Extraordinary Function and the Half-Diminished Seventh in the Song of the Wood Dove

[1] In the years following the debut of the Tristan chord, a number of works have continued the dialogue on how half-diminished sevenths function. Arnold Schoenberg famously noted that “there has been great argument over the question as to which degree [the Tristan chord] belongs” (Schoenberg 1911, 309–310).⁽¹⁾ While Schoenberg acknowledged the debate and confusion in 1911, he also pointed the way towards a process of understanding: “...essential to us is the chord’s function, and it reveals itself when we know the chord’s possibilities” (Schoenberg 1911, 310).⁽²⁾ Only recently have we taken Schoenberg’s words to heart and examined the various options inherent in half-diminished sevenths; only recently has our theoretical inquiry moved beyond elemental questions, allowing us to unravel the complicated musical contexts with which we wrestle.

I. Introducing the Half-Diminished Seventh

[3] Relying on conventional theory to address the musical practices of late chromatic harmony can be problematic because, as Carl Dahlhaus observes, “the essential element in the association of chords is semitonal connection and not root progression...chromaticism has achieved a degree of independence from its origins in alteration” (Deathridge and Dahlhaus 1984, 199; Kinderman and Krebs 1996, 4). By now, the analytical tensions this repertoire causes are familiar: the harmonic contents are often unyielding to classification in fundamentally diatonic systems, while individual pieces create their own stylistic tendencies (Proctor 1978; Kinderman and Krebs 1996). While classic studies on chromaticism concentrate on formal shape, more recent scholarship provides analytical entry points into the details, focusing on seventh chords instead of triads, obfuscation instead of clarification, and tension rather than release.

[5] More recently, Richard Bass describes how half-diminished sevenths cause us additional complications because we still consider them the product of linear motion when they occur outside their traditional contexts—that is, in forms other than vii⁷ or ii⁷ (Bass 2001, 41). Consequently, the chromatic chords from Example 2a are habitually classified as irregular, embellishing, or non-functional, often because we are unfamiliar with how they operate (Bass 2007, 73). Bass creates two categories for our seventh. The first, a half-diminished augmented sixth, notates as and occurs in major, as is the case in measure 2 of Example 2a. The second group, the half-diminished diminished seventh, spells the chord with and is specific to the minor mode, as in Example 1a (Bass 2001, 44). When one takes enharmonic equivalence into consideration, the chords are identical, thus making the primary distinction between them notational. Daniel Harrison catalogues the same pitch-classes as a part of the augmented-sixth family—a “dual German-sixth”—and considers the leading tone a coloristic element that Smith, Bass, Harrison, and I all agree adds an especially poignant touch to the chord’s functional palette (Harrison 1995, 184–185).⁽⁷⁾

[6] The first three chords in Example 2a resolve to C-major triads, where the leading tones ascend to the tonic and dissonances resolve appropriately. On the second set of staves, the same sevenths resolve to C-minor triads.⁽⁸⁾ In minor, the and add notational complexities to the voice-leading because they already exist as the diatonic and in minor, but aurally remains a common tone and all other pitches resolves by semitone.⁽⁹⁾ This study proceeds with the assumption that these chromatic sevenths are pivotal to our understanding of postromantic music, and that the solutions in Example 2a are merely the obvious ones. Add to them the multi-key enharmonicism, applied chords, and ornate deceptive resolutions bound to occur within this repertoire (Example 2b) and the possibilities expand dramatically.⁽¹⁰⁾

[7] We determine a sonority’s function by examining three elements: its context, root, and quality. Smith suggests our half-diminished seventh is a delicate dominant on the basis of its leading tone and context; both Harrison and Bass establish its similarity to augmented-sixth chords by placing some emphasis on its predominant moorings, without actually identifying it as such (Smith 1986, 124–126; Harrison 1995, 184–185; Bass 2001, 44). It follows that identifying this seventh by a root is bound to be troublesome. Like the family of augmented sixths—chords seldom identified by roots—giving the seventh a root is likely to further problematize it. The analyses that follow identify the half-diminished chord by its bass voice and function(s).⁽¹¹⁾

[8] The seventh’s functional composition leaves us with the initial impression that it is a multifarious changeling. Its contexts tend to further support this confusion and are homologous to two kinds of standard tonic prolongations: expansion by plagal means and expansion via a dominant. As is the case in diatonic music, the context of an individual scale-step can have an impact on its function, and a scale-step can maintain connections to more than one function. Outlined in Example 1b, the chord’s functional possibilities do not provide a single, obvious designation. The neighbor C’s descent to B seems to have clear predominant associations because it is a regular part of motion from a minor-mode or modally-mixed dominant preparation to V. Yet it also has a role in plagal progressions and tonic expansions involving vii°⁷ or its inversions, for in both, –– is a consistent voice-leading pattern. A similar functional configuration also applies to the upper-neighbor motion above the G, in the right hand of the piano arrangement. As a subdominant hallmark, the A neighbor can help to prolong the tonic plagally, yet because of its frequent use as the seventh in V⁷, may also create a hint of dominant function.⁽¹²⁾ That is, the we hear in V⁷ can be distinguished from the we hear as the root of a subdominant, and its interpretation in the half-diminished seventh is thus dependent on the chord’s context (Harrison 1994, 45–56). The G is also a common tone between the two chords and is therefore similar to the stationary in plagal relationships and to the in dominant-to-tonic ones. As a result, the unchanging has strong tonic associations and adds a third functional component to our seventh. This voice-leading is also reminiscent of what has become known as Schoenberg’s “Law of the Shortest Way,” for the motion is as slight as possible.⁽¹³⁾ In sum, Example 1b results in a sonority that has a similar number of dominant elements as it does subdominant ones, and creates this effect with function-specific voice-leading. We commonly acknowledge that diatonic chords have constituent scale-steps from two functions, while some sonorities may submit claims on all three. This half-diminished seventh has exactly that potential, for it is the lone half-diminished sonority to be comprised of scale-steps representative of all three functions. Surely the conflicting functional implications Schoenberg created were not lost on either his compositional or theoretical mind.

[9] Bass lines are equally important to our understanding of harmonic function (Smith 1986;