Schubert, part 2

This continues last week's post with further examples of the treatment of ^6 and the dominant ninth harmony in Schubert's waltz collections, D365 (1821) and D779 (1825).

D779n30. The ninth first appears in the pickup to bar 5, then is repeated as part of a simple arpeggio (notably without ^7) and is easily heard to resolve as ^6-^5 over I in bar 6.

D365_n12. We hear V9 unequivocally in bar 2, but there is no ^5 in bar 3 (we would have to imagine it). But there is no doubt in bars 6-7, where the figure is repeated an octave higher and the ninth resolves on the strong beat of bar 7. Note that the second inversion of I counts as a harmony for resolution of the ninth -- Schubert was quite fond of dominant pedal points, especially in his early Laendler, and he put all sorts of melodic figures above them.

D779n17. A textbook case of a true V9 harmony resolving directly, with a 6-5 figure over I.

D779n2. Almost identical to the preceding, except that the V9 is more strongly defined.

D365_n30. Like the above, and repeated on the dominant level at the beginning of the second strain.

D779n20. Like the above.

A Gallery of Simple Examples of the Dominant Ninth

I have published an essay titled Dominant Ninth Harmonies in the 19th Century: A Gallery of Simple Examples Drawn from the Dance and Theater Repertoires: link to the essay.

Here is the abstract:

In European music, freer treatment of the sixth and seventh scale degrees in the major key encouraged the use of independent V9 chords, which appear already early in the nineteenth century, are common by the mid-1830s, and are important to the process by which the hegemony of eighteenth-century compositional, improvisational, and pedagogical practices were broken down. This essay provides multiple examples of the clearest instances of the V9 as a harmony in direct and indirect resolutions.

Schubert, part 1

In an earlier post, I observed that "one can easily find all seven types of the dominant ninth in the waltzes of Schubert alone." Schubert, therefore, deserves to be an early entry in the repertoire documentation that is the main goal of this blog. The examples below are drawn from the Original-Tänze, D365, and the Valses sentimentales, D779. Both are miscellaneous collections of dances, D365 published in 1821, and D779 in 1825. Most have their origins in music improvised for social dancing. The dances are in both Deutscher (German dance) and Laendler style--sometimes both in the different strains of the same piece. The Laendler style dominates in D365, whereas D779 is much more mixed.

This is n3 in the Valses sentimentales, D779 (1825). Apologies for all the boxes—the examples for D365 come from an essay of mine on the sixth scale degree, Scale Degree ^6 in the 19th Century: Ländler and Waltzes from Schubert to Herbert (link). Here the impetus to ascent is as strong as it could be. A direct resolution within V in bar 5 is followed by a remarkable "one note too far" at the end of the long ascent over the strain.

D779n3, second strain. The ^6 in bar 7 (arrow) is somewhat like the preceding—an expressive element within the V harmony—but without the dramatic emphasis, to be sure. The question marks over B5 in bars 1 and 5 indicate the uncertain status of that note: on beat 1, is it a ninth; or is it part of a complicated neighbor figure; or is it a ninth that resolves within the chord to A5 on beat 3? Any of those explanations is plausible.

D365n13:

D779n2: Once again the ninth receives attention: E5 is on the downbeat of bar 3. It resolves immediately to D5. The fourth note in the bar, another E5, is a simple escape tone.

This is the second strain of D779, n14. Despite its resolutions into the underlying V7 chord in bars 6-7, the ninth is an essential element of the sound of these two bars.

D365n2, the best known of Schubert's waltzes in the 1820s and for several decades thereafter. Similarly to the preceding examples, F5 in bars 5 and 7 resolves within the V harmony but is given strong melodic emphasis that lingers as part of the sound. The figure also mimics earlier accented notes--see the various circled notes.

D365n31. What was said just above--about lingering as part of the sound--is even more true here, where Schubert gives emphatic attention to the V9 sound in bars 2 & 6 (boxed) and also to ^6 above I in bar 4.

Post continues on Monday next week.

Schubert, three more from D365

The dances in Schubert's first published collection, D365, were mostly written (or written down) in the two years prior to 1821; a few may have been composed as early as 1815. Several exist in single staff versions for violin. The seven examples here come from two sections of D365: an opening large group of Ländler, all of which are in Ab major, and the set of six Atzenbrugger Tänze, named for a summer vacation place visited by Schubert and his friends.

In number 1 (below), ^5 rises to an accented ^6, which reappears over the tonic two bars later. This is audible as an almost direct resolution because of the distinction in register--but I admit that the gap of two bars, causes me to hesitate a bit. But there is no doubt in the variant at (c), where the chromatic passing motion is expanded and ^5 follows just a bar later, the label "almost direct resolution" is obvious.

The tonic 6/4 as tonic-functioning in its immediate context—as in bars 3-4—is common in Schubert's dances, especially the Ländler, but not in those of other composers.

Note that the accented dissonance effect in bar 1 is repeated every two bars in the first strain. Thus, the 9 in V9 is linked to the milder 6-5 over I (or literally 9-8 over the bass Eb), to the very traditional 4-3 at (b), and even to the chromatic passing tone B-natural5 in bar 7. The flagged high note in bar 6 is a "one-leap-too-far" figure that is a cliché within the dominant of the cadence. (Here, the 4-3 that begins the phrase is overtopped by the leap up to Eb6.) To close the second strain, Schubert repeats the figure—with a dissonance (Db6) and timed to the two-bar groups of the first strain.

One can easily hear the first strain of no. 3 as a variation of no. 2, the famous Trauerwalzer. Another sentence, this first strain has a leap and passing tone figure at bar 1.3, repeated a step higher at bar 3.3, then again in bar 5.3. The second phrase is repeated to close the second strain, at (d).

In n13, an expanded V9 with a direct resolution at (a), repeated in the second phrase. The flexible treatment of accented dissonances that is typical of the waltz throughout the nineteenth century is already apparent here in Schubert. In the second strain, boxed at (b) and later, the dissonances are traditional accented passing tones. But if we regard these as parallel to the opening, then G5 is the dissonance and F5, the ninth of the chord, is the resolution.

Beethoven, Lachner, and Pechacek

This post begins a historical survey based on the seven categories I presented and discussed in earlier posts, beginning with this one: link.

Beethoven, German Dances, WoO8, were written for a public ball in Vienna in 1795. His Laendler (in WoO11 & 15), published a few years later (1799 & 1802, respectively), are so close to the traditional (that is, earlier 18th century) type that one can readily imagine he heard them, or music very like them, in taverns, restaurants, or open-air performances.

František Martin Pecháček, 12 Laendler for winds (1801). I have discussed them here in connection with ascending cadence gestures: link.

Theodor Lachner, 6 Laendler for pianoforte (1822). Lachner had a long career as organist and music teacher in Munich. The 6 Laendler are early pieces.

Count Gallenberg, Waltz. This was a popular piece in the first half of the nineteenth century. I took it from a pedagogical collection by Carl Czerny, but it can also be found in a number of anthologies for musical amateurs.
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Beethoven, Laendler, WoO15n3. The instrumentation is two violins and bass, a configuration that was sometimes called the "Linzer Geiger," after popular turn-of-the-century groups, but which was in fact common throughout the Germanophone south of Europe. Here, ^6 is what I called a "throwaway note" or "one note too far." In the usual textbook labeling, it's an escape tone.

Lachner, Laendler n2. The two circled bars show how the expressive figure of a rise to ^6 could be "contained" within stereotypical 18th-century cadential progressions: in the first case, over ii6; in the second, over IV. The traditional violinistic Laendler didn't use S or subdominant types: the harmonies were different arrangements of I and V only.

Lachner, Laendler n3, second strain. Here is the harmonic progression I just described above. In bars 1 & 4, ^6 is a colorful expressive note. In bars 3 & 7, however, I might well read the harmony a V9, especially in bar 3 as a delayed resolution to ^5 occurs in bar 4 (this would be category 2.1).

Pechacek, Laendler n7. Note the appoggiatura treatment of ^6 over I in bars 1-2. The ^6 over the dominant in bars 3 & 7 and also in the second strain I would probably regard as mainly melodic, as well.

Beethoven, Laendler, WoO11n2. Very similar to figures above.

Beethoven, Laendler, WoO15n3. In bar 7, perhaps the clearest instance of the "throwaway note" or "one note too far," as we get the model for it in the previous bar.

Gallenberg, Waltz, in Czerny, 100 Recreations. Sounds very Schubertian, by which I mean an urban waltz or Laendler of the 1820s.

Beethoven, Deutscher Tanz, WoO8n2. Here the neighbor-note configuration probably plays against the strong accent and the repetition of ^6 over I in the subsequent bars.

Beethoven, Deutscher Tanz, WoO8n8. My category 2.1, where ^6 over V resolves over ^5 in a parallel figure 1-2 bars later.

Pechacek, Laendler n1, second strain. Here are direct resolutions (category 2.3) and the occasionally seen impetus to an ascending cadence figure.

Beethoven, Deutscher Tanz, WoO8n2, trio. Direct resolutions (arrows) and a ^6 over ii6, as in Lachner above (circle).

Duration and sound, part 2

In a recent post (link) I wrote about the impact of duration and metric position on the definition of the dominant ninth chord. This post continues that discussion.

The seven categories I identified—the list is reproduced below—follow a trajectory from melodic to harmonic; that is, the ninth as a plainly melodic feature (1.0 and 1.1) to the presentation of V9 as a harmony with a direct resolution of the ninth into the fifth of the tonic triad or into ^6 over the tonic (2.3). I don't pretend that these categories have cleanly defined "edges" and are therefore ready labels for any possible example. Instead, they are better thought of as ranges on a continuum whose points would represent individual instances in the repertoire of 19th century music. The examples below the list illustrate.

1. Internal resolution (within the V chord)
    1.0. Element of melodic shape (step)
    1.1. Element of melodic shape (leap, off the beat)
    1.2. Element of chord, weak beat
    1.3. Element of chord, strong beat
2. External resolution (to the following chord, usually I)
    2.1. Indirect resolution to ^5
    2.2. Indirect resolution to ^6
    2.3. Direct resolution to ^5 or ^6

A first set of examples for the seven categories above:

1. Internal resolution (within the V chord)
1.0. Element of melodic shape (step)

1-0_Mozart_German Dances, K600n1trio. String parts only. Simple passing tones.

1-0_Mozart_German Dances, K605n3. String parts only. Simple passing tones, but on the beat. No effect on the underlying harmony.

1.1. Element of melodic shape (leap, off the beat)
1-1_Schubert, D779n5. The leap hints at arpeggiation -- more than hints in this context, where fifth leaps are ubiquitous. Although ^6 resolves immediately in bar 7, in bar 3 one hears it more easily as a delayed resolution to the next bar (category 2.1) and thus the entire bar could be regarded as a V9 harmony.

1.2. Element of chord, weak beat
1-2_Johann Strauss jr_op7 n1. The decorative "Laendler leap" dominates the melody here (see bars 2-4 and bar 8) and thus it is not a surprise to hear it in bar 6 as well, going past B5 to C#6.

1.3. Element of chord, strong beat
1-3_Josef Lanner_Pesther Walzer, op.093_n2. Here the sound of the dominant ninth is strong, but so is the figure of the appoggiatura/incomplete neighbor. I would not label bar two, in part or whole, as a V9. On the same grounds, I would not read bar 5 as Iadd6.  Notice at the end consequences of the expressive lifts throughout the strain: an ascending figure in the cadence.

2. External resolution (to the following chord, usually I)
2.1. Indirect resolution to ^5
2-1_Johann Strauss, jr_polka_op236, trio. One of the clearest examples of this figure I could find.

2.2. Indirect resolution to ^6
2-2_Schubert, D365_n1. The ^6 in bar 3 links back to and confirms the significance of ^6 on the strong beat of bar 1. In this case, I could hear bars 1 & 2 as Ab: V9.

2.3. Direct resolution to ^5 or ^6
The opening of the Act II Prelude in Wagner's Tannhäuser. No doubt about this one!

2-3_Schubert, D365_n13. A better case even than for D365n1 above.

As the two Schubert examples show, it is by no means uncommon to repeat ^6 at the moment of tonic resolution, in order to create a link back to the ninth of the V9 chord. Here it is in the third waltz from Johann Strauss, jr.'s Künstlerleben [Artist's Life], op. 316.

Reference: Richard Beyer, "Bemerkungen zu den Nonenakkord," Musiktheorie 11/2 (1996): 91-110.  Page 102 for the Tannhäuser example.

Duration and sound, part 1

In the previous post, I wrote: "The ninth above a V7 harmony can be categorized in two ways: (1) in terms of its resolution (and the distinction between what I call internal and external); (2) or in terms of its duration (that is, sound or "color" versus harmonic function)."

Both duration and metric position are represented in an almost direct sequence in types 1.1 through 2.2. These are reproduced below. In 1.1 and in 1.2, a & b, the ninths are eighth notes; in 1.2, c-e, the ninth is a quarter note; in 1.3, the duration is two quarters; and in 2.1 it is two or three quarters.

As I noted  in the previous post in connection with Figure 2.1e, faster tempi for dancing after about 1830 encouraged the writing of 16-bar and eventually 32-bar themes, in which the older basic idea of two bars frequently is four bars instead. A simple example is the famous Skater's Waltz by Emile Waldteufel (1882). The main theme is a very clearly formed 16-bar sentence:

The ninth of V9 is as prominent as it could be (arrows below). Also note that Waldteufel succeeds in stretching out the V harmony over four bars (boxed as bars 2-6) in a way that overlaps the four-bar ideas.

 The second strain is almost as well-known as the first. It is presented here in a "violin direction" score -- these were often used by small ensemble directors instead of the full orchestral score, and they played a substantial role in theatrical and film music performance as well. Note that the disposition of I and V harmonies is the same as in the theme, though the dissonances are missing. The two arrows show 9 as neighbor note, then as direct resolution into the fifth of the tonic chord.

Waldteufel continues the pattern in the first strain of the second waltz, where he reverts to the leap to the ninth familiar from early Laendler -- and even makes use of the "double play" of scale degree as ^6 over I, then ^6 over V, and here ^6 over I again: see the asterisks.

In another very familiar piece—the first strain of the "Waltz of the Flowers" from Tchaikovsky's Nutcracker (1892)—there is no V9, though he does bring forward the waltz's typical expressive rise, here to a diminished seventh chord over a tonic pedal. The point of interest, though, is that this is another very clear 16-bar sentence where the basic idea is four bars long, not two. (I've shown only the presentation phase -- that is, the first eight bars.)

The second strain continues the pattern of four-bar ideas -- see the boxes below. Here the dissonances are extraordinary -- and all diatonic!  The C# in bar 1, for example, briefly creates a I7 (that is, with major seventh)--a sonority we already saw in the first strain of the Skaters Waltz, bars 7-8. These kinds of diatonic dissonances had become common in the waltz repertoire by about 1880, so much so that a simple diatonic and consonant melody could be heard as contrast, a device often deployed by Waldteufel in particular.

In the third strain of the "Waltz of the Flowers," we finally hear a dominant ninth -- see the arrow in bar 6. The boxes show a two-bar basic idea this time—though one might well argue that these are really motive-sized chunks in this context, that is, smaller units, not ideas. The eight bars are the sentence phase of a sixteen-bar period.

On seven types of the dominant ninth

The dominant ninth chord belongs first of all to the history of music in the nineteenth century. There is a theoretical thread to the story in the eighteenth century, too, but that is almost entirely irrelevant to musical practice. And of course the ninth chord—along with other complex chords—is a common feature of Tin Pan Alley, Swing, and post-WWII ballad styles, but its treatment in those repertoires largely follows nineteenth-century practices (and is much more restricted than harmonic practices that follow from bebop).

Note 19 November 2018: See also an essay I have published titled Dominant Ninth Harmonies in the 19th Century: A Gallery of Simple Examples Drawn from the Dance and Theater Repertoires: link to the essay.      Here is the abstract: "In European music, freer treatment of the sixth and seventh scale degrees in the major key encouraged the use of independent V9 chords, which appear already early in the nineteenth century, are common by the mid-1830s, and are important to the process by which the hegemony of eighteenth-century compositional, improvisational, and pedagogical practices were broken down. This essay provides multiple examples of the clearest instances of the V9 as a harmony in direct and indirect resolutions."

I should also note that I am only writing about the dominant seventh with major ninth. The dominant seventh chord with minor ninth already had a place in 18th century music and is quite a different expressive entity, even though as a harmony it functions as a V in the same way as the dominant seventh with major ninth.

Nor am I concerned with the non-dominant ninth chords—these differ substantially from the dominant ninths and play only a very small role in 19th century music before about 1890. (Also see the note at the end of this post.)

The ninth above a V7 harmony can be categorized in two ways: (1) in terms of its resolution (and the distinction between what I call internal and external); (2) or in terms of its duration (that is, sound or "color" versus harmonic function).

Two main categories and seven types of the dominant ninth appear in the list below. These are arranged in a melodic to harmonic trajectory, that is, the "internal resolution" operates within a single V7 harmony where the 9 is a melodic element (1.0-1.3)—whereas the "external resolution" raises the possibility of V9 as a harmony (2.1-2.2 in the list below) and can sometimes truly supplant V7 with an independent V9 (2.3). As we will see, tension between melodic qualities and harmonic function is a constant with the dominant ninth, much more so in fact than it is with the V11 and V13 chords.

1. Internal resolution (within the V chord)
    1.0. Element of melodic shape (step)
    1.1. Element of melodic shape (leap, off the beat)
    1.2. Element of chord, weak beat
    1.3. Element of chord, strong beat
2. External resolution (to the following chord, usually I)
    2.1. Indirect resolution to ^5
    2.2. Indirect resolution to ^6
    2.3. Direct resolution to ^5 or ^6

I should warn against understanding this trajectory as a historical narrative for 19th century harmonic practices. In fact, all seven types occur in music throughout the century—indeed, one can easily find all of them in the waltzes of Schubert alone.

The examples below are generalized from the musical repertoires to be discussed in detail in subsequent posts. That most of the examples are presented as waltz fragments is a reflection of the central importance of that genre to the general adoption of the dominant ninth sonority.

1. Internal resolution (within the V chord)
    1.0. Element of melodic shape (step).  This first category is really here for sake of completeness: figures with ^6 as passing tone or neighbor in a complete neighbor-note pattern can be found throughout the eighteenth century. Only if the "ninth" was made to be of greater duration than its surrounding notes would there be any suggestion of the sound of the dominant ninth sonority.

    1.1. Element of melodic shape  (leap, off the beat).   Leaping to ^6 brings some attention to it not only as an expressive note but also as a potential chord member. In (a) and (b), the ninth relaxes back into the root immediately, in (c) it is left hanging, as if a free tone or a sort of "throw-away" note.

 
 1.2. Element of the chord, weak beat. Positioning the ninth on a beat strengthens the claims hinted at in the previous examples. In (b) and (d), the harmonic is certainly as well defined as the melodic. The old-fashioned suspension in (e), ironically works against the ninth, despite the considerable attention given to it in position and duration: the clichéd suspension figure—already more than 300 years old by 1800—demands it own attention.

    1.3. Element of the chord, strong beat. The same problem arises here as with 1.2.e: the greater duration of ^6, one might say perversely emphasizes rather than suppresses its melodic quality as neighbor note to ^5. Nevertheless, I am comfortable with representing the harmony as V with "9 — 8" to show that we are on the edge of the melodic/harmonic divide.

2. External resolution (to the following chord, usually I)
    2.1. Indirect resolution to ^5.  In these there can be no question that the dominant ninth is a harmony.

    In rare cases the indirect resolution to ^5 can be stretched to 3 or 4 bars. This figure is largely associated with music after Schubert's death. It's found already in Lanner and Strauss, sr., who are the first prominent composers to routinely expand the eight-bar theme to sixteen bars. It is possible that this change would have occurred anyway over course of time, but an immediate impetus was the speeding up of tempi for dancing beginning about 1830, the two main genres for this being the waltz and the galop.

    2.2. Indirect resolution to ^6. Although this can be found in Schubert, it's rare. The progression with a sustained ^6 over I begins to appear after about 1840 and becomes increasingly common—though never to the point of becoming a cliché—in the decades after that.

    2.3. Direct resolution to ^5 or ^6. Despite the design of my list and my comments, with their hints of historical trajectory, the proper dominant ninth harmony—as in the examples below—is heard emphatically (if, again, not often) already in Schubert, who clearly relished its distinctive sound and its striking expressive effect.

Note: Still another exclusion from this blog is the dominant ninth with altered fifth. These chords also begin to appear with some frequency in the 1890s. The version with raised fifth is more common; so, in C major G-B-D-F-A becomes G-B-D#-F-A, which happens to form a whole-tone scale pentachord also: D#-F-G-A-B. Less common is the dominant ninth with lowered fifth, so: G-B-Db-F-A. This one, too, can be spelled in scalar form as a whole-tone pentachord: F-G-A-B-Db.