Diminished chords are strange and exotic because they are symmetrical chords trying to function in an asymmetrical, tonal system.
Note:
bb7(Diminished 7) is the same as °7 (This note of the scale will also look the same as the 13th or 6th degree).
All notes a half-step above a chord tone are considered Harmonic Avoid notes, but are acceptable for Melodic use.
Tonal systems are asymmetrical which is the basis of tonal gravity. With Asymmetrical scales, the half steps are what define the system. The minor second is the strongest gravitational pull into Tonic that we have. The half-step of 7 to 1 is mirrored in the 4 to 3.
7 to 1 is what defines the Tonality. 4 to 3 is what defines our Modality (Quality of Major or Minor).
In a chromatic or symmetrical scale, any of the notes can be the 1 or Tonic.
Since the Baroque era, the Diminished chord, which comes naturally from Harmonic Minor (It’s the VII chord) is treated as an extension of the V7b9 chord and has a Dominant Cadential Function to the I chord.
For our examples let’s use the key of C Harmonic Minor.
If you take the Dominant Chord of the Key, in this case, G7, and keep building in 3rds G, B, D, F, another 3rd gives you Ab or the b9 on the dominant chord.
If you then remove the Root of the V7b9 chord then the third of the chord takes over as the new Root and you have B°7, which still resolves to the same I chord (Only now it’s up a half-step instead of down a fifth) and retains Dominant Cadential Function.
This is an Ascending Diminished chord with Primary Dominant Function because it takes the place of the primary dominant chord in the key and is one of our three types of Diminished Chords.
Let’s take a look at all 3 types now.
3 types of Diminished Chords:
1. Ascending diminished chords are diatonic (harmonic minor, 7th degree) and function either as Primary or Secondary Dominant. They contain the same tritone as the dominant chord and therefore have a dominant function. These are #I°7, #II°7, #IV°7, and #V°7. They can precede any diatonic chord except VII-7b5.
These Ascending/Descending types, when acting as passing diminished 7th chords, came about as a way to deal with parallel voice leading, or moving between adjacent diatonic chords. It’s a Passing Chord if it is prepared properly by the first chord, if it isn’t prepared then it is called an Approach chord.
2. Descending diminished chords (or chromatic approach chord) are Non-Diatonic/Non-Dominant and resolve to Diatonic chords through Chromatic Resolution or Voice Leading. These are bIII°7 and bVI°7. (The exception in Classical music is the bVI°7 because it can appear as an inversion of VII°7 and have a Dominant Function…This comes to light based on which direction it moves and where it resolves. In the example, it's functioning as bVI°7).
Note: The B in the Ab°7 chord is really Cb, and the D is really Ebb (E double flat).
3. Auxiliary Diminished ( an embellishment of I or V7) which have a Diatonic Root shared with the chord of resolution and are Non-Dominant (chromatic resolution) Diminished chords. These are I°7 and V°7.
Now let’s talk about Scales:
Remember the Chord Scale for our G7b9 comes from the fifth degree of C Harmonic Minor which is G Mixolydian (b9 b13) Also known as Phrygian Dominant. G | Ab | B | C | D | Eb | F | G
Anytime you see a b9 in a Dominant Scale you can always add in its compliment, the #9. So now we have this 8 note Chord Scale: G | Ab | A# | B | C | D | Eb | F | G
If we want this chord scale to represent B°7 (Remember our Diminished Chord is the V7b9 without the Root) now B is the root. The scale is still Mixolydian (b9,#9,b13) but now it’s spelled from the 3rd degree (sometimes called Diatonic Diminished).
This gives us B | C | D | Eb | F | G | Ab | A#(Bb) | B
The Scale Degrees are R, b9, b3(#9), b11(3), b5, b13, bb7, 7
This scale is useful for Diminished chords that have a Dominant Function because they are part of our Tonal world and Diatonic tensions are a great way to reinforce a given tonality.
For the Descending and Auxiliary Diminished Chords, we have a few options. If we want our scale sound to have a closer relationship to the home key then we can use versions of a Diatonic Diminished Scale.
This scale works for bIII°7, bVI°7, I°7, and V°7. The process is actually fairly simple. We can combine the chord tones of the Diminished Chord with the other scale tones from our home key to get variations of Diatonic Diminished scales.
So for example: If we take a bIII°7 chord in the key of C, the chord tones are as follows
Eb°7: Eb Gb Bbb(A) Dbb(C) and then add in the other scale tones from the home key of C we get Eb | E | Gb | G | A | B | C | D | Eb
The Scale Degrees are R, b9, b3, b11(3), b5, b13, bb7, 7
Notice that there is one tone we didn’t use, the F natural from the home key. This is an optional choice for the second degree of our Diminished Scale. So if we swap the E natural for the F natural then our scale is now Eb | F | Gb | G | A | B | C | D | Eb.
That natural 9th degree is a much nicer tension tone above the root than the b9. Remember that tensions a half-step above a chord tone are Harmonic Avoid Notes and tensions a whole-step above a chord tone not only sound great but also add a lot of richness to the Harmony.
The Scale Degrees now are R, 9, b3, b11(3), b5, b13, bb7, 7
Using the same process the bVI°7 only has one option for a Diatonic Diminished scale and that is
The Scale Degrees are R, b9, b3, b11(3), b5, b13, bb7, 7
The Auxiliary I°7 has two options with this process.
C°7: C Eb Gb Bbb(A) and which the home key scale tones added in we get
C | D | Eb | E | Gb | G | A | B | C
The Scale Degrees are R, 9, b3(#9), b11(3), b5, 5, bb7, 7
We can also swap out the E here for F and end up with a nicer scale because we have one less avoid tone C| D | Eb | F | Gb | G | A | B | C
The Scale Degrees are R, 9, b3(#9), 11, b5, 5, bb7, 7
The V°7 also gives us 1 choice with this process: G°7: G Bb Db Fb(E) plus the home key scale tones gives us G | A | Bb | C | Db | D | E | F | G
The Scale Degrees are R, 9, b3, 11, b5, 5, bb7, b7
….but we have another option for all of the descending and auxiliary diminished chords.
The Symmetrical Diminished/Whole-half/Octatonic scale (Yes, it has many names). This is considered, sonically, to be fairly aggressive, caustic, and “outside,” and is recommended to be used quite sparingly and only for a special effect. So you can essentially use this scale on any diminished chord if that is the sound you are looking for.
Another school of thought (to which I personally agree) is because it’s a Non-Functional scale (due to its symmetry) it can be used for Diminished chords with Non-Dominant Function that resolve Chromatically. This is a great scale for the Descending and Auxiliary Diminished chords!!
The Scale Degrees are R, 9, b3(#9), 11, b5, b13, bb7, 7
For extra fun, here are some Alternate Resolutions of Diminished chords: (Careful attention must be paid to the bass note here as it is always to the same note as the Root of the original chord of resolution. This consistent bass motion in the alternate resolutions helps the ear to accept the alternate chord).
#I°7 (normally to II-7) can resolve to V7 in second inversion C#°7 to G7/D (D is the Root of the original chord of resolution).
#II°7 (normally resolves to III-7) can resolve to the I chord in first inversion. D#°7 to CMaj6/E (E is the Root of the original chord of resolution).
#IV°7 (Rarely resolves to V7, and when it does it’s on a weak beat and therefore does not give the impression of V7/V) Normally this resolves to Imaj in second inversion(IMaj/5). F#°7 to CMaj6/G (G is the Root of the original chord of resolution).
#V°7 (normally resolves to VI-7) can resolve to VI7 which is the V7/II. G#°7 to A7
bIII°7 (normally resolves to II-7) can resolve to the II chords related V7 chord in second inversion. Eb°7 to G7/D (D is the Root of the original chord of resolution).
bVI°7 (normally resolves to V7) can resolve to I in second inversion. Ab°7 to CMaj6/G (G is the Root of the original chord of resolution).
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