Augmented Options

Aren’t we forgetting something here? We’re now well into chromatic harmony, yet we’ve hardly mentioned one of the four types of ostensibly diatonic triads: we’re up to speed with augmented sixth chords, but not the augmented triad. So what is this augmented triad all about? How do composers use it? How have we neglected it so long (and why do so many textbooks brush over it altogether)?

Recall that we have four types of triads that can be constructed with major and minor thirds alone:

• Diminished triad (minor third + minor third)
• Minor triad (minor third + major third)
• Major triad (major third + minor third)
• Augmented triad (major third + major third)

So the augmented triad is part of this set of possibilities, but apparently not an equal member, at least not in the eyes of common practice composers. Clearly major and minor triads are mission critical to tonal music, and so is the diminished triad, especially in its dominant function role (as vii^o and as a part of V⁷). The augmented triad is a slightly peripheral character in relation to those protagonists.

Always Chromatic?

Part of that rarity has to do with the structure of the major/minor system itself: III+ in harmonic minor is the only time the augmented triad appears in the major/minor system without chromatic alteration. This III+ triad is closely related to both the dominant (V) and minor tonic (i): in both cases, two scale degrees are held common and only one semitone distinguishes the chord tone which changes:

• III+ and V: [latex]\hat5[/latex] and [latex]\hat7[/latex] in common, semitone between [latex]\hat2[/latex] and [latex]\hat3[/latex];
• III+ and i: [latex]\hat3[/latex] and [latex]\hat5[/latex] in common, semitone between [latex]\hat1[/latex] and [latex]\hat7[/latex].

Overall, I’d say that the sound and usage of III+ typically suggests a dominant function. See what you think of the following example from the opening of Schubert’s “Der Atlas” (Example 1) in which:

• B♭ and D remain constant throughout ([latex]\hat3[/latex] and [latex]\hat5[/latex]).
• G moves to F♯ and back ([latex]\hat1[/latex] and [latex]\hat7[/latex]).
• This arguably gives the impression of a tonic-dominant alternation, but with very slight changes.

Here is the entire song:

Schwanengesang, D.957 by OpenScore Lieder

The small steps between these chords relate to a key part of the “parsimonious voice leading” that’s so important to the “Neo-Riemannian” approach to harmony, which seeks to account for the extended tonal relations that become more common in the late 19^th century. For more on that, see Neo-Riemannian Triadic Progressions. For now, let’s continue to look at some examples of the augmented triad in practice.

Rarely focal

The relatively peripheral role and the rarity of augmented triads may be thought to diminish its importance, though as the price of gold, diamond, and other rare commodities attest, that very rarity can be valuable. For Schoenberg, this makes the augmented triad “better protected against banality” than the diminished triad and seventh (1911, trans. ed. 1983, p. 239).

The idea of rarity also needs unpacking: when we speak of “rarity” in harmony, we usually mean that it is unusual to see that chord in a focal role. This speaks to Richard Cohn’s observation that “when an augmented triad appears in music before 1830, its behavior is normally well regulated and unobtrusive, tucked into the middle of a phrase rather than exposed at its boundaries, passed through quickly and lacking metric accent” (2012, p. 43).

This may be true in the general case, though that’s not to say there aren’t glorious counterexamples. Example 2 sets out such an example from the “mente cordis” section that concludes the “Fecit Potentiam” of Bach’s Magnificat (1723, 1733). This is a remarkable moment: not only is there an augmented triad at all, but it is introduced by nearly full forces, spanning the full register, and after a dramatic general pause which itself is preceded by a diminished seventh. You couldn’t hope to find a clearer, more dramatically foregrounded augmented triad in any repertoire.

Chromatic passing chord

Although there is only one diatonic form of the augmented triad (III+ in minor), there are clearly many more possibilities when we expand the remit to include chromatic alterations. Here too, however, some are more common than others. A particularly favored use sees the augmented chord as part of a chromatic passing motion from V to I in major, with the whole-tone step from [latex]\hat2[/latex] to [latex]\hat3[/latex] “filled in” with a chromatic semitone motion that gives a fleeing . This can appear in several ways:

• As a straightforward V–V+–I
• With another harmony on the initial [latex]\hat2[/latex]: e.g., ii–V+–I
• With or without sevenths: e.g., ii⁷–V+⁷–I

Example 3, from Fanny Mendelssohn Hensel’s Gondellied (6 Lieder, Op. 1, no. 6), sets this out. Measures 19–20 can be seen as a V⁶/V–V+–I cadence in A (or, with sevenths, V[latex]\mathrm{^6_5}[/latex]/V–V+⁷–I)​ where:

• the augmented chord appears in a dominant function;
• the crucial note of that augmented chord (B♯) is the raised supertonic, arising through chromatic motion from [latex]\hat2[/latex] to [latex]\hat3[/latex] (both in the voice part and doubled in the piano).

Here is the entire song:

Hensel, Fanny (Mendelssohn) – 6 Lieder, Op.1, No.6 – Gondellied by OpenScore LiederCorpus

The Augmented Triad​ as Figure or Ground in Liszt’s R. W. Venezia

Score on IMSLP

So far, we have seen examples of the augmented triad in diatonic form (III+), and as a chromatic alteration but with a clearly defined function (V+). Let’s now venture further into the chromatic territory and to pieces which use the augmented triad in a prominent, focal way. Liszt’s late music includes some fascinating miniatures, many of which heavily emphasize the augmented triad.^[1] R.W. Venezia is one such work, highlighting the augmented chord in general, and C♯ augmented [C♯, F, A] in particular. This chord receives such a weighting that it stakes a remarkable claim to a kind of overall primacy or tonicity that at least challenges and perhaps even vanquishes the corresponding claim from a tonal center (B♭).

Cohn (2012, 47), after Harrison (1994, 75ff.), discusses a similar emphasis of the diminished chord in Schubert’s “Die Stadt,” rightly observing that “rhetorical garments normally reserved for consonances” are used in this repertoire to afford dissonant chords a kind of surrogate tonic status (see also Morgan 1976). Those rhetorical strategies are well summarized by the pithy notion of “first, last, loudest, longest.”

R.W. Venezia begins with a C♯ augmented chord outlining, resolving by parsimonious voice leading to B♭ minor as the start of a rising chromatic sequence which ultimately turns into a long succession of rising (initially parallel augmented) triads that climax in a blazing, forte B♭ major. That forte section then moves through more parsimonious voice leading cycles before returning to C♯ augmented, now fortissimo. Finally, this C♯ augmented chord initiates a descent which deftly combines the pitches of B♭ minor and C♯ augmented [B♭, C♯, F, A], leading to an ambiguous close on a unison C♯. That final C♯ is repeated, carrying with it the ambiguity right up to the last note. If the second, final C♯ were a B♭, then the piece would come down more firmly in favor of B♭ minor. As it is, Liszt maintains the delicate balance and leaves us wondering which is the figure and which the ground.

In short, C♯ comes “first” and “last,” while B-flat probably wins in the “loudest” stakes, leaving “longest” as the primary vehicle of ambiguity. The augmented chord is used considerably more than the average for the time, even for Liszt (a considerably above-average user), though still not to the same extent as major or minor triads. Then again, the C♯ augmented triad specifically is used to approximately the same extent as B♭ major and minor combined, raising the case for it as “tonic.” Whether that is enough is open to debate; ultimately, I hear them in an amazingly effective balance where neither quite shines through.

Anthology Examples

This chapter has surveyed some claims about how relatively common or otherwise specific particular progressions are. But so far, we’ve just looked at examples. To make sense of this kind of claim, we ought to consider the overall case. We don’t have space here to go into that in detail, but this final section provides some direction toward extensive lists of further examples for you to explore.

First, here is an initial list of approximately 200 examples gathered from the literature. The list could be thought of as an augmented triad “canon”—those instances notable enough to have been mentioned in either the theoretical or historical literature. These repertoire occurrences are varied in function and tone. Many are indeed “merely” incidental appoggiaturas and decorations, while others are fundamental, referential sonorities; some are isolated cases, others are a core part of wider, recurring harmonic processes; some have an ambiguous role, others have a clear musical and even extra-musical meaning including topical associations which generally center on death, ambivalence, or mystery.^[2]

Second, head to the Harmony Anthology chapter for a list of moments in the OpenScore Lieder collection that analysts have viewed in terms of augmented chords. The list is sortable by composer, collection, song, measure, Roman numeral (figure) and key. Each entry includes a link to the score.

1. Head to the section on augmented chords in the Harmony Anthology chapter and pick one (or more) of the repertoire examples listed in which an analyst has identified the use of an augmented chord.
   • For that passage, make a Roman numeral analysis of the measure in question and one or two on either side (enough to establish a chord progression and some context).
   • Create one such harmonic analysis including the augmented triad provided (figure and key are given in the table).
   • If you disagree with that reading (as you may well do), then provide an alternative harmonic analysis without it.
2. Do step 1 for several cases and identify any that seem similar to each other, and to the above. For instance, for the cases given as V+ in the anthology, are many of them similar to the chromatic passing motion in the Hensel above? Can you find any dramatic examples like the Bach? Do you see any other recurring practices not described in this chapter?