It's been nearly a year (!) since my last partwriting help entry, so here's one on augmented sixth chords.
Augmented sixth chords are chromatic predominant chords. That is to say that 99% of the time, they occur immediately before a V chord (I'm not going to spend time in this post on the 1%--I will say that the exceptions behave as chromatic neighbor chords, usually to I). Augmented sixth chords are most common in minor keys, but do occur in major keys as well.
There are three kinds of augmented sixth chords that theorists commonly talk about, and they're named after countries: Italian, French, and German. The Italian augmented sixth chord consists of only three notes; the other two contain four notes. Both the French and German augmented sixth chords contain the Italian augmented sixth and one other note, so if you learn how to spell Italian augmented sixths, you should be able to find the other ones with relative ease.
To find an Italian augmented sixth chord, take the following steps:
1. Find scale degree 5 in the prevailing key.
2. Locate the pitches a diatonic half step* above and below scale degree 5. These two pitches will form the interval of a diminished third.
3. Invert that diminished third so that the pitches form the interval of an augmented sixth.
4. Include the tonic scale degree in the chord.
Let's try an example. Let's say we are in the key of G minor. Scale degree 5 in G minor is D. I'm going to locate the note a diatonic half step above D, which is E-flat, and the note a diatonic half step below D, which is C#. C# to E-flat is a diminished third; I invert that to get E-flat--C#. I add the tonic of the key to that chord, giving me E-flat--G--C#. Presto! An Italian augmented sixth chord.
In an Italian augmented sixth chord, always double the tonic scale degree--the middle note (in our example, G). This is the only unaltered (i.e., non-tendency) tone in the chord.
This method of finding augmented sixth chords also reminds us of how they tend to resolve. Since they're predominant chords (and rather intense ones at that), they will almost always resolve directly to V (there's one important exception that I'll discuss below). To resolve this chord, think of expanding the augmented sixth outward to the octave: in our example, the C# will resolve up by half step to D, and the E-flat will resolve down by half-step to D. In a manner of speaking, they go back to where they came from.
Notice that, in minor keys, the diatonic half step above scale degree five is scale degree six. In major keys, the diatonic half step above scale degree five is lowered scale degree six. This is often the source of a lot of confusion, since students are commonly told that augmented sixth chords are built on the lowered scale degree six. But if you think about finding the notes a half step above and a half step below the dominant, you'll be in good shape.
To create a French augmented sixth chord, take the Italian augmented sixth chord and add scale degree 2. Taking our example from above (E-flat--G--C#), adding scale degree two gives us E-flat--G--A--C#. Characteristic of the French augmented sixth chord is its two tritones; here, E-flat to A and G to C#. This is a good way to double-check your spelling. The resolution of this chord is the same as the Italian: the outer notes expand outward to an octave; the middle notes move to the nearest member of the dominant chord (G-->F#; A-->A).
To create a German augmented sixth chord, take the Italian augmented sixth chord and add the note a perfect fifth above the bass. In a minor key, this will be scale degree three; in a major key, you'll need to lower scale degree three by a half step. Taking our example from above (E-flat--G--C#), adding scale degree three gives us E-flat--G--B-flat--C#. To check the spelling of this chord, compare it to a dominant seventh chord. A dominant seventh chord built on E-flat would be E-flat--G--B-flat--D-flat. If we enharmonically respell the D-flat as C#, we have a German augmented sixth chord. This enharmonic equivalence is a special feature of the German augmented sixth chord that permits quick modulation to distant keys.**
Because of the perfect fifth in this chord, we must be careful when resolving it or parallel fifths will result. The German augmented sixth chord must always go through a cadential 6/4 on its way to V. The resolution is basically the same: the augmented sixth resolves out to the octave, and the middle two voices (in our example, G and B-flat) are retained to create the cadential 6/4.
The example below shows each type of augmented sixth chord as explained above, along with a good way to lead into each.
The fourth example is in G major and shows the required alterations. Be aware that the B-flat in the tenor in the augmented sixth chord may occasionally be spelled as an A#. (N.B. in the French and the first German examples, the ii 6/5 chords are both half-diminished; I didn't include the symbol.)
One final word: the labeling of these chords isn't quite standardized. Be sure to check with your teacher to see how they would like you to label them.
*By "diatonic half step" I mean pitches that are a half step away and have different letter names. A diatonic half step above G would be A-flat, not G#. Half steps that have the same letter name (like G and G#) are called chromatic half steps.
**For a great example of how this takes place, see the second movement of Beethoven's fifth symphony. Beginning in m. 23, Beethoven takes an A-flat dominant seventh chord (in context, a V7/IV) and, in m. 29, respells the G-flat as an F#, creating a German augmented sixth chord in the key of C. The chord leads into a cadential 6/4--V in m. 30, and by m. 31, we are in the distantly-related key of C major.
Augmented sixth chords are chromatic predominant chords. That is to say that 99% of the time, they occur immediately before a V chord (I'm not going to spend time in this post on the 1%--I will say that the exceptions behave as chromatic neighbor chords, usually to I). Augmented sixth chords are most common in minor keys, but do occur in major keys as well.
There are three kinds of augmented sixth chords that theorists commonly talk about, and they're named after countries: Italian, French, and German. The Italian augmented sixth chord consists of only three notes; the other two contain four notes. Both the French and German augmented sixth chords contain the Italian augmented sixth and one other note, so if you learn how to spell Italian augmented sixths, you should be able to find the other ones with relative ease.
To find an Italian augmented sixth chord, take the following steps:
1. Find scale degree 5 in the prevailing key.
2. Locate the pitches a diatonic half step* above and below scale degree 5. These two pitches will form the interval of a diminished third.
3. Invert that diminished third so that the pitches form the interval of an augmented sixth.
4. Include the tonic scale degree in the chord.
Let's try an example. Let's say we are in the key of G minor. Scale degree 5 in G minor is D. I'm going to locate the note a diatonic half step above D, which is E-flat, and the note a diatonic half step below D, which is C#. C# to E-flat is a diminished third; I invert that to get E-flat--C#. I add the tonic of the key to that chord, giving me E-flat--G--C#. Presto! An Italian augmented sixth chord.
In an Italian augmented sixth chord, always double the tonic scale degree--the middle note (in our example, G). This is the only unaltered (i.e., non-tendency) tone in the chord.
This method of finding augmented sixth chords also reminds us of how they tend to resolve. Since they're predominant chords (and rather intense ones at that), they will almost always resolve directly to V (there's one important exception that I'll discuss below). To resolve this chord, think of expanding the augmented sixth outward to the octave: in our example, the C# will resolve up by half step to D, and the E-flat will resolve down by half-step to D. In a manner of speaking, they go back to where they came from.
Notice that, in minor keys, the diatonic half step above scale degree five is scale degree six. In major keys, the diatonic half step above scale degree five is lowered scale degree six. This is often the source of a lot of confusion, since students are commonly told that augmented sixth chords are built on the lowered scale degree six. But if you think about finding the notes a half step above and a half step below the dominant, you'll be in good shape.
To create a French augmented sixth chord, take the Italian augmented sixth chord and add scale degree 2. Taking our example from above (E-flat--G--C#), adding scale degree two gives us E-flat--G--A--C#. Characteristic of the French augmented sixth chord is its two tritones; here, E-flat to A and G to C#. This is a good way to double-check your spelling. The resolution of this chord is the same as the Italian: the outer notes expand outward to an octave; the middle notes move to the nearest member of the dominant chord (G-->F#; A-->A).
To create a German augmented sixth chord, take the Italian augmented sixth chord and add the note a perfect fifth above the bass. In a minor key, this will be scale degree three; in a major key, you'll need to lower scale degree three by a half step. Taking our example from above (E-flat--G--C#), adding scale degree three gives us E-flat--G--B-flat--C#. To check the spelling of this chord, compare it to a dominant seventh chord. A dominant seventh chord built on E-flat would be E-flat--G--B-flat--D-flat. If we enharmonically respell the D-flat as C#, we have a German augmented sixth chord. This enharmonic equivalence is a special feature of the German augmented sixth chord that permits quick modulation to distant keys.**
Because of the perfect fifth in this chord, we must be careful when resolving it or parallel fifths will result. The German augmented sixth chord must always go through a cadential 6/4 on its way to V. The resolution is basically the same: the augmented sixth resolves out to the octave, and the middle two voices (in our example, G and B-flat) are retained to create the cadential 6/4.
The example below shows each type of augmented sixth chord as explained above, along with a good way to lead into each.
The fourth example is in G major and shows the required alterations. Be aware that the B-flat in the tenor in the augmented sixth chord may occasionally be spelled as an A#. (N.B. in the French and the first German examples, the ii 6/5 chords are both half-diminished; I didn't include the symbol.)
One final word: the labeling of these chords isn't quite standardized. Be sure to check with your teacher to see how they would like you to label them.
*By "diatonic half step" I mean pitches that are a half step away and have different letter names. A diatonic half step above G would be A-flat, not G#. Half steps that have the same letter name (like G and G#) are called chromatic half steps.
**For a great example of how this takes place, see the second movement of Beethoven's fifth symphony. Beginning in m. 23, Beethoven takes an A-flat dominant seventh chord (in context, a V7/IV) and, in m. 29, respells the G-flat as an F#, creating a German augmented sixth chord in the key of C. The chord leads into a cadential 6/4--V in m. 30, and by m. 31, we are in the distantly-related key of C major.