Some Notes on Analyzing Wagner: "The Ring" and "Parsifal"Author(s): David LewinSource: 19th-Century Music, Vol. 16, No. 1 (Summer, 1992), pp. 49-58Published by: University of California PressStable URL: http://www.jstor.org/stable/746619Accessed: 27/07/2010 15:06

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Rehearings

Some Notes on Analyzing Wagner: The Ring and Parsifal

DAVID LEWIN

Example la sketches the Tarnhelm motive from Das Rheingold as first heard; ex. lb sketches the modulating middle section of the Valhalla theme, again as first heard. For many years I had sensed some underlying relation be- tween the two passages, without being able to put my finger on it. In my recent book, Gener- alized Musical Intervals and Transformations, I tried to work out a suitable relationship using networks of Klang transformations. Figure 1 re- produces figure 8.2 from the book.' There is a misprint: what is incorrectly written as "(G ,-)" on the left of figure la should be written as "(G ,-)."

The bracketed harmonies on the figure are understood as interpolated transformational

stages in the networks. LT signifies Riemann's Leittonwechsel transformation: the two notes spanning the minor third of a triad are pre- served, while the third note moves a semitone to form a new triad of the opposite mode. The transformation SUBM makes a given triad the submediant in the key of the transformed triad. I was eager to assert SUBM between the opening and final harmonies of figure la; this made me assert B major, but not B minor, to be functional at the end of ex. la. (Wagner uses both major and minor harmonizations in the course of the Ring and Tristan.)

In the book (p. 178), I say that exs. 2a and 2b "make visually clear a strong functional rela- tionship" between the two passages, "a rela- tionship which it is difficult to express in words." The relationship is difficult to express because the analysis is bad. It is bad for at least three methodological reasons that I can spot. Criticism (a): There is no point asserting "a strong relationship" without being able to

19th-Century Music XVI/1 (Summer 1992). ? by The Re- gents of the University of California.

'David Lewin, Generalized Musical Intervals and Trans- formations (New Haven, 1987), p. 179.

49

19TH CENTURY

MUSIC a. Tarnhelm motive, Das Rheingold, sc. 3, mm. 37ff.

(muted Hn.)

-low TVn

IP"Jig b. Modulating section of Valhalla theme, Das Rheingold, sc. 2, mm. 5ff.

(Trpt., Tbn.) " "

WI (Tuba) I _ Tb

? V

-- resc.

--Die Burg ist ganz -sichtlich geworden.

L AV AV-btM S 1 64

?Fd r:im.24

L4

.

*

mnf ~~dim.pp

Example 1

specify just what the relationship is. All things are "related" in the Great Chain of Being. Crit- icism (b): Figure 1 does not lead us deeper into the music of ex. 1, or into other pertinent music, or into dramatic ideas about the Ring. Criticism (c): Figure la, as it stands, is techni- cally malformed by the criteria of GMIT. (The criteria are developed only later in the book, but that is beside the point in this connection.) While I felt the dissatisfactions of criticisms (a) and (b) most keenly, I was unable to make progress until I became aware of (c) as well; this

gave me a point of departure for improvement. Figure 2 will help us to explore the specific way in which figure l a is malformed.

It is true, as figure la asserts, that GO minor is the submediant of B major, and that the Leittonwechsel of G# minor is the subdomi- nant of B major. Symbolically, the equation of figure 2a is true: applying the transformation SUBM to the particular Klang G# minor has the same effect as applying, to that particular Klang, first the transformation LT and then the transformation SUBD. But the equation of figure 2b is not true. In general, if one applies

SUBM to a Klang, the result will not be the same as if one applies first LT and then SUBD. Figure 2c shows how this works when the Klang in question is, for example, C major; ap- plying SUBM to C major yields a different re- sult than does applying first LT and then SUBD. The chord of which C major is the submediant is not the same as the chord of which the Leit- tonwechsel of C major is the subdominant.

Because the equations of figures 2b and 2c are false, the functional equation of figure 2d is false. And so the configuration of arrows and ar- row-labels on figure la is malformed by the cri- teria of GMIT (9.2.1 [D], p. 195). As soon as I no- ticed the malformation, it occurred to me that the SUBM arrows of figure 1 were problematic in other ways as well. The SUBM arrow of figure la, for instance, was forcing me to assert B major and ignore B minor, where Wagner's music suggests both B major and B minor equally. Bringing B minor into figure la along with B major forms a suggestive analogy to the F major and F minor of figure lb. Then, too, why should I assert a SUBM relation in figure lb between Gb major and the bracketed Bb

50

REHEARINGS a) [(E, +)]

LT SUBD

tPAR

(G ,-) (E,-) (B, +)

SUBM

b) SUBM

[(Bb, -)] (F, -) (A, +)

SUB j PAR $PAR

(D,+) SUD ) (G, +) (Bb, +) (F, +) SSUBD

DOM SUBD

meas. 1-6 7 9 11; 13 141/2-20

Figure 1

Reprinted from Generalized Musical Intervals and Transformations by permission of Yale University Press.

a. true: (g#) SUBM = ([g#]LT) SUBD

B = ( E ) SUBD; correct.

b. false: (any Klang)SUBM = ([that Klang)LT) SUBD

c. false e.g.: (C)SUBM = ([C]LT) SUBD

e = ( e )SUBD ??; wrong.

d. false: SUBM = LT SUBD

Figure 2

minor? Why not assert a Leittonwechsel here, making another suggestive analogy between figures la and lb? Rethinking my analysis along these lines, I quickly arrived at the new network analyses of figure 3.

In these graphs the Leittonwechsel, subdom- inant, and parallel transformations have been abbreviated as L, S, and P respectively. The new analyses are much better than the old. They specifically respond to each of the three earlier

51

19TH CENTURY

MUSIC

a. b.

S S

e b B F

LP LP

P P P P

g [E] B D) GK----[bb] f (A?

L L

Figure 3

criticisms. In response to criticism (c), the graphs of figure 3 are well formed. I particularly emphasize this point because when a graph is well formed, one is apt simply to take that for granted. I want to stress once more that it was just this criterion which enabled me to work out the better analyses, with consequences we shall shortly examine.

The new analyses also respond to criticism (a). A very specific relationship can now be as- serted between the two passages: they admit of isographic analyses under the interpretations of figure 3. That is, the configurations of nodes and arrows are the same, on figure 3b as on figure 3a; furthermore there is a certain privi- leged way of relating transformations that makes the transformations of figure 3b analo- gous to those of figure 3a as they label their re- spective arrows. Here the privileged relation- ship is very strong-it is absolute identity. To the extent that transformations here play the role of extended formal "intervals," there is a quite precise sense in which figures 3a and 3b demonstrate the same tune in different modes. That is, they run through the same configura- tion of "moves," differing only in the place where they begin their journeys. One asserts a specific and very strong relationship when one makes precise a sense in which the Tarnhelm and the modulating section of Valhalla can

be described as "the same tune in different modes."

Finally, this way of regarding the two pas- sages leads suggestively deeper into the music, responding to criticism (b). One reason I had felt a relationship between Tarnhelm and Val- halla in the first place was that the two the- matic ideas grow to interact more and more as the Ring progresses. Example 2 shows the pas- sage in which one first becomes strongly aware of the interaction, the climax to act II, sc. 2, in Die Walkiire.

There is not space here to discuss the Tristan harmony which engulfs the opening A? minor, or the Gold motive at the end, or the fantastic rhythmic detail, or all aspects of the vocal line. That being said, one can hear clearly enough that the opening Tristan harmony enlarges Ah minor, and one hears E minor at the end. The large progression of Al minor to E minor evi- dently elaborates the first two harmonies of the Tarnhelm motive. Furthermore, the notes with stems up on the top staff of ex. 2 clearly consti- tute a transformation of Valhalla - the opening, rather than the middle section of that theme. Example 3 works the transformation out in some detail.

Example 3a puts the opening of the Valhalla theme in Al major and indicates the most ac- cented harmonic gesture of the two measures,

52

REHEARINGS WOTAN (mit bittrem Grimm sich aufrichtend)

So nimm meinen Se - gen, Nib - lun - gen Sohn!

3

3dim. ~- piup

Example 2: Die Walkii•e, act II, sc. 2, climax.

namely the inflection of the tonic by its sub- dominant.2 One gets from ex. 3a to ex. 3b by following the first descending P-arrow at the

right of the example: ex. 3b puts all of ex. 3a into the parallel minor. To get from ex. 3b to ex.

3c, one then follows the descending L-arrow: ex. 3c transforms the chords of ex. 3b into their

respective Leittonwechsels, starting from the third chord on. Then ex. 3d transforms the chords of ex. 3c into their parallels, starting from the fourth chord on. The effect of the var- ious vertical arrows is logged by the transfor- mational analyses that build up beneath exs. 3b, 3c, and 3d. The various transformations in- volved here, namely S, P, and L, are exactly the transformations involved in the earlier net- works of figure 3, networks that established a

strongly isographic relationship between the Tarnhelm and the middle section of the Val- halla theme.

Figure 4 emphasizes that aspect of the anal-

ysis by juxtaposing two networks. Figure 4a re-

produces figure 3a, the Tarnhelm analysis which is isographic to the middle section of the Valhalla theme. Figure 4b puts into analogous form the transformational analysis from be-

neath ex. 3d; this is the analysis of the Tarnhelm-infected Valhalla Kopf at "So nimm meinen Segen."

Figure 4 shows how the gradual corruption of the pure Valhalla theme, logged by the progres- sive transformational encrustations of exs. 3a, b, c, d, is actually the systematic working out of a transformational scheme already implicit within the middle section of the Valhalla theme itself; that middle section, in its isog- raphy with the Tarnhelm motive, already con- tains the potential for Valhalla's corruption. Just so does the progressive deformation of Dorian Gray's portrait merely log the potential for corruption already implicit in the narcis- sism of the beautiful youth himself.

Indeed, the "bitter rage" of Wotan in ex. 2 is aroused not so much by the frustration of his plan as by his dawning awareness of the corrup- tion necessarily inherent in the plan itself. The very idea of Valhalla contains at its center the source of its own corruption, and Wotan's be- coming aware of the fact here moves him be- yond political action, suffering, and anger to tragic self-awareness.

There is a significant technical feature of the work so far that contributes to problems in this sort of post-Riemann transformational anal- ysis. In figure lb we saw Gb major analyzed as the submediant of B? minor, whereas in figure 3b, an alternate analysis of the same passage, Gb major was analyzed as the Leittonwechsel of B? minor. One can easily imagine other con- texts in which one could assert yet other Riemann-type relationships between the two Kldnge. For example, Gk major is the parallel of

2The dominant harmony that supports the penultimate note of ex. 3a is omitted on the sketch. To include it, and to carry along its transformations through the later stages of ex. 3, would be to complicate the analysis needlessly for present purposes. The omission is not to be construed as an implicit assertion that less accented, smaller-scale har- monic features, such as those supporting melodic passing tones, are "less important" in some unspecified aesthetic sense.

53

19TH CENTURY

MUSIC

a.

it" Valhalla in Abmajor.

F? •

Put it all in parallel minor.

IDENT

b.

Valhalla in g minor.

I.W Apply Leittonwechsel to all chords from the third one on.

S1 I 1 [no. 3 on]

IDENT

C.

Next transformational stage. EVE

Apply parallel transformation to all chords from the fourth one on.

[no. 4 on]

LD

L

d.

W,1 :J

- I,

:; MFinal stage of example 2.

I I

L P

LP

Example 3: Transformations of Valhalla theme.

G' minor, which might progress along a chain of subdominants through D? minor, Ab minor, and E& minor to Bb minor; in this context one could assert Bb minor as "PSSSS" of Gl major. To sum the matter up, there is no unique Riemann-type relationship abstractly specified by the notion of starting at Gb major and ar- riving at Bl minor; the system makes a number of transformations conceptually available, each of which abstractly carries Gl major to Bl minor. In mathematical language, one says that the pertinent group of transformations "is not simply transitive."

Wagner interweaves such multiple relation- ships with particular craft. To explore some of his art we shall now examine a number of inter- related passages from Parsifal. Example 4a

shows aspects of the opening, which presents the Communion theme. The theme is written under one slur; essentially following Lorenz, I have articulated it into three sections, namely an incipit motive, the Schmerzensfigur, and the Spear motive.

Example 4b aligns beneath the Communion theme the first statement of the Grail motive in the opera. The alignment shows how the Grail harmonies reference and summarize salient features from the overlying incipit and Spear motives. The Grail, as heard in ex. 4b, does not reference the central Schmerzensfigur of ex. 4a at all.

Below ex. 4b appears a harmonic analysis. The final cadence, which involves character- istic scale activity not taken directly from the

54

REHEARINGS a. b.

S S

e -b e

LP LP

P P P P

g # [E] B g E [A]

L L

Figure 4

overlaid portion of ex. 4a, is analyzed using tra- ditional scale degrees, Roman ii, V, and I. Up until that final cadence, the M-arrows assert each harmony of ex. 4b as the mediant of the next. The chain of M-arrows coexists comfort- ably with the chain of falling diatonic thirds in the trombones, and with the regular rhythm of the harmonic changes during this portion of ex. 4b.3 Abstractly one could assert the progression from Ab major to F minor as a "relative" rela- tion, and likewise the relation from Db major to Bb minor. Since the progression from F minor to Dk major, however, cannot be ana- lyzed as a "relative" relation, such an analysis would break the chain just discussed. The break in the chain would feel particularly un- comfortable, because a smooth and homoge- neous transition from F minor to Db major, in the middle of ex. 4b, serves the very particular purpose of gliding unnoticeably over the missing Schmerzensfigur references. It seems awkward to draw attention to the lacuna, which would happen to the extent one hears the f-Db progression in the middle of ex. 4b as somehow specially marked. The critical point is all the more cogent when one observes that the most likely abstract candidate for an f-DM

relation here, other than the M-relation of ex. 4b, would be specifically a Leittonwechsel rela- tion. The Leittonwechsel is the most character- istic harmonic feature of the Schmerzensfigur in ex. 4a; there the Leittonwechsel supports a climactic downbeat when the high Ab moves to high G. To hear f-Dr in ex. 4b as a Leitton- wechsel would then be to draw particular at- tention to a Schmerzensfigur that is missing at this point, rather than to glide surreptitiously over its absence.4

Example 4c, also aligned beneath ex. 4a, shows the special role reserved for the Leitton- wechsel relation in the context of the Com- munion. Contour, dynamics, and floating- versus-beating metrics spotlight the climactic Leittonwechsel from A? major to C minor, and the return to Ah by Leittonwechsel. As ex. 4c suggests, the progression inflects the theme as a whole, not simply the Schmerzensfigur and its immediate continuation. The Schmerzens- figur is, to be sure, the special focus of the rela-

3The chain of falling thirds in the trombones is the source of the "Helpful Kundry" motive.

4If one plays over the incipit and Spear motives of ex. 4a without the Schmerzensfigur, connecting the end of the in- cipit bracket directly to the beginning of the Spear bracket, one can hear the f-D6 progression as a Leittonwechsel. One can specifically hear the agogically accented D6 of the Spear melody stepping up from the C within the incipit material, rather than stepping down from the Eb of the missing Schmerzensfigur. The analysis is latently possible to that extent and worth exploring to that degree.

55

19TH CENTURY

MUSIC

a. Communion motive, act 1, m. 1. incipit Schmerzensfigur Spear

I I O I

p f p pi__p

b. Grail motive, act I, m. 39.

PLcresc.

C. [ii V ]

p fA

L L

Example 4: Parsifal

tion; one wonders if Wagner was consciously exploiting a pun on Leidton.

Example 5a shows the consequent, C-minor variant of the Communion theme. Below this, ex. 5b aligns a succession of harmonies that can be inferred from the melodic activity - one must remember that the tempo for the written quarter note is "Sehr langsam." The harmonic analysis below ex. 5b shows how profoundly the structure of the theme has changed, in the pertinent transformational system.s At the very beginning of ex. 5b, the progression from C minor to Ab major is not analyzed as a mediant

relation, following the precedent of Ab -f at the beginning of ex. 4b; rather the c-Ab that opens ex. 5b is analyzed as a Leittonwechsel. That is because we associate the specific tonality-and- harmony of C minor, in relation to the tonality- and-harmony of Ab major, with the paradigm of the Schmerzensfigur in ex. 4c, and the large- scale Leittonwechsel relation that spreads out over ex. 4c therefrom. Unlike ex. 4a, the theme of ex. 5a is articulated by several different slurs; the first of these slurs sets off the opening c-At progression just discussed.

The leading tone of C minor appears climac- tically at the proper moment in ex. 5a. Because of the augmented second in the melody, sup- ported by the slurring of the theme here, how- ever, one does not hear C-minor return before the sforzando on the high B. Instead the Ab re- mains frozen in the melodic line, continuing to project Ab-major harmony, so that when the sforzando B? occurs, the effect is to change AT major to the parallel Ab minor, as indicated by the P-arrow below ex. 5b. As the exact intervals of the Schmerzensfigur are subsequently reca- pitulated, the earlier Ab of the melody in ex. 5a continues frozen under the B? , so that the im- plied harmony moves on from Ab minor to E major, via a new Leittonwechsel. The end of the Schmerzensfigur finally restores the me-

5One might go so far as to say that the analysis calls into question the extent to which ex. 5a should be called a "variant" of ex. 4a, rather than a new idea. Exploring the question, one notes that the two melodies, if analyzed as series of diatonic places, coincide exactly in their intervals up to the fourth note of the Spear motive. Both melodies rise a third from their point of departure, then rise another third, then rise a step and repeat the note, rise a step, rise a step, fall a step, and so forth. In the system of transfor- mations containing such gestures, the melodies have iso- graphic profiles. There is thus a profound divergence be- tween the diatonic world of the music and its Riemann- functional world. The reader will find that idea developed at greater length in my article, "Amfortas's Prayer to Ti- turel and the Role of D in Parsifal: The Tonal Spaces of the Drama and the Enharmonic CG/B," this journal 7 (1984), 336-49.

56

REHEARINGS a. Act I, m. 20.

44- -1-- - I -t$- -5- ---- b.

L P L P L P [V i] L

c. Act III, m. 1098.

p P L [ii V 1]

Example 5: Parsifal

lodic G, but by now the harmony has changed so that the melodic move from A6 to G sounds in a local context of E harmony: the effect is from E major to E minor, as indicated by the second P-arrow beneath ex. 5b. The Spear mo- tive returns us to the local tonic, now C minor, as did the Spear motive before, in Ab. In ex. 5a the C-minor version of the motive is changed so as to put extra emphasis on the early return of E6 in the melody; the change is supported by the end of the second slur in the theme. The overall harmonic effect, from E minor at the end of the Schmerzensfigur, is through C major and back to C minor via yet another L transfor- mation and yet another P transformation.

Overall, then, the transformations below the left side of ex. 5b go through a complete cycle of alternating Ls and Ps, starting and ending at C minor. Once C minor has returned, it is con- firmed by a scale-degree, dominant-tonic pro- gression as indicated, supported by the third slur of ex. 5a. The melody within that slur cre- scendos to another sforzando on the low B of that dominant, restoring the leading-tone func- tion of the B in C minor. By association of dy- namics, and by octave equivalence of extreme registers in the melodic ambitus, the gesture re- calls the earlier frustration of C-minor leading- tone function in the upper register at the climax, where we heard local A -major and local Ah-minor harmony.

The foregoing discussion has clarified, I think, what an error it would be to assume that the first arrow beneath ex. 5b should bear the same transformational label as does the first arrow beneath ex. 4b, simply because ex. 5a be- gins as a diatonic transposition of 4a. Example 4b shows a chain of diatonic mediant relations supporting the first and last sections of the theme; the chain of mediants is immersed in the larger-scale diatonic Leittonwechsel of ex. 4c, which bursts into the foreground to in- terrupt the chain of mediants during the Schmerzensfigur. Example 5b shows a thor- oughly chromatic chain of alternating L and P transforms, owing its closure to a mathemat- ical symmetry rather than a diatonic context. Example 5b may be regarded as a trope on the Schmerzensfigur, which provides both the L idea, and the idea of moving to C minor as a setting for ex. 5, whence the whole system of alternating Ls and Ps arises via the A -B rela- tion as discussed.6

Just as ex. 4b is the version of the Grail mo- tive that goes with ex. 4a, so ex. 5c is the ver-

6The reader is again referred to my article, "Amfortas's Prayer,"

a propos the diatonic-and-Riemannian worlds of

the drama. Important work on the form-building potential of L-and-P chains, and of such transformational algebra in general, has been carried through by Brian Hyer in a recent study, Tonal Intuitions in Tristan und Isolde (Ph.D. diss., Yale University, 1989).

57

19TH CENTURY

MUSIC

sion of the Grail that goes with ex. 5a. One sees how ex. 5c fits ex. 5a precisely because of the analysis that underlies ex. 5b. Example 5c oc- curs almost at the end of the entire opera, eight measures before the final chorus, at the stage direction "Allmihliche sanfte Erleuchtung des 'Grales"' (gradual soft illumination of the Grail).

In the Ring, the L and P relations of the Tarnhelm are involved in the corruption of Valhalla. In Parsifal the same transformations

become equally associated with suffering, minor, and chromaticism; however, they lead through suffering to salvation, durch Mitleid wissend. The musical difference, I think, is that the L and P relations of Parsifal chain together and eventually build complete cycles that return to their points of departure, as in exs. 5b and 5c. In the Ring, the open-ended application of LP rather disrupts and de- stroys, as in the relation of exs. 3d to 3a.

58