The first discord

In the history of Western music the dominant seventh was the first discordant chord to be used as freely as the consonant major and minor triads. It is also the first discordant chord that most people come across in their theory instruction.

For this reason it is a very well understood chord. The augmented sixth chord, however, is very poorly understood despite its clear similarity to the dominant seventh chord. It can be most easily understood by examining it in parallel to the dominant seventh type chord, which is how I shall approach it here.

The variety of names under which the augmented sixth chord has laboured also helps to obscure its understanding - in classical theory it is often referred to as the French sixth, the German sixth, or the Italian sixth. In jazz this chord is most frequently described and understood as a tritone substitution (of a dominant chord). The three classical names all refer to chords containing a root, a major third, and an augmented sixth, but differ in their choice of additional pitches: the German contains a perfect fifth, the French contains an augmented fourth, the Italian contains has no fifth or fourth (in four-part harmony, the third is usually doubled). Despite these differences the chords are functionally identical.

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The dominant seventh

If you build a four note chord, consisting of thirds, and you start on the dominant (or fifth note) of the scale, you will get the dominant seventh chord.

This chord is spelt 1 - 3 - (5) - flat7. (The 5 is bracketed because it is often missing from the chord and it can be sharpened or flattened without damaging or altering its function).

Over time the term "dominant seventh" referred to any chord which uses this formula, but whose root can be on any degree and not just the dominant.

The dominant seventh chord is felt to be unstable and actively seeks resolution. The main motive force of this instability is the diminished fifth between 3 and flat7, which seeks resolution to a major or minor third, with the seventh moving down and the third up. It is exceptional for the voices which make up the dominant seventh to move in any other way.

The most effective resolution of a dominant seventh is to a major or minor triad whose root is a fifth below. It can also resolve effectively to a minor triad a major second above. Resolutions to a major triad a minor second above and the first inversion of the major triad a major second below are also common:

Conventional resolutions of the dominant seventh:

Best Good Acceptable
         
G7 - C G7 - c G7 - a G7 - Aflat G7 - Fb
         
V7 - I V7 - i V7 - vi V7 - flatVI V7 - IVb

The resolution of the dominant seventh is frequently extended with the interpolation of a triad in second inversion which is built on the same bass note as the resolution chord. So, instead of V7 - I, we might get V7 - IVc - I (which, in the key of c major is: G7 - Fc - C).

The dominant seventh is frequently used as a secondary dominant so that it can be used as a chromatic chord which resolves onto a diatonic chord, without endangering the tonal centre. For instance all these chords can be consider to be part of the tonality of a major key:

I - IV | VI7 - ii | vi - II7 | V7 - I if it is heard as:

I - IV | (V7 of ii) - ii | vi - (V7 of V) | V7 - I

In c major these chords are:

C - F | A7 - d | a - D7 | G7 - C

The secondary dominant does not disturb the tonality because it resolves onto chords which are diatonic to the key. It is possible for secondary dominants to resolve to non-diatonic chords, and for the secondary tonality of which this dominant is a diatonic chord to be extended. In this case the secondary tonality can still be heard in relation to the primary tonality, but if the secondary tonality is extended for too long then we may well begin to hear the chromatic secondary dominants only in relation to their own key. That is, we will hear the music to have modulated - the point at which this happens is probably somewhat fuzzy and also dependent on the listener.

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The augmented sixth

The augmented sixth is a chromatic chord, in that at least one of its tones must be foreign to the key signature. This is because it contains the interval of the augmented sixth - an interval that is not found in the diatonic scale.

The dominant seventh is spelt 1 - 3 - (5) - flat7, while the augmented sixth is spelt 1 - 3 - (5) - sharp6. (The 5 is bracketed because it is often missing from the chord and it can be sharpened or flattened without damaging or altering its function.)

We can see how these two chords are represented on a keyboard by exactly the same notes. The difference between these two types of chord is in their resolution. In the dominant seventh the tritone in the chord is resolved to a third by the third moving up and the seventh moving down. In the augmented sixth this is reversed, so that the tritone is resolved to a third by the third moving down and the seventh moving up.

The most common resolution of the augmented sixth is to the major or minor triad a minor second below. It can also resolve effectively to a major triad a perfect fifth above:

Conventional resolutions of the augmented sixth:

Best Good
     
Dflataug6 - C Dflataug6 - c Faug6 - C
     
flatVIaug6 - V    
or flatIIaug6 - i IVaug6 - I
flatIIaug6 - I    

Like the dominant seventh, the resolution of the augmented sixth is frequently extended with the interpolation of a second inversion triad on the same bass note as the resolution chord. So, instead of flatVIaug6 - V, we might get flatVIaug6 - Ic - V (which, in c major and including the final resolution is: Aflataug6 - Cc - G - C).

Just as the dominant chord is used as a secondary dominant which resolves to a chord that is diatonic to the key, so is the augmented sixth. The only difference is that all augmented sixth chords are secondary, because they are all chromatic.

In common practice classical the augmented sixth is most frequently used so that it resolves onto either V or I. The most common progressions using augmented sixths are, therefore:

flatVIaug6 (- Ic) - V

flatIIaug6 (- IVc) - I and

IVaug6 - I.

In later classical music and jazz the augmented sixth is used to resolve to almost any chord which can be either directly or indirectly related to the main key centre. A familiar jazz style progression might use something like:

V7 - flatVaug6 | IVmaj7 - iimin7 | flatIIaug6 - Imaj7 which can be reinterpreted as:

V7 - (flatIIaug6 of IV) | IVmaj7 - iimin7 | flatIIaug6 - Imaj7

In c major these chords are:

G7 - Gflataug6 | Fmaj7 - dmin7 | Dflataug6 - Cmaj7

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Tritone substitution

Above we have compared the dominant seventh and its parallel augmented sixth chord. To achieve a complete understanding of this chord we now need to compare the augmented sixth and dominant chord whose roots differ by a tritone.

The active force in both the dominant seventh and the augmented sixth is the tritone found between the 3 and the flat7 / sharp6. The tritone in G7 is f - b, whilst the tritone in Dflataug6 is also f - b. So the augmented sixth and the dominant whose roots differ by a tritone, effectively resolve to the same chord - this means that one chord can be substituted for another. In jazz the process of substituting a dominant seventh chord for one whose root is a tritone away is known as tritone substitution.

For example the chord progression of a standard may be:

I | vi | ii | V7 | I

Using secondary dominants this can become:

I | III7 - vi | II7 | V7 | I

Using tritone substitution this may become:

I | flatVIIaug6 - vi | flatVIaug6 | V7 - flatIIaug6 | I

In jazz the tritone substitute augmented sixth is usually called, incorrectly (but quite pragmatically), a dominant seventh type chord.

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Enharmonic Substitution

Just as we can substitute a dominant seventh and an augmented sixth whose roots differ by a tritone, we can also substitute a dominant seventh chord and an augmented sixth with the same root.

Because the chords 1 - 3 - (5) - flat7 and 1 - 3 - (5) - sharp6 are both represented by eaxctly the same notes on the piano (i.e. in 12 tone equal temperament), one can approach one of these chords as a dominant seventh, but then quit it as if it were an augmented sixth, and vice versa. It is through the means of such an enharmonic substitution that we can effect enharmonic modulation.

For instance we could have a progression such as I - ii - V7, then quit the V7 as if it were actually an augmented sixth - with a progression like:

I - vi | ii - V7 / Vaug6 | viic - sharpIV | vii which should be reinterpreted as:

I - vi | ii - V7 / flatIIaug6 of V of vii | ic of vii - V of vii | i of vii

Relative to c major this is:

C - a | d - G7 / Gaug6 | bc - Fsharp | b

Or, reversing the process we could have a progression such as I - V7 - flatVIaug6, but then quit the flatVIaug6 as if it were actually a dominant seventh - with a progression like:

I - IV | V7 - flatVIaug6 / flatVI7 | flatII which should be reinterpreted as:

I - IV | V7 - flatVIaug6 / V of flatII | flatII

Relative to c major these chords are:

C - F | G7 - Aflataug6 / Aflat7 | Dflat

Using this method we can modulate quickly and simply from any key to another key differing by a minor second. Without using enharmonic modulation these two keys are mutually very remote - with a minimum of just two notes in common. Because of the subtelty and sophistry of this method, enharmonic modulation must be used with care as to its aesthetic effect.

Using enharmonic substitution many more, otherwise distant keys, can be quickly connected.