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In recent lessons (EP478, EP481), Brian used diminished seventh chords…
The dim7 chord is not exactly a new fancy 21st century jazz chord: you’ll find it abundantly in the music of Bach, Mozart, Beethoven, Haydn, … And the romantics used it almost too much! But its contemporary usage is somewhat less constrained than in the old days.
Let’s see what music theory has to say about this chord.1. Definition and construction
We are talking about the so-called “full diminished” chord here.
It is a diminished triad with an additional minor third; the chord therefore consists of minor thirds only. With respect to the root the chord formula is (R, b3, b5, bb7). The upper tone is a diminished seventh above the root. For example, C°7 = (C,Eb,Gb,Bbb).
This chord is not diatonic in major tonalities, but it is diatonic in the harmonic minor mode where it occurs on the 7th degree.Don’t let that “double flat” notation trip you off. It’s just the theoretically correct way to spell a diminished seventh interval. The interval above the C must be a diminished 7th. Since Bb is a minor 7th, we need to write Bbb: a minor 7th lowered by an additional half tone.
Having said that, in the equally tempered scale Bbb is enharmonically equivalent to A: it’s the same pitch. So although {C,A} is a major sixth and not a diminished 7th, you’ll often see C°7 spelled (C, Eb, Gb, A).One important characteristic of the dim7 chord is that it is equal to all its inversions! For example, B°7 = (B,D,F,Ab) gives B°7/D = (D,F,Ab,B). But B°7/D can also be spelled D°7. Similarly (F,Ab,Cb,D) can be written (F,Ab,Cb,Ebb) = F°7. And finally (Ab,B,D,F) can be spelled (G#,B,D,F) which is G#°7.
For this reason, there are only three distinct dim7 chords: C°7, C#°7 and D°7. All the other ones are inversions of these three chords.
On a guitar, take whatever chord grip for a dim7 chord and move it up or down three frets any number of times to get the inversions of that same chord.2. Usage
What can you do with a (full) diminished seventh chord?A. It can be used as a dominant or secondary dominant chord
The dim7 chord contains two tritones. For example, in B°7 = (B,D,F,Ab) there is the tritone (B,F) and the tritone (D,Ab). Since any tritone has two potential resolutions, the dim7 chord has four potential resolutions!The easiest and most common way to resolve a dim7 chord is to consider that its root is the leading tone of the resolving chord. For example, C°7 = (C,Eb,Gb, Bbb) would resolve to the major or minor chord whose root is a half tone higher than C, i.e. Db or Dbm.
Say you are in C Major and you want to “tonicisize” Am7 which is the vi chord. Usually you would do that with E7: C E7 -> Am where E7 is a secondary dominant chord.
But you can also do it with G#°7: C G#°7 -> Am7, which features a smoother voice leading. Note that G#°7 might as well resolve to A.
In functional analysis terms we would notate this: vii°7/vi -> vi.
Another way of looking at it is to realise that G#°7/E = (E,G#,B,D,F) = E7(b9). So we can view that G#°7 chord as an E7(b9) without root (the root would presumably be played by the bass). In functional analysis terms we would notate this V7(b9)/vi -> vi.But because G#°7 = (G#, B, D, F) is equivalent to all its inversions, it can also resolve to C (or Cm), to Eb (or Ebm) and to Gb (or Gbm).
In other words, the diminished 7th chord is also a pivot chord that allows modulations to very distant tonalities!B. It can be used as an embellishing chord or as a passing chord
Very often a dim7 chord is used to “resolve” to a major chord whose root is one of the chord tones of the dim7 chord. This is called “common tone resolution”.
For example:
I -> #ii°7 -> I (e.g. C -> D#°7 -> C)
or V(7) -> #vi°7 -> V(7) (e.g. G7 -> A#°7 -> G7)
Since the dim7 chord isn’t rooted on a leading tone it can’t function as a dominant chord in this case. But in each situation the dim7 and the resolving chord have a common tone. In the examples above, the dim7 chord is used to embellish the surrounding chords. It is somewhat comparable to a melodic appoggiatura.As a passing chord, the dim7 chord is often used between the iii chord and the ii chord; for example Em7 -> Eb°7 -> Dm. This is extremely frequent in bossa nova. This is not a common tone resolution because the resolving chord has no common tone with the dim7 chord, but look at the voice leading: (E,G,B,D) -> (E,G,Bb,Db) -> (D,F,A). See how smooth the voices move between chords?
In Gospel music, you will very often find #IV°7 -> I(c), that is to say the tonic chord in second inversion. In blues you will often have #IV°7 -> I7. In this case the #IV°7 is a passing chord, with a common tone resolution.
In a 12 bar blues you’ll often find a dim7 chord in the 6th bar; so instead of … | IV7 | IV7 | I7 … we have … | IV7 | #IV°7 | I7… In A that would be … | D7 | D#°7 | A7…
The D#°7 chord is (D#,F#,A,C) and the common tone is A.C. How Brian uses it
The lesson EP481 is in B Flat Major; Brian plays: Bb -> E°7 -> Cm F7 -> Bb F7
In functional harmony terms this is: I -> #IV°7 -> ii V7 -> I V7
That E°7 chord is a passing chord in this case; it has a common tone G with Cm.
Had he played a B°7 chord instead, it would have functioned as a secondary dominant resolving to Cm. Try this harmonisation and see if you like it!Later in the song (bars 13 and 14), he plays IV #IV°7 -> I, which is the common tone blues sequence mentioned above. The same thing happens twice in EP478.
3. Conclusion
Diminished seventh chords are versatile chords, very useful to spice up chord progressions!
They can be used as a (secondary) dominant chords, as embellishing chords or as passing chords. They can also be used as pivot chords for (distant) modulation. -
Jean-Michel,
Thank you for a very informative and thorough overview. I found the distinction of dominant/secondary dominant vs passing chord very helpful. The Bdim7 to Cmin resolution sounds good, also, but Brian’s Edim7 evokes that “Isn’t it a Pity” sound that is burned into everyone’s ear.
Could you do me a favour and explain “tritone substitution”? If full diminished chords have two tritones, I assume they can be substituted for two different dominant chords.
John-
A tritone, as you know, is an interval of a diminished fifth (b5), or augmented fourth (#4). It is called “tritone” because it consists of exactly three tones.
There is always one tritone in each major tonality between the 4th and the 7th scale degrees. For example, in C Major the interval {F,B} is a tritone (b5) while {B,F} is a #4. The tritone is the only interval that is equal to its inversion, so b5 = #4.In every major tonality there are two chords that contain the tritone: the V7 and the vii°(b7) (this is the half diminished chord). In C Major that is G7 = (G,B,D,F) and B°(b7) = (B,D,F,A). In both cases the tritone is the b5 {F,B}.
In the natural minor tonality there is no tritone; we get one by raising the 7th degree and turning the natural minor scale into an harmonic minor scale.Tritones are very dissonant and unstable intervals that call for a resolution of some sort.
The classical way to resolve a tritone is to make an augmented fourth even bigger and a diminished fifth even smaller.
For example, the {B,F} in G7 is a b5, so we’ll shrink the interval even further: B goes up to C and F goes down to E or Eb. If you put these notes in a C or Cm chord, you have a perfect (or authentic) cadence V7 -> I (or i). If you put them in another chord – typically Am, you have a deceptive (or interrupted) cadence V7 -> vi.
The vii°(b7) chord B°(b7) has the same resolution to C or Cm.Now take the Gb Major scale: (Gb Ab Bb Cb Db Eb F); the V7 chord is Db7 = (Db,F,Ab,Cb).
Being the dominant 7th chord, it (classically) resolves to Gb (or Gbm).
But look at the tritone in Db7: it is {F,Cb}… As you know, Cb is enharmonically equivalent to B. So, although spelled differently, the tritone in Db7 is the same as in G7. Being the same, it should be able to resolve the same way… So Db7 can also resolve (non-classically) to C! And for the same reason G7 can resolve to Gb.
Notice that the roots of the resolving chords (C and Gb) are a tritone apart!In practice then, whenever you have a dominant 7th chord you can replace it by another dominant 7th chord whose root is a tritone lower.
This is the famous tritone substitution.So we can have G7 -> C (Cm) or Db7 -> C (Cm).
We can also have Db7 -> Gb (Gbm) or G7 -> Gb (Gbm).Here is an example: A7 -> D7 -> G7 -> C can be replaced by Eb7 -> D7 -> Db7 -> C.
This is because Eb7 contains the same tritone {G,Db} = {G,C#} as A7, and Db7 contains the same tritone {F,Cb} = {F,B} as G7.
Note that the bass line descending by half steps creates a bit of a surprise and adds interest! But you may or may not find it appropriate depending on the context, the genre and… your personal taste!Summary:
Each tritone has two potential resolutions:
– the classical resolution leads to the cadences V7 -> I (or i) and V7 -> vi
– the non-classical resolution leads to the cadences bII7 -> I (or i) and V7 -> bV (or bv)
This works because V7 and bII7 contain the same tritone.A full diminished chord such as C°7 = (C,Eb,Gb,A) contains two tritones and therefore offers four potential resolutions!
A final word: although tritones are usually resolved one way or another, major chords with a b7 (i.e. chords of the form (R,3,5,b7) don’t always have a dominant function and don’t necessarily obey the cadences above. For example in the progression G -> B7 -> C the B7 is NOT a dominant 7th chord but a III7 (a chromatic mediant) going to IV. The tritone in B7 {D#,A} doesn’t resolve but rather melts away when D# goes to E and when A is ditched!
But this is another story…
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Thanks, JM. Does it make sense to say that whenever you have a dominant chord it can replaced by another dominant 7 chord whose root is a tritone lower OR higher, as the tritone is equidistant either way. That seems to cover the conversion from a 5th string root dominant to a 6th string root dominant and vice versa.
John -
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This is really informative stuff, J-M, thanks for posting it. Interesting issues too from John. It must be good for most of us to pause and think more about theory from time to time. It is probably worth mentioning that an earlier lesson from Brian, EP358, had some very useful practical suggestions about using dim7s in improvisation.
This may be pointing out the obvious, but the most effective and dramatic use of dim7s I know of is in Villa-Lobos’ Prelude no. 1!
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