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.

Foote and Spalding, Modern Harmony (1905) (2) note 1

In the previous post on Foote and Spalding's repertory examples of dominant ninth chords, I included this figure from their page 195:

This excerpt is certainly interesting, especially for its ascending move from the ninth, but Schubert's subsequent treatment of it in this variation movement from the A-minor sonata, D. 845 suggests that he was not thinking of it as a dominant ninth chord—or else we might say that he could have been in sympathy with those theorists who lumped the dominant ninth chord in with the dominant seventh and leading-tone seventh chords, and maybe even the ii chord (that is, any and all tertian entities that can be extracted from the dominant ninth chord).

Here is the context, the opening phrase of the theme's B-section, in which the ninth is part of a short "standing on the dominant" figure (the term is Caplin's; such figures to begin the B-section of a small binary or ternary form were stereotypical).

Already in the first variation, the bass changes the harmony to ii and thus A4 to the consonant fifth.

Variation 2: As in variation 1, but now the dissonance is gone!

Variation 3: G-F against Ab is brought very much into the foreground. The G is so obviously heard as an accented dissonant neighbor that the underlying chord in the first bar must be heard as vii°7.

Variation 4: Here the expressive idea of ascent takes over, but without the simple ^6-^7 figure of the theme. We can certainly hear the first bar as Ab: V9, with indirect resolution of the ninth in both fifth and sixth octaves in bar 2. Schubert continues to make the expressive point with the long scale that closes the phrase and leads to Eb7.

Variation 5: A predecessor to Schoenberg's fourth inversion of the ninth chord in Erklärte Nacht? No, a 2-3 bass suspension, A2-G2 against B3. And of course ^6 goes down, not up as in the theme.

Variation 5, end: As it would seem only Schubert can do, the end of the final variation leading into the coda turns unexpectedly magical. Not at (a), where he changes the mode to minor—but he does introduce a rising-scale figure that reaches Ab5 (note that the accented gesture is G and Ab). There is a source in the theme: the harmony is D minor with A4 at the top at the equivalent point that he reaches Db in this variation, but Schubert makes much more of it here than in the theme or earlier variations. At (b) we reach G5-Ab5 again, but now also get the reverse over dominant harmony. Then suddenly it is off into the sixth octave, A-natural, and a transcendent IV (no need for the triad's fifth; what we hear is without any doubt). Finally, at (d) even higher, but then with firm and continuing, if quiet,  descent into the final tonic.

Coda: Schubert isn't done yet. At (e), the old-fashioned turn to the subdominant in the prolongation of the structural tonic brings ^5-^6-^5 in F and so a little coloration of V9 in that key. At (f), Schubert reminds us of that transcendent IV from (c), again at (g), and even into the final seconds at (h).

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.

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* 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.

Foote and Spalding, Modern Harmony (1905) (1)

With this post, I leap ahead nearly to the end of the long 19th century. The point is to make a quick comparison with the various books up to 1850 discussed so far, before going back to survey the period from 1850-1900.

So far, the dominant ninth chord has been in a strange limbo, "invented" on the one hand as a result of Rameau's sub-posing a third below the fundamental of a seventh chord—as at (a) below—but, on the other hand, in form of the figure "9" at least, well established in thorough-bass (and therefore in the everyday activity of continuo playing)—"9", however, normally meant as at (b) below. The sub-posed third was already abandoned by Sorge in favor of the super-posed third that gave rise to the category of extended chords still found in textbooks today—as at (c), but a peculiar tension remained, given that the V9 chord was not a regular part of compositional practice (before popular genres like dances and dance-songs beginning in the first quarter of the 19th century), so that the viiø7 was recommended as the V9 without its root!—see at (d). The figures at (e1) and (e2) appear regularly in treatises when the dominant ninth chord is introduced, as we have seen, but though well recognized, and usually given its own chapter, the dominant ninth chord is then almost entirely ignored in exercises and assignments. In the few cases where it does show up, it is in form of the internal resolution of (e2), very rarely the fully independent harmony of (e1).

Arthur Foote and Walter Spalding published Modern Harmony in its Theory and Practice in 1905. Both were trained at Harvard. Foote spent his career as an organist in Boston, Spalding spent his as a member of the Harvard faculty.

Foote and Spalding follow the Weber/Richter tradition of Roman numeral labels but, like Richter, use figured bass for exercises. (Indeed, their volume overall shows a considerable debt to Richter's Harmonielehre.) Their employment of Roman numeral labels is exceedingly sparing, however, even in the chapters on modulation and even in analyses. On the dominant ninth chord, we note first of all that they give it considerable attention: a chapter of fifteen pages. (Eleventh and thirteenth chords are given their own chapter of five pages.) The dominant ninth chord is generated by adding a third to the seventh chord. Ninth chords can be built on other scale degrees, but Foote and Spalding dismiss those, saying they are really created by melodic figures such as suspensions (p. 153). "The dominant chord of the ninth is the one chiefly employed, and properly used is productive of admirable results" (p. 154).

Here are their first examples (p. 154). Note that under (1) & (2) they include the borrowed chord viiº7 in the major key (they refer to it as chromatic alteration, not borrowing or modal mixture). Under (3) & (4), they show ascending resolutions of the ninth without comment.

About Example 8, they say only that this resolution happens "not infrequently."

Like those of many other authors, their resolutions are a mixture of internal and external, as for instance in Example 8 above and in nos. 5-7 that precede it:

Foote and Spalding even allow downward leaps away from the ninth, thus showing their familiarity not only with earlier salon music but also with concert waltzes (such as those of the Strausses, Waldteufel, and others), comic opera, and operetta.

Although I have not made much of it in previous posts, all textbook authors give some space to chord voicings, in relation to the positioning of the ninth and usually in the context of discussing inversions. Foote and Spalding's comments are not unusual in this regard—for example, they reject the fourth inversion for the same reasons as earlier authors: the sound is harsh and/or the root of the chord must always be below the ninth. As a footnote, they praise one treatment by Wagner (p. 158):

The entire passage, which the authors call "splendid," is as follows (p. 137). It is meant to illustrate voicing in a sequence of seventh chords. As the boxed bars show, the ninth is internal to chord movements over a sustained cadential dominant.

I will reproduce and comment on additional examples in the next 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.

Kalkbrenner

In 1849, Friedrich Kalkbrenner published a practical instructional manual for pianists that combines the typical sequence in chord presentation with advice and examples for preluding, a nearly ubiquitous practice of improvising in the key of the composition before one performed in salon, recital, or even domestic music-making. It was only after the first World War that the practice largely died out.

Of the dominant ninth, he writes

This chord should be placed among the suspension chords, along with the eleventh and thirteenth, because it cannot be properly inverted, but because of its importance among the dissonant harmonies and the ingenious manner in which it is used, being presented in various contexts, we give it a separate chapter here. The ninth chord is nothing other than a dominant seventh chord to which a third has been added. (p. 26; my translation)

Oddly, however, Kalkbrenner's first example highlights a sequence of 9-8 suspensions, only reaching V9 at the end (boxed). Then he switches to the other extreme, with a sequence of dominant ninth chords that is very similar to one we saw in Dehn's Harmonielehre (1840).

And when he provides examples of preludes incorporating the ninth, the model (and of course the variants that follow) lack the V9 altogether:

Here are the first two variations:

The dominant ninth chord also plays no role in the nineteen exercises for preluding or the nine written-out preludes later in the volume.

Reference:

Friedrich Kalkbrenner, Traité d'harmonie du pianiste, Principes rationnels de la modulation pour apprendre à préluder et à improviser, Op. 189 (1849).  German edition: Harmonielehre zunächst für Pianofortespieler als Anleitung zum Präludieren und Improvisiren, Op. 190 (1849). Source: IMSLP; digital facsimile of a copy in the Staatsbibliothek zu Berlin.

Henry Lemoine, Traité (1833)

Henry Lemoine's Traité d'harmonie pratique et théorique (1833) is a perfect foil to E. F. Richter's "modern" Harmony in that Lemoine holds closely to the thorough-bass instructional system of the partimento tradition that dominated 18th century musical training and was only beginning to fade away by the mid-19th century. The emphasis is certainly on "pratique" and not "théorique": Lemoine is not concerned with the generation of chords; he restricts himself to off-hand comments about the opinions of Catel and Reicha, authors of the two harmony textbooks used in the Conservatoire through the first half of the century. He presents the chordal vocabulary in the same order as other textbooks but follows—and in some case even precedes—each with keyboard-based exercises.

The dominant ninth chord is presented in the familiar way (see below) Inversions are ignored.

 Lemoine's table of usable chords is as follows and is of interest because it includes the MM7 and the chromatic augmented sixth chords (in other words, the complete set he had introduced in the preceding chapters; in most other textbooks of the era, the augmented sixths are presented along with or just after the ninth chords but not included in the chord table).

Following the table is a preliminary "omnibus" lesson presented first with written-out chords (see below), then in several keys in the familiar figured-bass style of the partimento (I show only the first of these, in G major). The appearances of chords figured with "9" are boxed; these are all dominant ninth chords, prepared and then resolved internally.

Much of the last quarter of the book is taken up by a series of partimenti, in two sections, the first presumably by Lemoine, the second by earlier masters Cotumacci and Fenaroli. The first half of no. 17 in the first series is shown below. Despite the earlier presentation and despite Lemoine's indication that the exercises are "progressive," the dominant ninth is almost entirely absent. What we do find instead are 9-8 suspension figures. Of the seven figures with "9" below (boxed), six are of this type. The one with the arrow is a dominant ninth but can't really be said to function as one in context (note that is has no seventh). Below the example I have written out the first five bars of the third system for reference.

Reference:
Henry Lemoine, Traité d'harmonie pratique et théorique (1833). Source: IMSLP; digital facsimile of a copy in the Bibliothèque nationale de France.