Inversions, part 1

Discussion of inversions of the major dominant ninth chord typically stall on Arnold Schoenberg's famous needling of detractors about a fourth inversion chord in his Verklärte Nacht (see my post on several authors' analyses of the passage: link). But now that I am done with that ritual notice, let's move on.

Looking at examples from posts to this blog and from essays published on the TexasScholarworks platform, I found 25 instances, considerably more than I expected, though as we will see I have included a particular type that some readers may not accept as a proper inversion. The numbers were: first inversion 5; second inversion 17; third inversion 2; fourth inversion a questionable 1.

In the graphic below, I have shown G7 and inversions with simple voicing, then the same for G9, whose inversions are labeled a-d.

A weakness of the first inversion is the likelihood of its collapsing into the most commonly used inversion of V7: see (a1) below; a standard resolution to the tonic is at (a2). At (b1) the loss of the root turns the second inversion into viiø6/5. The standard resolution is at (b2) in five voices, at (b3) in four voices; it must be to I6 in order to avoid parallel fifths between the bass and the voice carrying the ninth of the chord. The "particular type" I mentioned earlier is at (b4). Before you complain--as some certainly will--that this doesn't excuse the parallels, let me remind us all of a very common dodge used in Renaissance-era counterpoint: 5-3-5-3, as at (b5). 

The figure at (b4) is of course a schematic form of the ubiquitous oom-pah bass. Its resolution nicely balances line and bass function; Schenkerians often represent this as shown below.

The third inversion--at (c1) and (c2)--has the smoothest voiceleading of the lot, with a pleasant pair of tenths between the bass and the voice carrying the ninth. At (d1) the fourth inversion collapses into V7; (d2) shows that this inversion leads to I6/4, (d3) that one can avoid the 6/4 with a mediant, but iii is the weakest of the major key's three minor triads and to make things worse is often used functionally as a dominant, which would make the ninth chord resolve internally.

 We begin with the first inversion. Here is an excerpt from the third waltz in Johann Strauss, jr.'s Künstlerleben [Artist's Life], op. 316:

And here is nearly the same in the trio from his father's Damen-Souvenir Polka, op. 236:

Again from Strauss Vater, in the trio of his best-known piece, the Radetzky March:

My added unfolding symbols give you the essence of the "particular type": it is ^5 (E2) that moves directly to ^1 (A2) in the bass, but ^7 (G#2) is given such emphasis that it will still be heard as resolving to ^8 (A2). The balance between line and function is perfect.

A march by Sousa, "The White Plume":

And finally another from Johann Strauss, sr., the second strain of the second number from Die Sorgenbrecher, op. 230, the most often played (or, at least, recorded) of his waltzes:

I will take up the second inversion examples in another post.

Johann Strauss, jr., late waltzes (1)

In the previous post I listed ten sets of late waltzes by Johann Strauss, jr., that I chose for examination. Here is that list again:

Op.407 - Italienischer Walzer
Op.410 - Frühlingsstimmen, Walzer
Op.423 - Wiener Frauen, Walzer
Op.424 - Adelen-Walzer
Op.437 - Kaiser-Walzer
Op.438 - Rathausball-Tänze, Walzer
Op.440 - Groß-Wien, Walzer
Op.453 - Hochzeitsreigen, Walzer
Op.461 - Gartenlaube, Walzer
Op.477 - An der Elbe, Walzer

Instead of going through these one by one, I have sorted examples by topic, or, perhaps more accurately said, by technique or device or figure. With the exception of a few slightly different figures and harmonizations in op. 410 (Frühlingsstimmen) and op. 461 (Gartenlaube), everything in these late sets of waltzes departs little if at all from the mid-1860s through early 1870s (at which point Strauss began focusing more on operetta), in the still-famous waltzes such as An der schönen blauen Donau, Künstler-Leben, Geschichten aus dem Wienerwald, Wein, Weib und Gesang, Tausend und eine Nacht, Wiener Blut, and Du und Du (derived from the operetta Die Fledermaus [1874]). That being the case, an inventory of techniques or figures involving the dominant ninth chord seemed more useful than analyses of individual sets. I have enriched the survey, so to speak, with occasional examples from his contemporary Emile Waldteufel and from the late waltzes of his father, Johann Strauss, sr.

1. Consonance/Dissonance and ^5, ^6.

The place to begin is with the play of consonance/dissonance in parallel figures involving ^5 and ^6. Here is the first strain of the first number of the Kaiser-Walzer [Emperor Waltz], op. 437 (1889). Apologies for the odd-looking score; it's a composite of score and ossia I made to show the harmonies more clearly. The consonant G5 in bar 1 is parallel to A5 in bar 5. We can—and should—take the A5 as an expressive "one-note-too-far" that provides the turn to the cadence (IAC), but at the same time the parallelism reinforces the sense that this is a chord tone, the ninth of V9. Note two features that are basic to Strauss's practice: the harmonies are exactly parallel in the two phrases—I (-?) I V, and V (-?) V I—and there is a strong descending scale-wise frame for each phrase. Though not relevant to the specific point here, I have marked the point (bar 12) where V (in other places, we'll see V9) is turned back, as it were, to ii. Similar figures are routinely used, as here, to make a turn toward the final cadence.

In Wiener Frauen, op. 423, the second strain of no. 1 reveals a second basic method: exchanging consonance for dissonance (or chord member for non-harmonic element). In bar 4, a conservative hearing for the 1880s would make Bb5 and E6 chord tones and D6 (the ninth) a dissonance. In bar 8, a conservative reading would reverse the second and third elements: D6 is a dissonance and C6 a chord tone. One finds hints of things like this even in Schubert, but the later waltz repertoire exploits the ambiguity at every opportunity and in every conceivable way, foremost with ^5 and ^6 but sometimes with the other scale degrees as well. In this particular case Strauss suggests a possible conservative reading, in that we might think of D6 in bar 4 as a non-harmonic note "left open" until its reappearance and resolution in bar 8. See the sketch below the score.

The same motive works differently in Waldteufel's Estudiantina waltzes, op. 191 (1883), the second strain of no. 1. Here the parallelism is strict: C#6 is an appoggiatura, B5 is a chord tone, then B5 is a non-harmonic note and A5 is a chord tone. The eight-bar unit does end with a direct resolution of a V9 chord.

From Strauss again: no. 2 in Gartenlaube, op. 461 (1895). As in the preceding, but now G4, as the ninth in V9, is paired with D5, as the third of the tonic triad. This time the turn in the consequent of this 16-bar theme comes early: where G4 changes from the ninth of V9 to the third of the IV chord.

From Strauss's father, Die Schwalben, op. 208, a late waltz set from 1847. The first strain of no. 4 suggests how the play of ^5 and ^6 helped domesticate not only V9 but also Iadd6. Here E6 resolves internally within I but the parallel note, D6, is consonant within V7, and C6 in bars 5-6 is a chord tone. Below the score I have added an indirect motion of E6 to D6; this gives the same kind of ambiguous weight to E6 as does the immediate resolution in bar 2.

From Waldteufel's op. 101, Myosotis (from the 1860s), an example of ^5-^6 play within a double neighbor figure, with attention given to E5 and thus the sonorities—the sound of—Iadd6 and V9.

From Strauss, jr., Kaiser-Walzer, op. 437 (1889), this time the opening of no. 2. A pleasant muddle of notes in the upper tetrachord of Ab major. The incomplete neighbor G5 (another label is "escape tone") is dissonant, suggesting a possible Imaj7, though the inversion (bass C) makes things less clear, but the parallel F5, also dissonant, is more plainly the ninth in V9. A long distance registral connection to F5 over the tonic in bar 9 brings still another suggestion of Iadd6.

From Waldteufel's op. 148, Violettes (1876), the first waltz. A simple 16-bar period where the consequent takes the melody up a scale degree and the harmony is I-V then V-I. In bars 6-8 and 14-16, we are invited to hear "conservative dissonances" as chord tones, thanks to the parallelism: D5 is a chord tone in bar 14, so perhaps is C5 in bar 6? Bb4 is a chord tone in bars 6-7, so perhaps is C5 in bars 14-15?

The second waltz. A "reversion" to clear dissonance/consonance pairs: F5-Eb5 in bar 1, C5-Bb4 in bar 2.

From Gartenlaube, op. 461 (1895), no. 4, second strain. The neighbor note figure about C6 is repeated about A5 above the tonic bass. Note also that B5 as a passing tone in the second bar of the strain suggests that G5 in bar 4 might be one, also -- in fact, to my ear, it really does sound like it.

From the Italienischer Walzer, op. 407 (1882), no. 1, second strain. Clear, parallel roles for the half-note pairs E6-D6 and D6-C6. The point of interest is in bar 7: A5 repeated, not G5. The boxes labeled b1 and b2 show another turn effected by harmony.

From Frühlingsstimmen, op. 410 (1883), no. 1, first strain. Still another instance suggesting Iadd6 (G5 in bar 3 is parallel to A5 in bar 9).

From An der Elbe, op. 477 (1897), no. 2, first strain. The thirds make this difficult to decipher. Some recurring elements, at least, are obvious: add6 in bar 1, the suggestion of Imajor7 in bars 1-2, and V9 in bar 4. The Iadd6 is firm in bars 9-10 (circled) and can even be understood as moving upward to D6, so ^6-^7.

Johann Strauss, sr., Radetzky March

The Radetzky March, op. 228 (1848), is the most well-known composition of Johann Strauss, sr. I am including it here partly for that reason, but partly also to begin making the point that there were repertoires other than the waltz in which the dominant ninth made inroads. Granted, these other repertoires--especially the polka--were directly influenced by the waltz practices of the 1820s and 1830s.

In general, marches were treated more traditionally than dance genres and the dominant ninth is relatively rare in them, but the Radetzky March, especially at the fast tempo it is usually heard today, is loosely aligned in its figures and expression with the galop, and figures from dance or theatrical music play a major role.

Note the parallelism of ^6-^5 over V then over I in the first strain (bars 5-6).

In the trio, we hear two direct resolutions of the ninth: see the arrows in the examples below:

First strain:

Second strain:

Johann Strauss, sr.

Johann Strauss, sr.—also called Johann Strauss I in the literature—was an excellent violinist who started playing professionally under Michael Pamer, the most important connection between the earlier waltz and Laendler traditions and urban practices after about 1820. Strauss then played under Josef Lanner, but soon formed his own band (in 1825) and enjoyed immediate success. The pieces below come from the last two years of his life; he died in 1849.

Strauss, sr. Damen Souvenir Polka, op236, second strain. An indirect—actually very nearly direct—resolution, thus either category 2.1 or 2.4 depending on how you hear it.

Strauss, sr., Die Sorgenbrecher Walzer, op230n2. Here Strauss puts such emphasis on E6, as the ninth, that it is not hard to imagine we hear a D6 over the subsequent tonic.

The remaining examples are also direct resolutions to the tonic (my category 2.3).

Strauss, sr., Wiener Kreuze Polka, op220

Strauss, sr., op236, first strain

Strauss, sr., Exeter Polka, op249 2trio

Strauss, sr., Die Adepten Walzer, op216n5

Josef Lanner

Josef Lanner is the one contemporary about whom we can be confident that he influenced Schubert's own waltz improvisation and composition. We know that Schubert heard Lanner’s orchestra in live performance, probably on multiple occasions and while Johann Strauss, sr., was still a member of the band.

Lanner, Trennungs-Walzer (1828), op19_n5, first strain. A curiously reversed resolution in bars 9-10. The circles throughout the strain show the overwhelming dissonance-resolution motive. In bars 9-10, however, the third of the underlying chord (D#5/D#6) is resolved to the ninth C#5/C#6!

Lanner, Flora-Walzer, op33_n4, first strain. Scale degree ^6 is a melodic element in each instance.

Lanner, Redout-Carneval-Tänze (second set; 1830), op42_n5, first strain. Similar to op19n5 in its motive, but now there is no "mistake" about the resolution of ^6.

Lanner, op19_n2. As in the previous example.

Lanner, op33_n4, second strain. Similar to one of the examples from Schubert in its sustained drive upwards culminating on the highly expressive ^6 as the ninth of the dominant.

Lanner, op42_n6. Three different treatments of the ninth, at (a), (b), and (c).

The remaining examples are all direct resolutions, that is, the ninth resolves not within the dominant but in the following tonic.

Lanner, op33_n5.

Lanner, op42_n5, second strain

Lanner, Alpen-Rosen Walzer (1842), op162 n3

Lanner, op162 n4

Lanner, Die Romantiker (1842), op167 n4

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.