Wagner (4), Siegfried Idyll

Wagner's Siegfried Idyll was composed in 1870; a private premiere took place that year, the public premiere in 1876, and the piece was published in 1878. About the use of the major dominant ninth chord, I have little that's new to say. The examples below show two distinct uses, literally soft and loud in cadences or climax points.

Near the beginning, arrival on V, then two treatments of V9, as V9 at (a), and as V9/V at (b).

Shortly thereafter, another "soft" moment: the sudden drop in dynamics and slowing of movement and harmony:

The remaining examples are all the typical treatment of V9 in climaxes.  At (d), the chord is in an approach to a cadence, which turns out to be deceptive.

At (e), V9/V in Ab major, resolved internally in its second bar.

At (f), C: viiø7/V--an "incomplete dominant ninth chord" that leads to a pedal dominant.

At (g) a very similar use of the "incomplete" chord; here C: viiø7 alternates with iiø7. At (h), a complete dominant ninth chord, as C: V9/V. It drifts off chromatically towards E major instead; I have sketched the voiceleading below the score.

Wagner (3), Tristan und Isolde, part 2

Here is a postscript, as it were, to the previous post. Eric Chafe observes that "the first of the dream chords of 'O sink hernieder' [reappears at the end] leading the duet to pass over into the f# tonality of Brangaene's warning" (2008, 268). Here are the two passages—beginning:

. . .  and ending:

In a later scene between Tristan and Kurwenal, the dominant ninth chord becomes thoroughly embedded in the full Tristan motive/phrase:

Finally, in the climax of Isolde's "Liebestod," the determined (and extended) progress toward the structural dominant and the 6 1/2 bars of the subsequent F# bass (as V in B major) support multiple rapid statements of the Tristan motive that eventually lead to the V9 of the cadence from the first page of the Prelude (but now in a major key). I have aligned the two cadences in a sketch below the score.

Reference:
Eric Chafe, The Tragic and the Ecstatic: The Musical Revolution of Wagner's Tristan und Isolde (2008).

Wagner (3), Tristan und Isolde, part 1

Tristan und Isolde (1865), as is well known, is a treasure trove of chromatic harmonies and expressive appoggiaturas, accented neighbor notes, and simply non-harmonic notes of more than usual duration. My interest in it here, of course, is specifically with respect to dominant ninth chords, and this is a good moment to remind the reader that I am surveying only major dominant ninth chords in this series, not minor dominant ninth chords; that is to say, not this (a), but this (b). There are *many* minor dominant ninths, half-diminished seventh chords, and fully diminished seventh chords to be heard throughout this opera.

I have written the chords in the peculiar key of Gb in order to trace its viiø7 (or V9 without a root) to the "Tristan chord": spelled as in Gb at (c), then as at the opening of the Prelude at (d)—also see at (a) in the example below. Later on, at the climax point of the Prelude,  the chord does appear spelled as F half-diminished7 and apparently acting as Eb: iiø7.

I certainly do not intend to add to the catalogue of solutions for the "Tristan chord" an enharmonically spelled C#9 chord with deleted root! The real point of interest lies elsewhere: first, in the dramatic tension between harmony and sonority in Wagner's insistence on the length of the G#4 appoggiatura and the brevity of its resolution note A4 (the only reasonable harmonic functional explanation for bar 2 is an augmented sixth chord that resolves to V7 in bar 3); second, in the continual shifting of roles between a pitch and its half-step neighbor. The initial ambiguity hints at this: is the long-held F4 a chord tone in bar 1 (part of a suppressed iv—which would make the progression a: iv-+6-V7), or is it an appoggiatura to E4 and thus the harmony in bar 1 is an incomplete tonic A3-(C4)-E4? By parallelism, bar 2 favors the second possibility, but observe that in bar 5 the long note is not heard as an appoggiatura but as a chord member of the preceding E7 (the same for B4 in bar 8: it is a member of the preceding G7 chord in bar 7). This shifting role for melodic elements is one of the hallmarks of Tristan und Isolde.

At (b) and (c) above, F#5 changes from the fifth of a B7 chord to the ninth in E9, which receives an internal ascending resolution, as sketched below:

By way of additional documentation, here are the subsequent few bars of the Prelude. The asterisks chart the profusion of non-harmonic notes of longer duration and traditional accented neighbor notes. The box shows the only possible V9 in this passage, and I think that V7 is more convincing here. But just as the first 17 bars suggested, the major dominant ninth chord is relatively rare -- that remains true for the opera as a whole: despite the dense textures of dissonant and complex harmonies, Wagner deploys the major dominant ninth for the same reasons and in the same places that we have seen many times by now in this blog: for an emotional surge in climaxes and near or in cadences.

Here is one of those, as tension rises while Isolde awaits Tristan's arrival (C9) and she sees him in the distance (F9).

Later, we hear Db9 (resolving internally) for "Liebe" to end Tristan's first phrase in "O sink' hernieder." Note that Tristan sings the ninth, Eb4.

Here are two more instances in the continuation; Eb9 over the continuing Ab-tonic pedal

And still another, at a climax point:

Wagner (2), Rheingold

An excerpt from the opening scene of Das Rheingold (1854). Although strongly expressive, it is not quite the same sort of dominant ninth chord as in the opening of Act II of Tannhäuser. The arrow points to the pedal tonic, and the chord above it would have to be considered a dominant ninth without its root. At least ^6 does resolve directly to ^5 (these are also doubled in the figuration).

A better example is from a little later, in what would have been a complete cadence in F major except for the deceptive close. Here the characteristic 19th-century cadential coloration of V with the ninth does at least give another ^6-^5 motive over the word "Rheingold."

In an exchange between the three Rhine Maidens, G: V9 in both major and minor forms is given particular attention:

And here is the first figure again, over its pedal C.

At the end, with the transition to the second scene, the dominant ninth becomes the central harmonic gesture for the pastoral sleep- (dream-) state of the gods Wotan and Fricka.

Eventually, the ninth in Ab: V9 resolves in an almost direct manner: see the boxed notes, arrow, and circled resolution.

Wagner (1), Tannhäuser

I included the opening of Tannhäuser, Act II, among examples in an early post to this blog: link. Von Wolzogen includes the passage in his tallying of leitmotives and labels it Glückseligkeit (happiness; or in this case perhaps better as ecstatic happiness). The emotion conveyed is Elisabeth's joy at returning to the Bards' Hall in the Wartburg castle, and the figure reappears more than once during her salute to the Hall (and of course to the immanent reappearance of Tannhäuser himself).

At (a) is the "undeniable" V9 chord with its direct resolution to I. At (b), perhaps the theorists' V9 without a root? I am willing to entertain the idea given the parallel to (a), but note that ^6 eventually finds its way down to ^5 before the dominant resolves. At (d), V9/V; I take this for a legitimate harmony because of the arpeggiation identified by the series of circled notes at (c)—von Wolzogen, by the way, includes these bars in his (thus rather long) leitmotif.

There are several "lesser" references to ^6 and V9. Here is one of them. This is again in the Prelude and involves a structural cadence:

The curtain rises, we hear the same music as the opening, including (a) and (b), and it seems clearly enough to refer to the Hall rather than to Elisabeth: she enters only at the end of the passage—but note that the very first figure she sings is a neighbor-note D5-E5-D5--at (e).

Near the end, she links herself and the Hall in the repetition of the opening passage -- quite literally, as she sings the melodic notes at (a') and (b').

The final cadence brings E5 very much to the foreground: see the three instances at (f). These are all internal resolutions, but just barely. The second is the most plausible; the first and third can easily be heard as direct resolutions with embellishment.

Heinrich Schenker, Harmonielehre (1906)

This continues from the previous post. I am tracing the line of influence from Sechter through Bruckner to Schenker and Schoenberg. As Wason summarizes the difference between these latter two, "if Schenker's Harmonielehre was written to build a 'bridge from composition to theory,' Schoenberg's was an attempt to build a bridge from Viennese Fundamental Bass theory to the new
music of the early twentieth century" (Wason 1982, 235). By 'bridge from composition to theory,' Schenker means that he intends his book to be comprehensive, neither merely speculative (or scientific) nor merely a series of mechanical exercises (Wason, 230).

The book, therefore, is in the traditional two parts: theoretical and practical. In the theoretical part, there are two divisions: systems (major, minor, modes) and intervals and harmonies. Under harmonies, there are three sections: three-note chords, four-note chords, and five- and more-note chords. These last are labeled "angeblich" (supposed or alleged). Nevertheless, Schenker gives sixteen pages to the dominant ninth chord and ten to the others.

He first criticizes the textbooks that allow a dominant ninth chord on the basis of stacked thirds but then restrict or forbid inversions. He then rejects the ninth chord as an independent harmony. In effect, it is a chimera, an accidental result of substitution (Vertretung). The three diatonic chords V, V7, and viiø7 share the diminished fifth ^7-^4 and therefore can substitute for one another (why the triadic vii° is missing is not clear) (1906, 249-251). He says that the space of the ninth these three chords share has deceived some into thinking that they can create a ninth chord from it (251; "Nun hat offenbar der Raum der None aber, innerhalb dessen die Vertretung der (verwandten) eindeutigen Akkorde sich abspielt, die täuschende Wirkung ausgeübt, dass man darauf verfiel, die Erscheinung unbewußt als eine Nonenakkordbildung zu kreieren"). This, of course, is no more an argument than those that reject inversions because they are "harsh"—it just offers us a different sort of statement of rejection of the ninth than we have seen in earlier authors.

Thus, although Schenker is said to have derived some of his system from Bruckner, his attitude toward the ninth chord is definitely more conservative, indeed is rather more negative even than Sechter's.

Schenker's repertoire examples—from Mozart, Chopin, and Wagner—are all about the minor dominant ninth, and so they are of less interest to us here. I will reproduce just one of them as a sample:

Reference:

• Heinrich Schenker, Harmonielehre (1906).    Source:  IMSLP; digital facsimile of a copy of unknown provenance. I did not have the Mann Borgese translation available at time of writing.
• Arnold Schoenberg, Harmonielehre (1912/3rd ed. 1922).   Source: Internet Archive; digital facsimile of a copy of unknown provenance.
• Simon Sechter, tr. C. C. Müller, The Correct Order of Fundamental Harmonies: A Treatise of Fundamental Basses, and their Inversions and Substitutes (1871).   Source: Internet Archive; digital facsimile of a copy in the Brigham Young University Library.
• Simon Sechter, Die richtige Folge der Grundharmonien, oder vom Fundamentalbass und dessen Umkehrungen und Stellvertretern (1853).   Source: Internet Archive; digital facsimile of a copy in the Wellesley College library.  
• Simon Sechter, Die Grundsätze der musikalischen Komposition. Part 1: Die richtige Folge der Grundharmonien, oder vom Fundamentalbass und dessen Umkehrungen und Stellvertretern (1853). Part 2: (1854). Part 3: (1854). Source: Google Books; digital facsimile of a copy in the Harvard University library.
• Robert W. Wason, Viennese Harmonic Theory from Albrechtsberger to Schenker and Schoenberg (1985). Reprint edition, 1995. Edited version of "Fundamental Bass Theory in Nineteenth Century Vienna," PhD diss., Yale University, 1981. I am using this last as a source because it is readily accessible to me.

General comments

This may be a good moment to pause the survey of treatises and textbooks in order to make a few observations of a more general kind and to restate the goal of the survey and, beyond that, the goal of this blog.

There is a progressive historical narrative to be told, but it is not one of smooth, incremental movement from triads and seventh chords (18th century) through triads with added 6ths and ninth chords (1850?) to elevenths, thirteenths, and even more complex harmonic structures (1890? 1900?). One does find such narratives even in textbooks beginning in mid-century, but "histories of harmony" become much more common later, when history became an important cultural idea. The extended tertian chord model—stacking thirds—was particularly amenable to such accounts. As Damian Blättler describes it: "The fact that the model’s chord types can be arranged in sequence —triads are followed by seventh chords, seventh chords by ninth chords, and so on—has been used both as a pedagogical sequence and as a narrative about the development of chord types" (2013, 6). In a footnote Blättler offers an example:

A particularly clear-cut narrative claim is made by Alfredo Casella: "[Jean Marnold once said that the only musical difference between romanticism and the 18th century dwindled down to a single chord: the dominant major ninth. There is much truth in this, even though it seems to reduce a century of music to a purely technical problem.] Assuredly the chord of the major ninth, introduced by Weber, gave a totally different complexion to the entire musical language of the 19th century. Nor is it less evident that the exploitation of this chord reaches its culminating point in Debussy. . . . The following harmonic concept [the augmented 11th chord], . . . it is only in Ravel that the new chord is finally used in a constant, conscious, and spontaneous manner.”    [the section at the beginning of the quote was added from the original publication to broaden the context]

The ninth, however, was already among the figures that continuo players needed to learn in the late 17th century, and when early 18th century writers tried to gain control of the large catalogue of figures, the ninth came along, too. In practice, the common figures of the ninth were relatively few:

(It is important to remember that these are figures designed for musical practice, not theoretical categories. Thus, 9-8 might mean 9-8 over 3 as in (1) above in one city, but it might mean 9-8 over 4-3 as in (2) in another city or region; it might also mean either (1) or (2) in still a third city or region, the continuo keyboard player being expected to make an appropriate choice according to the circumstance.)

All of these we would understand as linear formations (probably suspensions, but also appoggiaturas or accented neighbor notes), but Rameau essentially "invented" the dominant ninth as a harmony, first through his elevation of the status of the dominant, then through his notion of supposition and the subsequent reverse strategy of stacking thirds. Because of his influence, (almost) everyone after him accepted the ninth chord as a harmonic entity (recall, for example, that it is among the eight basic chords in Catel's Traité: link). Thus the ninth chord was not "introduced by Weber"—it was a theoretically accepted harmony, but one without any real presence in practice (according to the treatise authors).

In fact, thanks to the exploitation of ^6 in the major key, as Jeremy Day-O'Connell has documented, the dominant ninth harmony—in its characteristically complex position as sometimes linear, sometimes harmonic—was already a part of musical practice no later than 1820, especially in music for dance. Here, as a reminder, are several examples from Schubert. (At least some of these were not presented in previous posts or in essays published on Texas ScholarWorks.) I looked at his last published set, the Valses nobles, D. 969, generally regarded as intended more for performance than as accompaniment for dancing. In no. 11, at (a), is a direct resolution. At (b), note the parallel treatment of V7, and at (c) the realization of the ascent through the upper tetrachord, G5-C6, that was encouraged by freer—and this case expressively and structurally significant—treatment of ^6.

In no. 2, a plainly audible indirect resolution with unfolded thirds: F#5 to E5, D5 to C#5. In the cadence the figure encourages an open ending (IAC, not PAC, with the melody on ^3).

In no. 5, another parallel treatment of the type most common in the waltz throughout the century: ^6-^5 over the dominant (bar 9), then ^6-^5 over the tonic (bar 11). Here the ninth is resolved internally, and the chord in bar 9 has to be regarded as an inversion of V7.

In no. 1, at (a), the internal resolution is stretched over three bars (A5 in bars 4-5 to G5 in bar 7). As in no. 11, the upper tetrachord remains important: in the cycle of fifths sequence at (b), then in the dramatic rising cadence at (c).

In no. 4, the urge toward the upper register is treated a bit differently. At (a), an accented ^6 resolves internally, and within the bar, is repeated, then repeated again as the dominant in the cadence (bar 7). The design is a small ternary form. In the reprise, At (b), the same figure, but then carried up to the instrument's highest octave to end—at (c).

Finally, in no. 10, ^6 is an essential expressive element, but its harmonic expression is vi (in bars 4 and 12), not V9.

The dominant ninth chord as a harmony finds it way into the theatre indirectly through the dance (especially in waltz numbers) and becomes a cliché by the time of Offenbach's great successes beginning with Orfée aux Enfers (1858) and continuing through the 1860s, but we should also point to its prominent appearance in the first act of Wagner's Lohengrin (1854) and in the Prelude to Act II of Tannhäuser (1860). For the latter I presented the passage below in this post: link.

This idea of intensification of the major dominant seventh at climax points or in cadences persisted through the rest of the century and beyond, as did ^6 with both V9 and Iadd6 in music of pastoral, lyrical, or sentimental character. (In the dance and concert dance repertoire, the history of the dominant ninth is bound up with a remarkably free treatment of the scale's upper tetrachord.) Only in the 1890s did color and harmony-as-function reach parity in concert musics, and in this sense Casella was right that "exploitation of this chord reaches its culminating point in Debussy."

I do not expect any grand new revelations to emerge from the roughly twenty additional textbooks/treatises still to be surveyed and discussed in this blog. The idea is to fill out and complete the documentation, but I will be looking for additional repertoire examples, which will of course serve the main goal of the blog as originally stated.

Reference:
Damian Blättler, "A Voicing-Centered Approach to Additive Harmony Music in France, 1889-1940," PhD dissertation, Yale University, 2013.
Alfredo Casella, “Ravel’s Harmony,” The Musical Times 67, no. 996 (February 1, 1926): 124-27. (Cited by Blättler)
Charles-Simon Catel, Traité d’harmonie (Paris, 1802). Digital facsimile published on the Internet Archive. Source: University of North Carolina at Chapel Hill.   Note: An edition from 1874 shows no changes in text or examples for the dominant ninth. Source: Bibliothèque nationale de France at gallica.bnf.fr.
Jeremy Day-O'Connell, Pentatonicism from the Eighteenth Century to Debussy (2007).

Foote and Spalding, Modern Harmony (1905) (2)

Foote and Spalding's chapter on the ninth chords is distinctive for its generous number of examples from the repertoire, examples that show clearly the range and character of their own stylistic sources and assumptions.* One can see this already in their first page (p. 158). In Lohengrin below, G5 is strongly emphasized by position and duration, achieving the same kind of "climax coloration" that we found in American songs of the same period (see my essay Dominant Ninth Harmonies in American Songs around 1900: link). As with Wagner, Schubert moves the ninth (but ascending) over a stable dominant bass. The two brief excerpts from Beethoven are common instances from the era of the minor dominant ninth.

The next three examples are also concerned with the minor dominant ninth chord.

Amy (Mrs. H. H. A.) Beach's "Fireflies," no. 4 from Four Sketches, op. 15 (1892), has many dominant ninths, both major and minor. This short passage comes less than twenty bars from the end. Something of the flavor of the whole can be gotten by a slightly larger excerpt (see below). "Walküre" is a striking resolution of the minor dominant ninth, with ninth in the alto and fifth moving upward chromatically. "Parsifal" is a passing major ninth within a wedge shape: F-F#-G in the top voice, F-E-Eb in the bass.

Further comment on Amy (Mrs. H. H. A.) Beach, op. 15n4. Below is a slightly larger excerpt (bars -18 to -10). The passage quoted by Foote and Spalding is boxed; instances of the dominant ninth are circled: all but the last are understood as major dominant ninth chords, but see my final comments and the figure below the score. For the moment, notice the strongly marked direct resolution of the ninth in bars -11 to-10. The tonic reached in bar -10 is the final chord, prolonged by figuration to the end.

Here is a reduced view of the harmony and voice leading:

Obviously, this reduction isn't as good as it could be, since the move major-dominant-ninth to minor-triad is problematic. The composer "sneaks in" a minor ninth just before the chord change, and thus it would have been better to notate the entire example as follows:

Beach's "Fireflies" is one of those rare compositions before 1900 in which the dominant ninth is strongly motivic. Here is the opening, the ninth chords marked (minor in bars 1-2, 8; major in 5-6).

And here is a reduction of the harmony and voice leading:

More of Foote and Spalding's repertoire examples will appear in a subsequent post.

------------------
* Such generosity was not typical earlier in the 19th century, but I should point out that by the end of the century multiple examples from the repertoire were commonly used, either for practical compositional or analytical purposes, as with Foote and Spalding, or as examples of historical practices.

Reference:
Arthur Foote and Walter Spalding, Modern Harmony in its Theory and Practice (1905). Source: Internet Archive; digital facsimile of a copy in the UCLA library.