Monuments could be erected as totemic antipodes, polarizing the specters of theoretical discourse that engaged the attempt of a context in which to bear  light within the vessel of 16 brief, insouciantly passing  measures of music. 16 measures, that, hypothetically contained a hidden strand of harmonic species that would disrupt the way we experienced and analyzed music. 16 measures that ostensibly eroded that stratum of vestigial tonality keeping the entire dreadnaught of triadic-relations- by-fifth-roots, afloat. 16 measures that penetrated the psychological depths of a young philosopher, Friedrich Nietzsche, sanitizing the diodic oppositions of ‘true’ and ‘false’ to conjure from the depths of his own abyss, that truth which acts as the fragmentations of a prism casting differential grades of light and interpreted as colors unto the surface of the mundane artifices of ‘fact.’ 16 measures that lead the Sonic Prophet, Arnold Schoenberg, to declare the emancipation of all tonal relationships as equal brethren, no longer under the subjected  prepollency of the concentrically operating sovereignty of his self-perpetuating Sonic Egypt. 16 measures that demarcate the opening gesture of Wagner’s Vorspiel to Tristan und Isolde and eclipse a convergence of a tonally ambiguous and functionally reappropriated progression that restores tonal semblance some 6 measures later.

To assert that Wagner conceived this passage atonally is absurd. Equally, to posit that Wagner wrote an opening model whose merit and concerns were subjected to the standard by how it might be interpreted within a tonal context is equally absurd. Thus the intellectual pulse between these two ‘antipodal’ cogitations, and rather, its ability to subvert academic classification is the opening’s Raison D’etre. 

It is an example that transcends both Art and Science; Both the Poet and Professor. It is, as Nietzsche experienced, a tempestuous sorceress that in one gesture seduces with illusional dissipation, and in a transformative mythic exchange, evades it’s promises and intentions that dissipates, like a summer morning’s fog, with its commitments to resolution. As a mentor of mine, Hendrik Hofmeyr defines it, a ‘specious’ chord; That is, a harmonic object that represents something seductively misleading, like a Delilah in the shadows.

The source of the confusion of the opening is based on our desire to classify it as a tonal phenomenon; And this is not simply subjected to the position of this article. There are many structural levels in which Wagner is utilizing deception. Yet, as Carl Jung committed a life to illuminating, Symbols (and here I am not shy about including Roman numeral theory as a subject of evidence), are only a shorthand for conveying an unspeakable dialogue that is at both points unrelatable and inherently understandable in the context of the experience. That is to say, we have all had an experience which makes complete sense until someone asks us to describe it in words and images.  For this reason, symbols are a necessity of communication. For instance, what is more damaging to a political campaign? Spending many words to illustrate the points in which you disagree with your opponent, or simply applying the term fascist to him? Fascist here is a symbol that unlocks oceans of knowledge, associations, assumptions and allows us to remove the process of working out our proofs, as the conclusion has already been tested time immemorial. At the same time, those symbols trap us into a way of thinking that obscures the novelty of an idea that might require a new process of working out proofs. Thus, I propose that Roman numeral analysis is partially to blame for the millions of disparate and passionate opinions that lead to such heavy debate on the topic of the Tristan issue.

Here I will not deal with the Tristan chord itself, as it is one deception activating and activated by surrounding deceptions of larger formal units and smaller voice-leading units; Not unlike the cogs of a pocket watch. I will deal with the Tristan chord in a subsequent post elucidating Hofmyer’s erudite formalizations of foreground level harmony. For now, we head to the background.

For our purposes, we will focus on the first 22 measures of the piece, for at the downbeat, a metrically accented A major unannounced the unequivocal arrival of a half-cadence and thus the first moment in the piece where the retrospective material can be formally assimilated for consideration of a cohesive whole.

We open with a single A that expands to an E major chord in measure 3. How we get here is inconsequential to the analysis at present time. We shall make this segment a musical object in itself and refer to it as phrase 1. 

Phrase 2 starts in measure 4 and begins with a single B, a major 2nd above the opening note, a note that belongs to the harmony of the dominant as its associate

(an associate is the third member of any triad, i.e. its chordal ^5. Bases ^1, Agents ^3 , and Associates ^5 are a means of identifying functional deployments on chromatic spaces, posited by Daniel Harrison and will be given specific attention in another post.) 

The end of the phrase is a G dominant 7 which suggests the key of C. How can we be sure? A subdominant Major Minor quartad(sounding like a dominant 7) is not out of place in the music of this era. If this analysis is true, we would be in D melodic minor(Bb gives way to B natural) and would provide a link to the A major half cadence in measure 22(D minor). But if we look at the specious chord here, we have a chord that sounds like a half-diminished 7th in root position.When the Ab is enharmonically spelled G# all normality is returned. But this normality only lasts as a snapshot moment, a vertically plausible offering to the Roman numeral gods that call for tonal order on grounds of stacked thirds.

If this chord is G# half-diminished 7, and it is tonal, it can belong to A minor as the chromatically altered, though tonally correct leading-tone chord. By contrast, it can also belong to the key of F# minor as it’s supertonic half-dim. And, of course, F# minor is the relative minor of A major, which is the parallel of the A minor tonality that begins the piece. Thus a continuity is starting to lock in the analytical underpinnings.

But when we analyze the voice leading, and where the chord exchanges its tension, we end up with a different understanding. The Ab moves to G, which is the ^5 of C. If we are in C minor, then the Ab is ^6 moving to ^5. The half-step connection between ^6 and ^5 in the minor, you will remember from Reimann and his promoters, is the upper-leading tone converging downward on to the tonic associate(^5), while the lower leading-tone converges upward on the tonic Base(^1). So strong is this association of the leading-tone that ^b6 is the most common altered note in the Major, leading to chords such as the fully diminished 7th VII,  the minor subdominant IV, the Neapolitan 6th bII, and the deceptive Ab VI, entirely analogous to the ‘raised leading tone’ in minor keys, which can happen without disruption, Reimann establishes the reversal law of the leading-tone borrowed from minor in Major; 

That is,

 A ^6 can be lowered in major without disruption, and when used in cadential chords(fully-diminished quartad on VIII), it must!

 

 I illustrate this point to draw attention to the fact that it holds no bearing, as we said, whether we are in A minor, or A major, and here, that observation gains further weight.

 

We now must briefly consider chromatic alterations to consider the F# in the key of C. Whenever a key begins to modulate, if it will do so in the most natural way possible, it must pass through a series of keys that relate by fifth. If it is the upper fifth dominant, the plausibility of which is almost unerring in prejudice to establish this occurrence to be as plausible as the moon rising each night, then the ^4 always becomes ^#4. A further observation of this result is that so common is ^#4 that it can act within the key as a tonicization without the need to affirm it’s pretense through cadential confirmation, and thus no need to modulate as the effect of the alteration has become an extension of the blending of the tonal areas.

A related observation comes from the result of the loosening of the need for #4 to actually modulate, and here it is given attention as it will come up late in our discussion.

 Harrison, from his theory of Bases, Agents and Associates, has a term called ‘accompaniments’(relating to voice-leading accompaniments, proper) which are voice-leadings that are a byproduct or projection; Hofmeyr subsumes this idea as a focal point into the structure of the specious chord, albeit from a different vantage point, and thus ‘By the mouth of two witnesses the matter is established’ Deut 19:15. 

While I will explain them in detail in a further post, for now, it is enough to understand that a ‘mirrored’ voice leading is converging powerfully on to G. The Ab downward and from above; The F# upward and from below. Of course, Ab and F# exist in the Augmented 6th chord that is available to us in C minor, but the D and B obscure this analysis. If a French 6th, the D must move 2 semitones up to C, while if a German 6th, the movement is spread evenly, the D one semitone up to Eb and the B one semitone up to C. Notice this last voice-leading creates an important analytical parallel gesture, although harmonically they are difficult to explain. Faure exhibits a similar example in his first nocturne, where the byproduct of his voice leading creates a passing chord that is a quartal harmony, although it is easy to miss in perception, because our ear honors the ‘voice-leading accompaniment’ chords as satisfactory to musical coherence, despite their inability to be vertically applicable within the Roman numeral analysis.

These voice leadings can be considered as byproducts, and thus accompaniments of a contrapuntal fabric, but they do not help our understanding of Roman numeral ‘tonic’, ‘supertonic’, ‘mediant’, etc. And thus, briefly, we can first consider the usefulness of Roman numerals to aid in our understanding of the music of this late 19th-century character.

Let me be clear here, Roman numeral analysis is not synonymous with tonality. One adheres to presenting data in both our scalar system of diatonic integer labels: Tonic, Supertonic, Mediant, Subdominant, Dominant, Submediant, Leading-tone(Sub-tonic), 

AND 

in our alphabetic pitch labeling: A, B, C, D, E, F, G. Of course, both of these systems are SYMBOLS, are ARBITRARY, and only work so long as the composer channels his harmonic understanding through the funnel of the analytic tool. 

 

Meanwhile, a piece can modulate from Ab to E major through a means in which G# is Ab enharmonically, C(^3) moves downward to B(^5) reinterpreting the C as a ^b6 in E, and the Eb(^5 in Ab) is ^#4 in E moving to E. Notice that these two triads, which lay on opposite ends of the circle of fifths, exhibit analogous voice-leadings to the upper and lower leading-tones of the music of Haydn, Mozart and Bach, and yet, exhibit identical voice-leading processes of the Wagner, namely ^#4 and ^b6. These associations are highly problematic  in terms of explaining ‘tonic’ and ‘dominant’ relationships in the traditional sense, or even the scale degrees where C of Ab exists as ^3 to Ab but 6^ to Eb, and the voice-leading move from B from that C, shifts B, ^5 in E major, ^#2 in Ab. By contrast, B-C is a semitone movement. D to Eb is a semitone movement. Ab to G# is a consonant tonic to a consonant mediant. These chords are actually closely and intimately linked, despite what Roman analysis tells us. This is one reason that Forte’s pitch class theory is so useful, although, he himself made the error of presenting it in a treatise entitled ‘The structure of Atonal music’ and thus erroneously, if not involuntarily, related it to Schoenberg’s serial procedures. Of course Forte himself did not mean for this to be the case, writing articles on that examination of Pitch Class structures as a superior means to the analysis of the music of the late 19th and early 20th century, including a prominent article on Brahms C minor quartet.

Notwithstanding these distinctions, we should already observe that Roman numeral analysis, as a science for understanding the ‘reality’ of harmony, is being exposed by Wagner’s prelude as the true deception, at the cost of understanding that the method of analyzing reality, our reality itself, is the symbol for some truer nature.

 

With these considerations now swishing in our analytical tasting glasses, we are ready to gulp phrase 2. The F# never goes on to G, but we hear the G being prepared, and when the F# instead gives way to F natural, we understand it in two ways. A parallel semitone descent in the inner voices(a voice-leading accompaniment), and, that the F natural was the ‘True ‘ tone; meaning that the Ab is correct, as it is now belongs to the half-diminished leading tone chord in 42 position, in C(minor or major) while the C# that appears ‘tonicizes’  the D(which gives credibility to measure 22’s D minor half cadence).  It also assures an expectation by thematic motivation for that  C# to move unnaturally to C as a resolution. This is the transposition by fifth of the F#-F natural resolution, and is offset in the temporal dimension. The fact that we do not ever receive that C resolution is aptly understood, given the context of the unresolved nature of the vorspiel. Therefore, we can conclude that Phrase 2 is a phrase in C.

We now have Phrase 1 in A , and Phrase 2 in C. 

With the last phrase, it would do little to need to go into the level of detail that we did in the previous phrase, because we have already discussed complexities at the local level with the prior discussion. Phrase 3 starts at measure 8, and begins with pitch D. A third away from the previous phrase and a fourth away from the first phrase. Notice that Phrase 3 is the last Phrase before a dramatic resolution takes place. The initial D, again, links us to the D minor cadence at Measure 22. Likewise, Phrase 3 links itself further to Phrase 2 in that it ascends to B, the pitch that started Phrase 2. D can belong to A minor as the 7th of a dominant 7 chord as well, further linking itself to the dominant of Phrase 2 which opens with a B to a G#, AND,  is both the associate(^5) followed by the agent(^3) of  E major, which in turn is the dominant of A minor. By the end of this phrase’s specious chord transformation we end up with a B dominant 7, in the key of E major, or minor.

 

If the collection of these phrases is taken in truncated faction, we have a series of dominants that go nowhere. The dominants accumulate tension that discharges on the F major, which we will examine shortly, but otherwise, we are still at a loss for any overlording key or tonality. 

Let us return to the beginning to analyze the melodic content of the opening line.

If we follow the cello line(as would be in the conductor’s score) we can see that the line moves through a d minor triad with an accented dissonance on D# that leans and eventually falls on D(as an appoggiatura). Because the D# does not rise to E, we know that the enharmonic Eb is a more suitable label, and its true identity, as far as the melodic line is concerned. I say, ‘as far as the melodic line is concerned’ because the fact that it is a D# suggests that the vertical dimension has reinterpreted it, and this cross-sectioning of realities, is both a dramatic and analytical aspect of Wagner’s Tristan.

With this analysis, the figure is a D minor triad with a Neapolitan 6th chord acting as a predominant prolongation of tonic.

The melodic figure is near identical as an extrapolation of a more tightly-knit theme found in Beethoven’s Op. 31 no 2. 

The authenticity of the two examples to each other is uncanny. One can even account for the 3/8 time in the Beethoven verses the 6/8 in Wagner, as the result of the elided interaction between the two voices in Beethoven being ‘written out’ without the lower response in the Wagner.

 Furthermore, if we are of the Schenkerian school of thought, which I am, local, and long-distance projections can be analogous to each other. One can take I-V-I and intervene chords as voice-leading connections where no shift of harmony seems to have occurred. The Beethoven is a straightforward example in which the first 9 measures all represent tonic(The dominant of 4-7 are considered a prolongation; i.e. I-V-I does not imply a shift to dominant and harmony and back, but rather I emphasized by the contrasting V that connects two tonics). The first harmonic shift that we do hear,  is at the G minor, which then evolves into an Eb Major and, while we can make no functional sense of IV- bII we can say that IV and bII are ‘bound’ together through a voice-leading procedure; the D, of G minor being a retardation of the Eb of the Neapolitan 6th, before confirming the tonic in D minor(not pictured here). Of course we see the final chord in the above example is a dominant in inversion, and thus, must be connected as an incomplete neighbor, or a cambiata to the D minor(Eb and C# converge on D). Therefore the entire progression can be read as a D minor tonic I-bII-I, which really can then be assumed as a tonic with a prolongation by bII(meaning that bII is not acting in a predominant function) and thus it can mean simply tonic D minor.

 

If this analysis is correct, and I posit that it should be, we have a problem with the E major chord that manifests in the Tristan prelude in measure 3. But again, another prominent feature of late 19th-century music is to move in defiant opposition from regulated norms, which was not only philosophical and cultural, but spills over into analysis and style. That is to say, an opposition to what their classical predecessors would have done, and includes movement by thirds, rather than by fifths, weak cadences, and abrupt modulations based on enharmonic associations, rather than tonal distance.

The basis for the proceeding interpretation goes as far back to medieval theory, however, and thus should not be considered novel, except in the revolutionary way in which it is exploited. 

In the writings of church mode style there are two systems, Authentic and Plagal. While the distinctions concerned themselves with range, finalis, and reciting tone, for the theorists that came afterward, a synchronic observation dictated that these system’s governed the direction one moves to obtain a tonic. If, for instance, we have five notes on a staff, F-C and the B is natural, then the authentic system moves up to the finalis on C. If the B is flat, then the tonic is the F, and the projection of movement goes downward. 

What this meant for composers looking for new ways of saying old things, especially Brahms, is that Subdominant movement to Tonic could be established, not as a prolongation of tonic, as it would have been in the codetta of a theme closure in a Mozart Sonata, but a fully functional cadential progression. Sequences by ‘descending fifths’ became ascending; Dominant functions that utilized the subtonic, or Mixolydian variant dominant were employed; The lines between Major and Minor were all but obliterated, and pieces were written in the key of a particular tonic, with associative access to chords built in both the major and minor systems. As a consequence, composers became interested in playing ‘authentic’ verses ‘plagal’ systems against one another.

Similarly, if the opening A of the Tristan prelude is authentic, it moves to E. If it is plagal, it would move to D; To be sure, it does both at once. The melody suggests plagal, and the harmony suggests authentic. This is just another layer of the ‘deception’ of the dream world and the real world which Wagner plunges us into.

 

 

 

We can now compile the three tonal centers implied by the three phrases presented consecutively. 

Phrase 1: A

Phrase 2: C

Phrase 3: E

As a triad, it creates a high-level representation, or symbol, of A minor. And here, the A minor unequivocally suggests D minor, for while C# can exist in both minor and Major, C natural can only exist in the natural form of D minor. Thus the first 16 measures synergize into a metaphysical symbol for dominant of D minor.

A weaker signal of projection can be seen by assembling the dominant 7ths themselves. It is weaker because while the implied tonal areas relate to a Key, with both a tonic note and tonic triad, the dominant 7ths themselves are very specific to movement to a tonic, and don’t stand as representative as tonics themselves. None-the-less, the assembly based on the root of each dominant is:

Phrase 1: E

Phrase 2: G

Phrase 3: B

For reasons stated with the D minor, this reading can only assume A minor, though as we just stated, at a much weaker projection. Thus another unifying layer of authentic and plagal entanglement presents itself. 

In the first phrase an A note outlines both a d minor triad(plagal) and proceeds to an E dominant 7(authentic). A is the hinge by which these hypotheticals pivot. At a deeper structural level, the dominant 7ths at the ends of each phrase build an A minor chord that implies D minor, or E dominant 7 which implies A minor. Here, D is favored because A minor becomes increasingly hypothetical in its higher-level implication, by the reason stated above; Dominant 7ths point to tonics, rather than substitute for tonics.

One last feature to cogitate is that a series of dominants are chained together for 16 measures before releasing the tension they’ve accumulated, at measure 17. This is not unfamiliar to us analytically in even the most traditional methods. A sequence of dominant 7ths is understood as brief tonicizations of the next chord, and not “V7 of”, because the ear has no time to relate it to the tonic areas of which they seem to project; it is happening to fast. What we hear instead is a formal function being presented, not a tonality. Said another way, tonality is suspended briefly until the last dominant 7th discharges its accumulative tension on some tonic, which then establishes the key. To make sure my point is clear, we would speak of such a passage to a student, or the musically illiterate as ‘A series of dominants sounding one after the other” and not 

“The dominant of the dominant of the dominant of the dominant of the supertonic to the dominant of the dominant of the dominant of the super tonic to the dominant of the dominant of the super tonic to the dominant of the super tonic to a modulation to supertonic”

If we believe this distinction to be fair, that a chain of dominants briefly suspends tonality, then the Tristan prelude can be seen as a series of dominant charges that discharge on F major at measure 17. The fact that those dominants all imply keys that are subsumed into the ambassadorial roots that make up the dominant of D minor acts as  the anchor and sextant for us to navigate both analytically and perceptively.

What do we make of the F major chord at measure 17?

If it is true that a dominant accumulation can articulate dominant function without the need of a literal, or a Roman numeral explanation to its tonic, then so can the tonic assertion itself be enough to motivate our acceptance of it as tonic by its appearance after the dominant. 

There are too many examples to cite in this article, and I do not think it would be entirely productive, as the phenomenon exists so readily  in the music of Strauss, Reger, Wolf, Mahler, Scriabin, Busoni, etc, that we can understand even hypothetically through means of familiarity that composers and their audiences understood and employed the Tonic by assertion.

 The most poignant example is found in Schubert’s Bb sonata, D 960, in which a Bb tonic loses all sense of gravity when the second theme asserts itself in Gb major. No listener has ever been confused as to the meaning of the Gb, regardless if they understand theory or not. It is heard as a tonic by its assertion. The return to the first theme is approached by what, to our ear, we perceive as a preparation to modulate to Cb major via a Gb tonic becoming the dominant 7, through introduction of an E natural(Fb to our ear) of its subdominant(a plagal motion). Instead the Gb moves downward by semitone to F with a Bb major chord built over it, which sounds as though it is the embellished cadential 64 chord and in need of resolution to a dominant F major chord. Of course, that interpretation is completely obliterated when Schubert brings back the theme over the F, that is to say over the dominant harmony, and yet the ear has no problem removing our sense of an unresolved dominant function to allow the tonic to regain gravity through its assertion.

Again,  I stress that it is Roman numeral analysis that both helps us to understand the teleology of a progression and at the same time hinders us from hearing teleology in new ways. 

With that being said, in the case of the Wagner prelude, we can hear the F major chord at measure 17 as a tonic, not because it is preceded by its own dominant, but because dominant function spent 16 measures building up, including a repetition of phrase 3, followed by the prominent E#-F# insistent lingering before discharging on a triad without tension. 

But yhy this emphasis on E#-F#? 

In Phrase 1 we said that D# unconventionally  resolved to D, and thus revealed itself ever slightly as the tonic of a D minor melody. In Phrase 2 we discussed that F# did the same to F natural and thus revealed itself as belonging to C major as ^4(the chordal ^7 of G dominant 7). Phrase 3 is the only phrase that does not feature a species chord that resolves a pitch with a # resolving by a ‘lean’ downward to the natural version of the pitch. Yet, as we said, Wagner insists on moving E# to F# 5 times, even abandoning the cadential harmony that sets it, before he resolves the entire 16 measures to F natural. 

If he did resolve F# as an appoggiatura leaning downward so as to keep it consistent with both Phrase 1 and 2, which ‘tonic’ note would we land on?

F natural

 F#- F natural is finally related to phrase 2 and 1 in this way.

Phrase 1: D#-D = ^1 of Tonic

Phrase 2: F#-F = ^7 of Dominant

Phrase 3: F#- F= ^1 of Tonic.

We then understood again, like the Beethoven as a I-V-I equals a very elaborated, chromatic prolongation. Except we are on F major and not D minor. None-the-less, the lack of use of Mediant chords in progressions during the classical era is cited numerous times in that the Mediant sounds nearly identical to its Tonic with a slight coloring by ^7.

 But I will not assert that case here. I do assert that the functions of Dominant and Tonic have been expressed through the dominant accumulations of the first 16 bars, and the F major which stands as the first triad that feels like resolution. After all, on the criteria of tension and resolution and functional requirements of dominant and tonic, all metrics have indeed been checked and met. What doesn’t ‘work’ is the Roman numeral analysis. That is, that the F major is not preceded by a C dominant 7.

Knowing Wagner, one can only imagine this obfuscation would have brought him great joy. A tonic that is perceived, felt emotionally, though analytically it is absolutely absurd and difficult to explain, despite it sounding absolutely correct and ordained.

A Tonic by any other name would sound just as sweet!

Engraving of German composer and poet Richard Wagner (1813-1883) conducting. (Photo by Time Life Pictures/Mansell/The LIFE Picture Collection via Getty Images)

I will not continue further in the analysis for the sake of brevity, but to finish and assert my claims that tonality, function and key can stand outside of the confines of Roman numeral analysis we will observe just a few more foreground details. In the remainder of the example up to measure 22 of where our first traditional cadence appears, only a handful of accidentals are used. 

F#:

 which can be considered the modal compliment of D minor ^#3, utilizing the same tonic, different mode. This is congruent with keys being fusing the demarcation  between major and minor in this style, and as posited in the opening statements of the three phrases. Here the F# is being used in a D major chord and measures 18-19 and thus is consistent with the analysis of D tonic.

Bb:

Scale degree ^6, which as we already described as key-defining in that it is the upper leading-tone in minor which converges on the tonic associate(^5),  is responsible for subdominant chords as well. Here the Bb is used in both a G minor subdominant chord, and a C# fully diminished 7th chord, the latter of which unequivocally implies a D minor tonality as the leading-tone VII belongs to only that key. 

Eb:

The ^b2 or the Neapolitan root, which was also related to the Beethoven and to the opening phrase melodic content where we understood that D#-D is actually Eb to D, thus we can consider this motivic on varying structural levels. Of course, to confirm that this is an inarguable analysis, Wagner utilizes the Eb in none other than a Neapolitan 6th leading to an A major chord which is our first tonal cadence. We have at measure 19, a D major tonic moving in a plagal system, and thus obscuring tonality only slightly, as it transforms into a dominant 7 in 42 position to a C in 63 position, which hinders its chances to be established as a tonic, unless the dominant 7 and tonic appear soon in root position; They don’t. The C major instead moves back to its dominant, but that dominant is a G minor, and thus, we retrospectively assume the C and its dominant 7th to be nothing more than a tonicization of Subtonic in D minor, the G7 being a ‘false’ chord that returns back to G minor. The G minor itself is a passing chord between C major in 63 position, and what should be C major in root position, but, instead it invokes the Harmonic minor variant of the pitch, and is instally transformed into a dominant functioned leading-tone fully-diminished quartad in D minor. 

But here is where it gets interesting, and here we must back up. It was brought to my attention that the B that is suspended over the F major ‘tonic’ in measure 17 was problematic because B assumes F Lydian, which Wagner would not be thinking in and should then be considered an A minor deceptive cadence on VI; and It surely does sound that way through the lens of Roman numeral analysis. Still, I think ruling out that it probable that Wagner was not to have thought about the church modes during composition is highly suspect, because we are dealing with an opera that is set during a time period when a stylistic emphasis on the church modes would have been applicable, even appreciated, and one must imagine that this detail would not pass inconspicuously even in the most vestigial recesses of his genius; He was a man, after all, that researched for years, and was pedantic about details. Even though the story itself is of Celtic origin, and not primarily catholic in anyway, it is near impossible to separate ancient mythology with modal music. That being said, I will not make the claim that the B natural represents modal thinking. I think what is more accurate is that Wagner would have justified a use of modality if it served a deeper analytical purpose, through, precisely its inherent style attached to that medieval culture. 

For me, the B-A suspension represents motivic relaxation. Semitone ascension always implies a tension: ^7-^1 in Dominant to Tonic. But melodically, whole tone descension always implies a relaxation such as ^2-^1 in Dominant to tonic. Of course, with any tonic, lets say C major with an F# suspended over the resolution of E, that F# does not force our hearing into E minor(See example below). This is especially true when there are no other surrounding confirmations of an E minor tonality, in the same way that there is no reason for us to assume a deception in A minor in the Wagner, except on the basis of traditional hearing; And this is not the example in which one can rely on traditional hearing to assert a function.

Example 1. ^#4 does not interfere with tonic stability.

 

 

I am not implying that most people do not hear this F major resolution as a deceptive chord in A minor. What I am implying is that they do not have to. And for a piece of music that, out of the gate is not shy about formal ambiguity, it would be a grave oversight not to understand this potentiality as a vital device of Wagner’s prelude. Thus to invite access to a different hearing and understanding of these structures would be completely in line with the expectations that Wagner placed on his audience then and now; conversely, to eschew from a different hearing of tonality would be to the regret of Wagner.

Therefore I believe that an inverted motif is being deployed at the B-A. The ascending minor second, which permeates the entire melodic structure for the first 16 bars at every level, and has been stated to represent dominant accumulation culminating on the E#-F#, is reversed to a descending major second relaxation in which the dominant accumulation has been discharged on to the F major tonic that asserts itself. To be sure, the F major tonic is one of the most satisfying resolutions in all of western music and does feel as though we have just exhaled for the first time in ages; the suspension only aids in the perception of this ‘sighing’ gesture. 

At the downbeat of measure 21, the tonic of D minor is treated in the exact same way; A melodic ’sighing’ suspension from G to F, which again represents ^4- ^3. It would be hard  to argue that this is heard as a deceptive resolution. These chords are related at the transposition of third, exhibit both share two common tones, represent Major and Minor duality, and both have the exact same voice leading. One fascinating observation is that this D minor tonic is inarguably a tonic while the F major is open to discrimination against its tonic status, it is none-the-less accurate that the F major is phenomenally more pronounced as a moment of resolution; The d minor tonic almost goes by unnoticed despite it being preceded by a dominant functioned fully-diminished chord on its leading-tone, and signaling the onset of a proper half-cadence.

Lastly, the Neapolitan 6th chord transforms E to Eb and back to E for the half cadence on A major.  In measure 21 alone we have

Tonic: D minor with G-F suspension

Predominant: Eb in 63 position as a Neapolitan 6th

Dominant: in A major.

The  F major chord I  do continue to assert as a tonic function, despite the fact that it is not the tonic of D minor. It is however, associated to D minor as it is the mediant of D minor, which we also stated in relation between G minor and Eb major, that the chords related by thirds are assumed to be ‘extensions’ of whichever chord either

1. Appears lowest.  For instance, and E minor followed by a C major, would assume the harmony is C major, not E minor.

2. The surrounding adjacent harmonies that confirm one or the other. For instance, E minor followed by C major, followed by D minor followed by G major implies C major. If B major follows after E minor to C major, then we can assume we are in E minor territory, but it takes a lot to override the sense of C major as tonic, not Submediant.

Thus the entire opening to the first half cadence of the Tristan prelude is latently D minor.

Why is D minor important to Wagner?

It is well known that the real world is represented by A minor, and the dreamworld by Eb minor. These keys are not related to each other easily. Again, antipodal on the circle of fifths.

D acts as the transient gateway between these two keys. D is the leading tone of Eb and thus acts as part of a dominant structure to Eb. D is the subdominant of A minor, and thus acts as subdominant structure that can either emphasize tonic by prolongation, or introduce a plagal motion. In A minor, D is also used as the chordal ^7 of E dominant 7. While the G#, leading tone of A minor, acts as the subdominant of Eb. Between these two integral pitches, creates the transposition equivalent to the opposing keys: A-Eb is a diminished fifth. D- Ab/G# is also a diminished fifth.

A minor    subdominant –   D   – leading-tone   Eb minor

      leading-tone –   G#/Ab –  subdominant

D-Ab 

 

 

 

(Transposition of am-eb)

D minor effectively smooths the transition between the two keys while leaving us intoxicated and disoriented as it were. Listen to this progression in which only tonic, dominant and subdominant is used, and only those chords are used in both key. How convincingly they pass into each others tonic areas via the D and Ab, and yet, at the end of the piece, are thus able to stand in for each others dominant, but with a twist. Their tritone relation dissolves their gravity into equal status which the example highlights after going through two cycles of A minor-Eb minor via D minor, and pitch-class D and Ab

Example 2. A minor and Eb minor connected via D minor.