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 Bo 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 7th 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 Bo7 chord can be inverted fourfold and each inversion being the fundamental or tonic of a new diminished 7th chord:

From the inversion of the Bo7 chord we get the Do7, Fo7 and the Abo7, 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 Bo are a major 3rd apart, meaning that a Bo 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 Do, Fo and the Abo ; 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 7th 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 3rd degree; into an E7 by lowering the 5th degree; and into a G7 by lowering its 7th

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;

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:

using Chord Superimposition

Another common substitution of the tritone is to use the G7 b9 instead of the G7 that is present in the C major scale. This chord can be obtained by superimposing the Bo7 over the G7:

The G7 b9 obtained by superimposing a G7 and a Bo7 – a G7 | Bo7 polychord; resolving to C

If we superimpose the other diminished chords derived from the respective chord cycle, we will get the same G7 b9 chord since all the diminished chords have the same notes.

However, and as seen, the derived dominant chords are also a minor 3rd 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 G7 b9, G7 #9, G7 b9 (b5) and the G7 b9 add13 as the result of the G7|Bo, the G7|Bb, the G7|Db and the G7|E polychords, respectively.

Resulting chords from polychords Bo7 | 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 6th. The diminished chord cycle presents us with yet another possibility for dominant substitution.

Instead of using the diminished 7th, we will be looking at the half-diminished chord, the Bm7 (b5), which is the natural diminished chord formation based on the 7th 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 6th; 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

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.