Inversions, part 2

This continues discussion of inversions of the major dominant ninth chord.

Apologies for the overlapping boxes in this graphic of the opening of Franck's Violin Sonata. Boxes 1 and 2 include the second inversion of A: V9, each sandwiched between root position chords. The third "clears out" the chord momentarily by reducing it to a root position B minor triad.

Here is a passage from later on. The sounds over C#3 vary, with C#9 briefly touched in the third bar, though against a dissonant passing tone in the violin. The fourth bar gives us a#ø7, which becomes the upper part of the F#9 a bar later.

Now a secondary dominant ninth in its second inversion (MacDowell, To a Wild Rose). I've added the slurs in the bass to bring out the pattern in the harmonies: consonance to dissonance over the same bass in bars 1-2 & 3-4, then the reverse in bars 5-6 & 7-8.

And two examples of the unfolding bass figure: Sousa, Hail to the Spirit of Liberty, trio; James Scott, Broadway Rag. In the latter the boxes and arrows point to the common parallelism in a figure over V9, then over Iadd6.

For the third inversion, a waltz by Alexis Castillon and the introduction to An der Elbe, op. 477, Johann Strauss, jr.'s last published waltz set. There is expressive emphasis in Castillon's version, but as a harmony it is undercut by its middle position in a dominant.

In the second box below, a clever parallelism with a reversed harmonic progression, because of which the ninth (G5) resolves internally.

The best example for the third inversion, though, is in the "Serenade of the Doll" from Debussy's Children's Corner. Here is the second of three divisions of the B-section; it is made entirely of major dominant ninth chords, 15 of them, 9 of which are third inversions (indicated by asterisks (*)).

By way of a postscript: in the third division of the B-section, the F#9 returns to initiate a traditional cadence progression: E: V9/V drops the sharp to become ii13, then follow V7 and Iadd6:

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.

On Perfect Fifths and Complex Chords

 In a previous post (Bauer, Part 1), I created a chordal reduction and wrote the following about the last bars of the B section, leading to the reprise:

"Also, the V7/ii itself [see the final bars in the graphic below] can be explained by separating out the left-hand elements in bar 17 [at the farthest right]. The first thing we hear is in fact ii—not V—as iiadd6; only on the third quarter beat is the bass G2 sounded. Although the overall effect here is certainly that of a break, the harmony does offer some continuity."

The device that the composer uses in this passage is firmly within late-19th and early-20th century practice. Recall that the notion of the identity of viiø7 as V9 without its root goes back to the 18th century. By the time we reach an era where the voicing of sonorities becomes an important factor, it is not surprising to see what we might call a "play of functions," grounded in perfect fifths. In the graphic below, (a) is the major dominant ninth chord with the two P5s bracketed; (a1) and (a2) depict what Bauer does in "Epitaph"--that is, briefly drop the root and thereby "expose" the upper fifth D-A. I have filled out the scheme with V9#11 at (b), and V13 at (c). At (b1) is the common diatonic -2 voicing of V11, which offers a third P5. By the time we reach (c), there are four P5s, and--theoretically at least--any of the upper ones could replace the lowest fifth. As an aside, (a3) and (c5) as quintal chords lose almost all the character of the traditional V9 and V13.

Here are some additional examples of the play of functions and bass/upper-voice layering. The simplest type is the familiar common-tone modulation, a single note held between the two keys. Schubert uses it for a striking textural punctuation that announces the beginning of the second theme in the Unfinished Symphony, first movement:

Because the relationship is diatonic (B minor to G major), this passage often appears in harmony textbooks. Johann Strauss, jr., does something similar in the transition--moving from Eb major to Ab major--out of the second into the third waltz in Frühlingsstimmen ("Voices of Spring"; second box below):

Appropriately for our blog, he gives strong expressive emphasis to V9 in the cadence (first box) and in the transition, too (second box again). The cadential V9 is very prominent in the vocal edition of this waltz set:

Another textbook example--indeed, the one that almost inevitably shows up in a section on V9--is the opening of Franck's Violin Sonata. I wrote a long post about the entire movement in 2019: link. Franck briefly drops the root and third of E9 (box), creating a wonderful expressive effect that contrasts the simple minor triad against the fuller colors of the major dominant ninth on either side of it.

In an earlier post I referred to Brahms as "a genius at suggesting but avoiding the two characteristic chords of scale degree ^6: the dominant ninth and the add6" (link to post). The moment boxed below--from the Intermezzo in A Major, op. 118 no. 2--is a familiar style device of his that involves layering of bass and upper voices and "suggests but avoids" a directly stated V9/V.

In its "proper" form, the passage should have been built on one or the other of these: at (a), E in the bass is understood as a pedal point; at (b), the bass note changes to match the upper-voice chords and a V9/V is fully expressed. In both cases, I have inserted the tonic chord that Brahms only hints at with the bass A2.

Here is a version with the tonic chord repositioned so that the strongly marked IV6/4 remains on the first beat:

This compacted progression can be related to its opposite, where the bass does move as expected but the upper-voices don't correspond as neatly as one might like. The final cadence of the "Russian Dance" from Stravinsky's Petrushka is a famous example: C5 as the top note doesn't budge, nor does the A5 below it, as the bass pounds out a simple ii-V-I.

Given the presumed Impressionist influence on "The Epitaph of a Butterfly," it should be easy to locate examples of the "play of functions" in Debussy. Layering is of course a basic technique in his music, but as to using layers to suggest a change of function or modulation, my admittedly brief search has offered only this from the reprise in Reflets dans l'Eau ("Reflections in the Water"). A strongly defined Db: V9 (root and fifth circled) loses it root, perhaps by the second but certainly by the third bar, leaving eb7. The reverse process follows, as a b-flat minor triad is undergirded a couple bars later by a tonic fifth Db2-Ab2. 

Unlike Bauer's iiadd6, which gives an entirely plausible V7/ii–iiadd6–V9 progression, here it would be V9–ii7–vi–I, but better as V9–(ii7–vi)–I. The overall effect is not much different from that in the opening of Franck's Violin Sonata.

Harmony at the Ninth: The repertoire problem

 In a previous post, I outlined a harmony pedagogy that would place the ninth chord near the beginning of the curriculum, not—as is typically the case (if it's taught at all)—somewhere near the end. I also noted that my plan got into trouble at the point of choosing repertoire. I'll discuss the three main reasons here: (1) repertoire bias in the traditional theory core curriculum; (2) conflict between 18th/19th century and 20th/21st century theoretical models; (3) difficulty in finding entirely diatonic examples suitable for first-year theory classroom use.

To begin, I have assembled and posted to my Google Drive a list of all the musical examples for the five essays on the dominant ninth chord that I have published on the Texas ScholarWorks platform to date: 

V9 essays repertoire list. 

The essays are named at the beginning of the file, and abstracts and links are provided.

(1) repertoire bias in the traditional theory core curriculum

The historical narrative for classical music that prevailed through much of the 20th century was progressive, that is, it began from one point (usually medieval chant) and led by more or less regular steps forward into contemporary music. So, we have the first inklings of counterpoint around 1000 AD, eventually a perfected polyphony in the 16th century, an organized major/minor tonal system thanks to continuo practice and pedagogy in the later 17th and early 18th centuries, and a gradual expansion or break-down of that system through more complex harmonic relations and increased chromaticism in the 19th century, till we reached a fully chromatic model epitomized by twelve-tone and serial music. Despite this scheme, the heart of the story remained with the High Classical period (sometimes called the First Viennese School) with Haydn, Mozart, and Beethoven.

This is the narrative I learned as a young student. We had only just begun to acknowledge some of its problems even by the time I started college in 1968. For my purposes here, though, and beyond noting that these repertoire biases have barely changed in mainstream college introductory theory textbooks, the one point that is immediately relevant can be easily understood by a quick comparison of the repertoire list linked above with two textbook-based lists. The smaller of the two is derived from Kostka & Payne, 3rd ed. (even earlier than my 4th ed. copy!): David Temperley corpus study: see the bottom of that web page. The larger is the table of contents for the score anthology by Benjamin, Horvit, Koozin, and Nelson, Music for Analysis, 8th edition (2018).

Temperley extracts the 46 longest examples from the Kostka & Payne workbook. Of these, 29 are by Haydn, Mozart, Beethoven, and Schubert. For these 29, 11 are from piano sonatas, 3 from other pieces for piano, 9 from chamber music, 2 from concertos, 3 songs, and 1 opera.

Benjamin, Horvit, Koozin, and Nelson has 477 examples ranging from the 17th century to the present. Of these, 378 are prior to 1900, with 175 by Haydn, Mozart, Beethoven, and Schubert. For the 378, 49 are from piano sonatas, 12 from other pieces for piano, 32 from chamber music, 2 from concertos, 15 songs and vocal ensemble music, and 5 operas. In addition, 24 are dances in keyboard format, and 37 are from orchestral ensemble music (symphonies and overtures).

For reference, in Benjamin, Horvit, Koozin, and Nelson there are two examples from Johann Strauss, jr., while in Temperley's extracts from Kostka & Payne there are none—which points up the problem: there is very little intersection between their lists and mine, in which Johann Strauss, jr. and sr. dominate. Some important caveats: Apart from the Strausses, my study of the major dominant ninth chord is skewed toward the decades surrounding 1900. As I have noted in essays, I have generally looked at shorter compositions; for longer works, I use keyboard reductions rather than full scores but I haven't focused on large instrumental ensemble music and have done even less with chamber music. I have studied dances—especially polkas and waltzes—throughout the 19th century, not just Schubert dances. The historical circumstance that ascending cadence gestures, upper-register cadences, and clear treatment of the major dominant ninth all seem to have arisen in music for dance led me to the larger repertoires that incorporated them, beginning with opéra comique in the 1830s, then blossoming in operetta in the 1850s and later. In general, composers—including Schubert himself—would be more conservative when writing in the larger instrumental forms than in the popular forms of dance music and music for the stage. In another post I will report on my look at the Allegretto grazioso quasi Andantino in Brahms's Symphony no. 2 and at his Waltzes, op. 39. Even in the midst of the Schubert craze of the 1860s—to which he also contributed—Brahms was a genius at suggesting but avoiding the two characteristic chords of scale degree ^6: the dominant ninth and the add6.

(2) conflict between 18th/19th century and 20th century theoretical models

Textbooks still lump the “extended chords” together, in a model of progressive stacked thirds, even if, as Kostka & Payne remark in their 4th ed.: "Just as superimposed 3rds produce triads and seventh chords, continuation of that process yields ninth, eleventh, and thirteenth chords (which is not to say that this is the manner in which these sonorities evolved historically)." (!!) Jazz theory, on the other hand, doesn't bother with that, because the harmonic vocabulary is based on the dominant seventh with a variety of sounds, "tensions," and alterations built on it. In Mark Levine's Jazz Theory Book (1995), for example, "extensions" (9th, 11th, 13th) are listed in the glossary, but the ninth chord is never explicitly introduced in the text. Instead, it simply appears in the first example for the II-V-I progression:

This version of the opening of "Stella by Starlight" is a concise catalogue of the three main 9th chord types, but note that none of Levine's chord labels (above the score; mine are below in blue) indicates a 9.

Here are some additional examples drawn from different places in The Jazz Theory Book. My labels are below the score. The 9 is included in the fourth chord only because it is altered (G-nat = Fx).

(* I am grateful to UT-Austin doctoral alum and friend Joel Love for telling me about Levine's book. Link: His web page.)

(3) difficulty in finding entirely diatonic examples suitable for first-year theory classroom use

My first examples would, of course, come from Schubert waltzes, but it turned out to be difficult to find simple examples of V9 without also including chromatic chords. Here is the second strain of Valses nobles, D. 969, n11 (1828), with its "textbook perfect" V9 with a direct resolution. Bars 5-6 would require some discussion, however.

In their section on the dominant ninth, Benjamin, Horvit, Koozin, and Nelson include Strauss's Künstlerleben, one of the best known of his mid-period waltzes. I don't know what they say about it, as I don't have a copy of the anthology, but I can say that I find the choice of no. 3 particularly good because the ninth appears several times in different roles, and the only chromatic consideration is a relatively simple cadence to V at the halfway point. At (a) and (c) are internal resolutions (9 resolves within V). At (b) and (d) are "almost direct" resolutions (9 is held over the first part of I); the example below the score shows what a direct resolution would have been in (b). At (e) is the upward resolution of 9 that facilitates an ascending cadence. And at (f1) & (f2) is a very common device that flips the functional status of scale degrees ^7 & ^6: at (f1) ^7 is a simple chord tone and ^6 forms the ninth, but at (f2) ^7 is an appoggiatura and ^6 is a simple chord tone.

Simplified, correct, but not as expressive version of bars 6-8:

The question of repertoire choices appropriate for different levels can be explored through the repertoire list mentioned and linked to at the top of this post. I can add here that I have studied but have not yet reported on stage works from opéras comiques of the 1830s (mainly Adam, Auber) to operetta (Offenbach, Lecocq, Strauss), Savoy opera (Sullivan), and American operetta (Herbert) and musical (Kern). And of course there is something still to be said about that "genius of avoidance," Brahms.

New publication on dominant ninths and tonic sevenths

I have published The Dominant Ninth and Tonic Seventh in the Upper Tetrachord of the Major Key on the Texas ScholarWorks platform: link.

Here is the abstract:

Pieter van der Merwe, Derek B. Scott, and Norbert Linke have all written about the freedom with which nineteenth-century composers—especially those writing music for social dance and repertoires influenced by social dance—treated the upper tetrachord of the major key, an essential factor in the history of extended tertian chords and more generally in the history of still more complex harmonies. Examples total about 60; theirs and most of mine come from the 19th century waltz repertoire.

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.