Form and Structure

Week 2 of Analytical Techniques, Boston’s first graduate music theory course, uses Schenkerian analysis to look at the layers of form and structure of a piece of music. The lecture modules discussed surface design and how to look for changes within the design using musical character, texture, form, and other subtle clues. Examples from the lecture included Mozart’s Fantasia in C minor, K. 475, an excerpt from Hildegard von Bingen's Ordo Virtutum, Bach’s Prelude in C major from The Well-Tempered Clavier, the Presto from Mozart’s Violin Sonata, K. 526, and Beethoven’s Bagatelle, Op. 126, No. 1. The Application assignment looked at the construction of Hugo Wolf’s Das verlassene Mägdlein. Our discussion board post asked us specific questions about Felix Salzer’s analysis of Mozart’s Fantasia in C minor, K. 475. Finally, our assignment was to analyze the first movement of Beethoven's Piano Sonata No. 8 in C minor, Op. 13, "Pathétique" for structure and some Roman numeral analysis.

Application and Live Classroom 1

Prompt: As a way to prepare for this week's Beethoven Piano Sonata No. 8 in C minor, Op. 13, “Pathétique,"assignment, we will look at the Hugo Wolf song, Das verlassene Mägdlein, found on pp. 410–412 in the Burkhart. One might ask the question, "how does looking at a song help in understanding a movement of a piano sonata?" As is stated in this week's assignment, the goal of a good analysis is to find the salient features of a work-which can often be "quirky." This song, while on a much smaller scale than the Beethoven, certainly fits into this category. What can you discover about how this song is constructed? Look at the melodic and harmonic content, as well as the phrase structure. Compare the text with the form of the song. What is interesting about Wolf's use of register? Are the dyads in the first six measures isolated events, or do they reflect the larger harmonic motion? Is a "normal" Roman numeral analysis possible?

Discussion: I really struggled with the Application because I have no experience with Schenkerian analysis. To be perfectly honest, because the Application and Live Classroom sessions are not graded, I went into the Live Classroom having looked at but not analyzed the Wolf song. As it turns out, many of the questions asked in the prompt and by the instructor during the Live Classroom could be answered by just doing a harmonic analysis of the piece. Here are some key points I took away from the Live Classroom:

  • Discussion Question

    • Schenkerian Analysis is an attempt to strip away all of the surface detail to expose what is really going on in the underlying musical structure. The ultimate goal is to reduce it to its most basic elemental counterpoint. Reducing down to essentially a first species counterpoint exercise. Schenkerian Analysis completely removes the element of time (no rhythm). Takes a harmony and reduces a harmonic rhythm to a single event.

    • Two lines that imply harmonies in Schenkerian Graph (Think Bach chorale with inner voices removed. Considers steps as decorations, just leaving a few notes).

      • Structural melodic line

      • Structural bass line

    • Shows underlying voice leading. Gets rid of octave changes. See general harmonic progression over course of a piece.

    • Schenker found there are certain commonalities in tonal music (Mozart, Bach, Haydn)

      • Main melodic line tends to be scale degrees 3–2–1

      • Structural bass line tends to be Tonic–Dominant–Tonic

    • Some theorists believe modulation is a long tonicization—Schenker is one. Every key change is tonicizing something along the way. Every piece must return to its original tonic.

    • Harmonies are implied by pitches AND context.

  • Application

    • When writing about music, look for salient features. Find something interesting about the composition and focus on that.

    • Text is important to understanding the music.

    • Form: take a large musical structure and figure out how it segments

    • Surface Design: how do things look on the page? Big clue for beginnings and endings. Texture usually changes at section changes

      • Use of accidentals indicate key changes. Sometimes chromaticism is an isolated event (functional chord/modal mix). Key changes have consistent accidentals (Ex: D major will usually modulate to A major, so G# will occur). 

Discussion Board

Prompt: Begin by reading Alan Forte's article, Schenker's Conception of Musical Structure, (pp. 30–35), in Engaging Music.

Heinrich Schenker's theory of music and method of analysis have had a profound effect on theorists, composers, musicologists, and performers over the last several decades. Schenker's approach has its defenders and its critics, but nearly everyone who studies Schenkerian theory comes away with a deeper understanding of long-range musical process: contrapuntal, prolongational, motivic, and registral. The methods of proper Schenkerian analysis are beyond the scope of this course, although some reductive techniques may be adapted informally with success. Many of you may have already studied Schenkerian theory in some form, and many of you may have already developed opinions of the theory.

This week's reading from a classic Schenkerian analysis by Allen Forte, presents the basic concepts of Schenkerian theory and demonstrates the method of identifying long-range prolongational procedures, anchored by the Ursatz, or fundamental structure. We will not debate the usefulness or validity of the Schenkerian approach here. In this week's lecture, Felix Salzer's analysis of the opening of the Mozart Fantasia employs Schenkerian procedures less formally. The lecture also discusses the types of registral connections important to this approach. Ultimately, Schenkerian analysis goes beyond this to identify long-range linear (stepwise) connections between important structural tones, as well as connections by arpeggiation.

Study the example from this week's lecture, where Salzer's analysis is coordinated with mm. 1–26 of the score. Respond to one of the following questions:

  1. Why do you think that Salzer chooses G as the first structural tone of the long-range melodic structure, rather than the C which begins the piece? Give specific reasons that relate to the progress of the melody over time.

  2. From m. 4 through the rest of the excerpt, Salzer identifies G/F as the structural melodic tone, (note the stems and beams which signify importance). This note changes its meaning in relation to the chord it is in, (root, 3rd, 5th, 7th), and the contrapuntal structure, (interval with the Bass), several times in the passage. Discuss these changes and their implications for the music. F is, of course, a tritone from the tonic note C, so Salzer's analysis of its long-range structural importance implies a continuing sense of dissonance, or tension, with the tonic.

  3. The chords on G in mm. 14 and 18, which appear to be dominants, are shown in the analysis to be less structurally important than the dissonant chords which surround them. The second of these is discussed in this week's lecture. How does Salzer analyze these chords in his graph, and do you support the assessment in each case that these chords have no dominant association at all?

Response: I chose to answer Question 3.

The G7 chord in mm. 14 occurs in a line from mm. 10–16, as indicated by Salzer with downward stems in the bass clef. Beginning in mm. 10, Salzer indicates the following harmonic progression through mm. 16: BM, F#7/A#, A7, Fm/Ab, G7, Ebm, and F#7. If the G7 in mm. 14 was intended to be dominant, and thus analyzed as a structurally important chord, it would need to progress to a C chord. Instead, Salzer uses a slur in the bass to indicate a prolongation of I–V from mm. 10–16. The G7 chord also does not resolve as dominant chords typically do; while the seventh of the chord resolves down, the "leading tone" B descends by half-step instead of ascending. The A7, Fm, G7, and Ebm appear to be using motion by step and third to sequence from a comparatively weaker V6 in mm. 11 to a stronger V in mm. 16.

The G chord in mm. 18 is labeled as a neighboring chord to the F#7 that precedes it in mm. 16. Again, a G chord functioning as a dominant should resolve to a C chord. Instead, Mozart progresses to a Ger+6 in mm. 21 which resolves to F# in mm. 25. As mentioned in the lecture, the G chord in mm. 18 functions as an upper neighbor to the prolongation of F# from mm. 16–24. The G chord does not resolve to the Ger+6 in the way a dominant should resolve; the "leading tone" of B does not resolve up by half-step but is maintained.

Because of how the G chords fit contextually into their respective lines—prolongations of the F# dominant chord—and how the G chords resolve—"leading tones" not resolving upwards—I agree with Salzer's assessment that the G chords in mm. 14 and 18 do not function as dominant chords.

Assignment and Live Classroom 2

Prompt: The more one analyzes music, the more one comes to learn that every good work has an individuality which we should strive to capture in our analyses—its salient feature—that which makes it "tick." In most cases, rather than applying a one-size-fits-all approach for analyzing all music, or simply performing a Roman numeral analysis and identifying the form of a work, the approach concentrates on identifying what is important, even unique, to the piece under consideration. These may involve aspects of phrasing, melody, harmony, texture, register, long-range connection, form, and more. For this week's assignment, we will look at the first movement of Beethoven's Piano Sonata No. 8 in C minor, Op. 13, "Pathétique," found on pp. 264–270 in the Burkhart Anthology. The work is an example of sonata form with the inclusion of a slow introduction, (reminiscent of Haydn), and a coda, (very typical of Beethoven).

This movement does not always follow the "textbook" key relationships of a typical sonata. This does not, however, mean that the form is "irregular" in any way—it is merely one example of how the sonata principal has been applied in actual practice. You will find all of the normal constituent structural parts of a sonata here. Remember to keep in mind the idea of modal mix, as composers largely do not make the distinction between parallel major/minor keys, at least on a structural level. Pay particular attention to how the material unfolds in the recapitulation, particularly with respect to the 2nd theme. (It is always prudent to make a very close comparison between the recapitulation and exposition.) Beethoven's use of material from the introduction is also very interesting throughout the movement, as is the final phrase.

Directions

  1. Listen to and/or play through the music repeatedly until you know it well. Once you have familiarized yourself thoroughly with the music, analyze the large-scale structure of the piece. (Be sure to not get caught up in a measure-to-measure, blow-by-blow, analytic approach, at the start of the process.) Determine the boundaries of the Introduction, Exposition, Development, Recapitulation, and Coda, listing them clearly in some fashion, including measure numbers, in either prose or a simple chart, as you prefer.

  2. Analyze the next level of structure, which entails the main subdivisions of the four main areas. In the Exposition and Recapitulation, think about the succession of subsections and their usual melodic and harmonic associations, (first theme, bridge or transition, second theme, close). Carefully consider the key relationships employed! Material from the introduction comes back at various places in the movement as rhetorical interruptions. Consider the effect that these passages have on the form. It is always prudent to make note of the possibilities and the reasons for your choices. As in step No. 1, list the main subdivisions clearly in some fashion, including measure numbers, in either prose or a simple chart, as you prefer.

  3. Perform a Roman numeral analysis of the opening section of the movement included on the following PDF. (As the score is presented in a very compressed format in the Anthology, this passage has been reproduced in order to afford enough room to mark the score properly.) The bass line in mm. 17–18, (G–A–F–G) forms a cambiata-like figure that foreshadows the typical harmonic progressions of the succeeding Romantic Generation. Consider the following in determining these measures: what is the chord on beats 3–4 of m. 17? Does it resolve as expected? Does it act in tandem with the chord on beats 1–2 of m. 18? Do they both resolve together on beats 3–4 of m. 18? N.B.: even though you are not doing a complete Roman numeral analysis of the entire movement, you will need to think about harmony to answer the questions regarding form, etc. 

  4. Write answers to the following questions, each as a brief essay paragraph or two:

    • Discuss the main key relationships employed in the movement. Which sections do what is "expected?" Which do not? Be specific.

    • The return of material from the introduction at various places in the movement has been mentioned. Do these passages signal significant node-points in the architecture? What affect does the intrusion of "slow" material have in an otherwise quick movement? What is the primary relationship of the introductory material to the material of the movement proper? Why might Beethoven have employed these interruptions? 

    • What common harmonic device is in operation in mm. 245–249? How is the harmony in m. 250 different than m. 249? What affect does this device have on the perception of form at this particular point? 

Live Classroom: The second Live Classroom was pretty helpful. First, we discussed Week 1’s Assignment. There were only a few things I missed: labeling chords as they changed inversions, deciding whether or not something was a tonicization, and catching some of the German Augmented 6th chords. Then we moved into questions about the Week 2 Assignment which covered some good general points:

  • Normal Sections of a Sonata Form

    • Exposition

      • Theme 1: establish mood and tonic (not uncommon to be short, but can be long)

      • Bridge: (may begin as repetition of opening theme and modulates OR is completely new material, lots of falling-fifths progressions. Usually half cadence in new key)

      • Theme 2: solidly in new key, usually very different theme (change in texture and surface design)

      • Closing: fireworks with big cadence in 2nd key (goes on for a long time, purpose is to reinforce new key)

    • Development

    • Recapitulation

      • Theme 1 in orignal tonic

      • Bridge: reworked to stay in original tonic

      • Theme 2: stay in original tonic

      • Closing: stay in original tonic

  • Normal Key Centers

    • Major: modulate to Dominant

    • Minor: modulate to Relative Major

  • Node Point: most significant junctures between sections. (ex: In Ternary, where A meets B and B meets A

  • Strength of cadence comes from context, not necessarily type. Half cadences can be strong, typically end bridge sections, or setting up the arrival of the next section.

  • Progression: series of chords to get to final cadence. Prolongation is extending harmonies to avoid cadences

  • When something modulates, you will have a secondary dominant resolving to a new tonic that must get confirmed by an additional cadence. A tonicization does not get confirmed by an additional cadence

Assignment: Rather than post the entirety of my assignment, I’ll post my responses to Question 4 which carry most of the information covered in the other three questions.

Main Key Relationships: Beethoven does not follow the typical key relationships for sonata form in his Piano Sonata No. 8 in C minor. In a standard sonata form, the first theme introduced in the sonata is typically in the key of tonic (Benward & Saker, 2003, p. 129). The transition modulates to either the dominant or relative major—if the tonic key is minor. All other themes in the exposition typically remain in the dominant or relative major. In the recapitulation, all themes and transitions typically occur in the tonic key (p. 129). Beethoven begins with an introduction and the first theme of the exposition in C minor. Then, instead of modulating to the dominant, G, or the relative major, Eb, he modulates to Eb minor for the second theme, eventually mixing in the major mode in the closing material before returning to C minor. Beethoven also begins the recapitulation in C minor, but he modulates to F minor for the second theme rather than remaining in C minor for the entire section. The second theme of the recapitulation cadences in the key of C minor and remains there for the closing material and coda.

Benward, B., & Saker, M. (2003). Music in theory and practice (Volume 2, 7th ed.). New York, NY: McGraw-Hill.

Introductory Material: Beethoven interjects the introduction material between the exposition and development and the recapitulation and the coda. I believe these interjections signal significant node-points in the architecture due to their transitional nature in progressing from the concluding key of the previous section to the introductory key of the following section. The original introduction material is in C minor, ending on a half cadence to setup the first theme of the exposition in C minor. The second ending of the exposition is a D7 chord, tonicizing the G minor tonality of the interjection between the exposition and development. This first interjection tonicizes G through the use of F# fully-diminished seventh chords which transition to B7 by enharmonically spelling Eb as D# and resolving C down to B. The B7 chord is a half cadence concluding the interjection by tonicizing E minor at the beginning of the development. The second interjection removes the strong, fully voiced downbeats, and tonicizes G major, the dominant of original key of C minor. Some performances of this piano sonata, though not the recording of Alfredo Perl provided in the lecture material, also include the first Grave section during the repeat of the exposition. By including the introduction on the repeat, this places a significant node-point between each major structural section of the piece.

Pathétique refers to pathos and suffering (James, 2016, p. 5). The interjection of the slow, introductory material into the allegro molto con brio sections reveals this suffering. The half-step motion was a device typically used to show weeping (p. 9). I believe Beethoven intentionally used these interjections to not only transition between major sections of the sonata but to contribute to the overall sense of sadness and suffering.

James, J. (2016, November). Edexcel GCSE: Beethoven’s pathétique sonata. Music Teacher, pp. 1–10. Retrieved from https://www.rhinegold.co.uk/wp-content/uploads/2015/10/MT1116-scheme-KS4_Edexcel-GCSE-Pathetique-sonata-music.pdf

Harmonic Device: The harmonic device employed in mm. 245–249 is the falling fifths progression. The harmony beginning in mm. 245 progresses from Cm–F7–Bbm–Eb7–Ab. Then in mm. 250, the F# creates a Ger+6 chord in the key of C minor which progresses through a cadential 6/4 chord to G major, the dominant of C minor, and a half cadence concluding the second theme of the recapitulation. The device affects the perception of form by drawing attention to the cadence, creating an accelerated progression and signifying an end to a section or sub-section.

Comment

Burton Hable

Burton Hable is an instrumental music educator from Central Iowa. In 2013 he helped open Centennial High School in Ankeny, the first time in forty years that a school district in Iowa expanded to two high schools. He served there through 2018 as Assistant Director of Bands: conducting the 10th Grade Symphonic Band, directing the varsity Jazz Collective, co-directing the Centennial Marching and Pep Bands, teaching music theory, and providing individual and small group lessons to brass students in grades 6-12 at Prairie Ridge Middle School, Northview Middle School, and Centennial High School. During his tenure in Ankeny, enrollment in band grew from 450 to nearly 700, the jazz program expanded from four to seven ensembles, and ensembles under his direction were invited to perform at Iowa State University, Harper College, and the Veterans Day Parade in New York City.