Monday, June 27, 2005

Augmented Triads and Augmented Seventh Chords

The Augmented Triad is, along with the Diminished Seventh Chord, one of only two perfect symetric harmonic structures in the twelve tone system, as I mentioned in my previous post. Like the diminished seventh chord, the augmented triad has a dominant function and no real perceivable root except in retrospect after it has resolved. This is because, like the diminished seventh chord, any one of the three tones in an augmented triad can be interpreted as the leading tone, so it also momentarily suspends tonality as the diminished seventh sonority does. Unlike the all minor third diminished seventh which requires that a real root be added a major third below one of it's tones to get a fifth voice for four part harmonic canon composition wth a constant root bass, the augmented triad's all major third construction means that the root is the tone a major third below whichever tone is selected to function as the leading tone. This solves some problems associated with the diminished seventh, wherein all the four tones are active and require resolution, but others are created with the raised fifth degree (sometimes notated enharmonically as the flatted sixth) in association with a seventh, as we shall see.



On the top staff above I have demonstrated the theoretical origin of the augmented triad in the first measure: If a leading tone for the minor key is added to the fifth degree of the major triad on the bIII degree, an augmented triad is created. The root on the flat third degree is purely theoretical in the normal resolution for this chord, as can be seen in the following two measures. Here, there is the usual counterclockwise resolution of a Progressive root motion where the note C is interpreted as the fifth degree of the augmented triad, and not the sixth degree. The augmented triad is marked as enharmonic because it is spelled with a C versus a B-sharp, which makes sense since the note is tied over to become the third of the tonic triad. The augmented triad's normal resolution in the minor key, with it's two common tones, is very smooth; and coming from such a highly charged dissonant sonority, it is also very effective.

The real augmented triad - by that I mean the one in which the theoretical and real roots agree - is found in the major key where the fifth of the V triad is raised to get it. Here, there is only one common tone since the raised fifth resolves up to get to the third of the tonic triad, following parallel to the leading tone's resolution to the tonic degree. Again, there are no problems with a triadic environment in the upper stratum with a constant root bass below.

It is not until we try to employ an Augmented Seventh Chord that things get tricky. Using the enharmonic version from the minor key, the augmented fifth (flat sixth degree) sustains over to become the third of the tonic, while the seventh resolves down to become a third also. This results in a tonic triad with a doubled third. This is an irregular or hybrid transformation type. The same situation arrises in the major key where the raised fifth of the dominant chord resolves up by step to the major third of the tonic, while at the same time the seventh also resolves down to the second third. Obviously, this would ruin any harmonic canons if not dealt with properly. There are two ways to approach this and rectify the situation.

The first approach involves using the enharmonic version of the augmented seventh. Since the fifth is supposed to go to the root in a crosswise transformation, it follows that the raised fifth needs to get there in some fashion, or the harmonic canon will be interrupted (Unless the same irregular resolution is used in each place where the augmented seventh appears, which we'll cover later). Starting on the third staff, I have demonstrated the accented passing tone method combined with a delayed resolution of the seventh, or a 4-3 suspension resolution. This same method works in the major, where it now makes more sense to notate the raised fifth as the enharmonic flatted sixth. This is the chord I used penultimate to the resolution in the Theorem of Pythagoras sketch I presented earlier.

There is another way to handle this though. On the lower staff I have shown the seventh resolving down to the third while in the major the raised fifth of the dominant resolves up to the other third, then the passing tone figure is employed to bring the chord of resolution back into it's normative configuration. In the minor, this happens after the tied third occurs across the barline.

By understanding what all the normal and most natural transformation patterns are, unusual situations can be reasoned out and control can be maintained. There is no other way to write harmonic canons than by maintaining strict control over your transformation types in conjunction with employing repeating root progression patterns.

Since an augmented triad is symmetrical, any tone of it can be not only used as a leading tone with associated root a major third below, but any of the three tones can be lowered by a semitone to get any one of three different major triads. These can be used with or without a seventh as dominant function chords in suprise modulations. Also, augmented triads and augmented sevenths can be used to target secondary degrees of the key just like other forms of dominant function harmony: Secondary Dominants, Secondary Dominants with Diminished Fifths (Derived from so-called French Sixths), and Secondary Diminished Sevenths( Or V7(m9) sonorities in a five voice texture with constant root).

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