Bartók, For Children, “Sad Tale”

 Bartók, “Sad Tale” (For Children, vol. 2, no. 30). From Guide 2.

Here is another example of the analysis procedure. The form analysis at the right is repeated from §1. Next analyze the harmony—see the harmonic reduction and the formal bass-line sketch on the next page.

Harmonic reduction and bass-line sketch:

To begin working on the upper parts, isolate a formal unit (phrase or period), then locate and circle the initial tone, final tone, and highest tone [this last is boxed]. If the first tone is an anacrusis or pick-up note, the first accented tone may be taken instead; if the highest tone is a simple embellishing tone, the next lower or prominently placed tone may be taken instead. [That’s the case here, where F5 is a non-chord tone, neighbor to E5, so the “official” highest note is E5.] Make decisions based on what seems most workable or musically convincing at the time—remember that this procedure is informal. For the initial and final tones, always favor elements of the tonic triad.

For the second phrase, the high note F5 is again a non-chord tone. Because it is repeated and because it recalls the first phrase, I will take D5 as the high note (not marked as such).

The formal sketch in score form beams the middleground line for the theme (ending in bar 13) and slurs the same line as foreground ending in bar 6. In the repetition of the theme, the middleground line becomes the background line. The Bb4 of the second phrase (bar 7) is now an inner voice below D5.

If we choose the E5 instead—it is a chord tone after all—then we have a sixth-line, where “a” is a prefix (D5 to E5), “b” is a double neighbor figure, and “c” trades roles as D5 is the primary note and E5 is now a neighbor.

A third possibility is a registral or interval frame, shown as a triad beamed in the score (D5-Bb4-G4) but as an unfolded third (D5-Bb4) with a short line from the Bb down to G4. This forms a nice link to Bb4 in the second phrase.

I find any of these three versions easy to hear. One could argue for one or acknowledge the ambiguities.

Bartók, For Children, "Former Friends"

 Bartók, “Former Friends” (For Children, vol. 1, no. 3). Reproduced from Guide 2.

In §1.1 of the Guide, volume 2 (link to the file), we used a three-step procedure for harmonic (bass-line) analyses: sort the formal units, analyze the harmony, convert to formal Schenkerian notation. The last step was modified when necessary to a variety of alternative or informal modes of notation. 

I make use of the same three-step procedure for analysis of the bass and principal upper-part(s): step 1 is to sort the form elements; step 2 is to analyze and translate the harmony (that is, combine steps 2 & 3 from the bass-line procedure); step 3 is new: match the melody to the bass, with the optional step of untangling some or all of the inner voices. In this model, formal design is given the highest status, more than that of tonal hierarchies, and the traditional separation of bass and upper parts is maintained.

Here is more information from observation. Some of this may be useful further on.

The bass-line sketch for “Former Friends” is aligned with the score.

For the upper parts: in what follows I make use of text quoted from the original Neumeyer & Tepping Guide, chapters 4 & 5 (link to the file). We begin with informal upper-voice analysis.

A tone moves to any other in one of three ways: by step, by leap, or repetition. From these derive the three methods: lines, arpeggiations, and stationary or recurrent tones. All other melodic motions are combinations or specialized variants of these three

For the upper parts: isolate one formal unit: here it is the theme/sentence: bars 1-10. Recall that this piece consists of two statements of the theme. Locate and circle the initial tone, final tone, and highest tone [this last has an arrow pointing to it]. If the first tone is an anacrusis or pick-up note, the first accented tone may be taken instead; if the highest tone is a simple embellishing tone, the next lower or prominently placed tone may be taken instead. Make decisions based on what seems most workable or musically convincing at the time—remember that this procedure is informal. For the initial and final tones, always favor elements of the tonic triad.

Try to chart the essential motion between the initial and highest tones [very easy! an unfolded fifth A4–E5 at the very beginning], and between the highest and final tones. Give preference to a single line [overall a simple 5th-line in A minor with all the descent in the continuation phrase]. This line may have repetitions of tones or segments, may have neighbor-note figures attached, and may be chromatic or diatonic. The second segment (from highest tones to last) will almost always be a line; if so, connect its notes with a beam.

An optional additional step is to locate linear fragments in the inner voices. These will not usually run consistently from beginning to end, nor are they likely to be coordinated, note for note, with the principal upper-voice motions. [In this case, the A4 is consistent as the lower or inner voice throughout.]

The upper parts can be complex, with different voice-leading strands running through a single melodic line (and often appearing and disappearing). Only when the principal upper-voice motions are coordinated with the bass-line sketch do we have firm criteria for sorting and notating the different structural levels. A formal sketch is rendered as what Schenker called an Urlinietafel—“Urlinie table” or “score foreground,” a very practical way to keep the analysis close to the score and the aural experience of the piece. Once I transferred my analysis of the upper voices to the score, I made a few adjustments to the notation of the bass so that the two are coordinated. The notation overall still isn’t quite formal: notice that the beamed lines have both half notes and closed notes.

Bartók, For Children, “Flower Song”

Béla Bartók, For Children, vol. 1, no. 7 “Flower Song” [“Play Song”]. Note: “Flower Song” is the title in the first edition; “Play Song” is the title in the revised edition from the 1940s.

I examine this piece at length in §1.1 of A Guide to Schenkerian Analysis, Early 20th Century: link to the file. The goal there was to analyze the form design as it guided and was integrated with harmony. The end result of the work was a bass-line sketch.

Here we will work with both bass and upper parts, following the same three-step procedure: form analysis, harmonic analysis, sketch. To begin a form analysis, we recognize phrase and phrase-group levels. Phrases are "2" below, phrase-groups are "1". Note that the melody is identical in bars 1-8 & 9-16.

Since this is a simple melody and I am comfortable using William Caplin's formal-function labels, we identify the phrases as forming a sentence: repetition of a 2-bar motive in the first phrase ("presentation") is followed by a sequence-based continuation (Caplin calls that device "fragmentation"). 

Next we analyze the harmony. For more details and an alternative reading that gives more attention to bar 12, see the Guide narrative. Notice how Bartók makes a sharp contrast in harmony--effectively pedal-point tonic in bars 1-8 but then unstable over V in bar 9ff until the final tonic--while repeating the melody exactly.

 In a traditional Schenkerian analysis, we now try to match the hierarchy of the bass with a line or lines above. In this case, middleground lines (bars 1-8) and a background line (1-16) are the only possibilities, though we are obliged to think differently about priority in the third-motive (I picked the upper note in bars 1 & 3, but traced a line with lower notes in bars 5-7): this kind of inconsistency in tracing through voice-leading is routine in Schenkerian analysis).

Here are some aspects we haven't considered yet that would be obvious to an attentive listener and reasonably could influence our reading.

Fred Lerdahl's reduction method is based on local hierarchies of time/rhythm and harmony that are gradually built up over greater lengths. In bar 1, for example, I have removed the off-beat notes, and in the lower system I have prioritized the tonic on the first beat and connected it to the final tonic note. As I said in a previous post, unlike Schenker, Lerdahl doesn't require a specific shape in the final reductive level.

This is the tree diagram version of the system above, with a little more detail.

And this is a prolongational reading that is similar to the above. I have found such figures based on an upper-register ^8 to be surprisingly common in traditional European tonal music, going back to modal musics as early as the 16th century. See my comments on a similar one by Arthur Komar for a Bach Prelude in my Music Theory Spectrum article (2009).

My proto-background model, discussed at length in the same article and in this essay (link to the essay), has the ^8-^9-^8 figure (marked as ^1-^2-^1) but also preserves the obvious figures of the unfolded thirds, so that the first background is ^1/^3:

Briefly to the background and a generative model

 The practical work of our analysis of pitch design is reduction, or finding a larger-duration figure in a passage, expanding that work outward to encompass larger and larger durations, and organizing those in relation to each other. The system, however, in its foundation is generative and the goals of the method are interpretative; the ground of interpretation is the longest-duration figure, or the background. 

For Schenker it was the priority of line, all of them diatonic and very limited in number, and the priority of tonal progression rather than the rhythmic-metric groupings and articulations we call “form.” See his Free Composition (1935/1976).

For Felix Salzer, it was largely the same but as adjusted for a much broader historical account of European music. See his Structural Hearing.

For me, in that part of my work that concerns traditional tonal music, it has been the interval that precedes the line (following from “lines traverse intervals”), a re-positioning of the background, and an expansion of the number of middleground figures. 

For some others, the background is whatever results from the process of reduction (Fred Lerdahl argues this; for a concise presentation see chapter 1 of his Tonal Pitch Space [2004]). 

For many others still, including myself in my work on music outside of—and especially later than—the major representatives of the European Bach-to-Brahms repertoire, the background is integrated into a form- and motive-driven, still largely reductive process that can produce a variety of background shapes.

With respect to the current disciplinary status of prolongational analysis, Michael Buchler has written this, as part of a tribute to the late Carl Schachter. “. . .  with the recent falling-out-of-favor of prolongational (more broad than Schenkerian) analysis, [Schachter’s] analytical and theoretical voice [may be] known by fewer and fewer young scholars. . . . Those who decry the conservatism of prolongational analysis (a course I still love teaching, if in continuously evolving ways) should know that Schachter was hardly doctrinaire. He laid the groundwork for a changing practice, one that accounts for ever more musical features and that scrutinizes how we make musical decisions. . . .  [The] generalizability of his practice informs my own work in very deep ways.”. (Facebook post, 24 May 2026)

Briefly to goals and uses

 In practical terms, I distinguish between four modes or styles of analysis based on one’s priorities:

(1) as an aid for performance, which largely requires playing experience and skilled intuitions, not “readings.”

(2) as an active aid in listening, primarily knowledge of styles, music topics and conventions, repertoires, composers, and so on, along with the aural experience of melody, harmony, dynamics, texture, and tempo.

(3) as a method to identify and explain compositional mechanics or specifics (“explicate” is a technical term in literary pedagogy).

(4) as a device to provide beginning points or “windows” for “hermeneutics,” the verbally dominated work of interpretation, along with supporting details.

The last two of these are the natural focus of prolongational analysis. It is of limited, if any, value for the first two.

As was the case in the Guide to Schenkerian Analysis series (see the bottom of this post for more information), the goal here is to offer a coherent but flexible analytical, pedagogical, and interpretative tool for the musics at hand.

Nicholas Cook, in his classic but still decidedly relevant Guide to Music Analysis (1989) says the following: 

There is no reason why the normal conventions of Schenkerian analysis should not be replaced by others where this has some practical advantage, provided that the analyst makes it clear what conventions he is adopting or inventing—that is to say, that he makes it clear what he sees as being prolonged and by what means. Doing this can result in useful analytical results with music which is more or less a closed book for traditional Schenkerian analysis.         (Guide to Music Analysis, p. 59, emphasis added)

The value of this admonition for work with my principal repertoire is obvious (Cook himself offers a reading of a Debussy Prelude), but following directly from it is also a recognition of the role of analysis as interpretation. So long as it is hierarchical and so long as it includes background structures, prolongational analysis is never just objective in a work-out-the-algorithm sense: it is interpretive, and interpretation is never disinterested. 

Elsewhere I have used an analogy to illustrate this point. Thinking of it provisionally as explicating musical design, prolongational analysis gives us a background as the “theme” of a piece,** the mechanics of “how it works,” to be sure—what is being prolonged and by what means—but also our summary of “what it is about,” how it fits with the conventions we have adopted or invented. In other words, choice of a background figure inevitably reveals the point of the analyst’s narrative, his or her “thesis,” what he or she believes about this music and wants us to believe, too. I'll have more to say about theme and thesis in a subsequent post. You can also read about it here: Themes and Lines: On Practices in Linear Analysis of Music.

** “Theme” here does not mean the main melody of a musical composition -- that would be labeled a "motif" in literary terms. Yes, it is confusing.

----------

The three files of the Guide to Schenkerian Analysis series, with links and descriptions.

2018 November.  Guide to Schenkerian Analysis (2018-11-14)      Guide to Schenkerian Analysis

This essay is an introduction to Schenkerian analysis, one model for linear analysis/interpretation of music. This condensed version of an out-of-print manual, co-authored with Susan Tepping, provides the basis of an efficient learning experience and includes only the material from the original book necessary to that end. Two supplementary files contain appendices (File 2) and text and figures from the original book deleted from this file (File 3).

2025 December.  Guide to Schenkerian Analysis: Early 20th Century (2024-12-16)    Guide to Schenkerian Analysis: Early 20th Century

Methods for bass-line analysis that alter traditional Schenkerism are sometimes appropriate to European and European-influenced music from roughly 1890 to 1925. The examples are mainly drawn from Béla Bartók’s pedagogical collections for piano, principally For Children (1909; 1911), but also include work by Marion Bauer, Lili Boulanger, Samuel Coleridge-Taylor, and Roger Quilter, among others.

2023 October.  Guide to Schenkerian Analysis, File 4: Original (1992) Publication, Chapter 9 (2023-10-16)    Guide to Schenkerian Analysis, File 4

This continuation of the Guide to Schenkerian Analysis series include all the original publication’s Chapter 9, “Analysis of Music before Bach and after Brahms.”

Briefly to the principal repertoire

The primary repertoire for this blog is European and European-influenced music from roughly 1890 to 1925. 

By around 1890 the world of creative musicianship in European and European-influenced countries changed in very significant ways, not only with post-Wagnerism, but also, and perhaps more importantly, with the roots of an expanded tonal practice in Debussy, the rush to a radical chromaticism that reached its apex in the years just before WWI, the great flourishing of orchestral and other ensemble timbres, the rise—and reflection in publication—of music with characteristically syncopated rhythms, the incorporation of music into early cinema performance, and the early years of recording.

I believe we have reached a point in time where there is an educational—some are calling it moral—imperative to focus on music that is less than 200 years old and to give substantial attention to music in America (and some say well beyond America). The decisive turn away from older practices occurred 130 years ago, in the 1890s, with the dramatic expansion of timbral effects in Francophone countries (I include Russia here), of dense chromaticism in Germanophone countries, and of specific effects in nationalist movements. By the first decade of the 20th century, American composers had become prominent on the national and international stage, and the quintessential social dances of the 19th century—the waltz, polka, and galop—were either reinterpreted or abandoned for the tango, foxtrot, and one-step (rag).

An extraordinary variety of styles and compositional methods emerged in this quarter century, to which musics we have become accustomed since. As a reminder and as a simple example, here are a few compositions published in the year 1913: 

Marion Bauer, Up the Ocklawaha: Tone Picture for Violin, op. 6; Claude Debussy, Jeux; Rudolf Friml, High Jinks (musical); Victor Herbert, Sweethearts (operetta); Scott Joplin, (with Scott Hayden), Kismet Rag; Manuel Ponce, Doce canciones mexicanas; Max Reger, 4 Tondichtungen für grosses orchester (nach Arnold Böcklin); Erik Satie, Chapitres tournés en tous sens; Arnold Schoenberg, Sechs kleine Klavierstücke, op. 19; Aleksandr Scriabin, Piano Sonata no.10, op.70; Germaine Tailleferre, Berceuse for violin and piano; J. S. Zamecnik, Sam Fox Moving Picture Music, volume 1; and violin sonatas by John Alden Carpenter, Leland Cossart, Ernö Dohnányi, Erich Korngold, Daniel Gregory Mason, and Julius Weissman. 

Just as important for the first century of audio recording, here are some piano rolls published in 1913: 

Eugen d’Albert plays his music and works by Bach, Couperin, Korngold, Liszt, Rubenstein, and Sinding; Harry L. Alford plays Bach, Kunst der Fuge; Mike Bernard plays John Lindsay’s Aisha: An Indian Intermezzo; A. Brown plays Victor Herbert's "Won't You Be My Valentine?"; Debussy plays his Children’s Corner; Rudolph Ganz plays his music and pieces by Brahms, Chaminade, Glazounov, Godard, Grieg, Korngold, Saint-Saëns, Schumann-Raff, and Wagner; B. Goodall, selections from Sullivan's The Mikado; Enrique Granados, nine rolls of his music; B. Sarrazin plays Irving Berlin's "When You're In Town" (march); Ernest Van Dyck plays Silvio Hein's "The Maurice" (tango); Fanny Weiland plays Hugo Kaun's "Waldesgespräch," op. 78, and MacDowell's Virtuoso Studies, op. 46.

Pedagogy has shied away from the era for the obvious reason of complexity, but traditional practice and extensions and reinterpretations cover most of the ground, albeit at a cost if we insist on them in terms of some kind of absolute priority: earlier practices based heavily on 18th-century Italian pedagogical and performance-practice models have become myths of universal values, even supposed universal models of music cognition. Those myths are deeply embedded in Schenkerian analysis, the original form of prolongational analysis, too. The repertoire of this era teaches us to be more flexible for the sake of the best practical understanding. 

Introduction; work in progress

 Occasionally in my blogs and more often in publications to the Texas ScholarWorks platform, I make use of prolongational analysis, whose original form is Schenkerian analysis and which is sometimes referred to as linear analysis. 

This is a spinoff from two active blogs: Ascending Cadence Gestures in Tonal Music and On the Dominant Ninth Chord. The former was started in 2014 (introduction); the latter in 2015 (introduction). Both were themselves spinoffs from my long-running Schubert blog, Hearing Schubert D779n13, begun in 2009 and closed for new content in 2020 after more than 220 posts (link to the blog).

Though I say the two blogs are active, both have largely accomplished their purpose and I feel less incentive to add anything there beyond admin updates. 

Ascending Cadence Gestures reported on and continued a research project that began in the 1990s. To date I have found far in excess of a thousand published pieces of music with primary (structural) cadences where the principal melody rises in the end, where the upper register is the primary one throughout (centering about ^8), and/or where what I call a "wedge" figure combines rising and falling figures in different dispositions. 

On the Dominant Ninth Chord was meant as a historical survey and documentation of the dominant major-ninth chord in European and European-influenced music from roughly 1800 to 1950. My most recent posts on arranging manuals from the 1920s to 1940s seem to me to come close to finishing out the account.

Index

 I have just posted An Accumulated Index of Essays Published on Texas ScholarWorks. Link.

Abstract:

Here are lists of all my publications on the Texas ScholarWorks platform. The main topic areas covered are documentation and history of ascending and upper-register cadence gestures, similarly for the dominant ninth chord, form functions (after Caplin) for dance music, especially menuets of Mozart and his contemporaries, and linear analysis including Schenker. The file also includes repertoire lists.

Prolongational analysis plays a role in many of my essays, but I have also published a version of our Guide to Schenkerian Analysis (1992) along with a new essay applying the Guide's pedagogy to early 29th century music. Here are titles, links, and abstracts.

2018 November.  Guide to Schenkerian Analysis (2018-11-14)      Guide to Schenkerian Analysis

This essay is an introduction to Schenkerian analysis, one model for linear analysis/interpretation of music. This condensed version of an out-of-print manual, co-authored with Susan Tepping, provides the basis of an efficient learning experience and includes only the material from the original book necessary to that end. Two supplementary files contain appendices (File 2) and text and figures from the original book deleted from this file (File 3).

2025 December.  Guide to Schenkerian Analysis: Early 20th Century (2024-12-16)    Guide to Schenkerian Analysis: Early 20th Century

Methods for bass-line analysis that alter traditional Schenkerism are sometimes appropriate to European and European-influenced music from roughly 1890 to 1925. The examples are mainly drawn from Béla Bartók’s pedagogical collections for piano, principally For Children (1909; 1911), but also include work by Marion Bauer, Lili Boulanger, Samuel Coleridge-Taylor, and Roger Quilter, among others.

2023 October.  Guide to Schenkerian Analysis, File 4: Original (1992) Publication, Chapter 9 (2023-10-16)    Guide to Schenkerian Analysis, File 4

This continuation of the Guide to Schenkerian Analysis series has all the original publication’s Chapter 9, “Analysis of Music before Bach and after Brahms.”