Instructor Manual for Advanced Schenkerian st Analysis 1 Edition By David Beach. NOTE. (Lecture Teaching Notes Only)
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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 5 is 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 B4 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 B4 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 B4 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 B4, 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 B4, 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 B4, supported by IV, and from this B4 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 3 to 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
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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 fivethree. 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 2 does 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 - B4 - 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 2 and 1 in this lower octave.
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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, F5 (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. F5 then progresses to E5 via the descending third G5 - F5 - 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 2 1 supported 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 3 to the opening tonic chord and 2 to 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 3 is 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 F4 (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
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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 B4, 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 B4 (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 B4 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
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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 E 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
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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 5 in 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 5 is 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 5 is 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 2 is extended not by a single measure but by 8!
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Example A3.3
Analytic Graph of Schubert, Symphony No. 9 (II), 1-29
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Now back to our original example. In the consequent phrase, the motion to closure is by implication only (3 and 2 are 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 5 by 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.
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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 B4 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 B5 replacing scale degree 2. The b phrase prolongs the dominant and 2 (F5) by an ascending progression up to B5 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.
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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 F4 (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 F4 on the downbeat of measure 5 to the one on the downbeat of measure 7 and the corresponding bass from D2 (I) to F2 (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