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.

Schoenberg, Harmonielehre (1912/1922)

This continues and completes the series of posts tracing a line from Simon Sechter in the first half of the nineteenth century through his student Bruckner to Schenker and Schoenberg.

If Schenker took Sechter's ideas about scale degrees and chromaticism in one direction, expanding on them to reinterpret but also reinforce a traditional concept of harmony, Schoenberg went exactly the opposite direction from the same starting point. "In such matters as the existence of non-harmonic tones, the duration of harmonic steps and the notion of chords beyond the seventh, Schoenberg and Schenker could not be farther apart" (Wason 1982, 247).

Schoenberg's conversational, often satirical, style is on display in his chapter on the ninth chord, which begins

The 9th-chord is the stepchild of the system. Although it is at least as legitimate as the 7th-chord, it is still generally regarded as doubtful. It is hard to see why. The system begins to become artistic at the moment when it builds the minor triad in imitation of the major. Then, adding the seventh to form a 7th-chord, although not a necessary result of this first arrangement, is still a possible one. But if this is possible, then 9th-chords, 11th-chords, etc. are also possible, which would of course have the advantage that one could continue the system of extension by stacking thirds. (1922, 417; my translation)

He then spends some time poking fun at theorists' inconsistent treatment of inversions. That he accepts them is obvious from this passage near the end:

Of course, [inversions, such as the fourth inversion] no longer bother any serious people today. In [Strauss's] Salome quite a number of different 9-chords occur. . . . The student will easily find examples in the literature. There is no need to set special laws for [the 9th-chord's] treatment. Those who want to be careful can apply the laws that already came into play with the 7th-chords: that is, resolve the dissonance by step downward, make the root leap a fourth upwards. 

Finally, he says that altered forms of the ninth chord are "undeniably" useful as vagrant chords or in progressions involving vagrant chords, and he supplies this example:

Although this might suggest that even the dominant ninth chord type derives from the diatonic tonic ninth by alteration, in a previous example for ninth chords on secondary degrees, Schoenberg shows the dominant ninth chord first, then the others (including I9). In that respect, at least, he follows 19th-century theoretical tradition.

Reference
Arnold Schoenberg, Harmonielehre (1912/1922).   Source: Internet Archive; digital facsimile of a copy of unknown provenance.

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.

Simon Sechter

Next I want to talk about Arnold Schoenberg's Harmonielehre (1912/ 3d ed. 1922), but I need to precede that with posts on Simon Sechter, Anton Bruckner, and Heinrich Schenker. The reason for this is a trail of influence: Sechter established what is sometimes called Viennese Fundamental Bass theory; he taught Bruckner, who became professor in the Vienna Conservatory (he also taught in the University of Vienna) and at one time or another both Schenker and Schoenberg were his students. On the latter two, Sechter's influence is still strong, despite their radically different goals and attitudes.

Sechter taught in the Vienna Conservatory during the first half of the century. He was a composer, organist, and teacher who published a three-volume theory/composition textbook near the end of his life. The first volume is on harmony; the others are on melody, rhythm/meter, and counterpoint. Robert Wason gives a nicely compact description of Sechter's treatment of the ninth chord:

Sechter introduces the ninth chord after the suspension (Grundsätze, pp. 30f), for it is always the result of the 9-8 suspension, not third stacking. No chords beyond the ninth are discussed in the Grundsätze, although Sechter has a habit of referring to the "suspensions of the eleventh and thirteenth." The 9-8 is shown resolving over a held bass on the dominant, as well as with change of bass to the tonic. "Concealment" of the fundamental enables Sechter to explain such apparent progressions as VII7-I, and delay of the resolution of the ninth beyond the change of bass is used to explain such apparent progressions as VII7-VI6. Sechter also introduces the ninth chord into the sequence. (1982, 78n16)

Unlike most others we have encountered so far, Sechter does not attempt an acoustical explanation, whether by supposition or by stacking thirds, but he then effectively derives the independent ninth chord from suspensions (rather than separating the acoustical/stacked-third entity from suspensions, as other authors do). His first example shows the suspension, with preparation:

The next example leads to the independent ninth chord (that is, one that resolves directly) by means of a "delayed resolution" (verzögerte Auflösung). Like his contemporaries, he is obviously of two minds about this chord: "to the ninth, which is introduced here arbitrarily and really only delays the entrance of the octave, one can attribute an (admittedly inauthentic) independence, in that one calls
simultaneous sounding of root, third, fifth, seventh and ninth a ninth chord" (Wason 1982, 138; Sechter, vol. 1, p. 30; in Müller's translation, p. 59).

As do most other authors, he allows the other diatonic ninth chords in suspension figures and sequences:

Remarkably, he allows the dominant ninth to engage with the interpolated root needed to explain root progressions by second:

As demonstration that Sechter can be said to admit the dominant ninth chord as an independent harmony, even if "unofficially," the examples below show that it may be used to prepare a 6-5 (or 6-5/4-3) resolution. Note also that he explains the viiø7 chord in the now familiar way as the ninth chord without its root. "Verschweigung" is Wason's "concealment"; the word literally means "silencing."

Sechter's commingling of abstract fundamentals with passing-chord figures will have far-reaching consequences in Schenker (and will be roundly rejected by Schoenberg). In the second example below, we can see again the typical uncertainty about the status of the ninth chord--if it looks independent in the earlier examples, now it is the result of passing tones.

Sechter's student Anton Bruckner "promoted the conservative theories of his mentor despite his own compositional innovations. He did, however, introduce several new ideas into Sechterian theory, most notably his treatment of the ninth chord, which he considered a fundamental harmony rather than the result of a suspension" (Bernstein 2002, 791). This is hardly surprising for the later 19th century, but Bruckner apparently differed from Sechter not only in this, but from his mentor and almost other textbook writers in that he largely ignored suspension figures (Wason, 138-39). If Schenker saw something suggestive in the linearity promoted by Sechter's abstract fundamental basses, Schoenberg might well have seen in the intense vertical emphasis the path to his own denial of non-chord tones.

Wason summarizes the differences between Sechter and Bruckner on the ninth chord:

In Sechter's system the ninth is always the product of suspension, there are no inversions of the ninth chord, and scale-degree ninth chords can only occur in the sequence through delayed resolution of a suspension beyond the change of bass. Moreover, the dissonances of the eleventh and thirteenth do not form chords. In Bruckner's system, on the other hand, the ninth chord is a "fundamental harmony”; the eleventh and thirteenth are on some occasions the result of suspension, while on others they are part of a six- or seven-note chord on the dominant.  (142-43)

Reference:

• David W. Bernstein, "Nineteenth-century Harmonic Theory: The Austro-German Legacy," in The Cambridge History of Western Music Theory, ed. Thomas Christensen (2002), 778-811.
• Arnold Schoenberg, Harmonielehre (1912/1922).   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 source.

MacDowell, "Thy Beaming Eyes"

This is a second postscript to the post on Hull's Modern Harmony (1915). Among his examples is an excerpt from Edward MacDowell's "Thy Beaming Eyes," no. 3 in Six Love Songs, Op. 40 (1890). Here that is again:

Hull offers no context and no explanation for the harsh dissonance—arguably, much harsher in this voicing as a first inversion minor dominant ninth than any fourth inversion of the major dominant ninth!—and incongruously setting the word "Paradise." We will explore that here, as the song is rich in its treatment of ninth chords and their inversions.

The poems in Op. 40 are by William Henry Gardner and are largely simple expressions of love in a style that is a restrained version of sentimental songs from the late 1800s. "Thy Beaming Eyes," however, introduces irony. Its text:

Thy beaming eyes,
Are Paradise,
To me, my love, to me.
Thy trembling kiss
Is heavenly bliss,
To me, sweet love. 

But oh, thy heart!
It has no part,
With thee, my dear.
Tis strangely cold
And doth withhold
Its love, I fear. 

Thy beaming eyes,
Are Paradise,
To me, my dear.

The sentimental expression (in the opening at least) helps to account for the ninth chords (I have noted in earlier posts that major dominant ninth chords are more common in lyrical, sentimental genres), and the irony accounts for the increased dissonance.

"Passionately" and "loud" signal something unusual from the start, although one could say that "beaming eyes" and "Paradise" are worthy of intensified expression, the more so for sake of contrast with the familiar soft and sighing notes of the second phrase, "Thy trembling kiss . . .". Here "Paradise" is set to a second-inversion dominant ninth -- at (a). The ninth D5 is duly placed at the top, but the voice then doubles it (as a written D4) and resolves that note upward (while D5 remains in the piano part). That E4 remains in the subsequent A7 over C#.  The phrase ends with a plaintive "to me" on another dominant ninth, this time in root position with the ninth at the top in both voice and piano. With the following second-inversion C7, the ninth disappears more than it can be said to resolve (it's B-natural3 that's readily heard as moving to Bb3, and G—to which the ninth A might resolve—is already stationary in the bass). Whatever the explanations, both major dominant ninth chords here are prominent and striking in their voicings and treatment.

In the second phrase, we find the first hint of trouble: at (c) "kiss" is set to a version of the same dissonance that we saw in Hull's quote. Here it is heard not as a ninth, but as an F# diminished seventh chord with upper neighbor D4. At (d) and (e) the same chord pair as at (b) but now with forceful expression and the C7 in root position. Here the textbook writers' suggestions about the ninth chord as offering intensified expression are certainly realized.

The third phrase brings us to the poem's second verse. Apparently a reprise of the opening in the melody, the music quickly takes another direction, but not before "kiss" has become "heart" set to the same chord in the voicing of Hull's example -- at (f). At (g) I imagine a textbook writer might call this a dominant ninth with its root deleted. This is one of the few places in practice I might find that plausible. Supporting this hearing is the conversion of the ninth chord from (a) to the same half-diminished seventh at (a?).

The second phrase returns with harmonies intact—(b) through (e) below—but "kiss" and "bliss" are now "cold" and "withhold." The singer's final reiteration of the opening, then, is wistful and without much hope. It is here that the irony reaches its natural end-point, as "Paradise" is overtaken by the D minor ninth chord (this is Hull's example).  At the very end, note C9 and C13 in the cadence--at (h1) and (h2).

Schoenberg in Hull, Modern Harmony

A. E. Hull reproduces the famous fourth inversion of the dominant ninth chord from Schoenberg's Verklärte Nacht (1897).

The example is Schoenberg's own, no. 267 (p. 418):

Hull mistakenly assumes that example 273, below, is from Halm, but it is actually Schoenberg's rewriting of Halm's Ex. 97 (for that, see the previous post). Recall that Halm's position on the ninth chord was somewhat more conservative than most textbooks in the second half of the 19th century: the dominant ninth chord is a proper harmony, but may only appear as V9 and only in root position. Schoenberg ridicules the inconsistent and un-argued assertions about inversions of the ninth chord in textbooks, especially the ban on the fourth inversion as "harsh" (or, as Halm does, banning them all). Schoenberg turns this around, saying that what was ugly yesterday may be considered beautiful today and noting that his sextet was rejected for performance but then was premiered two years later and nobody noticed that there was a fourth inversion ninth chord (1912/22, 418-419). He also refers to multiple instances in Richard Strauss's Salome.

Extended, detailed discussions of Verklärte Nacht may be found in Swift 1977 and Lewin 1987. Swift notes that the longer progression of which the dominant ninth is a part is "more than a linking passage, for it returns at two crucial structural points. First, it is the harmonic scaffolding for the recapitulation of the first group sentence (mm. 181-87), and is in part responsible for the ambiguity and uncertainty of that return. Second, this 'uncatalogued dissonance' returns in the first part of the coda as part of a succession of important motives from the composition" (10-11). Lewin's exceedingly detailed discussion weighs a variety of potential analyses and implied progressions. He focuses particularly though on the chord-pair together as occupying the functional space of a leading-tone diminished seventh chord, a hearing one can recognize if one expands the context to include the subsequent chords:

At the asterisks are two enharmonically equivalent diminished seventh chords (see Lewin 52-53, for the derivation of the first one, where the chord tone is the Ab3 and A-natural3 is understood as a passing tone). Ultimately he settles for the idea of the functionally ambiguous vagrant harmony, pointing simultaneously away from D minor (deceptive progression) and toward it (note the inverted chaconne-bass figure starting from i 6/4: A2-Bb2-B-nat2-C3-Db/C#3-D3).

Here is still another possibility. At (a) below is Schoenberg's Ex. 267b, the root position of the Ab major ninth chord. At (b) are typical textbook voicings of the first three inversions (I took these specific ones from Catel and Bussler). At (c) is Schoenberg's fourth inversion with a partial resolution into an augmented sixth chord in D minor; note that Ab is enharmonically G#. At (d), an alternative: the same augmented sixth chord in D minor with raised 3 and 5 (D becomes D#; F becomes F#) and a cadential close follows. This is consistent with Schoenberg's strict, even radical, notion of monotonality: all chromatic chords are alterations of diatonic ones (such that even what we now commonly regard as secondary or applied dominants are considered altered chords), and it is also consistent with Schoenberg's notion of vagrant chords, or chords with multiple potential harmonic meanings and therefore potential progressions (these are diminished seventh chords, augmented triads and their derivatives, and the augmented sixths; see 1912/22, 288 ff., especially 296 ff.).

Reference:

• August Halm, Harmonielehre (1900).  Source: IMSLP; digital facsimile of a copy in the University of North Carolina Chapel Hill library.
• Alexander Eaglefield Hull, Modern Harmony: Its Explanation and Application (1915).    Source: Internet Archive; digital facsimile of a copy in the University of Toronto Library. The Halm/Schoenberg example perhaps is a hint of the loose mode of quotation from sources that eventually fueled public complaints of plagiarism.
• David Lewin, "On the 'ninth-chord in fourth inversion' from Verklärte Nacht," Journal of the Arnold Schoenberg Institute 10/1 (1987): 45-64.
• Arnold Schoenberg, Harmonielehre (1912/1922).   Source: Internet Archive; digital facsimile of a copy of unknown provenance.
• Richard Swift, ‘‘Tonal Relations in Schoenberg’s Verklärte Nacht,’’ 19th Century Music 1/1 (1977): 3-14.

A. E. Hull, Modern Harmony (1915)

Alexander Eaglefield Hull was a prolific writer, biographer, and encyclopedist on musical topics. His Modern Harmony: It Explanation and Application (1915) is atypical of his work in its focus on a technical subject, but its source must certainly lie in biographies of Scriabin and Cyril Scott that Hull was preparing at about that time (and published in 1916 and 1919, respectively).

Hull makes his advocacy of contemporary practices crystal clear at the outset:

The swift current of modern musical art during the past ten or fifteen years seems at first glance to have ruthlessly swept away the whole of the theories of the past. The earnest student may well be excused if he is bewildered completely on rising up fresh from his theoretical treatises to plunge into the music of actual life—of the twentieth-century opera houses, concert-halls, and music-rooms. . . .
      The whole of musical history . . . warns one against the too easy acceptance of the neatly turned epithets of persons who are . . . too indifferent to appreciate a new kind of music which claims at once wide sympathies and considerable powers of concentration. . . . Even on short acquaintance these modern musicians have too much method in their so-called “modernity” to be dismissed thus cursorily. It is the greatest possible mistake to view these modern schools as things separate from the art of the past. Indeed, most, of the new traits are legitimate growths out of the art technique of the acknowledged great masters. It does seem as if there were nothing new under the sun. As the principles of the twentieth-century Cubism in painting were well known some 400 years ago, so the modern methods of part-writing and chord-building all find their prototypes time after time in the pages of the great masters of the past.  (1-2; lightly edited)

Then Hull offers up a complaint frequently heard in the century or so from 1850 to 1950:

So much harmony teaching is founded on mere text-book formalities that there is little, if any, appeal to the evidence of the aural intelligence—the real arbiter in all matters of musical taste. It is the empirical method which makes the theory of the music of [recent] composers so difficult, and we cannot suppose that all of the explanations set down herein were present in the composers’ minds at the time of conception, or that they may even be acceptable always to the composers themselves. The system of teaching harmony by attaching names to the chords often produces an altogether false way of regarding music. No chord in itself conveys any meaning whatsoever. It can give a vague impression. . . , but thought in music can only be transmitted by chordal succession and forward movement, and the chord, however wonderfully arranged, has value only in this light. (4-5; emphasis in original)

Consistent with his approach—which simplifies discussion of harmony largely by removing complex labels—Hull has this to say about the dominant ninth and its inversions:

The unnecessarily forbidden appearance of the root in the inversions of the chord of the ninth tends to cramp part-writing, and the prohibition robs diatonic music of some of its most powerful effects. The root, which merely requires judicious placing and arrangement, may appear above the minor or major ninth with great effect. A wide selection of resolutions should be allowed.
For instance:
    (a) Both the major and minor ninth may fall a tone or semitone.
    (b) The ninth may remain.
    (c) The ninth may rise a chromatic semitone.
The case of (b) will be clearer still when the ninth is prepared, thus appearing as a pedal note. In all cases, so long as the ninth is satisfactorily resolved, the other notes are comparatively free. (18-19)

His example for (a)—see the arrow in the second bar—is from a song by Edward MacDowell, a piece so interesting in its treatment of the ninth that I will devote a separate post to it. For (b), see the beginning of the excerpt from the Verdi Requiem. For (c), look at the first chord pair from August Halm's Harmonielehrebuch [sic].

This last example is not in Halm's book. Hull is quoting from Schoenberg's Harmonielehre (1912), complete with the misspelling "Harmonielehrebuch" (properly it would be "Harmonie-Lehrbuch," although that isn't Halm's title, which is simply Harmonielehre).

Halm's example 97c is this. Schoenberg rewrites the progressions under (c). I will discuss his treatment of ninth chords in a separate post.

Halm's Ex 97c is actually meant as a negative example. He regards the V9 resolving to I (see his first examples under 97) as the only correct use of the ninth chord, in contradistinction to the dominant seventh, which he says has a much "softer" character and can move in almost any tonal direction. The two chord pairs under 97c show that one cannot reasonably apply the same traits to the ninth chord (Halm 1900, 118-119).

Reference:

• August Halm, Harmonielehre (1900).  Source: IMSLP; digital facsimile of a copy in the University of North Carolina Chapel Hill library.
• Alexander Eaglefield Hull, Modern Harmony: Its Explanation and Application (1915).    Source: Internet Archive; digital facsimile of a copy in the University of Toronto Library.
• Arnold Schoenberg, Harmonielehre (1912/1922).        Source: Internet Archive; digital facsimile of a copy of unknown provenance.

Castillon, 6 Valses humoristiques (1871)

Alexis de Castillon followed one of the familiar trajectories for a 19th century musician. From an aristocratic family, he was intended for law or the military but resisted and went into music instead. He studied at the Paris Conservatoire under Massé and Franck; among his friends was Saint-Saëns. Generally in poor health, he died young.


In de Castillon's 6 Valses humoristiques (1871), no. 1, the principal strain offers the rising line from ^5 in stark simplicity (beamed line), including V9 (boxed):

The design is ABCDAE, where E is a coda whose final phrase is recalls the opening with the melody in the left hand:

In no. 2, scale degree ^6, along with the occasional V9, is motivic. Here is the opening. The main motive is circled, a dominant ninth with direct resolution is in the first box, and a ^6-^8 figure in the cadence is in the third box.

At the end, a reprise of the first strain turns into one of those distilling or unraveling codas that are so common in 19th century instrumental repertoires. Here ^6 is the main attraction.

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) (3)

Here are more of Foote and Spalding's repertoire examples for the dominant ninth chord. These are from p. 160.

The Chopin example comes from the first movement, the second theme in the recapitulation—see the boxes in the third and fourth systems. It is indeed a proper major dominant ninth with a direct resolution (although with octave change). It is also an isolated instance, as nowhere else in the movement, or in the sonata, does the ninth chord play any role. In this theme, the far more prominent feature is the 13th (see arrows), which is a melodic rather than harmonic element but contributes a distinctive sound to the theme and so illustrates that characteristically uncertain positioning of the extended chords between harmonic and linear processes.

Incidentally, the ninth in the example above is not in the second theme in its initial presentation during the exposition:

George W. Chadwick's "Lovely Rosabelle" sets a short ballad from Sir Walter Scott's Lay of the Last Minstrel.  The form is that of a melodrama—like an operatic szena, alternating dramatic recitative with more formal sections of air or chorus melody. The example comes from near the end, where the chorus repeats several times text including "a dirge for lovely Rosabelle" (who has drowned).

The example isn't very convincing as a ninth chord. There are several better ones earlier in the piece. Throughout the 19th century, the major dominant ninth chord as a harmonic entity was more likely to appear in lyrical, sentimental, or even pastoral movements or passages, as here, with "soft" and "sad." Note especially the contrast between the vigorous, minor-key, martial music and this passage.

Here are two good textbook examples that Foote and Spalding might have used to better effect. Note the direct resolution of the ninth C5 in the soprano.

The ^6-^8 figure in the cadence was a common Scots-Irish touch. We have encountered it before in Macdowell's "To a Wild Rose": link to the blog post.

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.

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

I have already discussed Amy (Mrs. H. H. A.) Beach's "Fireflies," no. 4 from Four Sketches, op. 15 (1892), in the context of Foote and Spalding's repertoire examples for the dominant ninth chord. "Fireflies" is quite unusual in its motivic treatment of the minor dominant ninth, but isolated, interesting examples can be found in other numbers in the set. The contents are:

1. "In Autumn," Allegro ma non tanto with an epigraph from Lamartine: "Feuillages jaunissants sur les gazons épars" [Yellowing foliage on patchy grass]
2. "Phantoms," Allegretto scherzando with an epigraph from Hugo: "Toutes fragiles fleurs, sitôt que nées" [All fragile flowers, as soon as they are born]
3. "Dreaming," Andante con molto espressione with an epigraph from Hugo: "Tu me parles du fond d'un rêve" [You talk to me from within a dream]
4. "Fireflies," Allegro vivace with an epigraph from Lamartine: "Naître avec le printemps, mourir avec les roses" [To be born with spring, to die with roses]

All but no. 3 belong to the general class of scherzi, or more narrowly comic scherzos, "Mendelssohn scherzos," or even the scherzo mistereuse of theater and film music. In no. 1, the main key is F# minor. The first cadence to the parallel major includes a clearly defined V9/V whose ninth, C#5,  resolves indirectly to the same note over the dominant (perhaps a 13th by the standards of some textbooks).

In no. 2, the main key is A major. The beginning of the B-section, in Db major (enharmonically C# major, or III), carries with it some not-too-faint echoes of the waltz, and those may be responsible for the ninths in the three circled V-I figures.

In the principal cadence of the B-section we find one of those climactic V9/V figures—here, forte and appassionato—that are familiar from Beach's songs and many another 19th century composition. Although the melody leaves the ninth, notice that the left hand maintains it through the bar (see the arrow).

As a postscript, here is an excerpt from Anton Rubenstein's Romanze in Eb major, op. 44n1, as edited by Arthur Foote. The design is a bit unusual: A-B-A'-C, where A' acts equally as reprise and as acceleration toward C, which in its turn is equally thematic and cadence+coda. It is of interest here because it combines the rise to a climax (bar 7) with an anti-climax (sudden drop to pp at the registral highpoint) that is a very clear major dominant ninth chord.