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.

Brahms, Waltzes, op. 39, part 2

 In the previous post I showed the direct resolutions of the major dominant ninth (in nos. 2, 7, and 16), plus two others in no. 2. Here are the treatments elsewhere in the set.

The figure 9-8-7, very common in the waltz (especially Ländler) repertoire, occurs three times.

In no. 5 (see second system, second box; figure repeated in the final cadence):

I will discuss the other figures later in this post.

In no. 6 (three times via series of unfolded thirds):

In no. 10: in bar 4 after a scalar ascent from an initial V9; and in the final cadence, where thirds become sixths as 9-8-7 goes into the "right-hand thumb" voice.

A similar figure in no. 7 covers 10-9-8:

Now, to those other figures in no. 7. At (a), the cadence has no dominant ninth. The shape is repeated at (b)--and (b) is repeated, transposed and slightly altered, at (c)--and in these cases there is a ninth forming a major dominant ninth chord. The resolution, however, is ascending: C#5 goes to D#5 in the first instance and F#5 goes to G#5 in the second instance. I don't want to get into the problematic matter of influence, but in this one case I will venture to assert that Brahms borrowed this ascending gesture directly from Schubert. Note, too, that the ascending stepwise line from ^5 to ^8 is repeated in the final cadence against the 9-8-7 figure (see beamed notes in the left hand at (d)).

No. 7 also has an ascending resolution, and it is dramatic, with good metric emphasis to the ninth (see the arrow):

Where my first examples (in Part 1) came from the last waltz, my last examples come from the first, where we find (1) a variant of the (10)-9-8-7 figure in the closing cadence (box at the end), and (2) what I hear as a "just barely" sounding of the ninth in grace notes (boxes in the first and second systems), a characterization that is also justified in that the piece is played without pedal (left-hand staccati preclude it).

Brahms, Waltzes, op. 39, part 1

 The sixteen waltzes of Brahms's op. 39 (1865) manage only six direct resolutions of the dominant ninth chord, four of them in nearly the final bars of the last number. The two earlier examples are both obscured by registral shifts. (Direct resolutions, recall, are external, that is, the ninth over V is resolved in the following I, not before.)

Here is waltz no. 16; the score here lacks only the last phrase and cadence to C# minor.

The voice-leading is impeccable, though I should note that most composers before the 1890s do try to avoid the parallel fifths that can easily arise in resolving the major dominant ninth chord. The invertible counterpoint (cf. bars 1-8 with 9-16) is Brahmsian, not Schubertian!

The resolution in no. 7--see the boxes in the third system--has to be called direct but F#4 goes to E5, not E4, and the contrast is strong: the phrase before is a long descent (starting in the middle of the second system) and the phrase beginning with E5 is an equally strong ascent. I've checked the other versions (piano four-hands and two pianos) and neither has a simple resolution, though it would have been very easy indeed to add the extra notes.

The F#4 is repeated in the left hand (second box) and does move to E4 but the effect is a muddle of A major and D major, made worse if the pedal is held down. The pedal marking, incidentally, is in the manuscript. Note that the composer deleted several before that (arrow).

The other direct resolution is in no. 2, bars 16-17, or from the end of the B section to the beginning of the reprise of A. Here C#3 does go on to B2 but the placement of the ninth very nearly in the bass is unique (at least, I can say that I have never seen it elsewhere, not even in the more adventurous musics of the 1890s and early 1900s) and of course it is completely contrary to all advice about how to treat the major dominant ninth chord (recall that even inversions are suspect).

Two other points of interest in this score: (1) In bars 4-5, what I call an "almost direct resolution", where unfolded thirds clearly show the voice-leading as C#6-B5 and A5-G#5; (2) an expressive highpoint in the final cadence--a cliché of the waltz going all the way back to Schubert's generation--and an internal resolution, if one regards the entire bar as V and, even better, holds the pedal down (which I have never done; the "clean" sound of the higher register ii6 is more appealing).

In a subsequent post I will provide examples of the other internal resolutions and evasions.

Johann Strauss, jr., later waltzes (2b)

This series of posts began with one in September 2019 (link); a section 1 followed immediately, and section 2a shortly thereafter (link); today's post completes section 2 and the series. Here, in addition to music by Strauss, examples from waltzes by his contemporaries Tchaikovsky and Waldteufel are also presented.

The topic of section 2 is "Consonance/dissonance parallelisms and lines (mostly descending)."

Heading: ^8-^6.

In the second number of Strauss's Italienischer Walzer, op. 407 (1882), between the tonic triad with ^8 in bar 1 and the V7 with ^5 on the last beat of bar 8 lies a series of remarkable dissonances: the relatively rare I7 (the arrow in bar 2 points to ^7), an unequivocal Iadd6 in bar 3, a I with #^5 against an "indifferent" accompaniment, and a prolonged V9 where ^6 "relaxes" into ^5 internally but at the last moment.

Italienischer Walzer, op. 407 (1882), no. 2

Adelen-Walzer, op. 424 (1886),  no. 3b. Here is another I7, made all the more prominent by its hypermetric position. The dissonance is less daring than in the previous example, though, because B4 can be heard in retrospect as "passing" to Bb4 on the way to A4 over IV. The circled notes in bar 6 show a V9 where the ninth is internal--textbooks allowed such parallel sixth constructions (here A5-F6 to G5-E6). With the obvious anticipation of the tonic notes, we can fairly call this a direct resolution of V9.

Heading: line ^6 to ^3

Gartenlaube, op. 461 (1895), no. 3. we hear ^6-^5-^4 and briefly ^3 all over V. The register of ^3 (B5) is left open this way and we subsequently hear it over I when the 8-bar consequent starts up. Bar 12 = bar 4, but the register is immediately left open again, and this time it is picked up by the dramatic cadence chord, vii°7/V (circled).

Heading: line ^7-^3

From the beginning (no. 1, first strain) of the Italienischer Walzer, an indirect resolution of 7 (F5) to E5, so close and clear that it's the sort I like to call "almost direct." Note also that the full range of scale degrees over V is given (the bracket)—^7, ^6, ^5, and ^4.

Emile Waldteufel's Myosotis, op. 101 (1867), is a bit earlier than the late Strauss waltzes I have been discussing in this series. I have included it here to show that Strauss wasn't the only one to indulge in a delightful confusion of scale degrees and accompanying harmonies. The V9 resolution is direct (bars 6-7).

Heading: ^4-^1 (or farther)

Again Strauss: Hochzeitsreigen, op. 453 (1893), no. 2. The pre-dominant or subdominant-function harmony is given unusual prominence, and ^6 acts traditionally as a suspension dissonance (G5 in bars 1-2). As the melody continues down, past ^1, the 8-bar antecedent ends with an "almost direct" resolution of the ninth to ^6 in a Iadd6 harmony. Note also the ninth in V9/V as a cadence accent in bar 15 (not marked). As a point of interest—no V9 involved—I have also shown the waltz's final 8-bar consequent with its tonic ending. The overall design is 16 bar antecedent (itself a period--shown below--then 16 bar consequent, of which the final bars (or 25-32) are shown below.

Tchaikovsky, The Nutcracker (1892), Waltz of the Flowers. The confusion of scale degrees and their harmonies that we saw in Waldteufel's Myosotis is even greater in the second strain of the Waltz of the Flowers. In the antecedent phrase: the F#5 in bar 1 is fine, but what is C#5 exactly? What is E5? B4? D5? Things are just slightly better in the consequent phrase: G5, D5 and the subsequent quarter notes C#5 and A4, but what about F#5 and E5? A wonderful example of the freedom of treatment of melody in relation to harmony that Jeremy Day-O'Connell points out (in connection with a history of ^6), as also have Peter van der Merwe, Derek Scott, and Norbert Linke (I hope to complete an essay on their work before too much longer).

Heading: ^10-^7

Once again to Strauss: Kaiser-Walzer, op. 437 (1889), no. 3. I have remarked in earlier essays on the tendency to expand theme lengths in waltzes from the most conventional eight bars early in the 19th century (most of Schubert's, for example, but also early Lanner) to sixteen (late Schubert, Strauss, sr.) to thirty-two (Strauss, jr., and contemporaries). The most common design is effectively a 16-bar theme with two endings, where the repetition, with its second ending, is written out--see Hochzeitsreigen, no. 2, above for an example. In the Emperor Waltz, however, Strauss writes what I would call a true 32-bar period, where the two halves of the antecedent, bars 1-8 & 9-16, form a 16-bar sentence or antecedent-contrasting phrase. In that way, the distinctive opening of the antecedent doesn't return until bar 17 and the large design is clearly defined. I marked several things: at (a1) a line down from ^3 to ^7 (E6 to B5); at (a2)--the bracket--the considerable expansion of V with a ninth prominent in both color and position; at (a2)--box--and the arrow, C: V9 becomes G: V9 in the parallel position in the phrase; at (b), the theme closes in a quite conventional way.

Heading: Ascending

And, finally, to Waldteufel, Les Patineurs (1882), no. 1, the Skaters Waltz that is at least as famous as the Waltz of the Flowers and the Emperor Waltz. Here again the freedom of the scale degrees is remarkable, but now the motion is ascending and if anything the confusion of melody and accompaniment is greater. A brief hint of Iadd6 (bar 2) comes from ^6 anticipating its role as 9 in V9 (bars 3-4). The F#4 is still there over V in bar 6, but in the phrase parallelism it actually moves up, not down as we would expect in a resolution. It's not impossible to hear the G#4 as "resolving" to A4, but (1) it's interrupted by an expressive upper neighbor B4, and (2) the resolution is of melodic direction, not harmonic function. At the end, as a point of interest, I have included the second cornet's ascending line that is rarely heard over the melody in performance (F#4-G#4-A4).

Johann Strauss, jr., later waltzes (2a)

This continues a series of posts on ten late waltz sets by Johann Strauss, jr.

2. Consonance/dissonance parallelisms and lines (mostly descending)

In an earlier post (link), I made the point that 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. Although this is a general practice in the dance repertoire (especially but not exclusively in waltzes, and by no means only in Strauss), I am concerned here with a set of figures that instantiates it in a particularly clear form.     (NB: Some examples are repeated from the previous post but are discussed in terms of lines, not just the treatment of ^5 and ^6.)

Adelen-Walzer, op.424 (1886), no. 2. A simple example to begin. Here every note in the pair (circled) is a chord tone. The E5 in bar 2 is locally a passing tone, but in bar 3 it is clearly the ninth of V9 and it resolves directly to ^5 over I.

Figaro (polka), op. 320 (1867). Out of the normal order—a polka from the 1860s, not a waltz from the 1880s—but another excellent example of the descent ^8 to ^5 where ^7 descends rather than rises and ^6 as the ninth of V9 resolves directly, but here with the added detail of a hint of Iadd6.

Waldteufel, Je t’aime, op. 177 (1882), no. 4. From Strauss's contemporary and the leading waltz composer in Paris at the time, here is a figure that Strauss himself also makes frequent use of: a descent ^8 to ^5 over the tonic bass. In this case, ^7 and ^6 are both understood as passing tones, but the attention given each opens the possibility—fully exploited in other circumstances—for Imaj7 and Iadd6.

Eduardo di Capua, “O sole mio” (1898). Without question one of the most famous songs from the venerable Neapolitan Piedigrotta Festival. Here is the first phrase in the second half. One can certainly hear F#5 in bar 1 and E5 in bar 3 as very expressive (sighing) escape tones, but the turn to D5 to end the phrase suggests a different, longer-range possibility -- see the sketch below the score.

--sketch of the first phrase

Strauss, Kaiser-Walzer, op.437 (1889), no. 1b. In the second strain of no.1, we encounter what appears to be a much longer line but in fact is two lines moving (almost) in parallel, where ^8 descends to ^5, as we have seen in previous examples, while ^10 descends to ^8. Note the Imaj7 sound in bar 2, but also the complication of bar 3: certainly we would like to hear bars 3-4 as a neighbor note dissonance, B5 resolving to the chord tone A5, but then retrospectively B5 in bar 2 sounds very much like a preparation, so that we have the sound of a classic suspension figure: [dissonant] preparation (bar 2)-[reiterated] suspension (bar 3)-resolution (bar 4). In the modified consequent phrase, we have the same figure a scale degree lower: the harmony in bar 6 then is unequivocally V9 with a direct resolution. As a postscript, note the now-familiar turn in the harmony in bar 13 and the participation of the ninth and internal resolution in the dominant in bar 15.

An der Elbe, op.477 (1897), no. 2. I have already discussed this under the shifting consonance/ dissonance heading. It is copied here only as an additional example of the ^8 to ^5 descent.

Hochzeitsreigen, op.453 (1893), no. 1b. In bars 1-2, Imaj7 continues its distinctive role as perhaps-prominent-sonority-perhaps-harmony, while Iadd6 in bar 2 is plainly defined as a harmony through chord change and the step down in bar 3. In the parallel phrase (a2), B5 is definitely a chord tone and V9 is clearly defined as a harmony.

Hochzeitsreigen, op.453 (1893), no. 3. Here ^7 retreats to melodic status, while ^6 is given more prominence.

Rathausball-Tänze, op.438 (1890),  no. 1a. Scale degree ^6 is part of a defined Iadd6 harmony in bar 4, then the fifth of ii in bars 8-10, then the ninth of V9 in bar 14, and the root of vi in bars 15-16. Quite a journey for a single pitch! Note another instance of ^7 over the tonic in bars 13 and 20.

Gartenlaube, op.461 (1895), no. 4b. This was discussed in the previous post. It is reproduced here to show an instance of a long line, ^8 down to ^2, then ^11 down to ^5 in the parallel phrase.

Rathausball-Tänze, op.438 (1890),  no. 3. A 16-bar period, where the antecedent has a line running down from ^8 to ^5, points of interest being the unclear harmony in bar 4 and the almost direct resolution of the ninth in bars 6-7. The consequent picks up this line but then takes it down all the way through the octave. In William Caplin's terms, bars 10-16 are built on an ECP (expanded cadential progression, typically starting with I6 as in bar 10).

”O sole mio,” introduction. The figure from the second part (see earlier in this post) is used for the introduction in the published song. As in the preceding example, the line moves through an entire octave to conclude in a perfect authentic cadence.

This study of lines continues in the next 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.