Instructor Manual for Advanced Schenkerian Analysis 1st Edition Perspectives on Phrase Rhythm, Motiv

Instructor Manual for Advanced Schenkerian Analysis 1st Edition: Perspectives on Phrase Rhythm, Motive, and Form by David Beach

Instructor Manual for Advanced Schenkerian Analysis 1st Edition: Perspectives on Phrase Rhythm, Motive, and Form by David Beach

4 PART I CHAPTER ONE

THREE BASIC PREMISES The four examples demonstrating motion by step share a common characteristic. At the surface by which I mean note to note - the motion is predominantly by leap (arpeggiation); it is only by looking and listening beyond this level that we realize the motion of the various melodic strands or voices is by step. This perception is fundamental to understanding Schenker’s concept of structural levels.

Being aware of the treatment of dissonance - in this case the chordal seventh [V7] - is a crucial component in our understanding of voice leading; this is especially important in circumstances where the resolution is transferred to another voice, is delayed, or seemingly is omitted altogether. No matter how much I have stressed this in courses over the years, I am continually surprised by the number of students who forget or ignore such situations when analyzing a piece of music. Unusual treatment of the seventh, which is actually quite common, should be like waving a red flag in their faces! Example 1.2a demonstrates the temporary delay of resolution in the same voice, and the next two examples show the resolution occurring at two levels, initially transferred to another voice, then resolved in the same voice and register later. Example 1.3 is more complex, perhaps too difficult for some at this point. If so, omit it. In this instance I decided to begin with the underlying model and from it to show its unique representation rather than the opposite process, namely, to derive the underlying model from the music. Pedagogically I find it useful sometimes to approach an issue from a different perspective than normal.

The distinction between chord and [harmonic] scale-step or controlling harmony is tied to Schenker’s concept of voice-leading structure at multiple levels. This is demonstrated most clearly by Example 1.4b, the opening phrase from the second movement of Beethoven’s Piano Sonata Op. 10. No.1. Example 1.4c, the opening phrase of the development section from the first movement of Mozart’s Piano Sonata K. 333, is more difficult, since it involves substitution of chromatic chords for diatonic ones. Understanding the passing function of the C7 chord in the second half of the fifth measure of the phrase is most important. I expect this idea may, in some cases, require reinforcement or further explanation by the instructor.

MOZART, K. 333 EXCERPTS The point of this section is to demonstrate Schenker’s notion of motivic repetition at different structural levels. The commentary about voice leading is quite detailed, and, if appropriate for your class, you may want to simplify. The point is to demonstrate the similarities between the opening phrases of the first and third movements as well as the overall organization of the development section of the former.

Instructor Manual for Advanced Schenkerian Analysis 1st Edition: Perspectives on Phrase Rhythm, Motive, and Form by David Beach

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CHAPTER TWO The individual phrases selected for this chapter present some interesting analytical challenges, in some cases more difficult than the following antecedent-consequent pairs. This is true of the assignments at the end of the chapter as well. It is often a challenge for us as teachers to find the perfect example to illustrate a particular point that does not present at least one “problem” of some sort, since the music we are dealing with is very sophisticated. Each example is unique, requiring a unique solution, and it has always been my philosophy that it is better to confront students with interesting and challenging situations rather than file them away in a drawer.

PHRASES The initial example from the courante movement of Bach’s first Cello Suite is a closed phrase exhibiting a clear melodic descent of a fifth. A notable feature of this descent is the harmonization of scale degrees 4, 3, and 2 by a single chord, the dominant. The most unusual feature - the one requiring our special attention - occurs in the bass in the seventh measure, where Bach has written a D rather than the expected prepared C, possibly for purely practical reasons (D being an open string). C at that point would have made the following B inevitable, leading to an implied A over the written D as passing on to the concluding G. But Bach does not write the obvious, and we must adjust our analysis accordingly.

The first Beethoven example is often cited as a prototype of the musical sentence as defined originally by Arnold Schoenberg. Though Schenker did not employ this term, in part, at least, because he was not interested in describing formal types, it has generally been accepted today and thus has been adopted in this text.

The second Beethoven example, the opening phrase of the “Pathetique” Sonata, Op. 13, is more difficult to sketch than it first appears. Like the preceding example, it exhibits a linear ascent to the primary tone ( 5), only here arrival at the goal occurs in conjunction with a modulation to III. The difficulty lies in deciding how the first two measures fit into this larger scheme.

The opening phrase of the Brahms Intermezzo is an elaboration of a descending sequence of seventh chords. First I would like to stress my comment that the G 5 of measure 3 does not function here as a neighbor note to the following F5, but rather passes through it on the way to the following E 5. To be sure this E 5 is not the eventual goal, but its arrival coincides with a change of surface design, the initial statement of the descending third E 5 - D 5 - C5, which is subsequently repeated and extended over several measures. Second, it is important in dealing with this phrase to understand how Brahms has extended the passing note D 5 within the encompassing statement of this third. The result is an expansion of the phrase and a very subtle overlapping with the following consequent.

PARALLEL PHRASES (ANTECEDENT – CONSEQUENT) I will keep my comments brief here. The first four examples illustrate Schenker’s concepts of local interruption and closure. Two of these examples (the second themes from Mozart’s Sonatas K. 331 and K. 333) involve descents either to interruption or to closure by means of the cadential

Instructor Manual for Advanced Schenkerian Analysis 1st Edition: Perspectives on Phrase Rhythm, Motive, and Form by David Beach

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six-four. I mention this here only because the myth that the six-four is not legitimate support for scale degree 3 of the fundamental line seems to persist in some circles. There is no musical justification for this notion. The final example, the opening period from the third movement of Beethoven’s Piano Sonata Op. 10, No. 3, does not exhibit an interruption because the consequent phrase begins a step higher than in the first phrase and thus there is no restatement of the primary tone. And in the preceding example, the opening of Beethoven’s Piano Sonata Op. 57, there is no interruption or closure, but rather 5is retained throughout the antecedent and modulating consequent. Finally, I urge you to pay particular attention to the motivic parallels noted in three of these examples: the second theme from the first movement of Mozart’s K. 333, the opening period from Beethoven’s Op. 31, No. 2, and the opening of Beethoven’s Op. 57.

ASSIGNMENTS I will discuss the assignments in the order given at the end of the chapter. However, the two assigned phrases present specific “problems”, and for this reason I suggest they be discussed at the end of the other assignments.

TWO PHRASES 1. Beethoven, Piano Sonata Op. 31, No. 2 (III), 1-15 This phrase is a clear example of a musical sentence. The first eight measures present the basic idea, first the tonic form, which is repeated, then the answering dominant form, also repeated.

These repetitions are not written out in the graph (Example A2.1). This is followed by the continuation leading to the cadence. The hypermeter is quadruple; however, note that the phrase is fifteen rather than sixteen measures in length, resulting from measure 8 functioning both as the last measure of the second metric group and the first of the following continuation (indicated by the notation 4/1 between the staves in Example A2.1). More will be said about this in chapter three.

Example A2.1

Analytic Graph of Beethoven, Piano Sonata Op. 31, No. 2 (III), 1-16

I have notated the phrase as if it were a complete piece, which I will not do later when we consider phrases within larger contexts. The primary tone, F5 ( 3), which is established by the

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initial statement of the basic idea, is prolonged within the first part of the phrase (measures 1-8) by its upper neighbor. The slur from F5 (measure 1) to F5 (measure 8) indicates this area of prolongation, and the neighbor note G5 is notated in the graph by an eighth note. As noted above, measure 8 is simultaneously the end of the initial area of tonic prolongation and the point of departure for the continuation. Here the inner voice tone D5 is transferred to D6, initiating a series of descending thirds leading back to F5 and tonic harmony in measure 12. This is followed by a standard cadential pattern (cadential six-four to five-three), in which the leading tone substitutes for scale degree 2 in the descent to closure. The missing E5 ( 2) is supplied in parentheses.

2. Beethoven, Piano Sonata Op. 10, No. 3 (II), 1-9 This is a very complex phrase, the metric interpretation of which will be discussed briefly in the next chapter. Tonally it divides clearly into two parts, measures 1-5 and 6-9.

Example A2.2

Analytic Graph of Beethoven, Piano Sonata Op. 10, No. 3 (II), 1-9

The main melodic motion of measures 1-5 is a linear ascent from D4 to B 4 supported by a bass descent from D (i) to G (iv). Internal to this progression are two voice exchanges between the outer voices, which are notated in Example A2.2 by dotted lines to avoid possible confusion with the long diagonal solid line. At first it may not be clear how to interpret the covering F4 and G4 in measures 1 and 2, respectively, but as we continue it becomes clear that they are extensions of D4 and that the linear ascent really begins with the E4 in the third measure.

The second part of the phrase begins with a sudden shift to E5 in the top part, which is harmonized by a diminished seventh chord in four-three position. This leads to F5 (supported by o 7 of V), the melodic goal and climax of the phrase. It now becomes clear that the earlier motion to B 4 is an extension of the opening D4 and that the main melodic connection is from this D4 to E5, an association articulated musically by the repetition of a motivic idea. This E5 is a passing tone leading to F5, the primary tone. (In retrospect, we might now view the covering F4 in measure 1 as foreshadowing this primary tone.) The meaning of the long diagonal line is to show the association between the opening tonic harmony and this melodic goal. The slurs show the opening ascent of a sixth to B 4 embedded within the larger linear ascent reaching up to F5.

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Arrival at the primary tone does not occur in direct relation to a tonic harmony, but as seventh of the diminished seventh chord of V, which prepares the following cadential six-four. I have indicated the continuation of this F5 into the eighth measure by implication. But Beethoven does not do what we might expect here, but rather leaps back down to the lower octave to close on D4 with the leading tone substituting once again for scale degree 2, which is supplied in parentheses.

This is a rather unusual phrase in several respects, but totally comprehensible once the pieces of the puzzle fall into place.

PARALLEL PHRASES 1. Beethoven, Piano Sonata Op. 2, No. 1 (II), 1-8 This period is divided into two phrases of equal length. The first leads to an interruption, and the second completes the motion to local closure, notated in Example A2.3 as if it were a complete piece. The primary tone is A4 ( 3), though the covering tone C5 plays an important secondary role. In measure 1 this covering pitch is notated as an appoggiatura to B 4, the upper neighbor of our primary tone, thus making it easy to miss its significance. But in fact this appoggiatura generates a filled- in arpeggiation of the tonic triad, and this C5 is later picked up in measure 3 and returned to A4 via the passing tone B 4, completing the area of tonic prolongation just prior to the interruption. In the consequent phrase it is this C5 that prepares the covering motion to F5 prior to the cadential pattern leading to closure. From the F5 in measure 6 the top part arpeggiates to B 4, supported by IV, and from this B 4 the top voice descends a third to G4 ( 2) on its way to F4 ( 1).

Example A2.3 Analytic Graph of Beethoven, Piano Sonata Op. 2, No. 1 (II), 1-8

2. Mozart, Piano Sonata K. 494 (rondo theme) Like the previous example, the antecedent phrase progresses from 3to 2,and the consequent phrase completes the motion to local closure. Here, however, the phrases are six measures in length, and in both cases it is the repetition of the second measure of the phrase that leads to a clear division of the 6 into 3 plus 3. The antecedent phrase opens with a voice exchange between the outer parts establishing A5 ( 3)as the primary tone. The gesture of measure 2, repeated in

Instructor Manual for Advanced Schenkerian Analysis 1st Edition: Perspectives on Phrase Rhythm, Motive, and Form by David Beach

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measure 3, reverses this exchange, now filled in. The resulting melodic third A5 - G5 - F5 is then answered by a third a step higher leading to G5 ( 2). At the last moment the top voice leaps down to C5 in place of 2.In the consequent phrase G5 ( 2) is stated once again over the ii6 harmony, this time extended by a motion to the leading tone supported by the cadential six-four to five- three.

Example A2.4

Analytic Graph of Mozart, Piano Sonata K. 494 (rondo theme)

3. Mozart, Piano Sonata K. 310 (II), 1-8 Once again we are dealing with a period in F major with a fundamental structure of 3 2// 3 2 1 I V, I V I. Here, however, the fundamental line is stated in different octaves. The opening arpeggiation establishes A5 ( 3) as the primary tone. If we look ahead to the cadence at the end of the antecedent phrase, we see that 2does not occur in this upper octave, but as G4 supported by ii6 , which is then extended by a motion to the leading tone over V. I have supplied G5 ( 2) in parentheses in my graph (Example A2.5). If we now examine the intervening material, we see that the motion to G4 results from a linear descent in parallel thirds from C5 over A4. Note that I have interpreted the harmonic progression of measures 1-3 as controlled by the descending arpeggiation F - D – B (I- vi - ii6 ). The complete chord progression in these measures is I - V7 vi - I6 - ii6 . How do we determine the hierarchy? More specifically, what is the function of vi and the following I6 ? As a general rule vi in this circumstance functions as part of a descending arpeggiation as shown here. The support for the linear descent C5 - B 4 - A4 - G4 is I - V7 - vi ii6 . Here I6 offers support for a brief recall of C5. However, circumstances are somewhat different in the consequent phrase, where the bass arpeggiation in measures 5-6 is embedded within the larger connection between I and I6 supporting C5. This time it is C5 that prepares the descending third leading to 2and 1in this lower octave.

Instructor Manual for Advanced Schenkerian Analysis 1st Edition: Perspectives on Phrase Rhythm, Motive, and Form by David Beach

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Example A2.5

Analytic Graph of Mozart, Piano Sonata K. 310 (II), 1-8

4. Mozart, Piano Sonata K. 332 (I), 41-56 This time interruption and local closure are generated from 5,and in this instance I have notated the descents as middleground motions, since this passage is the second theme of a movement in F major. Considered in this larger context, the descents from G5 would be shown to prolong 2 supported by V in the home key. The main issue to be decided here is the function of F5 on the downbeat of the fifth measure in each phrase. Though it has been interpreted elsewhere as a neighbor to E5, I hear it in relation to the G5 in the second measure of the phrase. The descending third of measures 2-4 of the phrase occurs within a tonic scale-step and thus prolongs G5. F5 in the fifth measure is then a passing tone leading to interruption (eighth measure) or local closure (sixteenth measure).

Example A2.6

Analytic Graph of Mozart, Piano Sonata K. 332 (I), 41-56

5. Mozart, Piano Sonata K. 576 (I), 1-8 The primary tone, F 5 ( 3)is established in this piece by a combination of arpeggiation (D4 to D5) and a stepwise ascent involving a voice exchange with the bass. F 5 then progresses to E5 via the descending third G5 - F 5 - E5 with E5 supported by V. At this point the structure is identical to an interruption. However, looking ahead, we see that the consequent phrase does not begin again from the tonic, but a step higher. This is the same situation we encountered with the opening period of the Menuetto from Beethoven’s Piano Sonata Op. 10, No. 3. There is no

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interruption, and the dominant at the end of the antecedent phrase is interpreted as a divider, that is, as articulating the division between the phrases. Then consequent phrase then arpeggiates from E4 to E5 supported by supertonic harmony. E5 ( 2)is subsequently elaborated by arpeggiation to B5, and then at the cadence the leading tone temporarily replaces it. The overall tonal motion is continuous across both phrases ( 3 21supported by I – ii V – I) with the earlier motion to V embedded within this structure. This interpretation is reflected in the notation employed in Example A2.7. The diagonal lines show the association of 3to the opening tonic chord and 2to the structural dominant prior to closure.

Example A2.7

Analytic Graph of Mozart, Piano Sonata K. 576 (I), 1-8

6. Beethoven, Piano Sonata Op. 14, No. 1 (II), 1-16 In our final assignment for this chapter, the primary tone, G4 ( 3) is introduced after the harmony has moved away from the tonic. Initially 3is prolonged by a descending third with E4 harmonized by i6 . This is followed by a voice exchange between the outer voices reinstating G4 ( 3) and tonic harmony. This area of tonic prolongation is followed by a descending third leading to F 4 ( 2) supported by V, a motion that is subsequently repeated like an echo, thereby completing the eight measures of the phrase. The consequent phrase is stated an octave higher, and this time the motion continues to closure in this upper octave. A graph of these two phrases is provided in Example A2.8.

Example A2.8

Analytic Graph of Beethoven, Piano Sonata Op. 14, No. 1 (II), 1-16

Instructor Manual for Advanced Schenkerian Analysis 1st Edition: Perspectives on Phrase Rhythm, Motive, and Form by David Beach

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CHAPTER THREE Elsewhere I have noted that existing texts on Schenkerian analysis focus almost exclusively on Schenker’s understanding of pitch organization at multiple levels and on his description of the various techniques of prolongation. This is only natural, since these are the main focus of his mature work and that which has defined his legacy. But careful reading of his multiple works, including his last, Free Composition, reveals that he was interested in all aspects of musical organization - formal, metric, and motivic as well as tonal. One of my interests in writing this text is to bring all aspects of musical organization back into the discourse where they belong.

In this chapter we are considering two topics, phrase rhythm - the interaction of hypermeter and phrase structure - and phrase expansion. We have already observed hypermetric organization in several short sections of longer works, and I will continue to indicate the hypermeter in most of my graphs for the remainder of the text. There are times when this aspect of musical organization is regular and readily apparent, thus requiring no commentary. But, fortunately for us, there are many instances in the tonal repertoire where rhythmic events at this level are not regular. In the course of this book we will observe situations where a metric unit has been shortened or expanded, where two measures in a row are both heard as downbeat measures, and numerous instances of metric reinterpretation, where, for example, the final measure of a metric group or unit is heard simultaneously as the first measure of the next unit. All these situations are as important to musical organization and thus to Schenkerian analysis as, say, our understanding of voice exchange or reaching over.

I believe the discussion of metric reinterpretation in the text and the examples provided are perfectly clear, requiring no further explanation here. Likewise with phrase elision or overlap, which occur either with or without metric reinterpretation. The difference really comes down to whether the initial phrase ends on a weak or strong measure in the metric scheme. However, the one example I would like to comment on further is the opening phrase from the third movement of Beethoven’s Piano Sonata Op. 10, No. 3. We encountered this unusual phrase first as an assignment in the last chapter. You might recall that the first five measures involve a linear ascent from D4 to B 4, but then the top voice leaps up to E5 in the next measure. My analysis of this phrase (see Example A2.2) shows that this E5 is to be interpreted in the larger context as leading from the opening D4 up to the following F5 in the seventh measure. The reason we hear this connection between D4 (m.1) and B 4 (m.6) is the repetition of the opening motivic figure.

This repetition also affects our interpretation of the metric organization of the phrase. The hypermeter is quadruple, and we naturally hear measure 5, the arrival at B 4 and subdominant harmony, as a hypermetric downbeat. But with the leap to E5 and the repetition of the opening motivic idea in the next measure, we hear it too as a downbeat measure. There is a very important lesson in this for our students (and for us as well), namely, how important it is to be sensitive to the nuances of surface articulations, whether they be repetitions or the opposite, changes in the articulation. In our zeal to uncover deep structures, we too easily overlook important details. But it is often the details that can inform our choices about connections at deeper levels.

Our second topic is phrase expansion, examples of which fall into two general categories, those external to the phrase and those internal to the phrase. Instances of the first category, including extended upbeats and cadential extensions, are quite easy to spot. Though part of the phrase, they are considered to exist beyond the boundaries of the hypermeter, though if they are of sufficient

Instructor Manual for Advanced Schenkerian Analysis 1st Edition: Perspectives on Phrase Rhythm, Motive, and Form by David Beach

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length they may exhibit their own hypermeter. Normally, however, such measures are indicated by dashes, for instance where the goal harmony of a phrase is repeated for emphasis: 1 2 3 4 - - -. Likewise it is usually quite easy to hear or spot internal expansions once you are aware of their existence. These are of four types: 1) those arising from repetition of a segment of the phrase; 2) those resulting from avoidance of the cadence; 3) those arising from parenthetical insertions, which are normally differentiated clearly from surrounding material; and 4) written out decelerations. Examples of all types are provided in this chapter, and we will encounter several additional examples in subsequent chapters.

ASSIGNMENTS 1. Mozart, Piano quartet K. 478 (II), 1-19 The antecedent phrase (piano alone) is divided into two four-measure subphrases, the first of which features the descent of a fifth in the top voice. The function of the submediant chord in these four measures is shown in Example A3.1 to be part of a bass progression by descending thirds to Eq that leads to the cadence. The tonal motion of these opening four measures is embedded within the larger progression to the dominant in measure 8. The underlying harmonic progression of the phrase is I (mm. 1-4) - IV5-6 (mm. 5-7) - V (m. 8). Though the cadence in measure 8 has all the characteristics of an interruption, C5, which is subsequently replaced by the leading tone over V, is the result of arpeggiation from G5, the upper neighbor of 5.Thus the main melodic connection between the two phrases is not interruption, but prolongation of F5 by its upper neighbor.

Example A3.1

Analytic Graph of Mozart, Piano Quartet K. 478 (II), 1-19

Instructor Manual for Advanced Schenkerian Analysis 1st Edition: Perspectives on Phrase Rhythm, Motive, and Form by David Beach

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The main structural difference between the initial subphrases of the antecedent and consequent phrases is that in the latter the arrival at melodic closure (measure 12) is harmonized by vi, which is the middle member of a descending progression by thirds connecting I to IV, thus uniting the two subphrases more closely than before. This IV once again supports the upper neighbor of F5, from which point the melodic line begins its descent to closure. At the last minute closure is avoided by a deceptive motion to IV6 as support for 1.This results in a repetition of the neighbor note G5 and the following descent to closure, thereby expanding the phrase by three measures.

2. Mozart, Piano Sonata K. 332 (I), 71-86.

This closing theme is unusual in two respects: first, it begins from the upper neighbor of 5in the local key; and second, the initial phrase is six measures in length in a movement that to this point exhibits a clear quadruple hypermeter. Once again we see the function of vi as the middle member of a descending arpeggiation connecting I and ii6 . Here the progression I - V7 – vi supports the descending third G4 - F4 - E4, which is embedded within a larger descent of the same third spanning the entire phrase, harmonized by I …ii6 - V - I. See example A3.2.

Example A3.2

Analytic Graph of Mozart, Piano Sonata K. 332 (I), 71-86

The restatement of this idea involves three important changes. First, it is stated an octave higher.

Second, the upper neighbor of 5is stated over scale degree 1 (as a six-four resolving to fivethree), making even clearer its role. And third, closure is delayed at the last minute by a parenthetical insertion in which the descent from 5is repeated twice.

3. Schubert, Symphony No. 9 (II), 8-29, oboe theme The antecedent phrase, which leads to local interruption, is nine measures in length. This results from the repetition of the figure decorating B4 ( 2) and extension of the supporting ii6 chord for two measures, in which it is transformed via a chromatic voice exchange into a French augmented sixth chord leading to V. Example A3.3 shows this phrase as an expansion of 8 by counting measures 6 and 7 as 6 - . Note that Schubert does not shorten the following dominant by one measure to compensate. It is interesting to see how Schubert exaggerates this idea in the coda. Though I did not assign this later passage beginning in measure 340, I am including a graph of it here with the suggestion that you bring this passage to the attention of your students.

Here the supertonic harmony supporting the insistent repetition of the figure decorating 2is extended not by a single measure but by 8!

Instructor Manual for Advanced Schenkerian Analysis 1st Edition: Perspectives on Phrase Rhythm, Motive, and Form by David Beach

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Example A3.3

Analytic Graph of Schubert, Symphony No. 9 (II), 1-29

Instructor Manual for Advanced Schenkerian Analysis 1st Edition: Perspectives on Phrase Rhythm, Motive, and Form by David Beach

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Now back to our original example. In the consequent phrase, the motion to closure is by implication only ( 3and 2are supplied in parentheses) with E5 ( 5) always hovering above. What is implied here by context is stated clearly later in the movement. Note the metric reinterpretation here in measure 24, where the two phrases overlap.

4. Mozart, String Quartet K. 590 (I), 1-17 The score of this passage with interpretation superimposed on it is provided in Chapter Nine of the text (Example 9.1). It shows the prolongation of C5 ( 5) by its upper neighbor and identifies two important motivic ideas that are exploited by Mozart in this movement: x (the ascending arpeggiation to 5by all four instruments that opens the movement) and y (the dramatic descending scale passage to the low A, also stated by all four instruments). The first phrase is six measures in length, clearly divided into 3 plus 3. The ensuing phrase is 9 measures long, which can be understood as an expansion of 6 resulting from internal repetitions: 1 2 3 (2 3) 4 (4) 56 I have not included a graph of this passage, which involves a descent from C5 ( 5) to G4 ( 2). The voice leading is complex. C5 is reinstated in measure 8, but because of the addition of 7 to the tonic chord, this C5 gives way to B twice (first in measure 9 and then again in measure 11), though weakly (over a tonic pedal). Then in measure 12 B to “tossed” from violin 2 to violin 1 to cello, where it resolves to the low A in conjunction with motive y. This is then repeated. By implication, this A ( 3)leads to G ( 2) over V at the end of the phrase. It is then stated explicitly by the cello (motive x) at the outset of the following phrase.

5. Schubert, Piano Trio in E (I), 1-35 This opening section from Schubert’s second piano trio consists of three phrases, each 12 measures in length. The first two overlap with a metric reinterpretation (measure 12). The first is closed, and the second, which begins with a variant of the opening four measures, leads through the subdominant to the dominant. The material of measures 16-23, which is based on a new idea, prolongs the dominant. The third phrase then begins with a parenthetical excursion beginning in III (what Donald Francis Tovey would have called a purple patch!), the last measure of which pulls us back into the realm of E major. My purpose in assigning this rather complex passage is for the students to discover the phrase overlap with metric reinterpretation in measure 12 and the later parenthetical insertion. I have not suggested they attempt to do a voice-leading sketch of the structure at this point. It is simply too difficult.

Instructor Manual for Advanced Schenkerian Analysis 1st Edition: Perspectives on Phrase Rhythm, Motive, and Form by David Beach

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CHAPTER FOUR This chapter is a continuation of the previous two, the only difference being the inclusion now of contrasting material in our examples. It is important to realize, of course, that what we call contrasting material and label as “b” is often derived in some way from a. Even where that is not the case, there is continuity through the voice-leading connections. Consider, for example, the second theme from the first movement of Mozart’s Piano Sonata K. 280, our first example in this chapter. In the exposition this theme consists of two parts that are very different in their surface articulations, yet together they express a single unified tonal progression. Then in the recapitulation the connection between these two parts is expanded by a parenthetical insertion, an imitative passage based on motivic material from a.

The final example in the chapter, the opening section from the second movement of Schubert’s last string quartet, stands apart from our other examples. In my comments I stressed the virtue of using this type of notation - where the interpretation is superimposed on a metric representation of a score - to communicate your interpretation most easily to others, whatever the circumstance.

That is certainly true, but in fact I think it is the only viable way to communicate accurately in situations like this where, for example, the primary tone is never stated, but only implied. I suppose there is always a danger in raising a new idea at the end of a chapter; if that is the case in your class, then skip this example. My reason for including it is to demonstrate that there are other ways to communicate your interpretation of voice-leading structure and that, in fact, this alternative is sometimes far more effective than a traditional voice-leading graph.

ASSIGNMENTS 1. Mozart, Piano Concerto K. 491 (II), 1-19 The form of this opening section is: a (piano) - a' (orchestra) - b (piano and orchestra - a' (piano with orchestral support). The first two phrases are closed, but at a deeper level they prolong the primary tone G5 ( 3), first introduced on the downbeat of measure 2. Thus my notation in Example A4.1 shows these motions to closure at a middleground level. The primary tone is initially prolonged in measure 2 by a voice exchange with the bass before progressing to F5, This is followed by a leap back to the inner-voice tone B 4 supported by V, a motion that articulates the division of the four-measure phrase into two plus two. G5 is then reinstated over tonic harmony in the next measure, and the following motion to local closure now occurs an octave lower with the leading tone substituting for scale degree 2, which is supplied in parentheses in the graph. The orchestral statement of this material differs in two respects. First, the voice exchange is replaced by a progression to vi as part of a descending bass arpeggiation; and second, local closure occurs in this upper octave, this time with B 5 replacing scale degree 2.

The b phrase prolongs the dominant and 2(F5) by an ascending progression up to B 5 to prepare the introduction of the seventh of the dominant from above. Though it is this seventh that prepares the restatement of the primary tone in measure 17, I have shown this covering motion as an elaboration of the underlying interruption. I have also shown these seven measures as an extension of four. In the final phrase closure occurs in both octaves, but since we hear the piano in the lead here, I have shown its descent as primary.

Instructor Manual for Advanced Schenkerian Analysis 1st Edition: Perspectives on Phrase Rhythm, Motive, and Form by David Beach

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Example A4.1

Analytic Graph of Mozart, Piano Concerto K. 491 (II), 1-19

2. Beethoven, Piano Sonata Op. 2, No. 2 (II), 1-19 This theme by Beethoven is deceptively simple. Let’s begin with the form, which is ternary in design: a (mm. 1-8) - b (mm. 9-12) - a' (mm. 13-19). The a phrase is divided into subphrases, each four measures long. The first leads to the dominant, and the second leads to local closure.

The b phrase prolongs V with A4 in the top voice to introduce the seventh in preparation for the return. The final phrase, which combines elements of both parts of the opening phrase into a continuous (undivided) motion, is shortened to seven measures. A graph of the voice leading is provided in Example A4.2.

The primary tone F 4 ( 3)is established immediately, then prolonged by lower and upper neighbor notes before progressing to E4 supported by V. Our first significant challenge now comes in our interpretation of the second half of the phrase, and I suggest you ask your students to provide two interpretations, the point being to see if they understand the options. The harmonic progression of these measures is I - IV - I 6 - ii6 - V - I. The issue here is determining the function of the tonic chord following the subdominant. Is it part of a tonic prolongation followed by a standard cadential pattern? In this case we would connect by a slur the F 4 on the downbeat of measure 5 to the one on the downbeat of measure 7 and the corresponding bass from D2 (I) to F 2 (I6 ). This is certainly possible. Or is this tonic chord passing between IV and ii6 (IV5-6 )? The supporting evidence is of little help. Beethoven’s slurs would seem to support the first option, but the bass progression of an octave from G2 on the downbeat of measure 6 and the last-minute skip back to this G support the connection between IV and ii6 . To me this last piece of evidence is the clincher, and my graph shows the second option, which was, in fact, my initial reaction. The point I am trying to emphasize is that the process of analysis involves informed choices, but to do so you must first recognize the viable options.

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Example A4.2

Analytic Graph of Beethoven, Piano Sonata Op. 2, No. 2 (II), 1-19

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The b phrase presents no interpretive issues. As already noted, it prolongs V and its octave (A4), which introduces the seventh in preparation for the return to 3and tonic harmony. There is no interruption. The final phrase begins with a repetition of the opening two measures, the second of which is then treated sequentially, generating an ascending line that spans an entire octave to F 5 on the downbeat of measure 18. This is the climax of the phrase, marked ff by Beethoven. Here we are again at F supported by I6 followed immediately by a standard cadential pattern leading to closure. There can be little doubt that this point is the end of a tonic prolongation involving the octave progression F 4 - F 5, but does this invalidate our earlier interpretation of measures 6-7?

It certainly should make us re-examine our earlier interpretation, but I do not think it invalidates it. Circumstances have changed, as must our interpretation of the events. So my graph of these measures shows via the large slur the prolongation of 3by the octave progression F 4 - F 5 supported by the bass motion D2 (I) to F 2 (I6 ). Internal to this octave is a sixth G4-E5 harmonized by the progression ii - V. The motion to IV within this progression recalls the equivalent spot in measure 6, but here it seems to function within the local prolongation of ii.

The result of this reworking of the opening phrase is closure in the upper octave in the seventh rather than eighth measure. I hear the fifth measure of the phrase as a hypermetric downbeat, and it appears as if it is the acceleration to the goal of the phrase from this point that is the cause of the shortening of the phrase by this one measure.

3. Beethoven, Piano Sonata Op. 7 (II), 1-24 This entire movement is analyzed in Chapter Seven. See Example 7.12 and the accompanying discussion. Pay particular attention to the a' phase, which is expanded internally by delay of closure.

4. Beethoven, Piano Sonata Op. 14, No. 1 (II), 1-51 The first sixteen measures of this movement were given as the last assignment in Chapter Two. These two phrases are an antecedent-consequent pair, the first leading to local interruption and the second to local closure. We now have an opportunity to look at them within a larger context.

The overall form of this larger section is ternary, with each part consisting of two phrases, as follows: a (1-8) i- V local interruption i- V–i a' (9-16) local closure b (17-24) VI (I - V) b' (25-32) VI - iv 6 - V interruption a (33-40) i–V a'' (41-51) i – iv – V - i closure Rather than provide a detailed graph of the voice leading, I have produced a middleground graph (Example A4.3) that shows only the underlying motion of each phrase and how this all fits together into a larger structure. This graph involves what is normally referred to as “normalization”, in this instance realignment of events conceptually related but not stated together in the music, for example, placing the primary tone with the opening tonic harmony.

The opening two phrases establish a registral pattern of low to high, which is imitated by the b phrases, then reversed in the end to close in the original octave. The primary tone G4 ( 3)is

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retained as the top voice in the b phrases, the first of which follows the tonic to dominant motion of the initial phrase, here locally prolonging VI (C). The repetition of this phrase involves transformation of VI into an Italian augmented sixth chord resolving to V supporting 2.This motion to 2/V is shown as the structural interruption within this closed section. The next phrase, a repetition of the opening phrase an octave higher, reinstates the primary tone. The final phrase, which is expanded internally, then leads to closure.

Example A4.3

Analytic Graph of Beethoven, Piano Sonata Op. 14, No. 1 (II), 1-51

I have provided a detailed graph of this final phrase below the middleground graph. The primary tone is not present, but certainly understood conceptually, so I have supplied it in parentheses here. The C5 in the third measure is an appoggiatura (incomplete neighbor) leading to the B4 in the next measure as part of a diminished seventh chord of the following subdominant. The iv6 chord falls on a hypermetric downbeat, and it is the repetition of this emphasis on iv6 leading to the following voice exchange that stretches the phrase internally by two measures. The C5 resolves to the covering tone B4, while the earlier prolonged A4 progresses through G4 (cadential six-four) to F 4 ( 2) and on to E4.

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CHAPTER FIVE This chapter has a dual purpose: first, it is the culmination of material presented in previous chapters; and second, it serves as a summary and review of important concepts and associated terminology. One feature of previous chapters is the gradual expansion of formal aspects of musical organization, beginning with the phrase, then parallel phrases, and finally some examples of themes and musical sections incorporating contrasting material. We now concern ourselves with a particularly important musical scheme known traditionally as rounded binary, but viewed by Schenker, who was considering all this from a different perspective, as ternary.

Hence the unusual title of this chapter: Ternary (Rounded Binary) Form. The reasons for the different terms and conceptions of this formal type were made clear in the text, so they will not be repeated here. Suffice it to say that students must understand why this is so.

Let me suggest the following steps in preparing students to deal with the possibilities inherent in this formal scheme. When I speak of the first part, I mean that section designated as a (repeated); the second part, also repeated, consists of sections b and a'.

1. There are two basic types of rounded binary form: sectional, where the first part is closed (ends on the tonic); and continuous, where the first part ends on a harmony other than the tonic, normally V in the major mode and III in the minor.

2. Next we must consider the function of b within this scheme. If a is closed, then the content of b either prolongs the tonic and primary tone, or it leads to an interruption. If the form is continuous, the latter is the norm.

3. Finally we must consider the various characteristics of an interruption of the fundamental line. In all case the structure created by interruption is binary, the first including both sections a and b, and the second a'. For Schenker the formal scheme is ternary, a b a', but the underlying structure is binary, though I don’t believe he ever made that distinction explicit in his writings. With sectional binary, the interruption (if there is one) occurs in the b section. With continuous binary, we have two possibilities, depending on mode. In a major key, interruption occurs in the a section, and the b section then prolongs the dominant, frequently changing it from staple to unstable by addition of the seventh. In a minor key, the interruption occurs in the b section in conjunction with the arrival at V. It is important for students to sort all this out, because everything that has been said about continuous binary here has direct application to sonata form.

I will keep my comments about examples presented in this chapter brief, since I believe my explanations are sufficiently clear. Two of the examples include interesting manipulations of the phrase rhythm. The b section of the Schubert Impromptu contains an interesting contraction, a shortening of a hypermetric unit from four to two, within a chromatic voice exchange locally prolonging the subdominant. The Haydn Menuet includes both external and internal phrase expansions, external by extension of the cadence, and internal by repetition and later by avoidance of the final cadence. Finally, the Haydn Andante introduces a phenomenon we will encounter in later chapters, namely, the distribution of the fundamental line in different octaves and voices, including the bass. Though subsequent graphs “normalize” register, it is important for students to deal first with the unique characteristics of a musical work, including octave placement.

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If you are setting aside a week at some point for review, this is the place to do it. By the end of Chapter Five we have covered the important concepts and terminology associated with Schenkerian analysis. Part II, which follows, applies these ideas and techniques in different contexts.

ASSIGNMENTS 1. Mozart, Piano Sonata K. 331 (III), 1-24 This alla Turca theme is a clear example of a continuous rounded binary with interruption. The hypermeter is quadruple, but you will note that I have indicated the a' phrase as a continuous eight due to the harmony in the fourth measure, the augmented sixth chord, which propels the music onward. The first four measures feature an arpeggiation to the primary tone C6 ( 3)over a tonic pedal. Scale degree 3 then gives way immediately to 2over an E minor harmony (v), and in the next four measures the top voice descends a fifth to local closure in the key of the dominant.

The b phrase continues this linear descent, completing the octave B5 - B4 prolonging 2and the dominant. In this b phrase the hypermeter is maintained by repetition of the initial two-measure idea, which is treated sequentially. The a' phrase once again arpeggiates to C6, reinstating the primary tone, but due to the change in the bass and harmony in the fourth measure, the motion continues beyond this point to the sixth measure, where the bass arrives at C3 and the top voice, following a descent of a third, at A5, completing a voice exchange between the outer voices.

This is followed by a cadential pattern leading to closure in the lower octave, in which 2is approached by the descending third D5 - C5 - B4. See Example A5.1.

2. Mozart, Piano Sonata K. 545 (II), 1-32 This portion of a longer movement is an example of sectional rounded binary, in which the first part consists of parallel phrases and b prolongs the primary tone D5 ( 5) There is no interruption.

The initial phrase employs two motivic ideas, the descending arpeggiated fifth articulated in measures 2, 4, 5 and 6 by the dotted rhythmic pattern and the turn figure. The phrase opens with a linear ascent to 5,which is initially prolonged by a variant of the fifth motive descending from the covering tone G5, a projection of an inner voice, to the neighbor note C 5. Following restatement of D5 in the fourth measure, the descending fifth motive is stated a step lower, harmonized by the dominant with A in the bass. With the repetition of D5 in the next measure, it would appear as if this C5 is functioning as a lower neighbor. At a superficial level this may be true, but take care here to consider the proper resolution of the dissonant seventh, a point stressed in Chapter One. As shown in Example A5.2, the proper resolution of this C5 is taken by the bass in the next measure, delayed until the third beat. The result is a descending third D5 - C5 - B2, above which D5 is retained. This is followed by a descending arpeggiation from the covering tone G5, this time to Cq4 ( 4in the descent to local interruption), where each note is decorated by a turn figure. The consequent phrase follows the same path, this time leading to local closure.

Note that C5 in the descent occurs as the middle member of a descending arpeggiation supported by ii6 . Entrance of the following B4 is delayed until the third beat, sounding as an appoggiatura to the following A4, a characteristic Mozartian variant of the standard six-four to five-three. The diagonal lines in the graph show this rhythmic displacement.

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Example A5.1

Analytic Graph of Mozart, Piano Sonata K. 331 (III), 1-24

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Example A5.2

Analytic Graph of Mozart, Piano Sonata K. 545 (II), 1-32

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The b phrase, which prolongs 5,is more complex in its references to earlier material than it first appears. We might begin by examining the first four measures as a closed unit. Here the initial third D5 - F 5 is prolonged by its lower and upper neighbor notes, with the inner line metrically stressed. However, note that the bass line in the fourth measure continues by step down to F 3 on the third beat of the fifth measure, a motion reminiscent of the earlier bass motion to B2 in measures 6 and 14. This forces the motion beyond the fourth measure to its continuation, which supports a descent in thirds from A5 over F 5, the metric stress falling once again on the inner line. Once we look beyond the surface, this b phrase contains many of the characteristics of the a phrase transposed to the dominant key, but cleverly disguised. Most obvious is the parallel between the bass motions, especially the descent to the third of the local tonic chord, which here, like earlier, allows the introduction of scale degree five above it. The ensuing descent of a fifth is disguised not only by its weak metric placement, but also by the fact that its first two members, A5 and G5, are displaced by appoggiaturas; then the entrance of the following F 5 is delayed until the last minute, reminiscent of the cadence in measures 15-16. However, once you look carefully at the voice leading, the fifth indicated in the graph is clearly there. Finally, note the employment of motives from the a phrases here, both the dotted rhythmic figure and the turn motive, which is represented not only in its surface repetitions but also at the middleground level in the opening four measures of the phrase.

3. Mozart, Piano Sonata K. 331, trio The formal design of this trio is continuous rounded binary. However, as we shall discover, the underlying structure does not meet our expectation: there is no interruption. If the structure is “unusual”, so is my notation of it in Example A5.3, which is designed to show the underlying metric organization as well as the voice leading. The first part is sixteen measures long, an elaboration of an underlying eight-measure phrase resulting from repetition in the upper octave of its various components. The voice leading of the first four measures involves the ascending progression from A4 to D5. The next gesture descends a third within V7 of V, thereby transforming D5 into a dissonant seventh, which finds its resolution at the beginning of the final gesture of this phrase, which progresses by step to A4. Overall, then, the phrase opens up to D5, then descends by middleground progression back to A4, harmonized in the key of the dominant.

Our expectation is that the a' phrase will begin the same way, but instead Mozart initially prolongs A4, and from there the top voice descends gradually to closure. The result of this change in the first four measures of the a' phrase is an octave descent spanning the entire trio that is divided into a fourth and a fifth. The reason this octave is not shown as a fundamental line is that it prolongs D5, which in the bigger picture functions as the upper neighbor of C 5, the primary tone ( 3) of the Menuetto. This is shown clearly by Schenker in Free Composition, Fig. 35/2.

The b phrase prolongs the dominant. Here Mozart takes further advantage of the upper octave, the register of the earlier “echos”. A5 locally becomes the dissonant seventh of V of ii, and the subsequent dissonant unfolding from A5 to D 5 is answered by the third E5 to G5, the latter entering only as the bass progresses to Cq as part of an arpeggiation back to A. G5 then becomes the dissonant seventh of the dominant, and from there the top voice continues its descent through Fq5 to an implied E5 over the prolonged dominant, above which A5 is stated once again, then transferred to the lower octave in preparation for the return to a.

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Example A5.3

Analytic Graph of Mozart, Piano Sonata K. 331 (II), trio

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4. Schubert, Op. 142, No. 2, trio This trio belongs with the Impromptu discussed in the text (see Examples 5.5 and 5.6). Like the Impromptu, the formal design is sectional rounded binary. The graph provided here (Example A5.4) shows considerable detail, including chromatic passing tones. The local primary tone F4 ( 3) is established immediately and initially prolonged in measures 1-5 by a descending third from the covering tone A 4, in which the middle member of this descent, G 4, is introduced by its own third from above. The primary tone is then immediately transferred to F5 for a varied and expanded statement of this material. This time the return to F5 from the covering third is harmonized deceptively (vi), which progresses to ii - V - I as support for the continuation of the descent to local closure. This motion to vi anticipates the motion to VI in the b section.

The b phrase begins with a repetition of the initial idea, now in the parallel minor, a common procedure in Schubert’s music. This results in the modal inflection of the primary tone ( 3). The continuation begins in the upper octave, as before, but this time the covering A 5 progresses up to D 6. This is followed by the octave progression D 6 to D 7, the climax of the phrase, harmonized by the progression vi - V - I of VI (B ), which is written by Schubert as an A major chord for ease of notation and reading. But I have rewritten this to show its tonal function as the middle member of a descending arpeggiation to iv: I - VI - iv leading to V and an implied interruption with the leading tone substituting for 2.Meanwhile Schubert has remained on this A major chord for several measures, allowing the ear to adjust to this foreign territory and the builtup energy to dissipate.

5. Mozart, String Quartet K. 491, Menuetto The a phrase of this movement is ten measures in length with a clear duple hypermeter resulting from a repeated rhythmic pattern. The phrase opens with an arpeggiation to A5, from which point the top part makes its way eventually to local closure. The natural reaction is to take A5 as the primary tone ( 5), but there is a fundamental problem with this obvious choice. The descent from A5 (measure 3) to D5 (measure 7) occurs within a tonic prolongation (I to I6 ) followed by a cadence supporting E5 to D5. If A5 is the primary tone, where are scale degrees 4 and 3 in the descent to local closure? The only possibilities exist within the tonic prolongation of measures 37, so we must seek a different solution. As shown in Example A5.5, the fifth descent of measures 3-7 is embedded within a larger descent of a third from F5 ( 3)So there is a real dichotomy in this instance between surface articulation and underlying structure.

The b section consists of two phrases that overlap with metric reinterpretation. Together they prolong the dominant and 2,to which the seventh is added in preparation for the return to the beginning. (One might cite this as further support for the interpretation of F5 as the primary tone.) The first of the two phrases introduces 2,first harmonized by an A minor chord (v), then its dominant, from which point the top voice descends chromatically to B4, then A4 supported by i6 in the key of the dominant. Like before, this initial descent of a fifth is embedded within a larger descent, in this instance a diatonic version of the same fifth. The point of arrival, measure 22, is also the point of departure for a chromatic sequence of seventh chords progressing by descending fifths from V7 to the augmented sixth chord above B (enharmonically B 7 ), which resolves to the dominant.

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Example A5.4

Analytic Graph of Schubert, Impromptu Op. 142, No. 2, trio

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Example A5.5

Analytic Graph of Mozart, String Quartet K. 421, Menuetto

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PART II The principles of Schenkerian analysis – the concepts, specific techniques of voice leading, and terminology – are explained in the first five chapters, the last of which concludes with a summary and glossary. It is through this first part that the student acquires the basic knowledge and tools to apply them to the analysis of more extended works. Part II, then, is about applied analysis, organized by topic. Chapter Six focuses on selected short works by Bach, a brief digression from our underlying concern with classical formal procedures. An important feature of this chapter, one that can be applied elsewhere, is the recommended step of preparing a simple reduction as a preliminary step in developing an analytic graph of the structure. Chapter Seven is concerned with ternary form, first a consideration of extended rounded binary (a mid-stage in the transition between simple rounded binary as presented in Chapter Five and Sonata Form) and ABA form. Chapters Eight and Nine then deal with Sonata Form, the latter focusing on the idea of motivic repetition at multiple levels, and the final chapter is concerned with music as an expression of text. As suggested in the Preface to Advanced Schenkerian Analysis, I expect instructors to determine the selection and order of material from this second part based on the dynamics of their particular classes. I can imagine, for example, skipping directly to Chapter Ten if song is a particular interest, or to Chapter Eight if the focus is to be on Sonata Form.

The following commentary deals exclusively with my solutions to the suggested assignments.

Typically I will focus initially on aspects of formal organization, phrase rhythm, harmony and, where appropriate, text. Then I will turn to an explanation of my graph, explaining options and reasons for choices.

CHAPTER SIX 1. Little Prelude in D Minor (BWV 926) The formal-tonal organization is as follows: 1-20 Establishment of key and primary tone followed by prolongation of the tonic. The hypermeter is quadruple.

21-38 Prolongation of the dominant, internal to which there is emphasis on the subdominant. The final hypermetric unit in this section is extended from 4 to 6 measures.

39-42 An unexpected flourish (mini cadenza) on the tonic.

43-48 Tonal closure and extension of the final cadence.

The “puzzle” here is to determine the meaning of the four- measure return to the tonic (the brief cadenza) prior to closure in measures 43-45.

The opening eight measures comprise a tonic pedal over which the opening melodic A4 descends a third to F4; this is followed immediately by an apeggiation to F5, which is identified as the primary tone ( 3), since it from this F5 that the following motion unfolds. Example A6.1 shows the prolongation of 3by an octave descent F5 - F4 in measures 8-20, similar in some respects to what we have witnessed in the first two preludes in WTC I. Here, however, the octave is elaborated more extensively by projections of an inner voice above the main line. These occur in two pairs, marked 1. and 2. in the graph, the initial pair falling on hypermetric downbeats. The pattern then changes, continuing the descending motion in parallel tenths.

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Example A6.1

Analytic Graph of Bach, Little Prelude in D Minor (BWV 926)

The middleground octave descent prolonging F5 is answered by a descending sixth from E5 over a prolonged dominant in measures 21-38, internal to which D5 and B 4 in the descent are harmonized by VI and iv, respectively, neighboring the prolonged dominant. This brings us to the tonic flourish in measures 39-42. Looking ahead, we see that F5 ( 3) is reinstated in measure 43, followed immediately by closure in the upper octave. What, then, is the function of the tonic return just prior to this? The resolution of G4, the dissonant seventh of the dominant, to F4 in measure 39 is clear, and my graph suggests that the top voice, coming from the E5 in measure 21, leads to D5, though it is clear that this is immediately covered by F5 in anticipation of the return to 3in the next measure. This interpretation is clarified in the middleground graph provided as Example A6.2, which shows this tonic flourish as completing an initial motion to closure that is embedded within the overarching descent. It is important to understand, though, that the surface articulation of this tonic return counters any sense of completion, thus requiring the continuation to come to a satisfactory close.

Example A6.2

Middleground Graph of Bach, Little Prelude in D Minor

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2. Prelude in B Major (WTC I).

See David Beach, “The Submediant as Third Divider: Its Representation at Different Structural Levels,” Music Theory in Concept and Practice, edited by James Baker, David Beach, and Jonathan Bernard (University of Rochester Press 1997): 309-335. See Figures 9-14 and accompanying discussion.

3. Cello Suite I, Menuet I. My analysis of this movement is provided in two parts in Example A6.3, first a metric representation of the voice leading at level a and then a graphic representation of its structure at level b. Notes implied by context are supplied at level a in parentheses. In some cases these are obvious, as in measures 4, 13, and 15. However, the underlying harmony is not immediately apparent in measures 6-7. I have interpreted the C4 on the downbeat of measure 6 as displacing the following return to B3 and tonic harmony, followed immediately by a descent from A3 over an implied C3 below, that is, ii6 , which then leads to V on the downbeat of the next measure. The descent in thirds in measure 7 is then harmonized by V leading to I in the key of the dominant.

Note that the implied changes of harmony here fall on the second beat, more typical of a sarabande movement. Not shown in this reduction is the hypermeter, which is quadruple throughout.

The main issue in interpreting the overall structure of this movement is determining the function of the dominant in measure 8 and the modulation to vi (E minor) in measure 16. There are two possibilities: 1) that the dominant in measure 8 is structural, supporting 2,at least by implication, which is prolonged by subsequent motions to vi and IV before its return in measure 20; or 2) that the dominant in measure 8 is dividing, prolonging the tonic, and that the main tonal connection is from I to vi (m. 16) and IV (m. 18), arriving at the structural dominant and 2only in measure 20/21. I think the latter is the correct interpretation, the most compelling evidence being the return to B3 in measure 13 via its upper neighbor, a further development of a motivic component from the very beginning, and the subsequent descent of a fifth to the cadence on vi. This decision has a profound impact on the graph.

The graph at level b shows the initial prolongation of B3 ( 3)by its upper neighbor followed by the descent of a fifth from A3 to the cadence on the dominant. Following the double bar, B3 is reinstated by its upper neighbor once again, this time supported by an E minor chord in first inversion that leads to the cadence on vi. I have shown the underlying motion to this point as 5-6 above the bass note G2. The connection between vi and V is made via an intervening IV, which completes the large-scale descending arpeggiation in thirds from the opening tonic preparing the introduction of the structural dominant.. The prolongation of the structural dominant is accomplished in two stages, initially by an ascent by step from A3 ( 2) to D4, where the first two steps are elaborated by 5-6 motions and each 6 is introduced by the process of reaching over, and then by the descending third to the leading tone, where the passing G3 is given temporary consonant support by B2 in the bass.

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Example A6.3

Analytic Graph of Bach, Cello Suite I, Minuet I

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4. Violin Partita III, Menuet I Like the previous movement examined, the analysis of this Menuet is divided into two parts, a metric simplification of the voice leading at level a and an interpretation of the structure at level b. For the most part, the simplification at level a is self-explanatory. I have added solid and dotted brackets in measures 1-4 to show the exchange of parts (inexact in the dotted pair).

Beginning in measure 19, I have simplified the descending fifth sequence to a succession of chords, and I have interpreted the underlying harmony in measures 24-25 to be ii in four-three position, that is, over the bass note C (implied in measure 24), leading to V in measure 26. This is an awkward spot, where Bach breaks away from the established pattern to reintroduce A5, the seventh of the following dominant, in preparation for the return of G 5 and tonic harmony in measure 27. In this instance I have indicated the hypermeter above the staff at level a of Example A6.4 to show the gradual expansion of the established 4, first to 6 leading to the cadence on C (vi) in measure 18, and then to 8 in the following sequence leading to the dominant in measure 26.

There are some similarities between this movement and the cello movement just discussed, in particular the modulation to vi in the second part, but our interpretation of the underlying structure must differ to account for the return to tonic harmony and the opening material in measure 27. In this instance the dominant at the end of Part I (m. 8) is structural, supporting an interruption of the fundamental line. The modulation to vi occurs within the subsequent prolongation of the subdominant, where the seventh is introduced by a composed out 8 - 7 motion. As shown at level b, this is accomplished by a descending step progression of a ninth from B5 to A4 before the octave transfer to A5 in preparation for the return to the primary tone in this upper octave. Once 3/Iis re-established, it is prolonged by a return to the upper neighbor before leading to closure supported by the cadential progression ii6 - V - I in measures 33-34.

The intervening tonic chord is the result of passing notes.

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Example A6.4

Analytic Graph of Bach, Violin Partita III, Menuet I

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5. Partita in B , Sarabande I have suggested trying two interpretations of this movement, a reading from 5and another from 3.For the first, I refer you to David Beach, “Bach’s Partita No. 1 in B , BWV 825: Schenker’s Unpublished Sketches with Commentary and Alternative Readings, Music Theory Spectrum 30/1 (2008): 1-34. See example 8, p.21.

The first question that arises is the role of F5, first introduced in measure 1 and then picked up in measure 2, in the voice-leading hierarchy. At some level, this F5 descends by step to B 4 in measure 4, and eventually this B 4 progresses by step to F4 at the cadence on the dominant in measure 12. F5 is then picked up in measure 14, and, following an initial descent of a third, it progresses to E 5, first in measure 18 and then picked up again in measures 21-22. If one decides to read the fundamental descent from 5,this is surely 4.But where is the resolution of this E 5, which has now become the dissonant seventh of the dominant? It is transferred to the bass, where it resolves to D3 on the downbeat of measure 25. Eventually scale degree 3 is stated in the top part, resolving to C5 as part of the final motion to closure in measures 27-28. So a case can be made for a reading of the fundamental line from 5,which was my initial reaction. However, as noted above, this interpretation gives prominence to F5 and the initial descent in measures 1-4, which occurs for the most part over a tonic pedal. In retrospect, I believe my initial interpretation is incorrect and that a more logical reading of the deep structure is a fundamental descent from 3.

Such a reading is provided in Example A6.5.

Example A6.5 shows the descent from F5 in measures 1-2 initially to prolong D5 over a tonic pedal, which then descends a third to B 4. The C5 in measure 5 is then interpreted as related to the opening D5, and from this C5 the line continues its harmonized descent to F4. In this scenario, the overall descent in Part I is a sixth, not an octave, and the F4 at the cadence is understood as an inner voice, above which I have supplied C5 in parentheses. At the deepest level, then, the opening D5/I is understood to progress by step to C5/V, which is picked up immediately after the double bar. This C5 then progresses to B 4 over tonic harmony in measure 10, above which D5 ( 3) is reinstated by the descent of a third from the covering F5. The E 5 that is introduced in measure 18 and subsequently prolonged until its resolution in the bass in measure 25 eventually descends a third to C5 at the cadence. This is a very complex passage that should be studied carefully. In this interpretation the D3 in the bass is seen not only as the resolution of the dissonant E 5, but also as passing between C3 and E 3 in the bass. In fact, there is a large-scale step progression in the bass from the B 2 in measure 16 to the F3 in measure 27, which is highlighted by the extended stems and overarching slur in Example A6.5.

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Example A6.5

Analytic Graph of Bach, Partita I, Sarabande

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CHAPTER SEVEN 1. Mozart, Divertimento K. 563 (II) This movement is in extended rounded binary (ternary) form, similar to the second movement of the Piano Sonata K. 280 discussed in the text. The first part is divided into two extended phrases, identified in Example A7.1 by the roman numerals I and II; the phrases are separated by an eight-measure transition. The first phrase is divided into two parts, the first (mm. 1-8) characterized by the sustained chords and arpeggiation figure, initially stated by the cello and then embellished by the violin. The second part, which involves imitation between violin and cello, begins with the thirty-second note upbeat to measure 9, which takes us up to C6, identified in Example A7.1 as the primary tone ( 3). This second part is further divided into two subphrases: mm. 9-12, which concludes with the descent of a third from E 5 to C5, harmonized by a deceptive progression; and mm. 13-18, which ends with a perfect authentic cadence harmonizing the descent from C5 to A 4. The final measure of this phrase (m. 18) overlaps with the following eight-measure transition, which modulates to the dominant. The second phrase begins as an elaborated version of the opening idea, which leads to a brief dramatic digression in VI (C ) on its way to a perfect authentic cadence in the key of the dominant. Closure is avoided at the last minute, leading to a six-measure internal expansion of the phrase.

Example A7.1 shows the initial arpeggiation in the violin part from E 4 to E 5, above which C6 is then introduced. This is important because the inner-voice tone E 5 plays a significant role in this phrase. In fact, if Schenker were describing this movement, I believe he would say that the tonal space of this movement is C6 over E 5 over the bass note A 2. Immediately after C6 ( 3)is introduced, the melodic focus shifts back to E 5, which is initially extended by the descending third E 5 - D 5 - C5 harmonized by the above-mentioned deceptive progression, then reintroduced by its upper neighbor by the process of reaching over, that is, E 5 reaching up to G 5 to introduce the neighbor note F5 from above. This motion plays a significant role later in this movement, where it occurs a fifth higher and extended over a longer span to prepare the return to the opening. This phrase then ends with the descent of a third to closure in the lower octave, above which C6 is immediately restated.

The eight-measure transition descends from C6 to G5 harmonized by a progression leading to the key of the dominant. This brings us to the second phrase beginning in measure 26, where the lower two strings state the sustained chords while the violin arpeggiates up to G6, which is initially prolonged by its upper neighbor. This leads to a modal change (G 6) and the digression in C ( VI), which supports the descent G 6 - F 6/F 4 - E 4/E 6, again harmonized by a deceptive progression, where vi in C = iv in E ; this harmony is subsequently prolonged by a chromatic voice exchange transforming the minor subdominant into a German augmented sixth chord leading to the cadential six-four and five-three. Though a complex passage, I believe the voice leading is shown clearly in the graph. For reasons of space, I have not written out the sixmeasure expansion of the phrase resulting from avoidance of closure. If we now consider the overall motion from the beginning of the transition to the completion of the phrase, we see that the top voice has descended a sixth from C6 to E 5, divided into a fourth C6 - G5 (transition) and the third G5 (m.26) - F5 (m. 37) - E 5 (m. 44). At yet a deeper level of structure, the fundamental line is understood to progress from C6 ( 3)over tonic harmony to B 5 ( 2), supplied in parentheses in the graph, harmonized by V.

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Example A7.1

Analytic Graph of Mozart, Divertimento K. 563 (II), 1-44

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Example A7.2

Analytic Graph of Mozart, Divertimento K. 563 (II), 45-80

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A graph of the b section, an eighteen- measure digression prolonging the dominant, is provided in Example A7.2. Modal change, which was introduced in the previous phrase, beginning in measure 30, is reintroduced by Mozart at the outset of this b section, which opens with the initial idea – the sustained chords and arpeggiations in the cello part – in E minor with the top voice on B 4 ( 2). This leads via a German augmented sixth chord to a C major chord, which is extended over the next five measures. The function of this chord, which supports the upper neighbor of B 5, is ambiguous. Will it become the dominant of F minor (vi) or possibly a third divider between dominant and tonic, as occurs in other works by Mozart? Neither proves to be the case.

Instead the harmony progresses though a diminished seventh chord to ii in the original key, which then leads to V7 with the seventh transferred to D 6 in anticipation of the return to C6 several measures later. Now the function of this harmonically unsettled passage becomes clear, namely, to introduce the seventh above the fifth of the dominant ( 2): V5-7 .

2. Schubert, Impromptu Op. 90. No. 2, 1-52 The A section of this Impromptu consists of eight phrases grouped in a ternary design, the last extended by several measures to prepare the modulation to vi (B minor), the key of the B section. The formal-tonal design of the A section is as follows: a 1-8 I a' 9-16 I a'' 17-24 I b 25-35 i b' 36-43 III V7 trans.

44-51 a' 52-59 I a' ext. 62-82 I - i - III (= V of vi) Example A7.3 presents an interpretation of the voice leading up to measure 52. At first glance and hearing, the continuous eighth-note triplet motion and resulting octave displacements may seem difficult to interpret, but in fact the underlying structure is clearly articulated. First, note that there is one change of harmony per measure, which persists throughout this section except in the transitional passages. Second, note the relationship in phrase 1 of the outer voices of the tonic chords on the downbeat on measures 1, 3, and 5: G5 over E 3 to E 4 over G3 to G4 over E 3.

They are related by voice exchanges between successive pairs originating from and returning to the stability of tonic harmony supporting scale degree 3. I have identified the upper octave, G5, as the primary tone ( 3). If we set aside the passing harmonies in measures 2 and 4 for a moment, we see that the opening G5 progresses to F5, first harmonized by ii6 on the downbeat of measure 6, then by V7 in the next measure, leading to E 5 near the end of measure 8. Likewise, the G4 on the downbeat of measure 5 leads to closure in the lower octave. If we now go back to examine the opening measures in greater detail, we see that the tonic chord in measure 1 supports a descending sixth from G5 to B 4. In the next measure, the top voice progresses from A 4 down to B 3, though the defining interval here is the diminished fifth A 4 to D4, as shown in the graph.

This interval predicts a resolution to G4 over E 4, which is why I have supplied the G4 in parentheses in measure 3, though in reality the resolution is temporarily taken by the bass and G4 is not reinstated until two measures later by means of its upper neighbor. The “tricky” part of

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sketching this passage is deciding how much information to include or exclude. The following phrase begins the same, but closes only in the upper octave. In the graph I have identified a secondary line in the inner voice by means of a broken beam, the ascending fourth B 4 to E 5.

The third phrase is a replica of the first an octave higher.

As we find so often in Schubert’s music, the contrasting material begins with a modal change to the parallel minor, which involves a change of 3to 3.The first b phrase is eleven measures long, the first eight prolonging 3/i, and the next three consisting of a cadential pattern leading to local closure. The first eight measures comprise a descending fifth sequence of seventh chords, in which the upper two parts alternate 10-7 intervallic progressions above the bass, as indicated between the staves. The following variant of the phrase is in the key of G ( III). Here again the melodic motion begins from the covering tone B 4, but instead of descending to G 4 and on to local closure, as it had done in the preceding phrase, it ascends by step in parallel motion with the bass to G 5. This is followed by the retransition, which extends the dominant and its seventh in both octaves in preparation for the return of 3and tonic harmony. Overall, measures 25-51 progress from i through III (both supporting G ) to V7 (supporting the upper neighbor).

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Example A7.3

Analytic Graph of Schubert, Impromptu Op. 90, No. 2, 1-52

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CHAPTER EIGHT 1. Mozart, Piano Sonata K. 332 (I) There are several special features of this sonata movement that should be noted before we embark on a graph of its voice-leading structure; to aid in this discussion, I have provided a chart of its formal-tonal design in Figure A8.1. First, note that the initial theme has two parts, both of which conclude with a perfect authentic cadence, the second followed by a brief extension restating the descending fifth (scale degrees 5 to 1) in two octaves. This is followed by a transition (T1), which enters rather unexpectedly on C leading to D (forte) after a brief pause; this takes us to the expected goal, V of V, in preparation for the second theme. This second theme, which is a parallel period, was given as an assignment in Chapter Two. (See Example A2.6 for an interpretation of its voice-leading structure.) This is followed by a second transition (T2) that leads us once again to V of V. The following closing theme does not begin as expected from the tonic in the local key, but with the subdominant, and it ends with an imperfect authentic cadence. Its expanded repetition then achieves closure in the local key, which is confirmed by the following closing phrase. This third or closing theme was given as an assignment in Chapter Three. (See Example A3.2 for an interpretation of its voice-leading structure.) Since the second and closing themes have been dealt with previously, I will provide a graph here of only the first part of the exposition, the first theme and following transition.

The development section opens with an eight-measure phrase that is ostensibly a new idea, but, as we shall see, it shares characteristics with both themes 1 and 2. This phrase is then repeated an octave lower, followed by an extension that is based on the second transition (T2). The goal of this ascent back to the upper octave is the A major chord in m. 123, similar to what we have observed in the development sections of both the first and third movements of K. 280. Here the return to tonic harmony and theme one is achieved via an important connecting dominant. We will return to this later on. The recapitulation then follows the same order of events as in the exposition, the only change occurring in the transition to lead to V rather than V of V, thus keeping the remainder of the recapitulation in the tonic key.

A graph of the first theme and following transition is provided in Example A8.1. The hypermetric organization of both parts of theme 1 is quadruple. The movement opens with an ascending arpeggiation of the tonic triad to C5, which I have identified as the primary tone ( 5).

(More will be said about this later.) The gesture of mm. 1-2 is answered in mm. 3-4, but with a shift to the upper octave after the initial note, B 4, leading to F5 over A4. As shown on the graph, the main melodic motion of these opening measures is C5 - B 4 - A4 over a tonic pedal.

In the immediate continuation the descent extends to F4, above which C5 is reintroduced by its upper neighbor D5. When the right-hand part in mm. 5-6 is taken by the left hand, the right hand ascends by step back to A4, picking up the A4 from the second beat of measure 5. This ascent of a third from F4 to A4 becomes a clear link between the two parts of this theme. Once A4 is reestablished on the downbeat of measure 9, C5 ( 5) is re-introduced once again by its upper neighbor, while the inner voice completes its descent to local closure. Overall, then, we can trace a descending fifth across the twelve measures, broken into two thirds, above which C5 is retained.

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FIGURE A8.1: FORMAL-TONAL PLAN OF MOZART K.332 (I) EXPOSITION Theme 1 1a 1b Transition (T1) Theme 2 antecedent consequent Transition (T2) Closing theme statement expanded repetition Closing phrase DEVELOPMENT Phrase Repetition Extension RECAPITULATION Theme 1 1a 1b Transition (T1) Theme 2 antecedent consequent Transition (T2) Closing theme statement expanded repetition Closing phrase

1-12 12-20/22 22-40

I (PAC) I (PAC) leads to V of V

41-48 49-56 56-70

C (V): I - V I- V- I leads to V

71-76 77-86 86-93

IV - I

94-101 102-109 109-123, 123-132

I (= V in F)

133-144 144-152/154 154-156

I (PAC) I (PAC) leads to V

177-184 185-192 192-206

I-V I- V- I leads to V

207-212 213-222 222-229

IV - I

I

F: III

I

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Example A8.1

Analytic Graph of Mozart, Piano Sonata K. 332 (I), 1-41

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In some respects theme 1b is contrasting to 1a (new register and rhythmic articulation), yet the two parts are clearly related motivically as well as in their voice-leading patterns. It opens with the descending arpeggio of the tonic triads from 5in the upper octave, followed by the ascending third F5 - G5 - A5, a very clear reference to mm. 7-9. Following a second statement of the descending fifth idea, the inner voice completes its motion to local closure, as had occurred in the lower octave in mm. 9-12. This is followed by the two statements of the descending fifth that punctuate the end of the first theme, at the same time summarizing all that has come before.

The transition then begins unexpectedly after a brief pause with the introduction of a D minor chord (vi) supporting an arpeggiation to A5, creating not only a motivic link to the beginning (the ascending arpeggiation) but a registral link to theme 1b. Here the important inner-voice tone A5 emerges as primary, which is prolonged in the immediate context by its upper neighbor. The hypermeter is still quadruple, but in measure 31 the pattern changes to duple (3 x 2), an acceleration accompanying the push to the goal, V of V supporting G5. As shown in Example A8.1, A5 is prolonged by a descending third A5 - G5 - F 5 before resolving to G5 in preparation for theme 2, which subsequently descends a fifth to closure in the key of the dominant. Example A8.1 also shows that this melodic motion A5 - F 5 occurs in conjunction with a middleground chromatic voice exchange with the bass, a common occurrence in transitional passages. To understand this, you must realize that the controlling bass is F (carried over from the end of theme 1) and that the D minor chord at the beginning of the transition is the result of the voiceleading motion 5 - 5 – 6 above this conceptual bass note F. Speaking from a harmonic perspective, the tonic harmony at the end of theme 1 has become the pivot, the subdominant, in the modulation to the dominant. The subdominant in the new key is then prolonged by a chromatic voice exchange that transforms the F major chord into a German augmented sixth chord, which resolves to V in the new key.

Let’s return briefly to the matter of primary tone and underlying structure of this movement.

Both parts of theme 1 strongly articulate 5as the primary tone with a prominent inner voice that descends from 3to 1.Scale degree 3 then emerges as the top voice in the transition leading to scale degree 2 in preparation for the second theme. There is no strongly articulated connection between 5and 5,and I must assume it is the lack of a clear 4(B ) that has led some to interpret the structural descent from 3,which, in my mind, denies the inherent “fifthness” of each of this movement’s themes. Let me suggest, instead, that the structure of this movement is best understood as analogous to what we found in the third movement of K. 280, that is, a primary tone of 5that is retained until its descent in the recapitulation, below which 3progresses to 2.I think this interpretation of the fundamental structure is preferable either to reading a structural descent from 5to 2within the exposition, though I have done so previously, 1 or to ignoring the importance of scale degree 5 and reading a structural descent from 3.Indeed, 4is not strongly represented from a structural perspective in the exposition, but this is not the case in the recapitulation, where there are clear structural descents in both the second and closing themes.

A graph of the development section is provided in Example A8.2. The opening eight-measure phrase is related structurally to the first theme, and its opening resembles the way the second 1 See David Beach, “The Initial Movements of Mozart’s Piano Sonatas K. 280 and K. 332: Some Striking Similarities”,

Integral 8 (1994): 125‐146.

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theme begins from an inner voice, though here E5 is introduced by arpeggiation rather than directly. Structurally 5in the local key is prolonged by its upper neighbor while the lower third descends to local closure. I have also identified an inner-voice ascent over these eight measures from G4 to C5. This phrase is then repeated an octave lower, and the following extension, based on the second transition (T2), regains the original octave position by the process of reaching over. The goal of this motion is the A major chord (III ) in m. 123, and the underlying voice leading of the development up to this point is G5 - G 5 - A5 supporting the descending third in the bass C - B - A, harmonically V - It. 6 - III . Like both movements of K. 280 examined in the text, the space between V and I seems to have been divided into two thirds, C - A and A - F, which may be taken as an enlargement of the underlying design of the opening theme. However, when Mozart returns to this upper register with B 5 over the passing dominant in mm.131-133, the meaning of the A major chord as a goal is potentially changed. First, let me say that the way Mozart introduces this high B strikes me as mischievous. To this point in the movement, Mozart has avoided a strong statement of B ; now he states it tentatively, like a distant echo (piano) in this upper register, but he doesn’t resolve it there until m. 156! 2 So what are we to make of this? It strikes me that there is a fundamental dichotomy between the design and the underlying structure, though I suspect my colleagues might not agree with this assessment. The design, the division of the space between V and I by III , is clear. But the introduction of B 5/V suggests a different function of the A major chord, namely, to offer consonant support for the passing tone A5 between the fifth and seventh of the underlying structural dominant. Otherwise one is forced to interpret this B as the upper neighbor of the previous A5, a theoretically feasible solution, I guess, but one that seems forced rather than intuitively correct musically.

2 Mozart seems to be fond of leaving the seventh temporarily unresolved in the same register, thereby creating a

registral link across formal boundaries when it finally does resolve. See, for example, the end of the development section of the first movement from his last quartet, K. 590, where B 5 is left temporarily unresolved in that register. There can be no doubt about the primary tone in this movement. It is C5 ( 5).

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Example A8.2

Analytic Graph of Mozart, Piano Sonata K. 332 (I), 94-134

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2. Mozart, Piano Sonata K. 310 (I) A diagram of the formal-tonal plan of this movement is provided in Figure A8.2. The exposition consists of two distinct themes, the second followed by a closing idea that is repeated in varied form (with left- and right-hand parts inverted) and a codetta or final phrase that returns to the dotted rhythmic pattern of the opening idea. The first theme consists of an antecedent phrase that leads to the dominant in A minor and a consequent phrase/transition that leads to V of III. The second theme (in C major) has an unusual design, an opening four-measure idea followed by a nine-measure phrase that grows out of its varied repetition and which leads to a perfect authentic cadence in the new key. This theme was discussed in Chapter Three of the text; see Example 3.8 and the accompanying discussion. The closing idea then confirms the melodic arrival at scale degree 1 in the new key ( 3), while the final phrase not only returns to the rhythmic character of the opening but also anticipates the return to 5.The development section consists of an initial eight measures based on the opening idea followed by two sequences, the first leading to the subdominant, and the second leading to V in preparation for the return. The recapitulation follows the same order of events as the exposition with minor alterations, the main one being the recomposition of the consequent phrase of the initial theme to lead to the dominant in the tonic key. The remainder of the movement remains strongly rooted in the minor mode.

A graph of the first theme and transition to the second theme is provided in Example A8.3. The movement begins with a clear emphasis on E5 ( 5), which is identified as the primary tone.

Ostensibly this E5 is decorated by its lower neighbor twice in the opening measures, but, as indicated by my notation, a more accurate account of the voice leading shows this dissonant D5 leading to C5, above which E5 is superimposed. This may seem unnecessarily awkward to some, but I am being careful here to show the proper resolution of the dissonance. The top voice then moves to the upper neighbor F5 in measure 6, from which it descends as if to lead to an interruption. As shown in the graph, this descent divides into two lines, the lower one reaching to B4, but the upper one reaching only as far as D5. Instead of progressing to C5 over A4, as occurs in the equivalent place in the recapitulation, this resolution does not follow (as indicated by the V-like symbol in the graph) and instead E5 is once again re-instated via the lower appoggiatura D 5.

The consequent phrase begins like the antecedent, this time with E5 decorated by both neighbor notes, F5 and D 5. In the fourth measure B 4 is introduced and then transferred to the upper octave, a motion later repeated in the development section. This introduces A5, which then descends a third to F5 (the first two notes of which are elaborated motivically) in parallel tenths with the bass. This brings us to measure 14, marked calando by Mozart. The bracket above the graph here shows that what is being brought out is the double neighbor- note figure decorating E5. Furthermore, by delaying the entrance of E5 until the very end of the measure, we hear E5 associated once more with an A minor chord, albeit in passing and now as vi in the new key.

This gives way to D5 ( 4), which continues on to the inner-voice tone B4, immediately covered

by G5 over the dominant. Not shown is the extension of the phrase and theme 2, which descends a fifth from this covering G5 to C5 ( 3)in measure 35.

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FIGURE A8.2: FORMAL-TONAL PLAN OF MOZART K. 310 (I) EXPOSITION Theme 1 antecedent consequent = trans.

Theme 2 Closing idea statement varied statement Codetta/closing phrase DEVELOPMENT Dev. of theme 1 Sequence 1 Sequence 2 and ext.

RECAPITULATION Theme 1 phrase 1 phrase 2 Theme 2 Closing idea statement expanded statement Codetta/closing phrase

1-8 9-22 22-35

A mi. i - V I - V of III C(III): I6 - V - I

35-40 40-45 45-49

I I I

50-57 58-69 70-79

I 7 = Ger. 6 B7 - E7 - A7 A mi. iv – V

80-87 88-103 104-116

i- V i- V i

116-121 121-129 129-133

i i i

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Example A8.3

Analytic Graph of Mozart, Piano Sonata K. 310 (I), 1-16

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A middleground graph of the development section is given as Example A8.4. The first eight measures are based on a single harmony, the C major chord, to which Mozart adds the lowered seventh B , which is subsequently rewritten as A , creating an augmented sixth chord. Within these eight measures Mozart twice decorates the bass note C by its upper neighbor D , but the third time he writes C , even though this note functions in the immediate context as D . There is no clear explanation for this curious anomaly, except perhaps that Mozart was thinking ahead to the goal of the following sequence, the D minor harmony (iv) in measure 70. Returning now to the augmented sixth chord, it resolves to the B major chord in measure 58, the beginning of sequence 1, which progresses every four measures from B8-7 to E8-7 to A8-7 to the D minor chord in measure 70. A metric representation of the counterpoint of the first step in this sequence is given below the graph. There is a direct registral connection between measures 50 and 70, which continues through the next sequence to measure 74, the descent of a third G5 - F5 - E5 supported by the harmonies III - iv - V . This covering line prepares the return of 5,while the fundamental line progresses to interruption, as shown in Example A8.4. The second sequence is a diatonic progression by descending fifths leading first to an A minor chord, which offers consonant support for the passing tone E5 within the encompassing prolongation of iv by chromatic voice exchange. Note that the melodic approach to E5 in measure 74 is via its neighbors F5 and D 5, as occurred in the opening theme. In fact, the augmented sixth chord resulting from chromatic alteration of the subdominant is a vertical expression of these two decorative pitches. If we now look back over the entire development section, we see that the middleground structure, the descent of a third from G5 and the corresponding harmonic steps, are clearly articulated by changes of surface design. Corresponding with the major points of articulation is an acceleration of the harmonic rhythm: one harmony for eight measures (mm. 50-57), a change of harmony every four measures (sequence 1) to two harmonies per measure (sequence 2); once arriving at the goal (V), Mozart extends it for four measures, re-establishing the quadruple hypermeter.

Example A8.4

Analytic Graph of Mozart, Piano Sonata K. 310 (I), 50-80

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For both assignments in this chapter – the first movements of K. 332 and K. 310 – I have provided sketches of only parts of the movements. These plus the sketches supplied elsewhere in this document or in the text, cover most parts of their expositions and development sections. The next step is to investigate changes made in the recapitulations and how these affect the structural voice leading.

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CHAPTER NINE The one assignment in this chapter is to identify the established motive that pervades much of Beethoven’s Piano Sonata Op. 110 in the Arioso preceding the fugue. The motive in its complete form is 5654 3;sometimes it occurs without the initial scale degree, that is, as 654 3.The Arioso is written in the key of A minor with a Dorian key signature, requiring Beethoven to write the flat before F throughout. It is preceded by an eight-measure introduction: Adagio/recitative.

A detailed graph of the Arioso is provided in Example A9.1. The opening descent from E 5 to A 4 is answered by Gq4 to F 5, the upper neighbor, which returns to E 5 in measure 11.

(Remember that the Arioso begins in measure 9.) So the Arioso begins with an immediate reference to the neighbor- note feature of the motive. This is followed by a reaching up to A 5 to introduce the neighbor this time from above. As shown in the graph, the top sounding line then descends by step to C 5 on the downbeat of measure 13, completing a full statement of the motive. Measure 13 is also the beginning of the next phrase, and careful examination reveals the composing-out of an entire octave ascent from C 5 to C 6 in parallel tenths with the bass, above which a partial transposed statement of the motive is superimposed: A 6 - G 6 - F 6 - E 5 or 65 43in C (III). Transfer of the last note to the lower octave (E 5) returns the music to the point of origin. The third phrase now reintroduces the upper neighbor F 5, once again by the process of reaching over, which is followed by a stepwise descent to Gq4. The resolution of this dissonant interval F 5 - Gq4 would normally be to E 5 over A 4, which explains the parenthetical E 5 in the graph. Instead Beethoven transfers the resolution to an inner voice, E 4, and he goes out of his way to bring this to our attention by the insistent decoration of this pitch by both lower and upper chromatic neighbors. This final phrase is certainly the most complex to unravel, but we are aided greatly by Beethoven directing our attention to this inner voice. If we now follow this lead, we see and hear that this inner voice descends by step from E 4 to C 4, completing the motive. If our attention had strayed due to all that is going on above this line, it is pulled back by the extension of the phrase in parallel octaves with the bass, which brings the descent to closure and prepares the entrance of the following fugue subject, which no doubt is Beethoven’s reason for transfer to this register. (As an aside, note that the fugue subject ends with a clear reference to the motive.)

Meanwhile, the top sounding part above this line makes reference to the motive or parts of it in the original octave. Though the D 5 on the downbeat of measure 21 is approached from below, the graph suggests that we might also interpret it as related to the parenthetical E 5 two measures earlier, in which case we can posit a descent of the entire fifth to closure, covered one last time by the F 5 - E 5 reference to the motive.

Example A9.2 suggests how we might understand the entire Arioso as expressing a single overarching statement of the motive. The transfer of the final note of the partial transposed statement of the motive to E 5 in measure 16 signals a prolongation of that pitch from the beginning of the Arioso, that is, across two statements of the motive, supported by a bass motion from A (i) to C (III). The following phrase then progresses to the upper neighbor supported by the subdominant, which leads to V; the return to E is subsequently transferred to the inner voice over a tonic chord in first inversion. Understood from this perspective, measures 9-21 articulate only the initial part of the expanded statement, E 5 (mm. 9-16) - F 5 (mm. 18-20) - E 4 (m. 21), which is then completed in the final phrase in the inner voice. This is a prime example of what Schenker refers to as a motivic enlargement or “hidden” repetition.

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Example A9.1

Analytic Graph of Beethoven, Piano Sonata Op. 110 (Arioso)

Example A9.2

Middleground Graph of Beethoven Arioso

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CHAPTER TEN I will provide the text, translation and brief commentary about each of the four songs discussed below. Most of my commentary will be directed at the voice-leading structure of each setting and matters relating to their interpretation.

1. Mozart, “Ach, ich fühl’s,” The Magic Flute, Act II. Libretto by Schikanaeder.

At this point in the opera, Tamino, along with Papageno, have agreed to undergo the trials imposed by the priests of the temple. The first trial is silence, and though Tamino is allowed to see Pamina, he is not permitted to speak to her, and when she approaches, he signals for her to go away. This aria is Pamina’s response to this rejection.

Ach, ich fühl’s, es ist verschwunden ewig hin der Liebe Glück!

Nimmer kommt ihr, Wonnestunden, meinen Herzen mehr zurück!

Ah, I feel it is lost forever the joy of Love!

Never will hours of rapture return again to my heart!

Sieh, Tamino, diese Tränen fliessen, Trauer, dir allein.

Fühlst du nicht der Liebe Sehnen so wird Ruh im Tode sein!

See, Tamino, these tears flow for you alone, my beloved.

If you do not feel the yearning of love, then there will be rest in death!

Mozart’s setting follows the division of the text into two stanzas, the second greatly expanded by a nine measure insertion delaying closure. As we observed in the aria “Dies Bildnis ist bezaubernd schön” from Act I, which was analyzed in the text, repetitions of portions of the text are significant components of Mozart’s setting. The first two lines of text progress from tonic to dominant in G minor (mm. 1-5), and it is repetition of the second line of text that extends the dominant and the following brief transition to the key of B (III). The third and fourth lines, where Pamina speaks of rapture, is set in the new key, coming to local closure on the downbeat of measure 16. This phrase is also extended by repetition of the second of two lines of text, in this case three statements of meinen Herzen mehr zurück, each statement more elaborate than the previous one. The setting of the second stanza is more complex, involving numerous repetitions, not only of entire lines but of key words/phrases (dir allein, der Liebe Sehnen, etc). As noted above, closure is avoided by a nine measure insertion; here the final two lines of text and its various components are repeated several times. Even after closure has been achieved on the downbeat of measure 36, we hear two more statements of im Tode sein.

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Example A10.1

Analytic Graph of Mozart, “Ach, ich fühl’s”, Magic Flute

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In this text I have stressed the importance of hypermetric organization (or lack of the same) in works we have examined. In this aria we encounter an interesting situation, namely, that there is a perceived hypermeter, at least in its first half, but this does not correspond with the notated meter. I hear the entrances of the voice at the beginning of the first and third lines (Ach and Nimmer) as hypermetric downbeats, and after some experimentation I decided to renotate my graph in 3/8, that is, so that each of Mozart’s measures appears as two measures in Example A10.1. The aria then begins with an upbeat measure, and the first hypermetric downbeat coincides with Pamina’s entrance. This establishes a clear quadruple hypermeter in the renotated meter, which lasts until Mozart’s measure 20, where there is a metric reinterpretation. Though it is possible to continue in this manner, the hypermetric structure becomes less well defined in the latter half of the aria due to multiple repetitions. Perhaps this is a reflection in a way of Pamina’s increased agitation. I have a “solution” to these measures (measures 20-36 in Mozart’s score) written on my copy, but I have not transferred it to the graph, because I’m simply not quite sure.

This is an interesting problem for advanced students to tackle.

A graph of the opening phrase of the aria - Mozart’s setting of the first two lines of the text and the following transition - is provided in the top system of Example A10.1. The opening melodic note, D5, is identified as the primary tone ( 5), which is subsequently prolonged by its upper neighbor and then by a linear descent to A4 supported by the dominant. The repetition of the second line of text extends D5 and the dominant, which is followed by the harmonization of the upper neighbor of D5 as seventh of the dominant of III. This E 5 resolves back to D5, now harmonized by III, above which F5 is superimposed to initiate the next phrase.

The third and fourth lines of text, including the repetitions noted above, are set in the key of B (III). The overall melodic motion is a descending fifth from F5 to B 4, which is divided as follows. First F5 is prolonged by a descending third involving a transfer to the lower octave: F5 E 4 - D4; this is followed by an ascending fifth from the inner voice tone B 4 back to F5 over first inversion tonic harmony in the local key, followed immediately by the final statement of meinen Herzen mehr zurück. This is where the line descends to local closure, the notes of which are temporarily obscured by the elaborate setting. There is something ironic about this passage.

Indeed, Pamina is speaking about rapture, but the overall meaning of these lines is far from uplifting. The meaning of B major (III) in the larger tonal scheme is clear; it is part of an ascending bass motion from tonic to dominant. But the melodic emphasis on F5 and the eventual perfect authentic cadence seem almost a denial of reality. This is a dream world. The following duet between oboe and voice, where one can almost feel the sobs behind the tears, returns us to the real world of D5 and dominant harmony in the original key. We are, in fact, back where we left off at the end of the first phrase.

A graph of the final portion of the aria (beginning in Mozart’s measure 20) is provided on the bottom system of Example A10.1. As occurred in the opening phrase, D5 is prolonged by its upper neighbor, now over a dominant pedal, followed by a linear descent to an inner voice. D5, supported by tonic harmony in first inversion, is then reinstated via its upper neighbor, followed immediately by a descent directed toward closure, which is delayed by a deceptive progression initiating an extended insertion. I have not provided an interpretation of this interpolation, which provides an opportunity for several repetitions of the final two lines of text, for practical reasons of space.

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2. Schubert, “Du bist die Ruh” (Rückert) Du bist die Ruh, der Friede mild, die Sehnsucht du, und was sie stillt.

You are rest, gentle peace, you are longing and what appeases it.

Ich weihe dir voll Lust und Schmerz zur Wohnung hier mein Aug und Herz.

I dedicate you full of joy and pain to the dwelling place here my eye and heart.

Kehr ein bei mir, und schliesse du still hinter dir die Pforten zu.

Come to me and quietly close the gate behind you.

Trieb andern Schmerz aus dieser Brust!

Voll sei dies Herz von deiner Lust!

Drive other pain from this breast!

Let this heart be full of your joy!

Dies Augenzeit, von deinem Glanz allein erhellt o füll es ganz!

This tabernacle of eyes is brightened only by your radiance.

O fill it completely.

Schubert’s setting of these five stanzas has the following formal design: A (stanzas 1 and 2) - A (stanzas 3 and 4) - B (stanza 5) - B' (stanza 5 repeated). Each one of the musical periods ends with the repetition of the final line of text, and each, except the last, ends with a perfect authentic cadence in the tonic, which contributes to the sense of rest and peace. In the final section (B'), the vocal line ends on scale degree 5, leaving closure to occur in the piano part two measures later.

This larger formal scheme of A A B B' is reflected in the detail setting of A: a a b b'.

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Example A10.2

Analytic Graph of Schubert, “Du bist die Ruh”

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A graph of the crucial parts, but not all, of “Du bist die Ruh” is provided in Example A10.2. The top system shows the voice leading of the piano introduction (mm. 1-7) and A (mm. 8-26 = mm.

31-48); the lower system shows the voice leading of the B' section (mm. 68-82). The piano introduction presents the two components of the opening vocal line in order, first the neighbornote pattern B 4 - C5 - B 4 and then E 5 - D5 - E 5, the latter covered by B 5, itself an important feature of this song. In addition, there is a clear descending fifth from B 4 to E 4 identified in the graph. The initiating tone, B 4, is identified as the primary tone ( 5), and this descending fifth in the piano introduction anticipated the fundamental line of the song. In short, the seeds for all that follows is contained in this introduction, as we find so frequently in Schuberts songs. The basic hypermeter of the song is quadruple, though not expressed entirely clearly in this seven measure introduction. I have considered various options to explain this “irregularity”, including 1 - - - 2 3 4, which strikes me as the most logical, if indeed we must somehow understand this group of seven as an expansion of an underlying quadruple pattern. Looking ahead, it is interesting to note that the piano interlude following both A and its repetition, that is, mm. 26-30 and 49-53, is five measures in length. By this point in the song, the underlying hypermeter is well established. We hear these five measures as 1 2 3 4, 1 (or 1 2, 1 2, 1), and when the voice enters, the result is successive downbeat measures. An interesting tonal feature of this interlude is the interaction of c and cq ( 6 and q6), which not only introduces a negative element into the discourse but also anticipates the dramatic setting of the final stanza. These elements, both tonal and metric, suggest a sense of tension underlying what is otherwise a very peaceful setting.

The setting of the first two stanzas (A) opens with a four measure idea featuring the neighbornote patterns B 4 - C5 - B 4 and E 5 - D5 - E 5. This idea is repeated, clearly establishing the quadruple hypermeter. This is followed by a contrasting idea that further prolongs the primary tone by upper and lower neighbors. Repetition of this idea is extended from four to six measures, in which the final line of text, mein Aug und Herz, is repeated as the vocal line descends to local closure.

Following these local and larger repetitions, which have a tendency to create a sense of complacency, the dramatic setting of the final stanza, itself repeated in slightly varied form, comes as quite a surprise. The vocal line opens with the motion from 5to its upper neighbor, now C 5 rather than Cq5, but instead of returning to B 5, the line continues to rise through a series of superpositions and overlappings (reaching over). The goal of this motion is G5 supported by tonic harmony, but once again we are surprised by the addition of 7, propelling the music forward to A 5, the real goal, supported by the subdominant harmony. As shown in the graph, the rising sixth B 4 - G5 occurs within a tonic prolongation leading to IV, which provides support for 4in the following descent to closure. As noted above, final arrival at 1is left to the piano, the vocal line holding steadfastly to scale degree 5.

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3. Schumann, “Widmung” (Rückert) This song, along with the others in Myrthen, Op. 25, was written by Schumann as a wedding present for his bride, Clara Wieck. It expresses his deepest emotions and feelings for her. The Rückert poem consists of two verses, each of six lines, where the final word in each pair rhymes.

Schumann creates a ternary structure (A B A') from this by forming a third verse from the first five lines of the first verse and the last line of the second.

Du meine Seele, du meine Herz, du meine Wonn’, o du mein Schmerz, du meine Welt, in der ich lebe, mein Himmel du, darein ich schwebe, o du mein Grab in das hinab ich ewig mein Kummer gab!

You my soul, you my heart, you my joy, o you my sorrow, you my world in which I dwell, you my heaven in which I hover, o you my grave into which I eternally placed my grief!

Du bist Ruh’, du bist Frieden, du bist von Himmel mir beschieden.

Dass du mich liebst, macht mich mir Wert dein Blick hat mich vor mir verklärt, du hebst mich liebend über mich, mein gutter Geist, mein bess’res Ich!

You are rest, you are peace, you are sent to me from heaven.

That you love me makes me worthy, your glance at me glorifies me, you elevate me lovingly above myself, my good spirit, my better self!

The metric organization of this song is very regular. Following an upbeat measure, the hypermeter is consistently quadruple until the very end, where the final metric group of the vocal line is extended from four to six measures in the final descent to closure. As shown in Example A10.3, there is a metric overlap at this point of arrival (measure 39). The A section concludes with a perfect authentic cadence in the tonic key (A ). A potentially difficult decision for the inexperienced analyst is the choice of primary tone, because one could marshal evidence for either 5or 3.This could be an interesting topic for class discussion. Consider, for example, measures 11-13. There is a clear descent of a fifth from E 5 to A 4. This does not necessarily mean, of course, that the primary tone is 5,but we should know in advance how to interpret and notate our interpretation in either case. If 5,then 3in the structural descent to local closure occurs in conjunction with the cadential six - four. (Despite rumors to the contrary, this is a common tonal phenomenon.) If 3,then the cadential six-four is understood to support a passing tone in the descending third introducing 2.This does not answer the question, but it is important to understand these two ways of interpreting and notating this one progression depending upon our choice of primary tone. As it turns out, the choice is not all that difficult. Despite the emphases given to E 5 and its upper neighbor, it is C5 ( 3) that is given stable support by root position tonic harmony. If we look ahead to the B section, which is written in the key of E major (enharmonically F or VI), we see that it ends on an A major chord (IV) with C 5 in the vocal part. This C 5 becomes D 5, the seventh of the dominant in the original key, as preparation for the return to C5/I. Finally, note that in the piano postlude the gesture 321is stated twice. So in Example A10.3, the primary tone is identified as C5, and E 5 is shown to serve a secondary though important role.

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Example A10.3

Analytic Graph of Schumann, “Widmung”

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Example A10.3 shows the initial prolongation of C5 ( 3) and tonic harmony in mm. 2-6 by means of a voice exchange between the outer voices. E 5 is a cover tone and the function of F5 here is to introduce B 4, the middle member of the descending third C5 - B 4 - A 4, from above. (At the same time, the employment of F5 here strongly predicts either its return or that of E 5 later, which indeed is the case.) Immediately following this initial voice exchange is a reverse one reinstating C5 over A 2. With the addition of G 3 in the bass, this harmony leads to the subdominant, where there is yet another voice exchange between the outer voices involving the introduction of F5 from above. This F5 eventually leads to E 5 over tonic harmony in first inversion on the downbeat of measure 11, which is followed by the cadential progression discussed above. Meanwhile this F5 leads to B 4 on the downbeat of measure 10, a replica of the motion of mm. 4-5. The result is a varied statement of the original voice exchange, which I have indicated in the graph by dotted lines, since the descent in the top voice is to an inner voice covered by the motion to E 5. That is, this voice exchange is technically not “legitimate”, since it involves three voices, yet I felt it was important to indicate somehow the derivation of this passage from mm. 3-6. Finally, note the employment of F as coloration of the supertonic harmony in measures 5 and 10, which nicely anticipates the key of the B section.

The B section is contrasting not only in key ( VI) but in accompaniment and the slower pace of the vocal part, at least in the initial measures. However, after the first four measures, the voice leading of measures 18-23 is very clearly based on that of measures 3-7. That is, within the local key, 3and tonic harmony are prolonged by an initial voice exchange, followed immediately by its reverse reinstating 3/I. Internal to the initial voice exchange is an embedded one involving local prolongation of the supertonic harmony. Here and in similar situations care must be taken not to create a confusing jumble of lines in the graph. As already noted, this area of prolongation is followed by a motion to the subdominant in the local key, again involving a voice exchange between the outer parts leading to C 5 over A2. This A major (B major) chord is heard as II in the original key, and the C 5 becomes the seventh of the dominant (D 5) preparing the return to the primary tone and tonic harmony.

The initial six measures of the A' section are a repeat of mm. 2-7. The difference comes in the drive to closure, which follows immediately. Here the emphasis is given to the supertonic harmony instead of the subdominant as preparation for the following dominant, thus introducing B 4 ( 2). Following yet another voice exchange, 2is approached, at least by implication, from its upper third. Though I have supplied the passing C5 and following B 4 ( 2) in parentheses, they are actually stated an octave lower, while the voice makes one final reference to the covering F5 - E 5.

4. Schumann, “Frühlingsfahrt” (Eichendorff) See Jürgen Thym, “Text-Music Relations in Schumann’s Eichendorff song ‘Frühlingsfahrt’,” Chapter 3 in: Of Poetry and Song: Approaches to the Nineteenth-Century Lied (University of Rochester Press), 2010.

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5. Brahms, “Wie Melodien zieht es mir” (Groth) In addition to the brief commentary/analysis below, you should consult Edward Laufer’s analysis of this song in the Journal of Music Theory 15 (1971), 34-57.

Wie Melodien zieht es mir leise durch den Sinn, wie Frühlingsblumen blüht es, und schwebt wie Duft dahin.

Like melodies it flows gently through my mind.

Like spring flowers it blossoms And floats there like a scent.

Doch kommt das Wort und fast es und führt es vor das Aug, wie Nebelgrau erblasst es und schwindet wie ein Hauch.

But the word comes and expresses it and brings it to the eye.

Like grey mist it fades And vanishes like a puff.

Und dennoch ruht im Reime verborgen wohl ein Duft, den mild aus stillen Keime ein feuchtes Auge ruft.

And yet there lies well concealed in rhyme a scent which from its secret germ gently summons a damp eye.

The “it” in Groth’s poem is not defined. It is something intangible, like the idea of beauty. One imagines it, but words cannot adequately express it. Only through rhyme (poetry) can one convey its essence. Brahms sets the three verses in parallel fashion, by which I mean that each begins with the same material before leading to a different goal. In the first two verses, Brahms repeats the last line; in the last he repeats the last two lines. A graph of Brahms’s setting of the three verses is provided in Example A10.4.

The song opens with an arpeggiation to C 5 ( 3), which is introduced by its upper appoggiatura (incomplete neighbor). This is followed by a filled- in descending arpeggiation to F 4 supported by the subdominant harmony and then the chromatic passing tone Fq4, supported by II6 , which leads to E4/I in m. 5. This emphasis on the subdominant and its modal coloration (Fq) supported

by II is exploited by Brahms in his setting of verses II and III. This opening phrase is followed by a voice exchange between the vocal line and bass, further prolonging 3/I. These opening seven measures are repeated almost exactly at the beginning of the following two verses, and it is only their continuations that differ. In all cases the continuation is a variant of the preceding vocal line within the voice exchange. That is, the melodic idea has a similar rhythmic articulation and descending contour. Here, in verse I, the continuation leads to the dominant, which is subsequently prolonged by its own statement of this motivic idea, a setting of the repetition of the final line of text, und schwebt wie Duft dahin. Example A10.4 shows the underlying voice leading, which is somewhat disguised by octave transfers, to be 8 – q7 supported by V leading back to 3/I. This dominant is extended for a fifth measure, for the first time stretching out the clearly established quadruple hypermeter.

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Example A10.4

Analytic Graph of Brahms, “Wie Melodien zieht es mir”

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The continuation of the second verse extends the descent begun in measure 18 to F 4 supported by the subdominant in measure 22. Following the transfer of F 4 to F 5, there is a descent of an entire octave back to F 4, now supported by vi (m. 25). The two-measure extension of this metric unit from 4 to 6, which introduces the chromatic passing tone Fq4 once again, makes it clear that this motion to vi exists within a local prolongation of IV/iv leading back to I. In short, the continuation in this verse further develops the subdominant and its modal inflection.

In the final verse, the continuation beyond the voice exchange leads first to qVI (Fq) in measure 36, whereupon A4 is transferred to A5 to initiate a descent in parallel thirds. The harmony supporting this descent is qVI to II to the German augmented sixth chord at the end of measure 39, where the voice introduces Fq4 once again. This Fq resolves as expected to E4 (ein feuchtes), but the bass, instead of resolving to A to support a cadential six-four, moves chromatically up by step, above which D5, the upper neighbor of the primary tone, is introduced to lead to C 5 over tonic harmony in first inversion (a repetition of ein feuchtes). Now it becomes clear that the excursion to qVI - II - V, which supports an extension of the chromatic passing tone Fq, exists within a tonic prolongation. Once C 5 and tonic harmony are introduced, this is followed immediately by the closing cadence, with melodic closure occurring in the lower octave. You might recall that in the second verse the final metric group and subdominant harmony were extended from 4 to 6 measures due to a repetition of text. Here the extension of the final group is from 4 to 8 measures. Not shown in this graph is the four-measure piano postlude, which confirms closure with a plagal progression, further emphasizing the subdominant.

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INDEX OF MUSICAL EXAMPLES BACH Cello Suite I, Menuet I Little Prelude in D Minor (BWV 926) Partita I, Sarabande Violin Partita III, Menuet I

33-34 31-32 37-38 35-36

BEETHOVEN Piano Sonatas Op. 2, No. 1 (II), 1-8 Op. 2, No. 2 (II), 1-19 Op. 10, No. 3 (II), 1-9 Op. 14, No. 1 (II), 1-16 Op. 14, No. 1 (II), 1-51 Op. 31, No. 2 (III), 1-16 Op. 110, Arioso

8 18-20 7-8 11 20-21 6-7 56-57

BRAHMS “Wie Melodien zieht es mir,” Op. 105, No. 1

67-69

MOZART “Ach, ich fühl’s,” The Magic Flute Divertimento K. 563(II) Piano Concerto K. 491 (II), 1-19 Piano Quartet K. 478 (II), 1-19 Piano Sonata K.310 (I), 1-16 and 50-80 K. 310 (II), 1-8 K. 331 (II), trio K. 331 (III), 1-24 K. 332 (I), 1-41 and 94-134 K. 332 (I), 41-56 K. 332 (I), 71-86 K. 494, rondo theme K.545 (II), 1-32 K. 576 (I), 1-8 String Quartet K. 421, Menuetto String Quartet K. 590 (I), 1-16

58-60 39-42 17-18 13-14 51-55 9-10 26-27 23-24 45-50 10 14 8-9 23-26 10-11 28-30 16

SCHUBERT “Du bist die Ruh” Impromptu Op. 90, No. 2, 1-52 Impromptu Op. 142, No. 2, trio Piano Trio No. 2 (I), 1-35 Symphony No. 9 (II), 1-29

61-63 42-44 28-29 16 14-16

SCHUMANN “Widmung,” Myrthen Op. 25

64-66

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