well.
	I should point out here that having a major IV chord makes it harder to firmly establish the tonality in the minor key. When you hear a chord by itself, you don't know if it is the minor I in a minor key, or something like the minor VI in a major key. For example, the A minor chord could be I in A minor, or VI in C major, or the IV in D minor. What tips your ear off to the key is hearing the chord in relation to other chords of the key in a progression, *especially* in a cadence. I-IV-I and V-I type progressions are among the most useful for really rooting (excuse the pun) the key. An Am-D progression sounds like a II-V progression in G major more than it sounds like A minor.
	III. All Together Now So, which set of chords should you use? The way it typically works is that one uses a combination of chords from all three scales. I think the most common for "common practice" (classical-type music) are as follows:
	i: A, C, E (minor) (N/H/M) ii: B, D, F# (minor) (M) III: C, E, G (major) (N/H) iv: D, F, A (minor) (N/H) V: E, G#, B (major) (H/M) VI: F, A, C (major) (N/H) vii: G#, B, D (dim) (H/M)

where:

N = natural minor H = harmonic minor M = ascending melodic minor

	The augmented and diminished triads aren't used all that often, at least in common practice. For seventh chords, the likely candidates are:
	i: A, C, E, G (min7) ii: B, D, F#, A (min7) III: C, E, G, B (Maj7) iv: D, F, A, C (min7) V: E, G#, B, D (dominant 7, or 7) VI: F, A, C, E (major 7, or Maj7) vii: G#, B, D, F (dim7)
	The "preferred" chords for jazz and rock probably vary a bit from the "common practice" set, but I'll leave that for (someone else's) later lesson on chord progressions.
	C. The Diminished Seventh Chord The diminished 7 (dim7) chord is worth special attention. First, let's take a closer look at its structure:
	G# B D F \ / \ / \ / m3 m3 m3
	Yes, the dim7 is a stack of minor thirds. What's more, if you put another minor third on top (Ab), you simply start over (G#=Ab). Since it is all minor thirds, the chord is completely symmetric: it sounds the same in all inversions.
	The dim7 doesn't truly have a root: or one can say that it has *four* roots. If you invert G# dim7, you get B-D-F-G#(Ab), which you can see it is the vii7 (dim7) of C minor. Another inversion to D-F-Ab-Cb(B) gets you to the vii7 of Eb minor, while one last inversion to F-Ab-Cb-Ebb(D) brings you to the vii7 of Gb minor (or F# minor). This makes the vii7 chord very useful for modulating to different keys, related by relative minors. Thus, the G# dim7 can resolve to A minor, C minor, Eb minor, or Gb/F# minor. There are in fact only three different dim7 chords: G#-B-D-F, A-C-Eb-Gb, and Bb-Db-E-G. Note that none of these dim7 chords have any tones in common. Each one of them can resolve to four different keys, moving a half step up from any given note in the chord. Its a very useful chord, and somehow doesn't sound quite as dissonant as the augmented or half-diminished chords (IMHO).

References:

Acknowledgments:

Grant D. Green
grant_green@cc.chiron.com