Jody Nagel
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Pitch Structure and Dramatic Association in
The Murder Scene of
Alban Berg's
Wozzeck

 
 
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Pitch Structure and Dramatic Association in
The Murder Scene of
Alban Berg's
Wozzeck

 
by Jody Nagel
for Professor Douglass M. Green
The University of Texas at Austin
December 18, 1986.
 
The important atonal pitch structures of Wozzeck have certainly already been demonstrated and commented upon by many other writers. These include, of course, the groundbreaking works of George Perle and the important set-theoretic work on Wozzeck by Janet Schmalfeldt. The main purpose of this paper, then, will be to build upon the ideas of these writers, with an emphasis on the approach taken by Schmalfeldt, in order to show in detail the dramatic association of pitch structure and the dialogue between Wozzeck and Marie immediately preceding her demise.
 
First, however, it seems important to review the overall design of Act III, Scene 2: the "murder scene."
 
Wozzeck and Marie are walking at dusk along a forest path. There is a pond nearby. Marie would like to hurry home but Wozzeck says that she must be tired from walking and insists that she should sit down and rest with him for a little while. He speaks and acts so strangely that Marie becomes terrified. As Wozzeck draws his knife, she jumps up, trying to escape, but he manages to stab her and she dies. He bends over her, exclaiming the word "Todt" ("Dead"), and then he rises to his feet anxiously and silently rushes away.
 
Wozzeck's intention of killing Marie steadily began to form in Act II. He first notices her unexplained new earrings in Scene 1, and then he learned from the captain and the doctor in Scene 2 that she might be acting unfaithfully. After confronting Marie in the middle scene of the opera (II/3), Wozzeck cries out, "Mensch!" and is about to strike her when she screams the prophetic words, "Rühr' mich nicht an. Lieber ein Messer in den Leib, als eine Hand auf mich." ("Don't touch me. Better a knife in my body than a hand on me." - II/3, m.395.) Wozzeck has now been given the idea of murder consciously. In Scene 4, he sees Marie dancing with the drum major, and, in Scene 5, the drum major actually confronts Wozzeck asking him to drink with him to his new relationship with Marie. When Wozzeck refuses, the drum major easily forces him to the floor, choking him and leaving him barely alive. Wozzeck's idea of murdering Marie has now been completely formed.

This idea has, in fact, become an obsession for Wozzeck, and it is represented musically throughout the murder scene. It will be remembered that George Perle has identified a common sonority which closes each of the three acts. This cadential chord closes Act II in such a way that the pitches of the chord disappear one by one leaving one final low B-natural. This pitch-class is part of the tritone B-F. Werner König is quoted by Schmalfeldt as referring to this tritone as "the fate interval, the interval of the tormented creature," one whose "pitch relationship can recall a music-historical tradition (mi contra fa est diabolus in musica)."1 (König 1974, p.103.) The fateful tritone has significance throughout Wozzeck, but in Act III, Scene 2, it has extreme importance. The pitch-class B, foreshadowed at the close of Act II, is now found as an ostinato throughout the entire second scene of the final act, and Berg himself referred to this note as one of the five different "unifying principles" that govern each scene of the final act (Redlich, p.226).2  Perle refers to III/2 as an "invention on a note." This ostinato pitch-class B, then, here represents Wozzeck's obsession with killing Marie.
 

1 "Mi" refers to the pitch "B" as the third note of the diatonic (moveable) hexachord beginning on G, while "Fa" refers to the pitch "F" as the fourth note of the diatonic hexachord beginning on C.
2 The others are, of course, the unifying principles of the "theme" of Scene 1, the "rhythm" of Scene 3, the "six-note chord" of Scene 4, and the "equalized motion of notes" of the final scene. (Redlich, p.226.)

Additionally, the tritone's other pitch, F, plays an important role.

Throughout the murder scene (III/2), f is employed as a complementary tone-center: as the upper limit of the first sustained simultaneity in the orchestra (m.73); as a recurrent goal of motion (m.80); as the highest note or boundary note of segments of the vocal line. (Perle, p.139.)
Examples of Perle's indicated use of the note F are plentiful and are presented in the following excerpts.
 
1) "the upper limit of the first sustained sonority" (III/2, m.73). This example is Perle's, but actually this trichordal sonority (B, C#, F) quickly grows to include the higher pitches, Bb and D, so it is not his most significant example.
Example 1
 
 
2) "recurrent goal of motion" (III/2, m.80). Here, both notes of the fateful tritone are mirrored within the outer voices of the orchestra.
 
Example 2
 
3) Marie's first note of the scene (III/2, m.73).
 
Example 3
 
4) Wozzeck's first note of the scene (III/2, m.75).
 
Example 4
 
5) Marie's highest note of the phrase (III/2, m.76).
 
Example 5
 
6) Wozzeck's highest note and final note of a phrase (III/2, mm.84-85).
 
Example 6
 
7) Wozzeck's highest note of a phrase (III/2, m.89), and Wozzeck's final note of a phrase (III/2, mm.90-91).
 
Example 7
 
8) Marie's highest note of a phrase (III/2, m.93).
 
Example 8
 
9) Wozzeck's longest note of a phrase (III/2, mm.93-95).
 
Example 9
 
10) Wozzeck's first note of a phrase (III/2, m.100).
 
Example 10
 
The ostinato pitch-class B is itself also sometimes used in the vocal line in the way in which F has been shown to be used. Example 10 above exemplifies both notes of the fateful tritone in their use as "boundary notes." Not only do the pitches F and B constitute the first and last notes, respectively, of Wozzeck's line, they represent also the lowest and highest notes of an ascending line portraying the ascending moon and its resemblance to a bloody sword. The following excerpts contain B as the first or last note of the vocal line.
 
11) Wozzeck's final note (III/2, m.79).
Example 11
 
12) Wozzeck's final note (III/2, m.81-82), C-flat = B.
Example 12
 
13) Wozzeck's initial note (III/2, m.83).
Example 13
 
14) The solitary B, constituting the last note before the rising of the red moon (III/2, m.96).
Example 14
 
In Wozzeck's final words to Marie, and in her cry for help, the dyad B-F is clearly demonstrated. Wozzeck's line begins and ends with F, while Marie's "Hilfe!" is sung to pitch-class B, first in her highest register as she panics with horror, and then trailing off to her lowest register as she begins to die.
 
15) Wozzeck's first and last note F, Marie's note B (III/2, mm.102-103).
Example 15
 
It should be noted that the roles of the two pitches of the fateful tritone are reversed, according to Perle, in Act III, Scene 4, the scene where Wozzeck drowns in the pond nearby Marie's corpse.
The reiterated or sustained f in the top line of the orchestral part at salient moments in the formal design of III/4, as well as the prominence of f elsewhere in the scene parallels the reiterated or sustained b of the earlier scene, and just as f played a subsidiary but complimentary role within that scene, so b does within the later scene. (Perle, p.140.)
See, for example, III/4, m.220, where F is the highest note of the six-note chord, and III/4, m.246, where first the violin's and then the flute's ostinato octave leaps on F constitute the highest pitch of the passage.
 
Within the murder scene, form is generated based on the particular use of the ostinato note B. Each element of the dialogue between Wozzeck and Marie utilizes B in a slightly different manner. Perle formally divides III/2 into six sections. The present writer believes that the last section is enough differentiated and removed from the preceding sections that the labels A1, A2, A3, A4, A5, and B will be used to refer to each of the sections. The scene as a whole, then, is a two-part structure; the A-section includes all of Wozzeck and Marie's dialogue preceding the rising of the red moon. The B-section begins at m.97 as the red moon rises. This symbolizes red blood, and Marie's imminent death. The section begins with seven simultaneous octaves of pitch-class B accompanying the rising moon line.
 
Form
 
The ostinato occurs in each section as follows.
 
Section A1. The first section and the scene as a whole begins at m.73, but the low sustained B0 and B1 (the two lowest B's on the piano keyboard) actually began two measures earlier (in m.71) as the interlude following III/1 comes to a close. B0 is removed from B1 at m.73 and then rejoins B1 at m.75. In this section, Wozzeck convinces Marie not to hurry home but to remain and sit down with him for awhile.
 
Section A2. Starting with the last eighth-note of m.76, this section is characterized by B2 and its upper neighbor C#. The C#-B motion actually is prepared in the final notes of the bass clarinet on beat 2 of m.76. A written accelerando culminates on a trill between the two pitches, followed by a rapidly descending chromatic scale ending once more on B1, and then joined again by B0. Now Wozzeck suggests that Marie not walk further and make her feet sore. He observes that it is quiet and dark where they are (an ideal place for a murder).
 
Section A3. Beginning yet one more octave higher, on the second half-note of m.80, B3 is used as the point of departure and return for a "wedge," a characteristic Bergian structure where alternate successive notes become either further or closer to some fixed pitch. As shown in Example 2 above, the wedge is mirrored in the upper voice on the tritone complimentary pitch F. The section is pierced by regular occurrences of B6 in a solo violin (not shown in Example 2), this B6 anticipating the following section. At the end of the wedge, a written ritardando of the Cb-Eb trill comes to a finish as another octave of B is reached (B4). Descent from B4, B3, and B2 is made to B1. B1 is ornamented by its chromatic neighbors, C and A#, and is then followed by a further descent to B0 in the contrabass. Notice that the first of the contra bass' glissandos reaches upwards to F, once more stressing the fateful tritone.
 
Here, Wozzeck questions Marie as to how long they have known each other and how long their relationship will probably last. Marie says that she must go and Wozzeck asks her if she is frightened. He pretends to have no idea as to why she might possibly be afraid and his words are sarcastic: "But you are pious, and good, and faithful?"
 
Section A4. Each of the previous sections began with progressively higher octaves of B, and concluded by descending back to low B0. The steadily rising B creates tension as the scene unfolds. In Section A3, a hint of the upper register is given in the violin's softly articulated B6. Section A4 is preceded by a chromatic string glissando accompanied by a C-major glissando in the celesta and a Cb-major glissando in the harp, all lasting three quarter notes in duration. Beginning on the low B0, an ascent is finally accomplished all of the way up to a sustained octave tremolo on B5 and B6 in the violins and lasting throughout the section. The end of Section A4 is punctuated by three progressively shorter descending-octave ornamentations that produce the successive octave flutter-tongue tremolos on B3, B4, and B5 in the clarinet, trumpet, and flute (m.91, second quarter note, until m.92, first quarter note.)
 
Example 15b
 
With the B in a higher, "sweeter" register, Wozzeck says, "What sweet lips you have, Marie?" and kisses her. He continues, "I'd give up heaven and eternal bliss if I might go on kissing you. But I may not." The high B6-B5 tremolo in the violins comes to an end and, as described above, is replaced by the successive increasingly higher winds.
 
Section A5. The final section of A begins on the second quarter-note of m.92 as the xylophone initiates a regular interference of C-natural quarter-notes against the flute's flutter-tongued B5. Quickly however, the high register is lost once more as the trombones enter with B2 on the fourth quarter-note of m.93. A timpani tremolo then continues the B-C interference, now in the lower register, but halfway into m.44, a series of progressively shorter, articulated, ascending-octave ornamentations in the clarinet and bass clarinet replace the trombones and timpani:
 
      B2, B3, B4, B5       B2, B3, B4       B2, B3.
 
This octave pattern is the exact inverse of that found in the first violins at m.91, closing the previous section. In this section, Wozzeck asks Marie, "why are you shivering?" She replies, "The night dew is falling." Wozzeck says, "When one's cold, one doesn't feel the cold." Terrified, Marie says, "What are you saying?" but Wozzeck says, "Nothing," and they become silent.
 
The evolution of pitch-class B throughout the A-section, then, gradually ascended through the octaves, but finally ended in the lower register as Wozzeck himself utters the word "Nix" on B2.
 
Section B. The B-section begins as the moon begins to rise in m.97. It is represented by an ascending line in quarter-notes and repeated in stretto as a four-voice canonic fragment. Each of the lines is begun by a trombone and concluded by a trumpet, and each line begins one quarter-note sooner relative to the entrance of the preceding line. Marie's vocal part suggests a fifth part to the canon, but on her third note the time values are augmented to dotted quarter-notes.
 
Example 16
 
This canon is accompanied by the B ostinato in seven simultaneous octaves in the strings (B0-B6) and marked ppp. The rising moon seems to ascend through the atmosphere of Wozzeck's pervasive ideé fixe, represented by pitch-class B. In m.100, the octaves drop out one by one, from lowest to highest, and the discontinuation of each successive octave is punctuated by the harp. As the highest octave is dismissed, a timpani begins pounding a soft but insistent stream of B quarter-notes that increase in loudness to fff at the moment that Wozzeck kills Marie (m.103). The ostinato B then becomes increasingly softer until it is replaced by the harp alternating between B and its complimentary tritone-note F.
 
The final two crescendos on the single pitch-class B by the orchestra bring the scene to a close. The first crescendo consists of a rhythmic canon between wind and string entrances and takes place on the single pitch B3. The entrances of each instrumental group create the same rhythmic pattern that is found throughout the next scene. Here, the values are augmented by two as compared with the beginning of Scene 3.
 
Example 17
 
The violent chord struck at the beginning of m.114 contains the same six pitch-classes as found in the six-note chord of Act III, Scene 4. The bass drum sounds once more the rhythmic pattern of the following scene, this time with the same rhythmic values as actually found in the beginning of Act III, Scene 3.
 
The second crescendo on the pitch B utilizes four octaves (B1, B2, B3, and B4) and the crescendo takes place evenly in all instruments from ppp to fff.
 
The evolution of the pitch-class B within the murder scene can be summarized as shown below.
 
The Evolution of pitch-class B in Act III, Scene 2 of Wozzeck.
Example 17b
 
One final observation needs to be made. If we pursue König's idea that the B-F tritone, so important to this scene, represents an entire music-historical tradition, then we might as well remember what would be the proper voice-leading in a tonal resolution of this unstable dyad: namely, the leading-tone B would go to a C final. It must be noted that Wozzeck's final utterance of the scene is the word "Todt!" (m.106). It is sung on C3, a semitone higher than the timpani's B2. It is at this point that the timpani stops playing; Wozzeck's obsession has now been "resolved" by Marie's death.
Example 18
 
Now that the formal design of the scene has become more familiar, it is possible to consider in greater detail other musical devices and techniques used by Berg in order to reflect the dramatic situation prior to, and at the moment of, Marie's death. Consider the semitonal descent of the five-note chord at the end of m.73.
 
Example 19
 
The two highest intervals contained within this descending parallel structure are the same as those of the descending three-note structure at m.395 of Act II, Scene 3. The descending chord of m.395 is accompanied by a rising three-note structure in the lower register and, in fact, the upper five notes of, particularly, the chord on the first eighth-note of m.396 (II/3) is the same structure as that of m.73 (III/2).
 
Example 20
 
The descending lines of m.395 (II/3) occur when Marie says her important words, "Lieber ein Messer in den Leib,..." From this, an association is made in our minds between the knife and the chromatic line, and, from this point on, each time that the motive is used a suggestion at some level of awareness is being made of the knife. Associations of this type are referred to, of course, as leitmotive.
 

George Perle accounts for 20 musical fragments which have a leitmotivic nature throughout Wozzeck,3 and the descending line found at m.395 (II/3), at m.73 (III/2), and elsewhere throughout the opera, is referred to as "The Knife" motive.
 

3 For a complete list of leitmotive found in Wozzeck, see Perle, pp.96-117.

Of special interest in Act III, Scene 2 is the use of leitmotive at the actual moment of Marie's death. Nine distinct leitmotive are found in the eight-measure span from m.100 to m.107. Using the labels of Perle, they are as follows:
 
1. The Knife. m.100, beginning on the second half of the second quarter-note in the horns and bass trombone. First found in m.395 (II/3).
 
2. Wozzeck's Entrance and Exit. m.101, beginning on the last quarter-note in the piccolo. First found in m.427 (I/3).
 
3. Marie's Fear. m.103, beginning after the sixteenth-rest of the fourth quarter-note in the strings. First found in m.462 (I/3).
 
4. Drum Major's Posturing combined with the Seduction motive. m.104, beginning on the second sixteenth-note in the xylophone, horn, and strings. Drum Major's Posturing first found in m.666 (I/5); Seduction first found in m.673 (I/5).
 
5. Cradle Song. m.104, beginning on the second half of the second quarter-note in the piccolo. First found in m.372 (I/3).
 
6. The Earrings. m.104, beginning after the sixteenth rest of the third quarter-note in the strings. First found in m.7 (II/1).
 
7. Military March. m.104, beginning on the last quarter-note in the trombones and low winds. First found in m.334 (I/3).
 
8. Marie as Mother. m.105, beginning after the eighth-rest of the first quarter-note in the strings. First found in m.363 (I/3).
 
9. Marie's Endless Waiting. m.106, beginning on the second half of the third quarter-note in the violins, horns, trumpets, and flutes, and also in the harp. First found in m.415 (I/3).
 
In addition to those listed above, Wozzeck's Entrance and Exit leitmotiv is again found in m.107 in the bassoon, but in an almost perfectly inverted form and fixing the last two pitch-classes as an invariance. After the introductory Knife motive of m.100, then, the music surrounding the moment of Marie's death is framed by this Entrance and Exit figure. The inverted relationship, as well as a shift in register, suggests a "before" and "after" aspect to the way Wozzeck perceives his crime.
 
Example 21
 
The abundance of leitmotive contained in this passage recalls to mind the most crucial events found throughout the opera. In this final moment for Marie, as her life is ebbing away, thoughts of these events must rush chaotically through her head. The passage culminates with the ascending-fifths harmony, first found after Marie sang her lullaby and before Wozzeck arrived in Act I, Scene 3, and, according to Berg himself, the fifths express "her aimless and indefinable attitude of waiting, an attitude that finds its final solution only in death." (Redlich, p.272.)
 
Within the following excerpt, the above mentioned leitmotive are indicated. Perle refers to this passage as "an aggregate of leitmotive associated with Marie." (Perle, p.101.) It is equally significant that the music lacks leitmotive such as The Doctor's Motive, or The Captain's Motive, or any that are concerned with Wozzeck's associates exclusively. Before she dies, then, we musically "see" into the mind of Marie very clearly. By now she is no longer concerned with Wozzeck's hallucinations of Act I, or his lamentations concerning "Wir arme Leut." From the exact point in time that she is stabbed until she dies she thinks of her child (as suggested by the Cradle Song leitmotiv and the Marie as Mother motive) and she thinks of the drum major (as suggested by his Posturing motive, Seduction, The Earrings, and the Military March). The relationship of Wozzeck and Marie had already died.
 
Wozzeck, Act III, Scene 2, mm.99-107.
Leitmotive found at the moment of Marie's death.
 
Example 25a
 
Example 25b
 
Example 25c
 
Example 25d
 
Example 25e
 
Example 25f
 
In addition to the leitmotive found within the murder scene, Berg employs various other interesting devices that are based on systematic manipulations of some specific parameter. The most well-known of these devices occurs in Act II, Scene 3, as Wozzeck comes to Marie, confronting her with her unfaithfulness. He says, "...a sin, so thick and wide, its stink should be able to smoke the angels out of heaven!" Berg represents a suddenly escaped curl of rising smoke in m.380 (II/3) on the third quarter-note by accompanying a free ascending solo violin line with ascending lines in the solo cello, oboe, viola, and A-clarinet that are generated, respectively, from unfolding semitone-, whole-tone-, minor-third-, and major-third-interval cycles. The smoke "begins" on middle-C in all five lines. Just as rising smoke seems to have a homogenous, continuous quality about its ascent, except at it highest point where, swirling all around, it first breaks through clear air, the little ascending figure of m.380 (II/3) contains the interval cycles, representative of homogeneity, and the free, swirling violin line representing the smoke's cutting edge. It is no accident that, as the "angel-ridding" smoke reaches "heaven," the final note of each line contributes to a sonority built from stacked fifths. This interval-class-5 cycle has been used previously to represent eternity; it is found in the descending line of m.33, Act I, Scene 1, when the captain expresses fearfully, "Es wird mir ganz angst um die Welt, wenn ich an die Ewigkeit denk'." ("I get quite frightened about the world, if I think of Eternity.")
 
Example 22
 
A smaller example of unfolding interval cycles occurs in the murder scene in m.83 when Wozzeck asks Marie, "and how long do you think (our relationship) will last?" While the horns and the harp descend in octaves on the ostinato pitch B, the violins and violas, in parallel fourths, descend by major-sevenths with one final compound leap of the major-seventh's inversion, the minor-ninth (plus two additional octaves). Simultaneously, the cellos descend by minor-ninths with, again, one final compound leap of the minor-ninth's inversion, the major-seventh (plus two additional octaves). So the ordered interval cycles, 11, 12 (0), and 13 (1) are here unfolded; they are presented in such a way that the second and fourth pitch-classes (G and A) of the violin and of the cello are exchanged, and causing the octave G# of the third chord.
 
Example 23
 
A similar device occurs in m.90 in the third viola line, as once more Wozzeck refers to heaven. ("I'd give up heaven and eternal bliss if I might go on kissing you!") The ascending line consists of increasingly larger intervals. However, just as the free violin line of m.380 (II/3) added an "imperfection" to the system, there is one imperfection included within this systematically constructed line: the interval-classes 5 and 6 have been reversed. The reason for this may have been to avoid emphasizing the minor triad, C#, E, G#, C#, and its "doubled root" which would have occurred if interval-5 had preceded interval-6.
 
Example 24
 
In addition to the above instances of special pitch structures, Berg also occasionally employs systematically generated rhythmic structures. Beginning in m.91, as Wozzeck is shaken by the realization that he may not go on kissing Marie, the four-note figure in the horns, consisting of three sixteenth-notes preceding a longer note, is presented three times, each time beginning on a different metric subdivision of the beat (the 2nd, 4th, and 3rd sixteenth-note of the beat, successively).
 
Example 26
 
Rhythmic diminution, a process elaborately employed in Act III, Scene 3, in the "Invention on a Rhythm," is utilized also in the murder scene at one point. The four-voice progression found in the strings in m.94 is reduced to sixteenth-notes and immediately repeated in the following measure. It seems to represent a sudden "shiver" as Wozzeck tells Marie, "When one is cold, one doesn't feel the cold anymore! When the morning dew falls you won't feel the cold."
 
Example 27
 
It is now time to turn our attention to a more subtle use of pitch structures within the murder scene, namely, the use of pitch-class sets. From this point forward, pitch structures will be referred to using their set-type name, and each set-type is represented by its prime form as listed in Allen Forte's The Structure of Atonal Music.
 
A "set" differs from a "leitmotiv" in that a set is made of an unordered collection of pitch-classes. However, the particular assortment of intervals contained within a set-type can have an associative meaning equally important to that of a leitmotiv, though perhaps this "meaning" may be of a more general nature than that of a leitmotiv. This is an extremely important postulate and certainly not accepted by everyone that has contemplated on the matter. Let us remember, however, that the "unordered" notes of the major scale and the minor scale, as found in tonal music, are easily recognizable as to which mode is actually being used at any given moment. This is simply due to the specific internal intervallic structure of these pitch collections (and an emphasis given to the tonic and dominant scale-degrees). In music that is not tonal (nor based on some pitch-centric scale), the hierarchy of pitches in a set disappears, but not the identity of a given pitch structure. Within a given composition, then, associations between atonal set-types and extra-musical parameters are completely possible. They are of prime importance in Wozzeck.
 
A second assumption now needs to be stated: Inversionally related sets will have an equivalent associative meaning within a given piece of atonal music unless it is the inversional relationship itself that is used in a specifically differentiated manner. (The inversionally related major and minor triads are examples of how an equivalent set-type can have associative meanings distinct from each other; according to the rather ridiculous cliché, the major triad sounds "happy" while the minor triad sounds "sad.") If, however, the inversional relationship is not used with purposefully differentiated meanings, then the equivalent interval make-up of such sets will be considered sufficient for establishing identity. In Wozzeck, a set and its inversion possess the same associative meaning.
 
It is held, then, that the compositional use of equivalent sets, even if not perceived consciously by the listener, will have a subconscious affect on our associating between pitch collections and elements of the dramatic situation. Furthermore, we will consider subsets of important, associative sets to share in the associative power of the original set, especially if the cardinality difference between set and subset is not too large. There are several methods usable for the consideration of subsets, but the only one we will consider here stems from Forte's concept of the Kh-relationship. Two sets, A and B, are Kh-related if A can contain or be contained in B and A can contain or be contained in the complement of B. The requirement involving inclusion within the complement of a set adds a more exclusive aspect for the admission into a Kh-related family, and sets within a Kh family exhibit a strong degree of similarity. Thus, Kh-related sets have the potential of exhibiting an equivalent associative power.
 
The two most important sets, basically, of the entire opera Wozzeck are 6-34 [0,1,3,5,7,9] and 4-18 [0,1,4,7]. The first set is strongly related to Wozzeck while the second is associated exclusively with Marie. Janet Schmalfeldt, in her set-theoretic work on Wozzeck, offers a lucid argument concerning the evolution of these set associations. For now, let us review only the most important uses of these sets as found throughout the opera.
 
6-34 forms the cadential chord of Act I, Scene 1.
Example 28
 
George Perle demonstrates that each of the five character sketches (the five scenes of the first act) have a "principal tone center." (Perle, pp.130-31, 138-39.) The tone centers are:
 
    Scene 1      C#
    Scene 2      C
    Scene 3      A
    Scene 4      Eb
    Scene 5      G
 
The tone-centersExample 29themselves form a pentachordal subset of 6-34 and, indeed, the "missing note" F is one of the two even more important tone-centers of the entire opera: the B-F fateful tritone. The five character sketches each portray a person as to his or her relationship to Wozzeck. The relationship of the five tone-centers further establishes 6-34 in relationship to Wozzeck; the five characters are drawn into Wozzeck's world and together form the complex of variables that bring about Wozzeck's end.
 
The cadential sonority, too, closing each of the three acts, contains the closing 6-34 sonority of Act I, Scene 1, and, in addition, another representative of 6-34 as well. The two upper tetrachords alternate over a sustained perfect fifth. The two tetrachords, sharing two pitch-classes, together form 6-34. The second of these tetrachords (as shown below), along with the sustained fifth, form the same 6-34 that closes Act I, Scene 1.
 
Example 30
 
The important "Wir Arme Leut" leitmotiv is based on 4-19 [0,1,4,8] which is a prominent Kh-related subset of 6-34.
 
Example 31
 
Wozzeck's entrance theme in Act II, Scene 2 is based also on 6-34.
 
Example 32
 
These examples are provided to demonstrate some of the more important uses of 6-34. The identifiable feature of 6-34 is that it is almost a whole-tone scale (an "almost whole tone hexachord," according to Schmalfeldt). 4-18, on the other hand, contains no whole-tones at all, and is not Kh-related to 6-34. The set depicts Marie in her independence from Wozzeck. Her important lullaby, "The Cradle Song," is based on 4-18.
 
Example 33
 
The lack of whole-tones in 4-18 is the clue to recognizing the special individuality of this tetrachord. Just for a moment, let us consider all hexachords that contain four or more whole-tones within their interval vector. The whole-tone scale, 6-35 [0,2,4,6,8,10], contains six pitch-classes and six whole-tone intervals. If any one of these six pitch-classes is altered by a semitone, two of these whole-tone intervals are affected. Therefore, a hexachord cannot contain precisely five whole-tones. However, nine hexachords contain four whole-tones, and these will be referred to as the "whole-tone-saturated" hexachords. Interestingly, the chromatic hexachord, 6-1 Example 34 is one of these nine whole-tone-saturated hexachords. The whole-tone hexachords, as used in Wozzeck, seem to be associated with the character Wozzeck. Indeed, the chromatic semitonal descending "Knife" motive is seen to be related to Wozzeck; it too is based on a collection saturated with whole-tones.
 
These nine hexachords can be thought of in three groups: 1) those containing four whole-tones from the same whole-tone scale; 2) those containing three whole-tones from one whole-tone scale, and one whole-tone from the other whole-tone scale; and 3) those containing two whole-tones from each of the whole-tone scales. Group 1 (those containing four whole-tones from the same whole-tone scale) are the most similar to the whole-tone scale itself, and are given priority. Also, those hexachords containing the fewest semitones will be given priority. This, of course, leaves hexachord 6-34 [0,1,3,5,7,9] with the highest priority, and, indeed, it is the most important hexachord of Wozzeck. The nine whole-tone-saturated hexachords are as follows:
Example 36
 
Interestingly, Marie's 4-18 is conspicuously not found in a Kh-relationship with any of these nine hexachords. However, the important 3-3 trichord [0,1,4], which forms the basis for the "Marie as Mother" motive, is a subset of seven of the nine whole-tone-saturated hexachords including 6-34, and, of course, 3-3 is a very important subset of 4-18.
 
Example 35
 
As Marie sings "Komm, mein Bub!" using the 3-3 trichord, the trichord gains the association of depicting Wozzeck and Marie's child, and, therefore, helps illustrate the bond between them. The 3-3 trichord is also a subset of the Z-related pair 6-Z19 [0,1,3,4,7,8] and 6-Z44 [0,1,2,5,6,9]. These hexachords, according to Schmalfeldt, "provide pitch structural correspondents for the fatal bond between the two leading characters." (Schmalfeldt, p.226.)
 
Besides 6-34 (and other whole-tone-saturated hexachords), 4-18, 6-Z19/6-Z44, and all sets in a Kh-relationship with 6-34, 4-18, or 6-Z19/6-Z44, Schmalfeldt recognizes eight other important sets in Wozzeck. They are:
 
1) 4-14                  [ 0, 2, 3, 7 ]
2) 4-23                  [ 0, 2, 5, 7 ]
3) 6-Z47/6-Z25     [ 0, 1, 2, 4, 7, 9 ] / [ 0, 1, 3, 5, 6, 8 ]
These sets are basically diatonic in nature and add contrast to the predominantly atonal structures of Wozzeck. (Schmalfeldt, p.234.) 6-Z47, in particular, forms the first six notes of the captain's theme and is also the basis for the six-note chord of the drowning scene (III/4).
 
4) 5-15       [ 0, 1, 2, 6, 8 ]
5) 5-Z17     [ 0, 1, 3, 4, 8 ]
These are the basis of chord-III and chord-I of the "Hallucination" chords of Act I, Scene 2. (Chord-II is based on 5-19 which is in a Kh-relationship with Marie's 4-18.)
 
Example 37
 
6) 5-20      [ 0, 1, 5, 6, 8 ]
This pentachord forms the very first chord of the entire opera.
 
Example 38
 
7) 6-21     Example 39
8) 6-22     Example 40
These, according to Schmalfeldt, are the other important "almost whole-tone hexachords" in Wozzeck. As we have seen, this pair of hexachords, along with 6-34, constitutes group-I of the whole-tone-saturated hexachords.
 
The first of the following charts lists all Kh-relationships of the whole-tone fragment 5-33 [0, 2, 4, 6, 8], of Wozzeck's 6-34, of Marie's 4-18, and of the "bond" hexachord pair 6-Z47/6-Z25. The eight "independent" sets are also included. Sets shown in boldface are considered by Schmalfeldt to be important in Wozzeck.
 
The second chart lists Kh-relationships of sets with respect to the whole-tone-saturated hexachords. They are listed in the order of decreasing density. So, for example, 3-2 is found in all nine of the hexachords, 3-3 is in seven, and 4-6 is found in only one of these hexachords. Sets with no representation are listed last. These include Marie's 4-18 and all pentachords in a Kh-relationship with 4-18.
 
By cross-referencing the two charts, one can observe the interesting fact that all of the trichords and tetrachords in a Kh-relationship with 6-34 that are underlined (considered to be important by Schmalfeldt) are found to be in Kh-relationship with at least two other whole-tone-saturated hexachords as well. The important pentachords associated with 6-34 are found in at least one of the other whole-tone-saturated hexachords.
 
Each category of Kh-related sets is given a symbol. These symbols are used in the labeling of sets in the accompanying analysis in order to be able immediately to understand the significance of a given set. The symbols are defined as follows:
 
Example 43
 
Example 44a
Example 44b
 
Example 45a
Example 45b
 
Sets in no Kh-relationship to the nine whole-tone-saturated hexachords include, most notably, Marie's 4-18 [0,1,4,7]. It is also significant that the eight pentachords to be found in a Kh-relationship with 4-18 also have no Kh-relationship to the nine whole-tone-saturated hexachords; these include: 5-16, 5-Z18, 5-19, 5-22, 5-31, 5-32, 5-Z36, and 5-Z38. Of course, since 4-18 is not a subset of any of the nine whole-tone-saturated hexachords, neither will pentachords containing a 4-18 subset be a subset of the nine whole-tone-saturated hexachords.
 
Now that we are well-armed with information on what Schmalfeldt considers to be significant sets, let us pursue her manner of thinking by turning once more to Act III, Scene 2, and discovering how these set-structures operate prior to the moment that Marie dies. The first passage from the murder scene that we will examine from a set-theoretic point-of-view will be the "rising moon" line of m.97. This line begins in each of the four trombones after the longest silence occurring within the entire opera and, therefore, draws much attention to itself as it ascends through the very soft seven-octave "backdrop" of the ostinato B in the strings.
 
Example 41
 
The eleven-note trombone line, along with the final pitch-class B as found in Wozzeck's line in m.100, is packed with important subsets that were represented elsewhere throughout the opera. Schmalfeldt provides the following set-content diagram of the line (Schmalfeldt, p.217):
Example 46
The symbols accompanying each set-type indicate the Kh-families in which the set belongs, as defined in the above charts.
 
The present writer feels that of all of these sets, the first and last tetrachords (both of type 4-18, and shown in boldface in the above chart) are the most significant. The first trombone plays alone the entire first tetrachord without being joined by the second trombone until the fifth note. Likewise, each of the four trumpets concludes each line beginning one note earlier (relatively speaking) than the trumpet preceding it. Therefore, the final tetrachord is left sustained in the trumpets' fluttertonguing. The strings, oboes, and xylophone interrupt the trumpets in m.101 and draw the sonority to a close with an alternation between the 4-18 of the trumpets and an inversionally related additional 4-18.
 
Example 42
 
The alternating 4-18 tetrachords, representing Marie's words, "why are you shivering?", and also portraying her own trembling fear as she asks the last question she will ever ask, "what do you want?", occur a few brief seconds before Wozzeck stabs her.
 
The "rising moon" line is duplicated in the two vocal parts of mm.98-100. Marie sings, "How red the moon's rising," on the first hexachord (6-Z17). The aggregate-forming pitch-set of the second hexachord, having included the final ostinato pitch-class B (forming 6-Z43) is used by Wozzeck to "reinterpret" the sight for Marie: he says, "Like a bloody sword." The two hexachords, of course, are Kh-related to Marie's 4-18 since this tetrachord is itself a prominent subset of both of the hexachords. The prominence of 4-18 just prior to the act of murder reinforces the tension of the moment; it seems to suggest a smell of death, and its association with Marie has proven to be fatal.
 
Let us now turn once again to the beginning of the scene and consider in detail the pitch structure and dramatic association of the vocal lines, the text, and prominent accompanying instrumental passages. The contrast between sets in a Kh-relationship with Wozzeck's 6-34 [0,1,3,5,7,9] and Marie's 4-18 [0,1,4,7] will function as the basis for the analysis. It will be necessary to refer constantly to the set-analysis of the A-section of Act III, Scene 2, found in Appendix 1.
 
A1
The opening bassoon line (C, F#, Bb, D, C, A, C#) of m.73 in section A1 anticipates the ascending line of the rising moon at m.97 (G, C#, E, Ab, C, D, . . .). The bassoon line is a hexachord of type 6-15, while, as has already been shown, the first hexachord of m.97 is of type 6-Z17. Both are in a Kh-relationship to Marie's 4-18 [0,1,4,7], as indicated by the underlined pitch-classes.
 
Example 47
 
Indeed, the first four notes of the "rising moon" line (G, C#, E, Ab) do constitute 4-18. Marie sings, "Wie der Mond rot auf geht!" and the Kh-relationship of 6-Z17 to 4-18 firmly establishes an association with Marie. In the bassoon line, however, the last three notes (C, A, C#), of type 3-3, are in a Kh-relationship with Wozzeck's 6-34 and Marie's 4-18, and also with 6-Z19/6-Z44, the hexachords that exhibit traits of both Wozzeck and Marie, thereby binding the two characters. The final note of the line, nevertheless, is Wozzeck's C#, the monotone-pitch of Act I, Scene 1, ("Ja wohl, Herr Hauptman.") and here points to Wozzeck's obsession with killing Marie. The C# is sustained with the ostinato B, and finally with F, Bb, and D, forming 5-16 [0,1,3,4,7], a pentachord in a Kh-relationship with Marie's 4-18. Indeed, the tetrachordal subset B, F, Bb, D (4-18) is the same transposition as the important initial statement of the lullaby melody at m.372 (I/3). This pentachord contains no less than three instances of 3-3 [01,4].
 
Example 48
 
The initial sonority, then, includes Wozzeck's most important pitch, C#, Marie's most important tetrachord [0,1,4,7], three instances of 3-3, and also the fateful tritone, B-F. Marie tries to convince Wozzeck that it is time to go home. She sings, "Dort links - geht's in die Stadt" Example 49  This hexachord, 6-33, containing four whole-tones, is one of Wozzeck's whole-tone-saturated hexachords. The three successive dyads actually constitute three of the whole-tones, while the two lowest notes of the line form the other whole-tone. Marie is appealing to him for them to leave and therefore uses "his sound."
 
As she continues, "'s ist noch weit. Komm schneller," the Eb-clarinet plays a line to reinforce Marie (Ab, G, Eb, F#, C, etc.). This pentachord, 5-Z38 [0,1,2,5,8], includes Marie's 4-18 [0,1,4,7] (marked in boldface), and all but the initial grace-note do actually constitute an inverted form of 4-18 (G, F#, Eb, C). The melody sung by Marie is G, Bb, A, F# Example 50 which contains two inversionally related representatives of 3-3, the trichord binding Marie with Wozzeck.
 
Wozzeck replies, "Du sollst da bleiben, Marie." (F, G, A, G, F, A, C#), and he continues, "Komm, setz' Dich." (D, C, Bb.) Both of these whole-tone fragments taken together constitute 7-27 [0,1,2,4,5,7,9], which is in a Kh-relationship to the almost-whole-tone hexachord 6-32. Also, the first five notes Example 51 constitute 5-30 [0,1,4,6,8], which is a subset of 6-34 [0,1,3,5,7,9]. This pentachord is suggestive of Wozzeck's "entrance and exit" leitmotiv, and is actually used at the same transposition level found in Act I, Scene 3 (m.454) when he leaves Marie's presence. It is here used as his first line of the scene where he will leave Marie's presence forever. The whole-tone-saturated structures again reflect Wozzeck's primary hexachord, 6-34, and his primary purpose, which now begins to unfold as he tells Marie that he should remain there with him for a little while.
 
Marie becomes more urgent, proclaiming, "Aber ich mu ß fort." and using the pitch-classes (A, B, C, F, E). This diatonic pentachord is of type 5-20 [0,1,5,6,8], the type used for the first chord of the opera. It is now late in the course of events fated for Marie since the first act of the opera. Her words, therefore, take on a more permanent meaning ("I must go."). Wozzeck immediately says once more, "Komm," on the pitch F#. The combined utterances of Marie and Wozzeck (A, B, C, F, E . . . F#) are sung to the hexachord 6-18, a set in a Kh-relationship to Marie's 4-18. This is followed by two lines of moving sixteenth-notes in the winds. The upper line (Ab, Bb, C/Gb, F, etc.) is of type 5-24 [0,1,3,5,7], and the lower line (C, B, A, G, etc.) is of type 4-11 [0,1,3,5] and both are subsets of Wozzeck's 6-34. They provide strength to Wozzeck's command, "Komm."
 
A2
The second section begins on the last eighth-note of m.76. The sonority of this eighth-note (C#, E#, B, D#, G) is the whole-tone fragment 5-33 [0,2,4,6,8] and indicates Wozzeck once more. He sings, "Bist weit gegangen, Marie." on the pitches Example 52  The first six pitches (G, C, Ab, F#, E, D) and the last six pitches (C, Ab, F#, E, D, C#) are both of the almost-whole-tone hexachord 6-22 [0,1,2,4,6,8]. The seven-note collection, 7-15 [0,1,2,4,6,7,8], is itself the complement of, and includes, 5-15 [0,1,2,6,8], and this is the pentachord used as chord-III (F, E, D#, B, A) of the "hallucination chords" of Act I, Scene 2. This subtle reference to Wozzeck's unstable mental condition indicates that Marie not only has just walked too much ("Bist weit gegangen, Marie.") but, as far as he is concerned, has gone too far in her unfaithfulness as well. Wozzeck's obsession is once more indicated by sets saturated with whole-tones. Section A2 is distinguished by the use of the C# neighbor-tone to the B ostinato tone. The B of the fateful tritone, and Wozzeck's note C#, are joined in the trill beginning as Wozzeck says the name, "Marie." This welding of the B with the C# seems to represent the final indication that Wozzeck's (and Marie's) fate is now completely sealed. At this point, the first leitmotiv found within the scene occurs. The last four eighth-notes of m.77 portray "the knife" by descending semitones. The vertical structure of each of these eighth-notes forms 5-31 [0,1,3,6,9], which is in a Kh-relationship to Marie's 4-18 (indicated by the underlined pitch-class numbers).
 
Wozzeck says, "Sollst dir die Füße nicht mehr wund laufen.", as the "knife" motive concludes. Wozzeck's pitches are:
Example 53
 
The first three notes are part of the descending semitone segment of the "knife," but the middle pentachord (m.78) refers to Marie as much as do Wozzeck's words. It is of the type 5-Z18 [0,1,4,5,7], which includes Marie's 4-18. The G# is the "extra note" (not found in the 4-18), but it forms 3-3 [0,1,4] with the notes on either side of it. Marie's 4-18 is represented instrumentally (in the highest part) as well; the G# of the vocal line is omitted in the violin part (m.78), and the "knife" motive concludes very clearly with Marie's 4-18.
 
Example 54
 
Also to be noted are the parallel 3-3 [0,1,4] lines that accompany the last part of the 4-18 line (in addition to Eb-E-G, the next two lower voices plays Bb-B-D and E-F-Ab, respectively).
 
Example 55
 
These 3-3 lines conclude (m.78, beat 2) on the sonority Example 56 [0,1,2,5,7,8] = (F#, G, Ab, B, C#, D), which is of the hexachord type 6-18 and which includes 4-18. The heavy emphasis at the end of "the knife" motive on structures in a Kh-relationship with 4-18 [0,1,4,7] and its important subset, 3-3 [0,1,4], points to Marie much in the same way that an arrowhead points toward its victim. Wozzeck is already indicating his intentions of a painful death for Marie while he superficially expresses his concern for her tired, sore feet. His line concludes with (...Bb, Ab, Gb); the descending whole-steps (m.78, third and fourth quarter-notes), of course, reflect once more upon Wozzeck.
 
At the end of m.78, the ostinato B is joined by the sustained pitches, C and Db. The clarinet plays a line based on the remaining nine pitch-classes, thereby forming an aggregate, as Wozzeck sings, "'s ist still hier! Und so dunkel." The clarinet, at its climax in the center of the line (m.79, 3rd quarter-note), contains two imbedded 3-3 [0,1,4] trichords.
Example 57
 
The last four notes (Gb, Ab, Bb, F) of the clarinet are twice repeated in successively lower octaves in the bass clarinet and the contra bassoon. This tetrachord is of type 4-11 [0,1,3,5], which is an important subset of 6-34. The entire line, then, includes references to Marie (3-3) and Wozzeck (3-3 and 4-11) and seems to be an appropriate accompaniment to Wozzeck's observations concerning their mutual setting ("It's still, here! and so dark."). The repeated 4-11 segment, as it becomes lower and "darker," reflects Wozzeck's observation of the darkening night, but also, being Kh-related to 6-34, it portrays his own dark nature.
 
A3
The third section begins on the second half-note of m.80 and is characterized by the use of lines in the shape of a "wedge" between the outer voices, and by other ascending or descending chromatic semitonal lines suggestive always of "the knife." The ostinato pitch-class B is the point of departure or return for many of these chromatic lines. The initial wedge of m.80 contains the fateful tritone (B-F) as the point of departure for the two outer lines. In addition, however, the "chord" containing the B and F also contains pitch-classes C and Db. These two pitch-classes remain from the sustained tones of m.79. The other chords of this passage constantly return to this tetrachord (B, C, Db, F), which is of type 4-5 [0,1,2,6]. The other chords include structures built from 4-20 [0,1,5,8] and 4-19 [0,1,4,8], which are important subsets of 6-Z19/6-Z44, the hexachords containing elements common to Wozzeck and Marie. 4-19, along with two other chords from this passage, 4-11 [0,1,3,5] and 4-Z29 [0,1,3,7], are important subsets of Wozzeck's 6-34. The wedge, then, strongly portrays Wozzeck and serves as introduction to his next statement, "Wei ßt noch, Marie, wie lang es jetzt ist, da ß wir uns kennen." The entire phrase is built on the whole-tone-saturated hexachord, 6-33 [0,2,3,5,7,9] and uses the pitch-classes Bb, Ab, F, Eb . . . Db, Cb. The first tetrachord (Bb, Ab, F, Eb) is of the type 4-23 [0,2,5,7] and is based on a diatonic collection generated from four successive perfect-fifths. This tetrachord is sung by Wozzeck as he goads Marie, "Tell me, Marie, how long has it been..." This reference to time brings to mind the descending fourths that accompany Herr Hauptman's philosophizing, "Es wird mir ganz angst um die Welt, wenn ich an die Ewigkeit denk'" (m.33, I/1). Whereas Herr Hauptman's reference to eternity is depicted by nine pitch-classes from the interval-5 cycle, Wozzeck's more finite question to Marie involves only four elements from the time-symbolic circle of fifths.
 
The final clause sung by Wozzeck, "...that we've known one another." contains the descending whole-tone segment F, Eb, Db, Cb, a tetrachord of type 4-21 [0,2,4,6], which reflects Wozzeck's attitude toward his own question: he already sees the temporary condition of his relationship with Marie, and the whole-tone ending to the phrase is a reminder of Wozzeck's character and of his plan to end Marie's life. The shift from a cycle-of-fifths segment to a whole-tone segment indicates a departure from "objective, real" time to Wozzeck's subjective, distorted view of the situation.
 
Marie's answer, "Zu Pfingsten drei Jahre," is sung to the pitches Example 58  Each trichord is of the type 3-3 [0,1,4] and portrays Marie's union with Wozzeck. Her answer is quite sincere. She still does not know of Wozzeck's evil plan. Her two trichord-statements seem to reflect a desire on her part to satisfy Wozzeck's question with an honest answer. The two trichords combine to form 6-2 Example 59  which is one of the whole-tone-saturated hexachords, and which suggests a further desire on the part of Marie to appeal to Wozzeck's sympathy.
 
Wozzeck pushes his point further. He asks, "Und was meinst, wie lang es noch dauern wird?" The pitches he sings seem to mock Marie.
 
Example 60
 
The initial dyad (B, C#, B) resumes Wozzeck's line where he left off in m.82; this shows the continuity in his intentions for asking the two questions. However, the next seven pitch-classes imitate the answer Marie just gave; the pitch order and contour are preserved, and the final added D causes the last tetrachord to be Marie's 4-18. It is as if the use of her "property" is a purposefully disrespectful gesture, and this instance of Marie's 4-18 sung by Wozzeck seems to be incredibly spiteful on his part. The question succeeds in tormenting Marie, and she exclaims, "Ich mu ß fort." Her dyad (C#, D#, C#) imitates Wozzeck's dyad (B, C#, B) from the beginning of the same measure (m.83). So Marie's exclamation, "I must go," has several shades of meaning. First, she must leave to go home. Secondly, however, her statement is an implied answer to Wozzeck's question, "How long will it last?" "I must go" is meant by Marie to mean that their relationship must come to an end. She must leave the relationship behind for her own sanity; emotionally, she has already left Wozzeck.
 
The final 4-18 of Wozzeck's line joined with Marie's dyad (C#, D#) form 6-Z17 [0,1,2,4,7,8], which contains yet another 4-18 fragment. The two 4-18 subsets are inversionally related and contain maximum pitch-class invariance.
 
Example 61
 
Marie's 4-18, which generally represents her individuality, is now being dominated by Wozzeck. So her words, "I must go," also represent a fatalistic statement, as Wozzeck's intentions draw ever nearer to their end.
 
In m.84, Wozzeck asks, "Fürchst Dich, Marie?", and the tetrachord used is Bb, Ab, F, D, which is of type 4-27 [0,2,5,8], a subset of 6-34. Wozzeck's 6-34 Kh-related subset, 4-27, causes Marie even more fear as he asks her if she is afraid. He continues tormenting her, "Und bist doch fromm?" The two phrases together  form 7-31 [0,1,3,4,6,7,9], which contains no less than three instances of Marie's 4-18 [0,1,4,7].
 
Example 62
 
As Wozzeck says the name "Marie" (m.84), along with the syllable immediately before and after the name, he sings the same 4-18 that concluded with the C# of Marie's "Ich mu ß fort."
 
Example 63
 
He continues, "Und gut! und treu!", and uses the pitches D, C, F#, F, which form 4-Z15 [0,1,4,6], an important tetrachordal subset of 6-34. These questions are accompanied by a solo double bass playing three portamentos involving the pitches B, F, Bb, and C#, which constitute 4-Z29 [0,1,3,7], another subset of 6-34. His questions actually represent his accusations that Marie is not pious, or good, or faithful, and the continued use of 6-34 subsets, and a mocking use of Marie's 4-18, continue to dominate the musical representation of Wozzeck as he prepares to kill Marie.
 
A4
In the fourth section, the ostinato is shifted to the high register and approached from the lower register by a rather lengthy glissando. Under the ostinato high B, there unfolds a series of triadic structures that sound "sweet" as Wozzeck sings, "Was du für süße Lippen hast, Marie!" (m.86). The upper voice of these chords (F#, A, F#, D, Ab), in the first solo viola, consists of the trichord 4-Z29 [0,1,3,7], which is a subset of 6-34. His melody begins A B C D F# G F Eb, which is a representative of 8-27 Example 64 and which is in a Kh-relationship with 6-34. (6-34 is contained in 8-27 in two different ways, as indicated by the short lines given both over and under the pitch-class numbers.) As Wozzeck says the name "Marie" at the end of m.87, he uses the same rhythm (eighth-note plus quarter-note) and pitches (Bb and A) as he did when, under pressure in the doctor's presence, he cried out, "Auch Marie! Marie!" (mm.606-608, I/4). This semitonal suggestion of 3-3 [0,1,4] is reinforced instrumentally: as Wozzeck says "Marie," the first viola plays G, F#, Eb. The G is accented and draws attention to the imbedded 3-3 trichord contained within the viola line. Also, the second phrase of the viola trio, beginning on the second eighth-note of m.87, has as its first chord D-F-Bb, which, along with the ostinato B, forms the transposition of 4-18 contained within the opening pentachord sonority of this scene and found first in Marie's "cradle song" (m.372, I/3).
 
The first viola continues its line with two more imbedded 3-3 trichords, the second of which is increasingly reinforced by four clarinets.
 
Example 65
 
Wozzeck continues, "Den himmel gäb' ich drum," which is sung to the pitch-classes Example 66 The hexachord is of type 6-22 [0,1,2,4,6,8], which is one of the whole-tone-saturated hexachords. The last three pitch-classes form another 3-3 trichord; it is at the same transposition, but in a retrograde order, as the second of the viola's previous imbedded 3-3 trichords.
 
Wozzeck's sentence, "I would give up heaven..." is important. It is the first time in the scene that he refers to himself in the first person. Previous sentences have been in the second person and directed toward Marie. The sentences within the scene sung by Wozzeck up to now have been:
 

"You must stay, Marie." "Come sit down." "You've gone far, Marie." "You shouldn't make your feet sore walking." "Do you know, Marie, how long we've known each other?" "How long do you think it will last?" "Are you frightened, Marie?" "But you are pious, and good, and faithful?"
 
Accompanying Wozzeck's first-person statement, in m.89 in the 3rd violas and initially also in the trombones, there is a complete whole-tone scale followed by one semitone: Example 67  This, of course, contains Wozzeck's 6-34 [0,1,3,5,7,9] and is actually the only instance of a complete 6-34 in the entire murder scene.
 
His next clause, "und die Seligkeit," sung with the pitch-classes (Bb, D, Ab, G, C#), is on a pentachord of type 5-19 [0,1,3,6,7], which is in a Kh-relationship with Marie's 4-18. He concludes, "wenn ich Dich noch oft so küssen dürft!", sung with the pitch-classes Example 68 which consists of a 3-3 trichord (F#, F, D) followed by a 5-Z36 pentachord [0,1,2,4,6]; 5-Z36 is also in a Kh-relationship with Marie's 4-18.
 
The heavy emphasis of 3-3 and 4-18 throughout Wozzeck's conditional statement ("I would give up heaven...") expresses his longing to be close to Marie. There are a few suggestions of 6-34, as described above, in the apodosis of Wozzeck's wish. However, in the protasis ("...if I might go on kissing you"), the above-mentioned 5-Z36 [0,1,2,4,7] (Kh-related to Marie's 4-18), here given, is in a Kh-relationship with none of the nine whole-tone-saturated hexachords. Wozzeck is hopelessly separated from Marie by his unstable mental condition, and, as he yearns for her kisses, there is nothing in the final pentachord that suggests a bond between them.
 
Example 69
 
The two contrasting halves of the conditional statement, the first containing whole-tone-saturated elements while the second does not, depicts clearly the gulf existing between Wozzeck and Marie.
 
In m.91, he decides, "Aber ich darf nicht!" Sung with the pitch-classes C, D, Eb, D, C, this 3-2 trichord [0,1,3] is a subset of Wozzeck's 6-34, but not of Marie's 4-18. Nor is it in a Kh-relationship with their "common hexachord," 6-Z19/6-Z44. So, as Wozzeck decides that he better not kiss Marie, the melodic structure relates exclusively to Wozzeck, not at all to Marie, again depicting their separation.
 
A5
The final section of the A-section begins on the second beat of m.92 as the xylophone adds a disturbing C dissonance against the B ostinato. The C "interference" is perpetuated in the timpani trill of m.93. Wozzeck is no longer thinking of kissing Marie. He begins by asking Marie, "Was zitterst?" He uses the pitch-classes E, A, G, forming a 3-7 trichord [0,2,5], which is another one of the four trichords contained in 6-34, but not found in a Kh-relationship with either Marie's 4-18 or the 6-Z19/6-Z44 "common hexachord." (Besides 3-2 [0,1,3] and 3-7 [0,2,5], 3-6 [0,2,4] and 3-9 [0,2,7] are the only other trichords exclusively found in 6-34 and not in 4-18 or 6-Z19/6-Z44.) Also, the 3-2 trichord of m.91 and the 3-7 trichords of this section happen to be two of the four trichords contained within all nine of the whole-tone-saturated hexachords. (The other two are 3-6 [0,2,4] and 3-4 [0,1,5].) This suggests that there is something unique about the structure of Marie's 4-18, which, as we have said, contains no whole-tones. The total lack of 4-18-related structures, in this section immediately preceding Marie's death, is an indication of Wozzeck's dominance at this point, and of Marie's impending doom.
 
After Wozzeck asks Marie if she is shivering, Marie answers, "Der Nacht-tau fällt.", in m.93. She sings the pitches (G, D, F, G), reinforced by the same pitches in the harp. These pitch-classes are another representative of 3-7 [0,2,5], and come as an answer to Wozzeck's equivalent trichordal question. Wozzeck whispers morbidly to himself, "Wer kalt ist, den friert nicht mehr." He sings Example 70  The first dyad (G, A, G) connects his thought to his previous question, which also ended with (A, G). The main clause ("den friert nicht mehr") is sung with the tetrachord (Bb, D, E, C#), a representative of 4-12 [0,2,3,6] and a subset of Wozzeck's 6-34. The entire hexachord is of the type 6-Z29 [0,2,3,6,7,9], which is in a Kh-relationship to Marie's 4-18. Wozzeck's statement, then, can refer both to Marie and to himself: the physical coldness of Marie's corpse, and the chilly emotional quality of Wozzeck's horrible plan.
 
Wozzeck continues by imitating Marie's concern about the falling night dew: as she had sung (G, D, F, G), Wozzeck, in m.94, now begins his next thought, "Dich wird beim Morgen-tau nicht frieren," with the same pitch-classes (F, G, D, F). The phrase concludes in m.95 with (Eb, D, Eb, D, C), the pitch-classes constituting the 3-2 trichord [0,1,3], which is, as said above, related to Wozzeck's 6-34 but not at all to Marie's 4-18.
 
Finally, Marie sings, "Was sagst Du da?", with the same 3-7 [0,2,5] trichord that Wozzeck used in m.92 (E, A, G, G).
 
The emphasis of 3-7 in section A5 clearly relates to the 6-34 of Wozzeck and to his imminent murder of Marie. Wozzeck' answer to Marie, "Nix.", is sung on the ostinato pitch B. Together with the pitches of Marie's question (E, A, G), the B forms tetrachord 4-22 [0,2,4,7], which, again, is a subset of 6-34. In conclusion, let it be said that the music of this scene is constantly referring to the 4-18 tetrachord of Marie and the 6-34 hexachord of Wozzeck. To the person who insists on saying, "But Alban Berg knew nothing about set-theory - this is all nonsense," it will be said, "You have missed the main point concerning set analysis." Berg obviously did not know the terminology, but he did have a great ear. He intuitively deemed some sounds more appropriate for a given character or a given situation, and some sounds appropriate for others. The internal make-up of the sounds associated with Wozzeck contain many whole-tones, even if they are not always displayed prominently. Berg saw fit to give Marie a sound devoid of whole-tones so that a contrast could be drawn between the two most important characters.
 
In Act III, Scene 2, the two main characters are brought together one last time, and left forever separated. This is the reason that representations of 6-34 and 4-18 are found interspersed throughout the scene. It would not be correct, however, to suggest that one of the two sets dominates. Most of the music is new in this scene, not found earlier within the opera. This was necessary in order to create a musical fabric perfectly designed to portray the complex relationship at this final moment between Marie and Wozzeck.
 
Bibliography
 
1.  Berg, Alban; Wozzeck - Vocal score, (Vocal score by Fritz Heinrich Klein),
     © 1931, 1958 by Universal Edition A. G., Wien.
 
2.  Forte, Allen; The Structure of Atonal Music,
     © 1973 by Yale University, New Haven.
 
3.  Perle, George; The Operas of Alban Berg, Vol. I / Wozzeck,
     © 1980 by the University of California, Berkely/Los Angeles.
 
4.  Redlich, H. F.; Alban Berg - The Man and his Music,
     ©1957 by Abelard-Schuman LTD, New York.
 
5.  Schmalfeldt, Janet; Wozzeck - Harmonic Language and Design,
     © 1983 by Yale University, New Haven.
 
 
Example 71
Example 72
Example 73
Example 74
Example 75
Example 76
Example 77
Example 78
Example 79
Example 80
Example 81
Example 82
Example 83

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