Dominant Chord Substitutions

     The importance of the tritone to functional harmony was already discussed and considering that chords can be replaced in their function, as long as they share common tones, it is not hard to imagine that the dominant chord (V⁷) and its tritone can also be replaced in terms of function. The most direct diatonic substitution of the dominant chord is the diminished chord – i.e. replacing a G⁷ with a B^o still shares the common tones B, D and F, maintaining the presence of the tritone.

Using Diminished Chords

     The diminished chord can be found in the major scale when thirds are stacked over the 7^th degree of the scale – the leading tone. The structure of a fully diminished chord is symmetrically built in minor thirds which can be used to divide an octave in four equal parts – B, D, F and Ab and then returning to B. This means that the same B^o7 chord can be inverted fourfold and each inversion being the fundamental or tonic of a new diminished 7^th chord:

     From the inversion of the B^o7 chord we get the D^o7, F^o7 and the Ab^o7, all sharing the same notes and thus the same tritone. These chords are the natural substitutes of each other:

Diminished seventh chords sharing the same tritone

     Further implications arise related to the modulation process – going from one tonality to another; although these matters will be dealt with in other blog posts.

     The G⁷ and B^o are a major 3^rd apart, meaning that a B^o can be easily substituted by a G⁷, only by adding a major third interval below B, while maintaining all the other common tones. That said, the same can also be applied to each new diminished chord – to the D^o, F^o and the Ab^o ; and thus infer new dominant chords as well:

Adding a major third interval below the root of every diminished chord, transforming the B⁰ into a G7; the D⁰ into a Bb7; the F⁰ into a Db7; and the Ab⁰ into a E7

     But there is another way we can get the same dominant chords instead of going through the diminished chords cycle. Interestingly enough, if you lower by a half-step each of the chord tones from a diminished 7^th chord, one at a time, you get the same dominant chords:

The B⁰⁷ turns in to a Bb⁷ by lowering the first degree; into a Db⁷ by changing the 3^rd degree; into an E⁷ by lowering the 5^th degree; and into a G⁷ by lowering its 7^th

     As you can see, because of the diminished chords cycle we have got not only three new diminished chords – the D⁰, the F⁰ and the Ab⁰ that can naturally be used as substitutes of the B⁰ in the C major tonality;

Different Diminished Chords Resolving to the Tonic – Final chord is G⁷ to C

but also, three new dominant chords that can be derived from them – the Bb⁷, the Db⁷ and the E⁷. All of these chords are also a minor third apart from each other and can be used to replace the G⁷ when resolving to the tonic:

Different Dominant chords resolving to the tonic, starting with G⁷ to C

Using Chord Superimposition

     Another common substitution of the tritone is to use the G^{7 b9} instead of the G⁷ that is present in the C major scale. This chord can be obtained by superimposing the B^o7 over the G⁷:

The G^{7 b9} obtained by superimposing a G⁷ and a B^o7 – a G⁷ | B^o7 polychord; resolving to C

     If we superimpose the other diminished chords derived from the respective chord cycle, we will get the same G^{7 b9} chord since all the diminished chords have the same notes.

     However, and as seen, the derived dominant chords are also a minor 3^rd apart from each other and their superimposition over the V⁷ will produce different chord results. In effect, we will have a Bb, a Db or an E over the G⁷.

     These polychords can be interpreted as altered dominant chords; the G^{7 b9}, G^{7 #9}, G^{7 b9} (b5) and the G^{7 b9} add¹³ as the result of the G⁷|B^o, the G⁷|Bb, the G⁷|Db and the G⁷|E polychords, respectively.

Resulting chords from polychords B^o7 | G⁷ ; Bb7 | G7; Db7 | G7; and E7 | G7 – resolving to C

Using minor chords with major 6^th

     The last example I will be providing for dominant chord substitution is the minor chord with a natural or major 6^th. The diminished chord cycle presents us with yet another possibility for dominant substitution.

     Instead of using the diminished 7^th, we will be looking at the half-diminished chord, the Bm⁷ (b5), which is the natural diminished chord formation based on the 7^th degree of the C major scale. Functionally, the half-diminished chord cycle can also be used as dominant chord substitutes but when you look at the chord tones of a Bm⁷ (b5), you have a B, D, F and A. The first inversion of this chord can be considered as a Dm with a B on top – a major 6^th; spelled as a Dm⁶.

Inverted half-diminished that can be interpreted as a minor chord with major 6th – resolving to C

     As it is expected, if you move the same chord in minor thirds cycle, we will have the Dm⁶, the Fm⁶, Abm⁶ and the Bm⁶, and all of these can be effectively used as dominant chord substitutions as they all have leading-tones and tritones that can resolve to the tonic or to other chord tones belonging to the tonic chord.

Tritones are represented in red while leading-tones are in orange

Minor chords with major 6^th resolving to the tonic Cmaj – Starting in Bm⁶ and moving in a minor thirds cycle

summary

     In the following representations you will find a run-through of all the mentioned chords that can be used as substitutes of the dominant chord (V⁷) and its tritone, using G⁷ as reference and excluding the altered dominant chords:

     All these chords have tritones in them causing a tension that needs to be resolved. This means that they can be used to achieve the same finality of the dominant chord, which is to confirm or give strength to a target chord we wish to emphasize because of its contextual importance – see cadences.

     On the risk of feeling overwhelmed by all this information, the chords you choose to use should always depend on the harmonic context and feel that you wish to convey and this should always be your guideline.