It is central to Wagner’s style that his musical “objects do not go into their concepts without leaving a remainder,”Footnote 1 which is to say that in any account of how the musical details (the “objects”) fit into a formal or analytical account (the “concepts”), something is left over which cannot be accounted for (the “remainder”). This is true as much in what the first half of this essay labels its “formal properties” as in what the second half calls its “harmonic and motivic structures.” Part of what I mean by this is that, in Carl Dahlhaus’s words, “Wagner the philosopher was at odds with Wagner the man of the theatre, for whom only what was seen on stage could count.”Footnote 2 Generally speaking, the theoretical schemes, some of them grandiose, that Wagner concocted around the time of the protracted composition of the Ring were at best only partially realized in the music – and then mostly in the early stages of the cycle. But I mean something more specific, too. Wagner did not treat the forms and genres that previous generations had granted each composer as an artistic inheritance – recitatives, arias, ensembles, “numbers,” and “scenes,” as well as chords, chord progressions, cadences, and so on – as empty vessels suitable for his music to be poured into. Such a manner of composition would value the musical form more highly than the musical content. For Wagner, dramatic and musical content took priority, and, if from time to time his content is housed in a more or less recognizable form, it is so only because the form emerges from the exigencies of the content itself: there is some apparent dramatic or musical need to create a certain form. The “remainder” which is left when Wagner’s musical objects go into their concept presents itself as something that cannot be fully explained by an analysis, even remains resistant to it – and this gives his music a peculiar fascination.Footnote 3
This chapter examines the forms and structures of Wagner’s music for the Ring in two broad circuits.Footnote 4 By form I mean the musical “shapes” that Wagner employed in these four operas: traditional operatic forms such as arias and ensembles, Wagner’s own theory of the “poetic-musical period” and the use of Stabreim, and the various strophic and “symphonic” forms he used. The looser shapes formed by his use of leitmotif, associative tonality, and narrative interlace will also be briefly introduced here. Broadly speaking, these “forms” establish connections with the traditions which were handed down to Wagner from his chosen musical and literary sources. In the second half, the focus on structure turns attention to Wagner’s idiosyncratic reconstruction of tonality, a structure which is loose in the sense that it imposes no particular form on a piece of music, and rigid in the sense that it insists on one, and only one, way of closing a piece satisfactorily. Far from abolishing this system, as is sometimes supposed, Wagner worked exclusively within it. But if an analytical attempt is made to squeeze his music into a tonal space that in some ways resists its entry, something richly implicative is left out. The comprehensibility of Wagner’s forms explain his broad accessibility – particularly relative to later revolutionary composers such as Schoenberg and Boulez – and the “remainder” left behind by the failure of his structures to entirely correspond to the expectations of the systems they work in explains in large part the magnetic effect he has had on radical artists and thinkers of the last century and a half.
Formal Properties of Scenes and Acts
(a) Periods and Stabreim
Even at the local level of organization, the structure of a melodic phrase, the music of the Ring marks a departure not only from operatic precedent but from most of Wagner’s own previous work. His librettos partly explain his musical choices. An early intention, outlined in Opera and Drama, was that his chosen poetic structure should dictate elements of the structure of the music and so create a “poetic-musical period.” The poetry of his librettos was based on an old model of German alliterative poetry, Stabreim. Believing that this form connected to a primordial essence of the human spirit, Wagner judged that it would further his artistic aim to clear away the alienation of contemporary society and create a new conceptual space for humans of the future. Thus, according to his theory, the stress patterns of the poem ought to regulate stress patterns in the music: The lines of the poem should have some correspondence with the lines of music. It is fair to say that this ambition was not achieved, but the manner of its failure has interesting musical and dramatic consequences.
Carl Dahlhaus draws attention persuasively to the paradox that Wagner’s emphasis on Stabreim is quite immaterial and at the same time the cause of his rejection of regular musical periodicity.Footnote 5 Classically, Stabreim has a regular number of strong accents in each line of poetry. True to character, Wagner adapts or distorts his model: his lines have two, three, or four stresses. Had he used Stabreim classically, then his musical units might have more closely resembled the so-called phrase-structure of the Classical style in music, the predominant formal principle of vocal music up to Wagner’s day. In a musical period, an “antecedent” phrase states an “incomplete” version of a basic musical idea (incomplete because it ends with an imperfect cadence, from chord I to chord V) and is followed, or answered, by a “consequent” phrase which gives a “complete” version of the same basic idea (now closing with a perfect cadence, V–I). But Wagner’s irregular poetic rhythms produce a notable irregularity in his musical phrase-construction.
Dahlhaus cites as an example of this irregularity the setting of the opening of Waltraute’s narration in Götterdämmerung act 1, scene 3 – a moment to which I shall return. In the ten poetic lines which begin “Seit er von dir geschieden / zur Schlacht nicht mehr / schickte uns Wotan” (“Since he separated from you, Wotan has not sent us [Valkyries] into battle”), the poetry varies between two and four stresses, and each line is set to music varying between half a bar and two bars long. In the absence of an obvious pattern to any of this, Dahlhaus concludes that “it is no overstatement to call it musical prose.”Footnote 6 It would be incongruous, to put it mildly, to hear a phrase structure like the opening of Beethoven’s “Ode to Joy” (which is a Classical period) emerging from the mouth of Waltraute, but we should pause to note why that is so. The dramatic quality of such music would be compromised by a musical form whose frequent and predictable cadences emerge from an aesthetic of balance and symmetry that is at odds with the fragmented psychological modernity of Wagner’s characterizations.
(b) Sentences
The periodic phrase structure that was an essential feature of earlier music was not, however, the only premade phrase structure available to Wagner. The main alternative phrase structure in the eighteenth and nineteenth centuries is one that Schoenberg called the “sentence.”Footnote 7 In this, a basic idea of around two bars’ duration is immediately followed by some kind of repetition (e.g., literal or on the dominant), after which there is a continuation containing two essential elements: “liquidation,” a breaking up of the idea into smaller constituent parts, and finally a cadence. The effect of the sentence is to state an idea, fix it in the mind through immediate repetition, develop it (which often involves a fragmentation of the basic motif), and build anticipation of a cadential punctuation to terminate the idea: a very rough similarity obtains with the syntactic structure of a linguistic clause, although there is no sense in which a musical sentence communicates anything definite beyond itself. And there is another approximate relation between this idea and the Bar form that Alfred Lorenz famously identified in Walther’s Prize Songs in Die Meistersinger and then applied as a general principle across Wagner’s entire operatic output.Footnote 8 Lorenz’s “Bar” is a notoriously vague term, and derives such explanatory power as it has from that vagueness (it is, in the disparaging sense used by Karl Popper, more or less “unfalsifiable”), but the greater precision of the concept of the sentence makes that a more useful tool for examining Wagner’s “musical prose.”Footnote 9
In Wagner’s sentences, the basic move is to create a loose form with the proportion short–short–long (corresponding to the classical sentence’s basic idea–repetition–continuation). Wagner may insert additional repetitions of the basic idea, and the close might be attenuated (the cadence might not be a perfect cadence, for instance) or absent altogether, but the shape can still be discerned. The first meaningful vocal statement of the cycle (see Example 4.1), Flosshilde’s criticism of her sisters’ careless watch over the gold, offers a simple illustration. The opening two-bar basic idea (bb. 158–9) is given an immediate, lightly varied repeat (bb. 160–1), and is followed by four bars of continuation (bb. 162–5) which lead to a perfect cadence into B♭ at the start of the next phrase (b. 166).
Example 4.1 Das Rheingold, scene 1
In pursuit of the ideal of “endless melody,” whose most elementary principle is the suppression of cadences at the end of phrases (or the effect of a cadence in the vocal part which is not matched by cadential harmonies in the orchestra), Wagner very frequently loosens this relatively tight sentence structure. And yet, in a manner that is so often a feature of his style, Wagner’s break with convention often retains that convention as a kind of necessary negation, a means of drawing attention to the break he is simultaneously making. The opening of Götterdämmerung gives an example of such a sentence (see Example 4.2).Footnote 10 As at the opening of Rheingold, Matthew BaileyShea notes that the traditional elements of sentence structure are present: a basic idea (in the orchestra, bb. 27–8), a repetition (bb. 29–30), and a continuation (bb. 31–5). But the traditional sentence’s built-in expectation of some kind of closure at the end of the continuation section would be inapt in this dramatic context. All onward drive is absent here: the slow tempo, subdued dynamics, and queries from the Norns (“What light is that there?” “Is the day already dawning?” etc.), all contribute to a sense of stasis. Time does not press here: It must wait. The sentence form in this case is therefore used not to generate motion towards a close, a clearly bounded temporal unit, but a more gradual progress of development and rumination, a musical phrase hovering almost outside of time: hence the continuation’s failure to reach a cadence. In the repetition of the basic idea, too, Wagner dramatizes the moment. Instead of the simply varied repetition of the Rhinemaiden’s line in Example 4.1, “the upper part [of the idea] rises up a third while the harmony is shifted down a third (E♭ minor to C♭ minor). Thus, the basic idea is not just repeated, it is developed.”Footnote 11 The audience’s subconscious awareness of the classical model of the sentence, with its drive towards closure, can thus be summoned up by Wagner only to be negated: as he pours the musical object (the phrase) into its concept (the sentence), we press up against a certain remainder – a sense, perhaps unnoticed at first, but gradually building, and often becoming intense, of desire for a resolution. As BaileyShea observes, “what is most important with regard to Wagner’s sentences is that they generally point toward a specific cadence, even if that cadence itself is ultimately denied.”Footnote 12 Or, to put it another way, what is important about Wagner’s phrase structure is the way that even on its own, without reference to the harmonic structures which inflame its effect, it can seem to arrest the passage of time in an appreciable and effective way, and make the audience will the drama to continue.
Example 4.2 Götterdämmerung, Vorspiel
(c) The “Poetic-Musical Period”
Although the musical period was of no use in the Ring, Wagner’s conception of the poetic–musical period,Footnote 13 which is a kind of huge expansion of this model, served him as a workable pattern from the beginning of Rheingold until the end of act 2 of Siegfried (after which the influence of the composition of Tristan was felt and he moved to a “symphonic” kind of organization which will be discussed below). In the poetic–musical period, Wagner could stretch the desire engendered by his use of the sentence across entire scenes and acts, effectively stretching the concept of musical time a hundred- or two-hundredfold. The fundamental ideas of the poetic–musical period are that longer sections of the poetry should be written as sections of music; that the musical sections should be unified by a more or less consistent exploration of melodic material, harmony, tempo, and meter; and that the period should be brought to a conclusion with a cadence. Much of this definition accords with the requirement of a Classical period, except that while it would be expected that a period should last around eight bars, a Wagnerian poetic–musical period could last for hundreds of bars. Small-scale symmetries, and their inappropriate concomitant aesthetics, could by this means be eradicated, and the forward drive of the drama could become extended, and punctuated by less frequent cadences.
Act 1, scene 1 of Siegfried offers a good illustration of how the poetic–musical period works.Footnote 14 There are eight poetic–musical periods in the scene, with a transition between periods 4 and 5, and a coda after period 8. The dramatic/musical aim is to offer sufficient cadential punctuation for the action to progress from moment to moment, but not so much that the scene itself is broken into separate parts: In theory, there should only be one dramatically obvious perfect authentic cadence (a V–I cadence with the first scale degree, 
, as the final melodic note: the strongest form of cadence in classical tonality) at the end of the scene. Such cadences sometimes appear in the middle of periods, but they are not spotlit by any significant dramatic effect. The effect may be compared to Shakespeare’s practice: A typical scene in Shakespeare may include several couplets, and yet the couplet which typically closes each scene has a different quality, because a character leaves the stage or the location shifts. Substitute perfect authentic cadence for rhyming couplet and the poetic-musical period’s attitude to musical closure is more or less understood.
After the orchestral Vorspiel, Mime’s “Zwangvolle Plage!” begins the first period of scene 1 with a strong cadential motion, effectively VI–V–I.Footnote 15 This period has a loose ABA structure, with a central section focusing on Fafner before a return to the opening music and a vocal cadence onto the tonic of this period, B♭, on the words “schmied’ ich ihm nicht!” (“I can’t forge it!”). This is an example of a quasi-aria form encountered occasionally in the Ring. The first statement of the melody and text establishes a particular mood, as in a Classical aria (here, Mime’s frustration, elsewhere, Fricka’s complaint about Wotan’s infidelity),Footnote 16 which receives a contextualizing contrast in its middle section (here, Mime’s concern about the dragon, in Fricka’s Lament, her memory of Wotan’s earlier care for her), before the opening melodic idea, sometimes with the same first line of text as before (“Zwangvolle Plage!”), returns to initiate what in a traditional form would be a closing section of the form. But in obedience to the subordination of the poetic-musical period to the dramatic arc of the scene and act, the repeated A section tends to degenerate and fail to achieve a cadential close. Here the failed cadence is archetypal. As so often in Wagner’s style, Mime’s line has a cadential shape: It falls to the first scale degree (
, B♭) as if expecting the orchestra to affirm a perfect authentic cadence. But the orchestra enters with a shimmering minor third, E–G, forming a diminished triad with Mime’s concluding B♭. The dramatic effect is to punctuate but not to arrest the flow: The orchestral harmony keeps us moving into period 2, Siegfried’s prank with the bear, which is in G major.
Period 3 starts with the same kind of cadential opening as period 1 had done. Here there is a dramatic ground for the musical gesture. As Siegfried smashes Mime’s latest attempt at forging a sword, we hear the first perfect authentic cadence of the act so far: Siegfried’s line “Den schwachen Stift nennst du ein Schwert?” (“Do you call this puny pin a sword?”) ends on the dominant of G minor (V/g) and closes into that key (I/g) for the beginning of the new period. The typical poetic-musical period pattern is developing through this scene: The beginning of periods are clearly marked either by a cadence into the new key or by a refusal to cadence in the old one; periods end without a cadence of their own.Footnote 17 Period 4, Mime’s “Als zullendes Kind zog ich dich auf” (“I brought you up as a suckling baby”), is opened up by means of a soft but clear V–I cadence into its tonic, F minor, and ends as period 1 had done with a vocal cadence contradicted by the orchestra: Mime’s “der hastige Knabe mich quält und hasst!” (“the hasty boy fears and hates me!”) closes with a 
–
gesture, C–F, but the orchestra enters on a chord of D♭7 in place of the normative F minor. After an interlude, during which Siegfried reflects on what he has learned from Mime and then mocks his song, the second half of the scene proceeds in like fashion with four more periods that have cadentially articulated openings and relatively open endings. By the time the scene’s coda begins with Siegfried “Aus dem Wald fort in die Welt ziehn” (“I’ll move out of the forest into the world”) in B♭ major, we have heard 1,190 bars with only one dramatically foregrounded perfect authentic cadence (at the point Siegfried breaks the sword) – the kind of cadence that Classical tonality might expect every eight bars or so. Even at Siegfried’s swashbuckling departure – “dich Mime, nie wieder zu seh’n!” (“never again to see you, Mime!”) – the orchestra refuses a perfect authentic cadence to match the cadential expectations of the melody: A powerfully cadential V6-4–V5-3 motion is answered not by I but by a surprising II4-3. The tonic B♭ returns after eleven bars of Mime’s frightened response, but the musical flow is not interrupted by a perfect authentic cadence even at this highpoint of the scene. Briefly alone, Mime’s despair is interrupted – and so, appropriately, is his putative drift towards a B♭ minor perfect authentic cadence – by the Wanderer, and a lurching perfect authentic cadence not to close scene 1 but to open scene 2, in A major, for the next period.
The poetic-musical period enabled Wagner, for much of the composition of the Ring, to ensure that individual dramatic moments are grasped clearly by the audiences, without the risk of breaking an act into numbers or scenes. Until his motivic technique and harmonic language passed through the prism of Tristan, composing scenes by means of a sequence of cadentially opened – but normally not cadentially closed – periods remained a pliant form for the composer.
(d) Strophic and “Symphonic” Structures
After the composition of Tristan, Wagner’s harmony, which will be the focus of the second half of this essay, became more complex, and this new complexity engendered ever more complex structures. The next scene of Siegfried, the riddle contest between the Wanderer and Mime, shows one form that had already served Wagner in earlier moments such as Wotan’s Monologue in Walküre. Here, periods can take on the additional quality of being strophic repetitions of the same or similar material. This form often augments the ruminative, uncertain, troubled, or obsessive quality of dramatic moments such as the riddle contest, Wotan’s dilemma concerning Siegmund, his honor, his power, and the curse on the Ring, or the Norns’ struggle and ultimate failure to foretell the future in the first scene of Götterdämmerung.Footnote 18 Across such strophes, a single variegated cadential structure might be presented, in which the stopping points en route to the final perfect authentic cadence each serve a distinct dramatic end. In Wotan’s Monologue, for instance, the first strophes sit gloomily on a string of unresolved dominant pedals for several minutes until, through a massive effort of will, the god lumbers up to the point of a conclusion: “Nur Eines will ich noch: das Ende!” (“I only seek one thing now: the end!”), a ♭II–V progression terminating on a loud, jabbing dominant chord and a silence generally marked dramatically by directors (Chéreau in Bayreuth in 1976 had Wotan clasp and arrest the motion of a Foucault’s Pendulum; Kupfer in Bayreuth in the 1980s and 1990s had a vast chasm open suddenly and noisily at the center of the stage, never to close for the remainder of the cycle). Instead of resolving to the expected A minor (a resolution anticipated by the same motion seventy-two bars earlier: a perfect authentic cadence in the middle of a strophe), Wotan repeats the word “das Ende” and reflects that Alberich, too, seeks that end – which means that Wotan must think again. Another stage in the harmonic progress therefore begins. The harmony slips chromatically to its hexatonic pole (a concept I explain below), E major, and a new strophe is underway. When Wotan reaches his final decision at the end of the sequence of strophes to close the scene, he completes the A minor cadence by the same means he abandoned here: ♭II–V–I.Footnote 19 But it is not, of course, the same A minor it was before: it has passed through the fire of his harrowing indecision to emerge transformed by the process.
Still larger forms than this became possible – even necessary – as a result of changes in Wagner’s harmonic language and the density of his leitmotivic counterpoint between Siegfried acts 2 and 3. Where acts had previously been formed of scenes composed of periods (individual parts of which were often written in sentences), from act 3 of Siegfried on, acts are constructed as longer “movements,” often four to six of them, joined by orchestral transitions. The old poetic-musical period had created a formal isomorphism between the poem and the music, but on this new “symphonic” form of construction, individual “movements” might no longer correspond to the boundaries suggested by the poem – and could even cross over the boundaries between scenes. But as with Wagner’s expansion of the Classical concept of the sentence for his new dramatic purposes, his “symphonic movements” will not be misunderstood if they are seen to be expansions of the principle of the poetic-musical period: they retain the period’s deferral of closure and its subjection of part to whole, while at the same time repudiating its attempted alloy of the forms of poem and music.Footnote 20
From the foregoing it should be apparent that Dahlhaus was exaggerating the case when he wrote that “from Rheingold onwards, the basis of Wagner’s musical form is no longer syntactic but motivic.”Footnote 21 It is nevertheless true that the Ring was a climacteric in the use of both leitmotivic technique and its corollary, associative tonality (the association of, say, D♭ major with Valhalla, and B minor with the curse). Although neither forms nor structures as such, these features of his language – melodic and tonal signifiers, respectively, of a labyrinthine network of personal and thematic interactions – enabled Wagner to establish connections over the longest range with dramatic events seen on stage in earlier evenings, or even to moments that are never staged. It is in the nature of these associations to suggest still further possibilities: events that are not only not presented dramatically but not even alluded to in the narrative. Here there is no hope whatever of a musical analysis answering once and for all questions about what a moment “means”: Even as capacious a conceptual container as the Ring cycle cannot answer questions that can emerge as a remainder when a character or an idea is summoned up by a leitmotif or tonal association and the music decanted into the form. When Alberich returns to the cycle in act 2 of Siegfried, having last been seen in Rheingold scene 4, he brings with him motifs that forge connections across the entire span of music between those two points, and indeed reach further into the past and future. These motifs create a narrative texture that Wagner took over from his medieval literary sources, a technique known as “interlace narrative.”Footnote 22 Imponderables that emerge when these musical gestures impress themselves on consciousness come destabilizingly fast:
[W]hat adventures have befallen him since he bribed a woman into bearing him his heir Hagen (and when did that happen in relation to his humiliation in Rheingold scene 4?). Has he been living alone? Did he raise his son in a community? Where is his son now? Just offstage attending to business of his own, or lost to Alberich altogether? … We are also invited [to] ask how is it that Hagen manages to ingratiate himself with his half-siblings the Gibichungs and why his father is out of the picture. Has Alberich done the Gibichungs some untold wrong or was he simply absent from most of Hagen’s childhood so that the Gibichungs never had any need to spurn him?Footnote 23
Here the only proper critical response is probably to acknowledge defeat. At least the immense deferral of closure in Wagner’s sentences, poetic-musical periods, strophes, and “symphonic movements” in each case finally reached a conclusion in a cadence which certified finality. But the resonances opened up by the techniques of leitmotif and associative tonality are potentially inextinguishable. We cannot close down this world because it is too rich, too real, too far beyond our ken.
Harmonic and Motivic Structures
The interlace structure found echoes in literary modernism in the work of writers who much admired Wagner. These included James Joyce, who used it to create depth in Ulysses (sometimes also making connections with Dubliners), and Marcel Proust, who populated a vastly rich fin de siècle world with the technique in A la recherche du temps perdu. But arguably Wagner’s greatest contribution to early modernism in music was his chromatic distension of tonal space. The most readily graspable aspect of Wagner’s chromaticism, familiar to many music lovers, is the saturation of his post-Tristan harmony with what is generally simply called chromaticism. As interesting, and as expressive, as his individual chords or their sequence often are, an increase in the spectrum of harmonic colors does not on its own constitute a musical revolution. The fact that almost all of the harmonies Wagner used can be described in terms of traditional harmony, and that the great majority of his chords are actually triadic (i.e., simple three-note chords such as E minor and G major) indicates that, in principle, what is interesting about his chromaticism is not the chords he chooses but the structures he forms with them. Specifically, what makes Wagner’s achievement so impressive is the development of a new chromatic technique that restructures the classical relations between the normal diatonic chords in “tonality,” the name given to the system of harmonic organization that took on a definite form around the time of Bach and still persists in popular and film music today.
Wagner’s exploitation of the potential of a radically reordered tonal landscape links abstract musical shapes to arresting dramatic gestures. Although the details are sometimes complex, in principle the relation between the one and the other is normally easy to apprehend. In the same way that the close reading of aspects of a poem such as rhyme and imagery can deepen the appreciation of, and the pleasure taken in, a poem, so does the examination of musical detail enrich one’s intellectual and emotional response to Wagner’s Ring. But more than this, music analysis also enables us to see why radical thinkers, from the modernist artists of the early twentieth century through to leftist critical theorists of the early twenty-first, such as Slavoj Žižek and Alain Badiou, have found Wagner’s music as compelling a vision of a revolutionary new world as any created in the nineteenth century.Footnote 24
The Effect of “Failed” Resolutions
A brief diversion into two of Wagner’s non-Ring operas will establish a broader context for his harmonic practice in that cycle. One of the most familiar and over-examined examples of Wagner’s chromatic revolution is so engrossing in its instrumental voicing, its inversion, and its immediate harmonic context that it has come to stand as the quintessence of nineteenth-century experiments in harmony. Example 4.3 shows the opening three bars of Tristan und Isolde in short score. Famously, the “Tristan chord” of b. 2 (F-B-D♯-G♯), resolves onto a dominant seventh chord in b. 3 (E-G♯-D-B), itself a dissonant chord which seems to require a resolution onto the A minor that is implied by the first three, unharmonized, melodic notes of the opera. The question of how the Tristan chord should be parsed in terms of traditional tonal harmony has been the subject of lengthy and ultimately inconclusive discussion.
Example 4.3 Tristan und Isolde, opening
I do not propose to take a view on what this chord “is,” or how it does or does not function in its context. Whatever the answer to such questions, the chord certainly lends the opening of the opera its immediately gripping effect of representing, and evincing from the audience, a state of unresolved desire. What I find a more interesting question is why a desire that is frustrated throughout the Prelude is felt to be “satisfied” in some sense by the final bars of the opera, in which the Tristan chord resolves through an E minor chord (E-G-B, as opposed to the E-G♯-B-D dominant seventh of b. 3 of the Prelude) to a tonic chord of B major (see Example 4.4). Wagner seems to slip an experiential paradox into these two musical moments: In the first moment, a nonresolution to A minor makes the audience partake of the frustrated desire of the tragic lovers; in the second moment, a nonresolution to A minor makes the audience join the lovers in the “night’s wonder-world” in which, finally, their desire is transfigured and fulfilled. How is it possible that the failure of the Tristan chord to resolve to A minor can result in irreconcilable expressive outcomes? It cannot simply be that the opera ends with a radiantly scored B major chord. (That was a resolution that, in act 2, the lovers had achieved vocally just at the moment that King Marke arrives to interrupt their tryst, but which the orchestra flatly rejects.) Surely, for a “happy” resolution, the correct chord for Wagner to have chosen would have been A major, not B major. There has to be some reason why, in Wagner’s chromatic structuring of tonality, a resolution from the Tristan chord to B major “is,” paradoxically, as satisfying as a resolution from the Tristan chord to A major. Like his lovers, tonality itself seems to have been transfigured here, and turned into something it was not before this moment.
Example 4.4 Tristan und Isolde, conclusion
Revolutionizing Tonality
In gestures like this, which crop up throughout the Ring and Parsifal, Wagner effects a dialectical reconstruction of the basic principle of tonality, which might be expressed as a maxim: However far it strays, the harmony in a piece of music should return to the tonic. In failing to resolve from the Tristan chord to A major, it appears that Wagner has violated this principle, but I would argue that he has instead reformulated it thus: However far it strays, the harmony in a piece of music should return to a transformed tonic. In the music of Wagner and his followers, tonality remains in place as the ideology of music, but its inner construction is distorted, as I will exemplify in an examination of the Valhalla motif from the Ring, which evinces an extraordinary range of chromatic transformations. In preparation for that analysis it is useful to consider Steven Rings’s analysis of the transformations of the grail motif from Parsifal. Here the essential parameters of Wagner’s technique show up very clearly.
Example 4.5 shows the grail motif at its first appearance in bb. 39–41 of the Prelude. The harmony could not be more purely diatonic: Descending by thirds, the bass supports a conventional motion from I. It reaches a predominant chord ii in the middle of b. 40, and cadences via a second-inversion dominant seventh onto the tonic in b. 41. The A♭ chord I at the start of the phrase resolves, classically, to A♭I at the end of the phrase. Example 4.6 shows a transformation of this motif from act 3, during the orchestral music accompanying the uncovering of the grail. Now the diatonic music has become structurally chromatic – but note that, as usual, the chords are still triads: E♭ major, B minor, G major, E♭ minor, A♭ major, and D♭ major. The curved arrows below the stave are a shorthand which indicate how Wagner transforms the chords into each other. E♭ major becomes B minor by means of a chromatic transformation known to modern music theory as a “hexatonic pole” (“H” for short). Richard Cohn has defined this as “a progression (in either direction) between a major and a minor triad that features semitonal motion in each of the three upper voices” (here, E♭→D, G→F♯, and B♭→B♮).Footnote 25 After converting B minor into G major by changing just one note – the F♯ leading note (“L” for short) rises a semitone to become a G – there is another H shift to E♭ minor. In Cohn’s view, hexatonic poles frequently create an uncanny effect (the Freudian unheimlich), which is here dramatically apt, since the uncovering of the grail is a moment of other-worldly, transcendent encounter for the knights of Monsalvat. What this analysis reveals is how Wagner moves from chord to chord (a feature of the surface of the music), but it does not shed much light on the working of his tonality (a feature lying below the surface, to use the normal metaphor).
Example 4.5 Grail motif, original version, from Parsifal, act 1
Example 4.6 Grail motif, transformed version, from Parsifal, act 3
Rings insightfully notes that Wagner actually retains the I–vi–IV–ii–V7–I chord progression from the motif’s opening presentation but adds that those chords are not all in the same key. In order, E♭ is chord I of E♭ (I/E♭); B minor and G major are, respectively, vi/D and IV/D; and E♭ minor, A♭7, and D♭ are ii/D♭, V7/D♭, and I/D♭. Ring’s theoretical explanation of how Wagner transforms this theme is that he retains the chord function but changes the actual sounding pitches. This is quite an extraordinary transgression of the rules of tonality, and yet listeners generally recognize that the music is still tonal, in the same way that when Scrabble players play by their own rules (say, awarding five bonus points to a player who places a musical word), the game, however much it flouts the rules, is still recognizably Scrabble. Abstractly, what was previously considered formless has become form: An impossibility has been made actual.Footnote 26
Normally, every scale degree in a key has a specific and unbreakable association with a particular pitch class, and this allows tonality to impose a rigorous functional order on musical reality. So, in the key of C major, the first scale degree (
) will always be a C in some octave, the second scale degree (
) will always be a D, and so on. Similarly, the triads built on those scale degrees will always be associated with a chord function: So the G-B-D triad (built on
) will always be V in C major. Thanks to this cinching together of scale degree and pitch class – which we normally do not think of as a significant matter – tonality is able to work like a well-ordered traditional society, where every chord knows its function in the whole, and the preeminence of the tonic (the hegemonic element) cannot be called into question. For every function, there is a single name: With the function “dominant” goes the name “G major.” Similarly, in society, with the function “ruler” goes “monarch.” Wagner’s chromatic transformations effect their revolutionary change by breaking the link between scale degree and pitch, between function and material reality. It is a musical correlate of his political ideas, a handing over of tonal power to “the wrong pitches,” which has the effect of breaking the hegemonic control of the old pitch rulers. Such musical gestures never have a single meaning, but the radicalism of this particular composer invites the speculation that it is as if the function “ruler” in some society were retained, but now the name that goes with it is “General Secretary of the Communist Party.”
Rings’s theory is much more abstract than this. He observes that Wagner performs a kind of transformation in which the scale degrees retain their “qualia,” their character within the key (what I have been calling “function”), while the actual pitches have been changed. In this transformation of the grail motif, the pitches in chord vi have been pulled down one semitone from what they should have been in a traditional tonal space: a chord of C-E♭-G has become B-D-F♯, and yet both “are” chord vi. For short, we can write this transposition in the following way: (vi, C minor) has transformed into (vi, B minor). The pitches in chord vi have therefore dropped down one semitone, which we can write for short as (vi, −1).Footnote 27 In the same way, the chord of G major which ends b. 1098 is a chord (IV, −1). By the middle of b. 1099, with the arrival of the chord of E♭ minor, there is an additional slip of a semitone, so that we hear the famous Dresden Amen cadence, ii–V7–I, in the transformed form (ii, −2)–(V7, −2)–(I, −2), i.e., the same chords, but down two semitones. Wagner therefore has his cake and eats it: Tonality strongly orders the entire progression, but the “unbreakable” link between scale degree and pitch class has been broken. The D♭ at the end “is,” in some uncannily transfigured sense, the same as the E♭ which opened the phrase. The uncovering of the grail might indeed have such a disorientating effect on the believers who behold it, but this musical effect, not unique to Wagner but one which he makes extraordinary use of, need not be tied so specifically to any particular meaning. Indeed, as is this case with his treatment of leitmotif, Wagner’s harmonic structures can mean many things at once.
Transformations of the Valhalla Motif
Example 4.7 shows the Valhalla motif in its first presentation, at the opening of scene 2 of Das Rheingold. The fortress is newly built, its gleaming crenellations (blinkenen Zinnen) imbued with a nobility and power that is as yet uncorrupted. The musical presentation encapsulates these qualities: chorale-style chords are “sung” by a brass choir of Wagner horns, tubas, and trombones, all playing in a very soft (sehr weich) tone, while harps pick out chords I and IV in a stolid processional sequence that strongly establishes D♭: I–IV–I–V–I.
Example 4.7 Valhalla motif, “prime form,” from Das Rheingold, scene 2
Compare this presentation to a later version of the motif in the Ring (Example 4.8). It comes from the scene in Götterdämmerung in which the Valkyrie Waltraute futilely petitions her sister Brünnhilde to return the Ring to the Rhinemaidens, to lift the curse from the gods.Footnote 28 In the latter, we can see how greatly Wagner can disfigure his motifs without them becoming completely unrecognizable and so achieve very different dramatic effects. By this point in the cycle, the bright major-key feel of the original has been darkened. In place of D♭ major, the motif opens with a diminished chord, A♮-C-E♭-G♭, but the falling melodic third, and the rhythmic profile (strong emphasis on the first and second beats of the bar), as well as the text (Waltraute sings that Wotan is in Valhalla with the splinters of his spear), are enough to indicate the connection with the old motif – and an invitation to reflect, both in the moment of hearing and afterwards, on the state of the corruption of that world’s old certainties.
Example 4.8 Valhalla motif, “Tarnhelm form,” from Götterdämmerung, act 1, scene 3
There is a delay before we hear the second part of the motif, originally the proud melodic rise B♭–D♭–E♭–F. When it comes, the final melodic step is denied, and the final cadence is no longer the reassuringly final perfect cadence of Das Rheingold: now it is an expectant imperfect cadence, I–V, in the key of F♭ minor (F♭–C♭). What has happened, in fact, is that the Valhalla motif has been fused with the Tarnhelm motif. As is clear from Examples 4.8 and 4.9, the harmonies of the last two bars of the Tarnhelm motif and the new form of the Valhalla motif are identical, albeit with different spellings for the two last chords: f♭/e–c♭/b.Footnote 29
The motif has become mysteriously hybridized, with the head of Valhalla and the body and tail of the Tarnhelm. As Wotan himself notes in Die Walküre, act 2 scene 2, the owners of these two objects – Wotan and Alberich – are each other’s obverse, and in music such as this we can hear and feel that quality. But this distorted form of the motif also catches the sense, from the gods’ perspective, of the “bad transformation” that has occurred, the destabilizing of the divine order by the Proteus-figure, Alberich, whose shape-shifting, represented by the Tarnhelm motif, had led to his capture and the curse which Waltraute now desperately wants to be revoked by Brünnhilde. In Keith Warner’s staging for the Royal Opera House in London in 2009 and 2012, the dramatic point was underlined by the setting of this scene inside a gigantic Tarnhelm: in this production, the Tarnhelm in Das Rheingold was a windowed cube worn on the head, and here it was simply magnified to fill the entire stage.Footnote 30
Example 4.9 Tarnhelm motif, from Das Rheingold, act 1, scene 2
By Götterdämmerung, it has become clear to everyone (apart, it seems, from Waltraute) that the preeminence of Valhalla and its gods is over. There can no longer be a resolution into that old lynchpin tonic, in a V–I cadence, because the world’s corruption – symbolized by Alberich’s Tarnhelm but initiated by Wotan himself – has reached a stage that leaves no possibility for restoration. In Die Walküre, though, the corruption is not yet complete; Wotan knows that his supremacy is imperiled, but it still hangs together – just. For as long as he remains the god who can influence mortals such as Hunding and Siegmund, and command the fearful respect of the Valkyries, he can extract dark humor from his current predicament. This is how we find him at the center of his monologue, in Die Walküre act 2 scene 2, as he mordantly bequeaths to Alberich’s son, Hagen, the void splendor of godhead (der Gottheit nichtigen Glanz; see Example 10).
Example 4.10 Valhalla motif, “cursed form,” from Die Walküre, act 2, scene 2
Immediately before this “cursed form” of the Valhalla motif, Wotan bewails his inability to father a free human being, which he finds ironic given the ease with which Alberich achieved it. An orchestral fanfare on a keening diminished seventh chord on F♯ (F♯-A-C-E♭) is resolved at b. 981 onto a chord with a root one semitone down: an f7 chord.Footnote 31 Here, as in the grail motif from Parsifal, Wagner’s chromatic harmony opens up a rift between the scale-degree “function” and the pitch-class “name.” In the middle of b. 981 the tonic of this phrase, which had been an F, slips a semitone to become an E (
, –1). The brightening of the mode to the major (E) is perhaps an ironic correspondence to Wotan’s blessing to Hagen (it coincides with him singing “Segen”). In any case, the remainder of the phrase reverts to the minor, still retaining the one-semitone-down transposition. The phrase concludes on the tonic, E minor, with a similar melodic rise to its original form in Das Rheingold, but now the final “cadence” is II–I, not V–I: We hear the tonic at the end of the phrase (in contrast to the doubtful close of the Götterdämmerung version discussed above), but its status is a little hazy. The music thus reflects Wotan’s new, deflated vision of the world order: Valhalla’s position is weakened, but not yet terminally, and Hagen’s power, should he attain it by winning the Ring, will not be of the same kind, or same potency, as Wotan’s. Hence there is a poetic elegance to Wagner’s tweaking of the point of cadence: The leap and fall that characterizes the fifth gap in the perfect cadence of the original has now shrunk to a major second: Hagen, the son of a dwarf, lacks both the stature and the majesty of Wotan. In the Boulez/Chéreau centenary Ring at Bayreuth the ironic effect was beautifully enhanced by Wotan’s act of kneeling, holding his cloak – swiftly made to resemble a diminutive human form – by the scruff of the neck as he grants his sour blessing.
Conclusion
In these moments from Götterdämmerung and Walküre we see a motivic transformation which does a particular form of dramatic work, which is to say it has a dramatic function in its own particular moment. But at the same time, it interacts with a harmonic transformation that has a more general, or universal, quality, as its use in Tristan and Parsifal instantiates. This is why it is wrong to pin this revolutionary sundering of the scale degree/pitch class (or function/name) unity too tightly to a particular dramatic symbol such as the transformative power of the Tarnhelm. What is common to all the occasions in which Wagner uses chromaticism to form a revolutionized tonal space is the dialectical shape of his musical argument. On the one hand is the declaration, as it were the founding principle of diatonic tonality, that however far it strays, the harmony in a piece of music should return to the tonic. On the other is chromaticism’s emancipatory declaration that no pitch, no name, should be assigned any particular place in the whole; each element should be free to exist on its own terms, without being subjected to a purpose that fixes power in a predictable place. These declarations are irreconcilable, and Wagner does not – as Schoenberg and his followers did – decide in favor of the second over the first. Instead, his harmonic language effects a mediation: By moving dialectically between the conformity of one system and the relative anarchy of the other, he retains tonality’s sense of order – its loading of tonicity with a sense of “home” or “security” – but allows new actors to occupy roles that were formerly closed to them. The great expansion of his forms through the poetic-musical period and “symphonic movements” contributes to this new possibility by freeing up space in the moment – where clear resolution is no longer required – for a fracturing of tonality to take place. So, in Walküre or Parsifal a drop of a semitone can create a “flat-side” rupture of the old ideology, to allow Hagen briefly to sit on Wotan’s throne or to reflect the Monsalvat knights’ uncanny encounter with the divine. And in Tristan a “sharp-side” rupture, rising two semitones, can transform what might seem like a loss – a failure to resolve to the “tonic” A major – into a victory: B major now “is” A major, and the couple have been emancipated from the repressive Day of A minor into the freedom of Night’s B major. In all these cases, whatever their particular concerns, there is something universalizable in the brief, transcendent views opened up by Wagner’s harmonic structures, something which has had, and may very well retain, a strong appeal to radical thinkers. At points such as these, his harmony is a coup d’œil of a transfigured world.
