C. K. Harris, "Climb a tree with me" (1912)

From March 2026: A post with information and links to galleries of simple ascending lines and to other essays of mine published on the Texas Scholarworks platform: link.

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Charles K. Harris, "Climb a tree with me" (1912). It might not seem very promising to begin a song on climbing with an octave's worth of descending tonic-chord arpeggio, but there is a clue in the answering phrase, "As we climbed long years ago." The lower ^5, as Eb4, goes up to a firmly held ^6, and "all the birds sang" with ^7 suggests going further. In the end, the proto-background interval of the octave (shown with the unfolding in bars 1-4 and again later) maintains Eb5 while its lower element Eb4 closes to Ab4. This is not a wedge--Eb5 stays put and the principal line is the one that proceeds from Eb4.

Given the intervallic frame, it's not surprising that the common expressive ascent in the upper register should be easy to manage. Here is my alternate or second ending, following the model of songs discussed in a previous post: link.

J. R. Europe, "I've got the finest man" (1912)

 James Reese Europe, "I've got the finest man" (1912). A proto-background with repeated shifts between the registers, one of the clearest examples I've seen. Overall a wedge figure with the descending line from ^3 above and the ascent below but occupying all of the final phrase. (In this it is very like van Alstyne's "Why Don't You Try": link to the post.) See at the bottom of this post for traditional Schenkerian notation.

Wedge figure with ^3 (making a V13) subbing for ^2:

Harris, "Don't Blame Me"

Charles K. Harris, "Don't Blame Me" (1911). Another instance of a clearly defined proto-background, ^5/^3 here. Note the nicely presented interruption (bars 6–8) where both elements are cleanly positioned in the voice-leading--and there's even a direct resolution of the ninth in V9/V! (See bar 7, last beat, into bar 8.)

I am, however, primarily interested in the final cadence, which is one of those awkward lines that's not a line, as a very strong rising scale figure to begin the final phrase breaks as ^6 goes *down* to ^7. 

The alternate ending I have made below would have been very likely in performance, in the manner I have mentioned a number of times now based on what we know about singers' practices during this era. This song, indeed, really asks for that ending with its long scale followed by the emphatic "Don't blame me."

Harris and Williams, "What's the Matter with Father?"

 Charles K. Harris and [ ] Williams, "What's the Matter with Father?" (1910) A pronounced proto-background ^5/^1 and a simple ascending line. Note ^9 as a suggested alternate for ^7 over the dominant in the final cadence.

Grieg, Larvikspolka, EG 101 (1858)

Presumably a collected piece of social dance music. Larvik is a city in southern Norway. The design of this polka is the very common ABACA of social dance music, beginning with contredanses in the late 1700s and then spreading to almost all other types. The ABACA can be almost indistinguishable from a small ternary form (ABA) with trio (C) and truncated reprise (A), though the "trio" is only one strain, not the two we usually find in the familiar Classical instrumental repertoire of sonatas, etc. The equally common case used here has A as a single principal strain, B a first "trio" in the subdominant key, and C a second trio in the relative minor. (In the contredanse repertoire C is almost always in the parallel or relative minor, which fact might suggest that Larvikspolka is a traditional tune, not a newly composed one from the 1850s). The modern notation is by "Sigerland" and is available on IMSLP: link.

I hear a primitive rising line in A:

In the first iteration of A, however, an inner voice is pushed above (F4 to F5) and the unfolded B4-F5 closes into C5-E5--see below. We can then trace the voices in the two trios. The C5-E5 interval remains stable in the first trio B, except that E5 moves up to F5. In the second trio C, G4 becomes A4/A5 and C5 remains stable.

A synoptic view, then, is as follows:

Note: I have "collapsed" two aspects into one, as the line ^5-^7-^8 is easily understood based on the proto-background ^5-^8.

Lehar, The Merry Widow, Act 1 Ball-music

Franz Lehar, Die lustige Witwe / The Merry Widow (1905), Act 1 Ball-music. This single waltz strain is to be played offscreen under conversation, but also ad libitum, meaning it can be left out (the same music appears later in the score -- a recording I listened to recently included the first statement but dropped the second one). The design is a 32-bar period (common in waltzes after about 1860, but also found regularly later on in marches, one-steps, and rags). The first 16-bar phase is one of those awkward units where period or sentence might apply equally well, depending on how you take the identical rhythms but different melodic shapes.

A triadic interval frame is established quite clearly -- circled at the beginning below -- and is returned to at the end of the first 16-bar phase -- circled at the beginning of the second system. In the second 16-bar unit, the triad is shifted upward -- circled across the second and third systems -- and overlaps with a simple scalar progress through the octave, with a registral drop on ^3. See the next example.

Here is a schematic of the triad frame (as proto-background) and a parsing of the octave line in the final six bars.

Chaminade, Passacaille, op. 130

Chaminade's Passacaille, op. 130, was published in 1909, shortly after her successful tour to the United States, where the highlight was a performance of her own Concertstück with the Philadelphia Orchestra. The Passacaille belongs to a genre of Baroque keyboard nostalgia, to which composers in several countries contributed but which was especially favored in France. Chaminade's Menuet Galant, op. 129, was published at the same time.

By the title, the composer refers loosely to French Baroque keyboard styles, not to the ground-bass variation form. Her op. 130 is in triple meter, as was traditional for the passacaille, and in rondeau form with theme and couplets, though she treats this design loosely, the overall effect being of a ternary form. The first 48 bars are repeated in toto to close the piece.

The opening 16 bars give strong priority to a proto-background ^3/^5, as the unfolded intervals show. Note especially the line from within reaching up to B5 in bars 15-16.

Bars 17-32 are a contrasting B-section, 33-40 a retransition that points toward ^3, which duly arrives in bar 41. The abbreviated reprise then traces a simple rising line twice and does it emphatically into the cadence.

Offenbach, Pomme d'api (1873), nos. 2 & 4

Gustave acknowledges Rabasten's demand that he abandon his unsatisfactory girlfriend in "Mon oncle ne vous fâchez pas" (no. 2). The design is ABABA, the text's three quatrains presented as 1 2 1 3 1. The strong focus on the melody's outer notes invites hearing a proto-background ^5/^8, as Ab4-Eb5 (written) -- see the opening period below.

In the first reprise, the frame is temporarily expanded upward to include Ab5--see the final bars of the example below--but the fifth frame is not disturbed.

In the final reprise, on the other hand, the frame is again expanded upward to include Ab5, firmly now thanks to Gustave's final note. (In Neumeyer 2009, I call this device ADDINV; here the result is a tonal frame of three pitches, Ab4-Eb5-Ab5, after the fifth is inverted and its fourth added on top.) The change happens quite directly, as you can see, without the inclusion of a line -- see the reprise below -- and a proto-background is the most musically satisfying large-scale figure for the number.

Number 4 is a trio about cooking dinner: "Va donc, chercher le gril!" (in the operetta's Scene 7). A traditional multi-section form, the trio begins with an Allegro vivo for all three singers. "Mais, que ferez-vous de ce gril?" follows, a brief scena/recit between Gustave and Catherine. "Nous mettrons le gril sur le feu" is much longer, beginning as a Moderato 16-bar period (between Rabastens and Catherine), after that a contrasting B-section for Catherine and Gustave, who then repeat the 16-bar period, but—as the example below indicates—without completing it, as Catherine gives comic emphasis to "grilled lamb chops." The presto coda that follows is the point of interest here. It consists of an eight-bar theme (period) that is repeated (plus a short orchestral codetta). Both statements of the theme include a rising line in the cadence -- these are boxed in the score below. Gustave sings the figure the first time, then all three offer it in the high-spirited finish.

As it happens, the presto may have the expressive effect of a coda, but in form-functional terms it is not a coda. William Caplin distinguishes between expansion and extension: essentially, the former happens within a theme, the latter after the theme's cadence. Codas are properly extensions, "added on" after the structural cadence. But in this case the presto expands the consequent of the 16-bar theme and only then provides the structural cadence itself.

To show how this works, here is the initial presentation of "Nous mettrons le gril sur le feu." Note that the closing cadence is to the dominant -- and coincidentally features an internal rising line as well.

Here is an abbreviated scheme that shows the design of the reprise consequent + presto first phrase.

The structural cadence, of course, happens on the repetition of the presto's 8-bar theme:

Three more from Ball's Musical Cabinet

Ball's Musical Cabinet was published in two volumes. The three pieces discussed yesterday are from volume 1. From volume 2, I have chosen three more: "The Carpet Weaver," "Peggy Ban," and "The Tank." The first two of these are well-known tunes, like those in yesterday's post. About "The Tank," I know nothing more.

"The Carpet Weaver" is unusual in its boundary play, a Schenkerian term for melodic figures above the basic line. Here we would assume through the first phrase that the focal pitch is F#5, but in the second phrase of both theme statements, F#5 disappears, and attention goes entirely to the lower register, the end result being a mirror, ^8 down to ^5 and then back up again.

On the other hand, in the second half F#5 gains considerably, but the usual B-section contrast (at "vow'd") and the melodramatic long note (at deny'd him") are still not enough to displace the octave (that is, D5) as the focal note.

"Peggy Ban" (better known as "Peggy Bawn"). The play of ^3, as F#5, above the focal note ^8 is very similar to "The Carpet Weaver."

I've isolated the interval frame (which I would take to be a proto-background) in this version:

"The Tank" is a curious piece -- no song, it is highly violinistic, which character it promptly announces with the octaves in bars 1-2. I put it down to an eighteenth-century contredanse, perhaps put in by the publisher because there was empty space on the page (I have seen more obvious insertions in other collections of the period). Note that every phrase is different. Thus, each strain is what Caplin calls an antecedent + continuation hybrid. I use the term "galant theme" because this particular hybrid is especially common in virtually all types of instrumental music from roughly 1750-1800. Periods are more likely in contredanses (a fact reflected in the themes of many finales in Classical period sonatas and symphonies), so in another sense, then, "The Tank" is unusual.

The second through fourth phrases are quite distinct from the first: all have interesting—but differing—plays on ^3 and ^5 (as F#5-A5).

JMT series, postscript

In May of this year, I started a series of posts that discussed compositions mentioned in the notes to my article "The Ascending Urlinie," this being the 30th year since its publication in the Journal of Music Theory. The two introductory posts are here: link; link. A further administrative post appeared in early September: link.

Since the series has necessarily been about Schenkerian analysis, I think it's important to stress here again that the blog is by no means restricted to that method or its issues. Referring to documents published on the Texas Scholar Works platform, I recently wrote "In this and other essays, a broader range of examples was made possible in part because the selection was not so constrained by abstract Schenkerian background models and their idealist voice leading. The result is a much better picture of musical practices over the several centuries separating 16th-century bicinia (two-voice pieces mainly for pedagogical use) from nineteenth century waltzes, polkas, and other instrumental and vocal compositions" (2017, 4). I have sometimes used a traditional Schenkerian method for pieces with clear focal tones that connect plausibly to rising cadence gestures, but equally or more often a freer model of reading lines and their patterns where I thought that provided better information. I have used my proto-background model when register, stable intervals and their transformations are particularly evident, and in the absence of analytic method I have used the simple, familiar model of style statistics and comparison where rising cadence gestures appear but their connections to pitch-design context aren't clear.

As the preceding suggests, although the hunt for rising cadence gestures began thirty years ago in an effort to justify and document the ascending Urlinie, it has evolved into a broader and more consequential historical project. That rising cadence gestures are far more than exceptions to the rule (even in narrowly constrained Schenkerian terms) has been obvious long since, but the historical narrative of these gestures in European and American music-making is a work in progress.

Reference:
Neumeyer, David. 2017. Ascending Cadence Gestures in Waltzes by Joseph Lanner. Link.

JMT series, part 10 (Beethoven, Op. 22, III)

I intended this originally as a response to an article by Jason Yust; the menuet movement from the Piano Sonata, Op. 22, is the author's main example: link. There is, however, little to be said from the standpoint of traditional Schenkerian analysis, as Yust's goal is to rationalize the orthodox form of the theory, and therefore the analysis of Op, 22, III, assumes a priori Schenker's analysis from Free Composition and seeks to formalize it. Broadly, his position is similar to Matthew Brown's rationalization of Schenkerian theory (2005). Brown rejects the ascending Urlinie with a bit of circular reasoning; Yust doesn't engage it at all. The closest he comes is a critical note on the waltz ninth in this menuet's Urlinie: "Neumeyer (1987) . . . considers G to be an ascending passing tone rather than an upper neighbor. According to his interpretation, the G and A at the end of m. 7 are successive notes in a single voice, even though they both are sustained as part of the dominant ninth harmony over all of mm. 5–7" (2015, n33). More on that at the end of this post.

Yust does mention my article on proto-backgrounds (2009). As I noted above, he belongs among the "rationalizers" of Schenkerian theory (and so do I--in Neumeyer 2009, at least); he summarizes the earlier history very well (in paragraphs 0.1.1 & 0.1.2, and introductory paragraphs to subsequent sections). Although I can hardly claim to have offered a formalized theory in Neumeyer 2009, I did focus on a generative model (that is, building out from the background through transformations), which Yust also favors. Here is a sample, his Example 15; I have removed its analysis of the bass to show only the reading of the treble parts. The specific aim of the work is to portray contrapuntal melody (2 or more part-writing "voices") in a single diagram or figure (which presumably can then be subject to computerized comparisons). Level 0 is the "chord of nature" and is indistinguishable from one of my proto-backgrounds. At Level 1 the passing tone C is represented as a digression from the interval; then a second voice appears--as a hierarchically subordinate voice it is shown below the primary voice. Level 2, so to speak, harmonizes the two voices, drawing them together into a single diagram. The only comparison I can possibly make is to say that, in my view, Level 0 could just as easily have had the fourth F5-Bb5 instead of the third Bb4-D5.

In the details of his analysis, Yust brings out motivic thirds, beginning with the pick-up gesture. In my view, the fourth is more prominent, tying together accented notes at the beginning, F4-Bb4, and then being repeated. Stretched to a fifth -- one can hear the stretching in Enat5 -- the fourth can still be heard as a shadow within the compressed thirds that follow and continue throughout the continuation phrase. This theme, incidentally, is in the antecedent + continuation design, which Caplin regards as a hybrid but which I have found to be fundamental to 18th century galant style and have re-named the "galant theme" (link).

A reading using proto-backgrounds is not kind to my JMT analysis of the theme as using the registral variant, ^5-^6-(reg.) ^7-^8, since the stable interval would strongly imply/imagine ^5 (as F5) at the end. See below.

Thinking of the proto-background more abstractly, the initial fourth could be recovered -- circled notes below -- but the registral variant of the Urlinie would be undercut by this version, as well.

I still do think that a registral variant (link) is not difficult to hear in this theme and in the reprise (below), but it is obviously not compatible with a reading based on proto-backgrounds, which are after all biased in favor of registral definition and stability.

Note on the note: "Neumeyer (1987) . . . considers G to be an ascending passing tone rather than an upper neighbor. According to his interpretation, the G and A at the end of m. 7 are successive notes in a single voice, even though they both are sustained as part of the dominant ninth harmony over all of mm. 5–7" (Yust 2015, n33). I have written about the "waltz ninth" many times by now--here's a (link) to a recent post in this JMT series. Yust's criticism is the same as the one I've just made with respect to proto-backgrounds and does tend to undermine the registral variant. The waltz ninth is another matter. Nineteenth-century practice is broader--more creative and expressive--than eighteenth-century proscriptions. At (a), the ninth as neighbor note; at (b), the directly resolving ninth, a cliché in the waltz repertoire by no later than 1830. Note that the essential Schenkerian melodic note, C, is nowhere to be seen (or heard) -- in four-part writing of ninth chords, one leaves out the fifth. At (c), the figure that applies to all three "extended" chords: keep the seventh below the newly added top note in ninth, eleventh, and thirteenth chords. At (d), the voiceleading for the rising line with waltz ninth, understood as at (e) splitting the ninth in two; the same at (f) in Schenkerian notation.

References:
Brown, Matthew. 2005. Explaining Tonality: Schenkerian Theory and Beyond. Rochester: University of Rochester Press.
Neumeyer, David. 2009. “Thematic Reading, Proto-Backgrounds, and Registral Transformations.” Music Theory Spectrum 31 (2): 284–324.
Yust, Jason. 2015. "Voice-Leading Transformation and Generative Theories of Tonal Structure." Music Theory Online 21/4: link

JMT series, part 6b-3

This continues from yesterday's post to examine linear analyses of Beethoven, Symphony no. 1, III, and also to discuss its pervasive figure of the rising fourth.

In the previous post, I noted that Schachter's analysis of tonal structure was "bizarre, in my view radically un-Schenkerian." The sense of this assessment is apparent enough in the background/first middleground (63), which I have reproduced and annotated:

Far more (on traditional terms) mechanically and (in my view) musically plausible readings are shown below.

One can, of course, always read from ^3. This analysis takes the E5 in bar 3 as its focal tone--not unreasonable as it is the endpoint of the tonic prolongation in the opening phrase. The reading positions the "flat-key" area within a dominant prolongation, which matches our expectations about tonal design and formal functions. And the ending is conventional too, though ^2 must be implied (not shown that way, here) if one is taking the first violins, first oboe, and first flute as the line. There is a simple ^3-^2-^1 in the first horn and viola. Details of this reading may be found on my Google Drive page: link.

The traditional reading from ^5 fits the music as well as the one from ^3, with the exception that ^5 appears in the first obviously non-tonic moment (I've whisked that away in the graph, but you can see it in the score -- top of the previous post). This graph also shows more clearly that V in the retransition has been replaced by iii (as iii6/4).

A descending line from ^8 is not possible, but one can hear a stable ^8 -- surrounded by neighbor notes -- if one takes the strongest shape of the opening, the rising fourth motive, and chooses its goal tone as a long range focal tone. Details of this reading may be found on my Google Drive page: link.

The rising fourth motive and the persistent register play make a reading with a proto-background quite convincing. For more on proto-backgrounds, see my essay on Texas Scholar Works: link.

Finally, a reading meant to support the previous two, but I think also quite strong on its own. The fourth motive is stated three times, as three 2 bar ideas, in the first strain. A cadential gesture finishes. In the B section, the motive is continually present, as an obvious inverse, then expanded to a sixth in the approach to the cadence on bII. After that, the original and inverse are combined in the "codetta" to the Db cadence. A distorted version in the retransition is followed by the 14-bar expansion of the main theme in the reprise (bars 45-58), where the motivic idea is heard six times before the cadence formula. In the second half of the coda the rising motive and the falling melodic formula are opposed.

The three main cadences (not counting the one in Db major or bars 67-76) have versions of the same rhythmic figure and falling shape. At (a), the accented bar is on V/V. At (b), it is on the cadential dominant 6/4, but at (c) it is on the tonic -- the cadence came before it this time. It is this motivically driven dramatic plan that allows us to hear the final bars and not the earlier formula as the proper end of this menuetto/scherzo.

References:
Schachter, Carl. 2000. “Playing What the Composer Didn’t Write: Analysis and Rhythmic Aspects of Performance.” In Essays in Honor of Jacob Lateiner, edited by Bruce Brubaker and Jane Gottlieb, 47-68. Pendragon.