19b Lesson - Common-tone diminished chords

Augmented sixth chords act as functional substitutions for pre-dominant and occasionally dominant chords, so in both of these cases, you can assign those chords a primary function of dominant or pre-dominant. The chord that you will study below does not fulfill one of the three primary functions; instead, it embellishes and elongates a different chord, similar to a tertiary function chord such as a passing or pedal chord.

It is possible to think of this chord using tertian harmony, but its voice-leading determines its construction.

Listen to and then analyze the following three progressions. The first is the most straightforward example of this chord, and each example gets progressively more complicated. As always, start your analysis with leadsheet symbols and then provide Roman numerals when possible. In each progression, study the chromatic chord to answer the following questions:

• How would you describe its construction?
• How does it function? (e.g. tonic, passing, etc.)
• Does it have tendency tones, and if so, how do they resolve?
• If you were to compare it to a diatonic or chromatic chord that normally fulfills this function, which chord shares the most commonalities with it?
• Does this embellishing chord work for all types of chords (i.e. major, minor, etc.)? If not, why?

Conclusions

Each of these three phrases contains one chord which does not function like any chord that we have studied thus far.

• The first phrase shows the most basic usage for a common-tone diminished chord; it establishes the key through a I-V-I progression and then arpeggiates the I chord. On the downbeat of the the third measure, however, a diminished seventh chord appears that does not function as any diminished seventh chord we have seen. Typically, fully-diminished seventh chords act as a dominant function of the following chord, relying on resolving the root of the diminished chord up by half-step to the root of the next chord. In this case, you can see a D#^o7, which, if it were a secondary leading-tone chord, would resolve to a chord with the root of an E–in this key, it would likely be a vii^o7/iii. Instead, this diminished seventh chord shares a common tone with the root of the chord to which it resolves. The notable features of this resolution though, are that the other three pitches resolve smoothly by step-wise motion to the pitches of the I chord. You could analyze these as neighbor tones, but as we saw when studying pedal and passing chords, it would be simpler and clearer to analyze this as a tertiary function (i.e. chords that extend function), because this group of non-chord tones form a recognizable chord.
• In the second example, we find the same chord on the downbeat of the third measure, but in this example, it is embellishing the V chord instead of the I chord. It shares the same voice-leading principles as the previous example did with the I chord–three neighbor tones and one common tone–as the previous example, but instead of being built as #ii^o7, it is now a #vi^o7 that decorates a V chord.
• The last example is more complicated. The progression begins with a I chord moving to a vi chord, but instead of going to a diatonic predominant, it moves to a V⁶/V. This does not go directly to a V chord, however, and instead passes through a strange diminished seventh chord on the beat 3 of the second measure, an E#^o7. The neighbor tones of the previous example are altered here to instead become passing tones. The chord still has many commonalities to the previous examples, though, in that it is still a diminished seventh chord that is surrounded by the same harmony on both sides and shares a common-tone with those chords.

Common-tone diminished chords

The chromatic chords above are examples of common-tone diminished chords. We will label these chords as ct^o7.

Common-tone diminished chords:

• Are a stack of minor thirds that create a fully diminished seventh chord.
  • When you encounter these in an analysis, you will likely assume that it is a secondary leading-tone chord, but you will quickly notice that it does not resolve correctly as a secondary function.
• Can be used to embellish any major triad or dominant seventh chord.
  • ct^o7 most often embellish either I or V (and V⁷).
  • These chords do not work well for non-major triads because there will be more than one common tone. For example, a minor triad would have two common tones with its ct^o7, and because the ct^o7 is designed to create movement, this weakens its purpose.
• Share a common tone with the root of the chord to which they resolve.
  • It is common for the same chord to precede the ct^o7, but not a requirement.
  • There are examples of composers using a ct^o7 that uses a common-tone that is not the root (e.g. shares a common tone with the chordal fifth), but these are considerably rarer.
• Have three non-common tones that resolve by step to the closest chord tone.
  • For major triads, this means that the chordal fifth will likely need to be doubled.
  • For dominant seventh chords, each non-common tone resolves by half-step to the closest chord tone.
• Do not have their own primary function (i.e. tonic, dominant, pre-dominant) and instead extend another chord’s function.
• Are always labeled with only ct^o7.
  • They have no standard inversion, so they do not require an inversion figure. As with all fully diminished seventh chords, they can be enharmonically spelled in four different ways, and the voice leading of the passage will determine how the chord should be spelled.

The two most common ct^o7 chords are those that embellish the I and V chords. These will most likely be spelled as #ii^o7 and #vi^o7 respectively, because these provide the correct voice leading.

We technically already had a way to label these chords: they could simply be labeled as a pedal chord. If you review our discussions of pedal chords, they are tertiary function chords that share a common tone with chords on both sides. Tertiary function chords extend the function of one of those chords, so common-tone diminished chords fit that description perfectly. Admittedly, ct^o7 can occasionally appear while only having a common tone with a chord on one side, as we saw in the third sample phrase, but this is a rare usage of an already infrequently-used chord.

Common-tone diminished seventh chords happen just often enough that they have received a special name. This is simliar to the Neapolitan and augmented sixth chords, in that those could also be handled through other means–mode mixture for the Neapolitan and non-chord tones for the augmented sixth chord. But because these chords occur with some frequency, theorists have created a special nomenclature to provide a short cut in their analyses.