CHAPTER 6
Threni: Large-Scale Musical-Poetical and Formal Row Employment with Objects

Threni: id est lamentationes Jeremiae prophetae

Considered from any angle, Threni is a monumental work. Threni, written in 1957-58, is the largest of any work that Stravinsky wrote after The Rake's Progress. Threni requires a huge orchestra (2.3.3.0-4.1.3.1, sarrusophone, timpani, tam-tam, piano, celesta, harp, and strings), six soloists (SATTBB), and a four-part mixed chorus. Although Threni is only the third composition (after Canticum sacrum and Agon) in which Stravinsky employed twelve-tone technique, it is his first entirely twelve-tone composition.

Stravinsky explores many aspects of twelve-tone technique in Threni. His row treatment includes combinatoriality, set rotation, permutation, incomplete row usage, and large-scale formal row usage. An Object-Oriented Analysis of Threni explains many of Stravinsky's row choices and their subsequent compositional treatments.

The Prime form of the row is taken from the first aggregate sung by the soprano soloist, beginning in M. 5. Although this row is not the initial row in the work, Stravinsky acknowledged that this form is the Original form on which the rest of the work is based (Roman Vlad, Stravinsky (London: Oxford University Press, 1960), 214.). The Prime form is indeed the home row of this work, since it is the basis for the foundational rows used throughout Threni. Table 49 shows the standard twelve-tone matrix for Threni.

   int:   +5   -1   +3   +3   -4   +5   -3   +5   -4   +5   +1   

       I-0  I-5  I-4  I-7  I-10 I-6  I-11 I-8  I-1  I-9  I-2  I-3  

 P-0   Eb   Ab   G    Bb   C#   A    D    B    E    C    F    F#   

 P-7   Bb   Eb   D    F    Ab   E    A    F#   B    G    C    C#   

 P-8   B    E    Eb   F#   A    F    Bb   G    C    Ab   C#   D    

 P-5   Ab   C#   C    Eb   F#   D    G    E    A    F    Bb   B    

 P-2   F    Bb   A    C    Eb   B    E    C#   F#   D    G    Ab   

 P-6   A    D    C#   E    G    Eb   Ab   F    Bb   F#   B    C    

 P-1   E    A    Ab   B    D    Bb   Eb   C    F    C#   F#   G    

 P-4   G    C    B    D    F    C#   F#   Eb   Ab   E    A    Bb   

 P-11  D    G    F#   A    C    Ab   C#   Bb   Eb   B    E    F    

 P-3   F#   B    Bb   C#   E    C    F    D    G    Eb   Ab   A    

 P-10  C#   F#   F    Ab   B    G    C    A    D    Bb   Eb   E    

 P-9   C    F    E    G    Bb   F#   B    Ab   C#   A    D    Eb   

The row, which has ic3 between the first and last pitches, creates three Torus-shaped objects when projected. These objects are shown in Table 50 (First Object), Table 51 (Second Object), and Table 52 (Third Object).

     A                                           A
       E                                       Ab
         F                                   Eb
   I-6     D                               G     R-3
             B                           D
               Eb                      F
                 Bb                  C
                   C#              E
                     Ab          C#
               RI-6    C       Bb     P-3
                         G   B
 foundational             F#                       extended
 rows                   F   C#                     foundational
 P-0, R-0,     R-0    C       D       I-3          rows
 I-0, RI-6          E           B                  also include
                   B               Ab              RI-3 and R-9
                 D                   C
               A                       G
             C#                          Bb
   P-0     Bb                              F      RI-3
         G                                   A
       Ab                                      E
     Eb                                          Eb
       Bb                                      D
         B                                   A
   I-0     Ab                              C#     R-9
             F                           Ab
               A                       B
                 E                   F#
                   G               Bb
                     D           G
               RI-0    F#      E     P-9
                         C#  F
                           C
                         B   G
                R-6    F#      Ab     I-9
                     Bb          F
                   F               D
                 Ab                  F#
               Eb                      C#
             G                           E
   P-6     E                               B      RI-9
         C#                                  Eb
       D                                       Bb
     A                                           A 

    Bb                                          Bb
      F                                       A
        F#                                  E
  I-7     Eb                              Ab    R-4
            C                           Eb
              E                       F#
                B                   C#
                  D               F
                    A           D
              RI-7    C#      B     P-4
                        Ab  C
                          G
                        F#  D
              R-1     C#      Eb    I-4
                    F           C
                  C               A
                Eb                  C#
              Bb                      Ab
            D                           B
  P-1     B                               F#    RI-4
        Ab                                  Bb
      A                                       F
    E                                           E
      B                                       Eb
        C                                   Bb
  I-1     A                               D     R-10
            F#                          A
              Bb                      C
                F                   G
                  Ab              B
                    Eb          Ab
             RI-1     G       F      P-10
                        D   F#
                          C#
                        C   Ab
               R-7    G       A      I-10
                    B           F#
                  F#              Eb
                A                   G
              E                       D
            Ab                          F
  P-7     F                               C      RI-10
        D                                   E
      Eb                                      B
    Bb                                          Bb

   B                                           B
      F#                                      Bb
        G                                   F
  I-8     E                               A      R-5
            C#                          E
              F                       G
                C                   D
                  Eb              F#
                    Bb          Eb
              RI-8    D       C      P-5
                        A   C#
                          Ab
                        G   Eb
              R-2     D       E      I-5
                    F#          C#
                  C#              Bb
                E                   D
              B                       A
            Eb                          C
  P-2     C                               G      RI-5
        A                                   B
      Bb                                      F#
    F                                           F
      C                                       E
        C#                                  B
  I-2     Bb                              Eb    R-11
            G                           Bb
              B                       C#
                F#                  Ab
                  A               C
                    E           A
             RI-2     Ab      F#    P-11
                        Eb  G
                          D
                        C#  A
               R-8    Ab      Bb     I-11
                    C           G
                  G               E
                Bb                  Ab
              F                       Eb
            A                           F#
  P-8     F#                              C#     RI-11
        Eb                                  F
      E                                       C
    B                                           B

De elegia prima

Threni consists of three large formal sections. The central section is further subdivided into three subsections. Each of the large formal sections takes its text from a different chapter of the Biblical book of Lamentations: "De elegia prima" sets portions of the first chapter, "De elegia tertia" parts of the third chapter, and "De elegia quinta" selections from the fifth and last chapter.

Post-Tridentine settings of the Lamentations of Jeremiah that are intended for liturgical use make use of the words from nine lessons in the Matins of Maundy Thursday (Lamentations 1:1-5, 1:6-9, 1:10-14), Good Friday (2:8-11, 2:12-15, 3:1-9), and Holy Saturday (3:22-30, 4:1-6, 5:1-11). Stravinsky, not intending a liturgical performance, chose the portions of Lamentations for Threni himself based on his sense of form and drama.

However, Stravinsky does follow the liturgical tradition of setting Lamentations in one respect: he sets the Hebrew letters. Each of the five chapters of the Biblical book of Lamentations is an acrostic poem. In chapters one, two, and four, each line of the acrostic begins with a successive letter of the Hebrew alphabet. Thus, each chapter has twenty-two verses, one for each Hebrew letter. Chapter three contains sixty-six verses, every three of which begin with the same letter. Therefore chapter three is a triple acrostic. The fifth chapter of Lamentations also has twenty-two short verses, but it is not an alphabetic acrostic and so its translation uses no Hebrew letters. In his setting, Stravinsky follows Roman Catholic tradition by including the Hebrew letters (except for the fifth chapter), which were maintained in Jerome's Latin translation to show the acrostic pattern.

Table 53 presents the Latin words and King James English translation of the first movement of Threni, "De elegia prima." Stravinsky's alterations to the Latin text are designated with square editorial brackets [ ].

Table 54 shows the form of the first movement of Threni, "De elegia prima," listing all the rows employed.

Incipit

The first five measures of Threni are a short instrumental introduction. The oboes and first violins play the R-0 row as the clarinets and low strings play RI-6. After the rows begin, they spread through the orchestra. Both rows begin with the pitch F#, the last note of the Prime form of the row. In the Incipit and throughout Threni, Stravinsky sets up F# as an important pitch and establishes the rows beginning on F# as important forms that will recur throughout the piece. Table 55 shows the rows used in MM. 1-5 as located on the First Object (from Table 50).

 A             A
 
         RI-6
 
        F#
 
         R-0
 
 Eb            Eb
 
 
 
        C
 
 
 
 A             A

In MM. 5-18 the vocal and instrumental parts shift the importance from F# to Eb and to the rows beginning and ending on Eb. This shift to Eb is brought about by the first statement of P-0 in Threni, sung by the solo soprano, and the first statement of I-0, sung by the alto. Both P-0 and I-0 begin with Eb. The first oboe plays R-0 (beginning on F#), the second oboe R-9 (beginning on Eb, both oboe rows are completed by the clarinets), the clarinets RI-3 (beginning on Eb), and the trombones RI-6 (beginning on F#). The harp and cellos double vocal pitches. Row relationships caused by the beginning and ending pitches in the network of rows at MM. 5-18 create a solid formal base for the entire work: the extended foundational rows all taken from the First Object. Table 56 shows the row relationships of the extended foundational rows.

   A             A
 
 
  RI-6
          F#              extended
    R-0                   foundational
                 RI-3     rows
 P-0
   Eb            Eb
 
  I-0            R-9
 
          C
 
 
 
   A             A

Note that the rows that Stravinsky employs in the Incipit are an extension of the same foundational rows that he uses in the smaller twelve-tone works (P-0, R-0, I-0, and RI-6). Along with the four foundational rows, he also includes all of the rows beginning on the first pitch of the Prime row of the work: Eb (RI-3 and R-9, as well as P-0 and I-0 already in the foundational rows). These six rows, related to each other by beginning and ending pitches, are the extended foundational rows for Threni.

Stravinsky's use of these six extended foundational rows is an appropriate setting of the poetic text in the Incipit. Just at the moment that the Incipit announces the entirety of the rest of the work "the beginning of the Lamentations of the Prophet Jeremiah," all the extended foundational rows are heard at once. This simultaneous row statement solidly centers the row collections for the entire work, as will be shown below. Also, the Incipit is formally important because the Incipit is the only instance in Threni in which Stravinsky combines all six extended foundational rows simultaneously.

ALEPH

The first Hebrew letter, ALEPH, in MM. 19-22 uses the row RI-6. This simple row statement demonstrates Stravinsky's typical use of the Inverted Retrograde, or the Retrograde Inversion beginning on the last note of the Prime form (F#). Interestingly, Stravinsky opens ALEPH as he began the opening measures of Threni, with a row beginning on F#. Table 57 illustrates RI-6 in the First Object as employed in MM. 19-22.

 A             A
 
         RI-6
 
        F#
 
 
 
 Eb            Eb
 
 
 
        C
 
 
 
 A             A

The pitches and rows from MM. 23-61 are repeated with new text in MM. 73-107, and 120-165. The clarinets and low strings play I-0 in MM. 23-32 as the chorus speaks the poetic text. The clarinets, horns, and strings play I-6 in MM. 33-41. In MM. 42-61 the tenor soloist and bugle repeat R-0 as the strings and upper voices from the chorus repeat RI-0. Again, Stravinsky uses the same foundational rows that he employs in his smaller works. Here, Stravinsky explores all the foundational rows and their retrogrades except for P-0. Table 58 shows the rows used from the First Object in MM. 23-61, 73-107, and 120-165.

    A             A
 I-6
 
   RI-6
           F#             all foundational
     R-0                  rows and
                          their retrogrades
                          except for P-0
    Eb            Eb
 I-0
 
   RI-0
           C
 
 
 
    A             A

BETH

For the letter BETH (MM. 62-65), Stravinsky employs rows outside of the First Object for the first time in Threni. This letter, as in the previous letter ALEPH, employs just one row. Here the RI-10 row from the Second Object is used. The Second Object, the frame pitches of which are a half step higher than the First Object, is used perhaps as a precursor to the half step motive in the top tenor line in the following "Plorans ploravit" section ("She weepeth sore"). Table 59 shows the RI-10 row in the Second Object as used in MM. 62-65.

 Bb            Bb
 
 
 
        G
 
 
 
 E             E
 
 
 
        C#
                         "she weepeth sore"
                RI-10
 
 Bb            Bb

Two solo tenors sing the foundational rows from the First Object in MM. 66-67. In M. 66 the first tenor sings R-0 and the second sings I-0; in M. 67 the first tenor sings RI-6 and the second sings P-0. Therefore, the first tenor centers on the rows starting on F#, while the second tenor centers on those beginning on Eb. Note the abstract symmetry of the row presentation in these two measures as shown in Table 60: in M. 66, R-0 and I-0 both move "down" along the object (from F# to Eb to C), whereas in M. 67, P-0 and RI-6 both move "up" along the object (from Eb to F# to A).

             A             A
 
 
            RI-6                   return of
 tenor 1            F#             foundational
              R-0                  rows
 
          P-0
 tenor 2     Eb            Eb
          I-0
 
 
                    C
 
 
 
             A             A

HE

For the first time in Threni, Stravinsky employs rows from two objects at once for the letter HE (MM. 68-72). For this third letter in the work, the vocal parts sing P-7 from the Second Object simultaneously as the instruments play I-0 from the First Object. The instruments borrow two pitches (6 and 12) from the vocal parts to complete their row. The departure to the Second Object may underscore the implicit separation in text "inimici" or "enemies," because throughout Threni Stravinsky uses rows from the Second Object when the poetic text mentions enemies. Rows from the Second Object are not used during the singing of the actual poetic text in MM. 76 ff., because Stravinsky uses the same music three times for different texts in MM. 23-61, 73-107, and 120-165. Stravinsky repeats the music for his settings of ALEPH, HE, and RES(H). He sets more of the words from these verses than the excerpts that he uses for BETH and CAPH.

The choral statement of P-7 in MM. 68-72 relates to the previous presentation of a row from the Second Object, RI-10 in MM. 62-65, in that both rows begin on Bb.

CAPH

In the letter CAPH, MM. 108-111, Stravinsky employs a row from the Third Object for the first time in Threni. Here the rows RI-0, R-0, and P-11 are played simultaneously in the strings, with sporadic doubling in the vocal parts. The R-0 and RI-0 forms from the First Object both end on Eb. P-11 is from the Third Object. Just as Stravinsky employed rows from the First and Second Objects at once in the third letter (HE), for this letter he uses rows from the First and Third Objects. This accretion of rows used in the letter is an example of additive progression, which Stravinsky will continue to exploit further in Threni. As the movement progresses, and in later sections of Threni, Stravinsky tends to move farther and farther away from the First Object and its foundational rows. Table 61 shows the rows used in MM. 108-111.

            F#
    R-0
 
 
 Eb
 
 
   RI-0
            C

 Ab
 
 
 
           F
 
 
       P-11
 D

MM. 112-113 displays Stravinsky's most complicated object employment in "De elegia prima."As in MM. 66-67, two tenors sing four rows, but the rows here are different. In M. 112, the first tenor sings R-11 from the Third Object as the second sings P-0 from the First Object; in M. 113, the first tenor sings I-0 from the First Object as the second sings RI-5 from the Third Object. The Object mixture represents the furthest collectional departure in "De elegia prima." This mixture of Objects, and the collectional discord resulting from the mixture of foreign and foundational rows, also musically depicts the words "for I have become vile."

Table 62 and Table 63 show the rows used in MM. 112-113. The symmetry of the row presentation is analogous to the symmetry in the previous tenor duet in M. 66-67, except in the earlier case all the rows are from the First Object (R-0 and I-0, then RI-6 and P-0).

            F#
 
 P-0
 
 Eb
 
 
 
            C

 Ab
 
 
 
           F
 
           R-11
 
 D

            F#
 
 
 
 Eb
 
 I-0
 
            C

 Ab
 
           RI-5
 
           F
 
 
 
 D

RES(H)

In RES(H), the final letter of "De elegia prima," Stravinsky returns to the rows of the First Object. Similar to the Incipit (MM. 5-18), where all rows beginning on Eb were heard simultaneously, here for the letter RES(H) in MM. 114-119 all forms starting on F# are heard at the same time. The first violins play P-3, the second violins I-3, the violas R-0, and the cellos and basses RI-6. The vocal parts double pitches from the instrumental parts sporadically, as they did for CAPH (MM. 108-111). Table 64 shows this return to the foundational forms for the last letter in this movement. The return to the foundational rows serves as a formal closure. But, because the closure here favors F# only and not Eb, the closure is not final. Stravinsky reserves a stronger closure for the final measures of Threni.

   A             A
 
 
   RI-6          P-3      all rows
          F#              beginning on F#
    R-0          I-3
 
 
   Eb            Eb
 
 
 
          C
 
 
 
   A             A

The opening movement of Threni ends with the third and final repeat in MM. 120-165 of the material from the First Object first heard in MM. 23-61.

Summary of "De elegia prima"

Of all the movements in Threni, "De elegia prima" yields most readily to analysis with rows projected onto Objects. All the rows used in "De elegia prima" are from the First Object except for RI-10 (BETH, MM. 62-65), P-7 (HE, MM. 68-72), P-11 (CAPH, MM. 108-111), and R-11 and RI-5 (Vide from CAPH, MM. 112-113).

Stravinsky uses rows from the Second and Third Objects for specific formal events. In the case of "De elegia prima," Stravinsky employs rows from the Second Object for the letters BETH and HE, and rows from the Third Object for the letter CAPH. The first and last letters in the movement, ALEPH and RES(H), use rows from the First Object. The remainder of the movement is written using rows from the First Object, except for Vide from CAPH (MM. 112-113), which includes rows from both the First and Third Objects.

Appropriately, the particular rows within the Second and Third Objects that Stravinsky uses in "De elegia prima" are related to each other by hinging on the first or last pitches of the row, as can be seen from the examples of the objects above. The rows from the Second Object both begin on Bb (BETH RI-10, and HE P-7). The rows from the Third Object all begin or end on F (CAPH P-11, and Vide from CAPH R-11 and RI-5).

Structurally, the rows from the Second and Third Objects establish different regions than the standard sets of rows in the First Object. Stravinsky's use of these regional departures using different objects parallels the motion into different key areas in a classical tonal composition. Stravinsky uses rows from the First Object, and especially rows beginning and ending on Eb or F# (the first and last notes of the Prime form), as structural centers from which other rows depart, and to which they return at the ends of movements and at important internal events. Departure into rows in the Second and Third Objects is formally further removed than rows in the First Object. Table 65 lists the Objects used for each subsection of "De elegia prima."

De elegia tertia

The harmonic structure of most large-scale tonal music diverges from the foundational or central key area in the middle portion of the work. Analogously, the objects employed by Stravinsky in "De elegia tertia" increasingly diverge from the foundational rows of the First Object. In addition, however, the foundational rows are employed throughout as a formal reference and structural foundation. "De elegia tertia" is in three sections: Querimonia, Sensus spei, and Solacium.

Querimonia

The first part of "De elegia tertia" is Querimonia or "complaint" (MM. 166-193). Querimonia is in four sections, each consisting of the chorus singing Hebrew letters accompanied by trombones, followed by an increasing number of soloists singing the Lamentations text (from one to four). The rows for the chorus and trombones are from the First Object (for the possible exception of BETH, see below). The soloists take rows from all three objects, often showing a symmetrical or otherwise ordered method as shown in the discussion below.

Table 66 shows the rows employed in and the form of Querimonia.

Table 67 presents the Latin words and King James English translation of the first part of "De elegia tertia:" Querimonia. Stravinsky's alterations to the Latin text are designated with square editorial brackets [].

ALEPH

The first of four subsections in Querimonia is ALEPH (MM. 166-172). The letter breaks up two row statements into three parts (MM. 166, 168, and 170-171), as the sopranos and altos sing the P-0 row and the trombones play I-0. The solo bass sings the Monodia with RI-6 rot2 and P-0 rot3 in M. 167, R-0 and I-0 in M. 169, and R-0 in M. 172. All the rows in ALEPH are from the First Object, thus reinstating its importance as manifest in "De elegia prima" as also the central or foundational area for "De elegia tertia." Table 68 shows the rows employed in MM. 166-172.

    A             A
 
 
   RI-6                   return of
           F#             foundational
     R-0                  rows
 
 P-0
    Eb            Eb
 I-0
 
 
           C
 
 
 
    A             A

BETH

The second of the four subsections in Querimonia is BETH (MM. 173-178). The letter for this section is set as chords (harmonically), with one note per syllable for the first two statements of the letter (MM. 173 and 175). Therefore, the rows that Stravinsky used are extremely difficult to determine in relation to the rest of the work. For example, M. 173 has notes that could be from either of the hexachords P-1a or I-6a; looking for aggregates in M. 173 and 175 does not provide a definitive row analysis. The third statement of the letter in M. 177, while containing many pitches from the hexachord I-0b, further eludes row analysis.

The row use in the two-part canons of this section is more obvious. In M. 174 the tenor soloist sings P-0 rot1 followed by I-6 rot1, both from the First Object. The bass follows a minor sixth below, in canon with the tenor, singing P-4 rot1, and I-10 rot1, both rows from the Second Object. Here, Stravinsky sets up a pattern in his object use by beginning with the First Object and ending in the Second Object. Stravinsky's first canon in BETH, then, is an exploratory journey with no return, beginning in one object and ending in another. Perhaps the journey to another object underscores aging or the one-way progression of time spoken of in the words "My flesh and my skin hath made me old."

In the second two-part canon (M. 176) the bass leads with I-0 rot2 followed by RI-7 rot2. The tenor follows a minor sixth above, with I-8 rot2 and RI-3 rot2. Here the bass begins in the First Object (I-0) and the tenor follows with the Third Object (I-8). The bass then leads with the Second Object (RI-7) and the tenor concludes with the First Object (RI-3). In this manner Stravinsky sets up a complete symmetrical journey through the objects ending with a return to the home object, perhaps to depict the word "circumdedit" or "compassed."

In the last two-part canon (M. 178), Stravinsky explores the combinatorial possibilities of hexachords from several rows from different objects. Stravinsky divides the hexachords not in two halves, but internally and asymmetrically. The tenor leads the canon with P-5 (5-10), then RI-0 (9-12 and 1-2), and finally R-0 (3-12 and 2-1). The bass follows the canon a tritone below with P-11 (5-10), then RI-6 (9-12 and 1-2), and finally R-2 (3-12 and 2-1). In this complex mesh Stravinsky creates many combinatorial aggregates, shown in Table 69.

According to the objects, the construction is symmetrical: The tenor leads with the Third Object, then the First Object; the bass follows with the First Object then the Third Object. This exploratory journey begins and ends in the Third Object, and thus returns like the first two-part canon in M. 174. At the same time, the journey ends in the Third Object. Therefore, each of these three two-part canons ends in a different object area: The Second, then the First, and finally the Third.

Several examples of word painting occur in BETH. In M. 174 note the wide leaps for "contrivit" or "he broke." The rows are rotated, and rotate even further away from the pure forms to underscore the text "He built against me and encompassed me" and "he has set me in dark places." Perhaps Stravinsky's use of combinatorial aggregates, a technique prevalent in Schoenberg and used no where else in Threni, for the words "He hath set me in dark places, as they that be dead as of old" is a compositional homage to Schoenberg.

VAU

The third of the four subsections in Querimonia is VAU (M. 179-187). In VAU, Stravinsky uses canon in three parts to explore different cyclic presentations of rows and hexachords. The first two canons in VAU use rows related by ic5, the last canon by ic4. Since the objects for Threni are generated by ic3, the three-part canons in VAU based on ic5 or ic4 engage rows from different Objects in each voice.

The rows of the letter are R-0 in the sopranos and altos; yet difficult to determine in the trombones due to their vertical (harmonic) note presentation.

Continuing Querimonia's pattern of adding another canonical voice for each letter, Stravinsky presents canons in three voices in VAU. In each of the three of the canons in VAU, the vocal parts sing rows from all three objects, one object in each voice.

A musical-poetical conjunction appears at the words "he has also broken my teeth," where Stravinsky depicts the words with broken fragments of rows. In M. 180 the tenor leads the canon with the hexachord R-2b (9-12 and 8-7) followed by an incomplete hexachord P-0b (8-12). Note that D (P-0 note 7) is missing from this statement, and the same respective pitch is absent from the following voices as well (bass 1 Ab and bass 2 Eb). Furthermore, even if these hexachords were complete, they would not form aggregates, since two pitches repeat in each hexachord. The bass voices follow the canon quickly each a perfect fourth below. Bass 1 sings R-9b (9-12 and 8-7) followed by P-7b (8-12). Bass 2 sings R-4b (9-12 and 8-7) followed by P-7b (8-12).

The hexachords employed in M. 180 change objects midway through in each voice at the words "cibavit me cinere" or "covered me with ashes." The tenor begins in the Third Object (R-2) and ends in the First Object (P-0). The bass 1 begins in the First Object (R-9) and ends in the Second Object (P-7). The bass 2 begins in the Second Object (R-4) and ends in the Third Object (P-2).

Additionally, the systematic row shifts in M. 180 reinforce ic5 in that the voices enter and conclude symmetrically in descending perfect fourths. Another aspect of the symmetry in M. 180 occurs where the first hexachord in each voice is transposed down a whole step and reversed, albeit the order of pitches is not maintained.

In the second three-part canon (M. 182) the tenor leads with P-2 (5-12 and 4-1), followed by the bass 1 a perfect fifth lower singing P-7 (5-12 and 4-1), and finally the bass 2 again a perfect fifth lower singing P-0 (5-12 and 4-1). The voices end with pitches related to each other as descending perfect fifths, and so the rows reinforce ic5 just as in M. 180. Note that the unusual row ordering turns to retrograde for the final four pitches to depict the text "bonorum" or a return to the former "prosperity." The tenor is in the Third Object, the bass 1 in the Second Object, and the bass 2 in the First Object.

Like the other two three-part canons, the third three-part canon, in M. 184-187, begins with the tenor leading, but this time each voice enters an ic4 apart. The tenor sings RI-10 (6-12 and 5-1), the bass 1 follows a major third below with RI-6 (6-12 and 5-1), and the bass 2 finishes with RI-2 (6-12 and 5-1). The order of the pitches in each row is just as in M. 182, where the order was 5-12 and 4-1, with the addition of a single pitch. The change of order occurs on the word "mea" or "my" for the syllabic presentation of the text "Periit finis meus, et spes mea a Domino," or "my strength and my hope is perished from the Lord." The tenor is in the Second Object, the bass 1 in the First Object, and the bass 2 in the Third Object.

ZAIN

The last of the four subsections in Querimonia is ZAIN (MM. 188-193). Again, an additive pattern of canons is at work in Querimonia, and this final section has four voices. However, the canons here are double canons, in which two pairs of voices sing canons simultaneously. The letter is made up of the P-0 row in the sopranos and altos, and the I-0 row in the trombones. Returning to some of the foundational rows is appropriate for this, the last of the four subsections in Querimonia.

In M. 189, the first canon begins in the bass 2 with RI-3 and R-9. The tenor 2 follows the first canon a perfect fifth above with RI-10 and R-4. The second canon begins in the bass 1 part with RI-6 rot3, followed by the tenor 1 a minor sixth above with RI-2 rot3. The first canon bass 2 is in the First Object, the tenor 2 is in the Second Object. The second canon bass 1 is in the First Object, the tenor 1 in the Third Object.

In M. 191, the leading and following voices exchange roles. The first canon begins in the bass 1 with P-10 and R-10, with the tenor 2 following a tritone higher with P-4 and R-4. The second canon begins with tenor 1 singing RI-1 and RI-4, with the bass 2 following a major sixth lower with RI-4 and RI-7. All the rows here are from the Second Object, and all either begin or end on G (RI-4 spans E to G, P-4 G to Bb, R-4 Bb to G) or E (RI-1 C# to E, P-10 C# to E, R-10 E to C#, RI-4 E to G). The unity of the rows from a single object is perhaps appropriate of "memoria" or the "remembrance" of a previous single object-state (from the first of the four subsections ALEPH and from "De elegia prima"), however the remembrance of the original First Object is blurred, and the Second Object is used in its place. (Stravinsky used rows from the Second Object to depict weeping and enemies earlier.) Remembrance is also parlayed through the row succession, in that the voices of the second canon trace their rows back on themselves, i.e. a row is followed by its retrograde (bass 1 P-10 to R-10, and tenor 2 P-4 to R-4).

In the previous two double canons, one leading voice started before the other, but in the final double canon in M. 193, both canons begin at the same time. However, the voices that follow do not enter at the same time. The first canon begins in the bass 1 with RI-6 rot5, and the tenor follows a tritone higher with RI-0 rot5. The second canon begins in the tenor 1 with R-9, and the bass 2 follows a minor ninth below with R-8. All the rows are from the First Object except the bass 2, which is from the Third Object. The bass 2, entering last, comes in at its pitch level and not in the First Object as a surprise. This unexpected entry by the last voice to finish the canon enhances the inconclusive ending of Querimonia, appropriate for the first of three parts in "De elegia tertia." In addition, the text of this canon is set appropriately, as the words "therefore I have hope" recall the First Object. However, the setting is incomplete and tainted by the bass' single statement of the Third Object.

Just as in "De elegia prima," here Stravinsky uses the rows in the Second and Third Objects to establish different regions from the foundational rows in the First Object. In Querimonia Stravinsky sets the Hebrew letters with rows from the First Object (with the possible exception of BETH). The canons explore interval relationships outside of ic3, on which the Objects for Threni are based. At the same time, however, Stravinsky maintains a balance between which Objects are used simultaneously and in succession. Table 70 lists the Objects used for Querimonia.

Sensus spei

The second of the three parts of "De elegia tertia" is Sensus spei or "Perceiving hope" (MM. 166-193). Sensus spei is a setting of eight Hebrew letters and their corresponding Lamentations text from chapter three of the Biblical book of Lamentations. Chapter three, the triple acrostic, contains sixty-six verses of text in comparison with the twenty-two verses of the other four chapters of Lamentations. Formally, Stravinsky sets aside the strict additive canons of Querimonia in favor of a large-scale formal structure made up of three statements of each of the eight letters. In between the statements of the letters, Stravinsky inserts the Lamentations text in various methods with a timbral palate of much greater variety than any heard thus far in Threni.

Table 71 presents the Latin words and King James English translation of the second part of "De elegia tertia:" Sensus spei. Stravinsky's alterations of the Latin text are designated with square editorial brackets [].

The Hebrew letters of Sensus spei employ pitches, one or two at a time, from a single row (RI-3). The row is from the First Object and is significant because of its relationship to P-0: both rows begin on Eb and end on F#. RI-3 is also one of the extended foundational rows Stravinsky used in the Incipit. Table 72 lists all the rows employed in Sensus spei.

HETH

As in the beginning of "De elegia prima" and "De elegia tertia", Stravinsky generally opens formal sections with rows from the First Object. HETH, the beginning of Sensus spei, is no exception. In the Latin text for MM. 194-203, the rows used are I-0, RI-6 rot2, and RI-6. In contrast with the previous section's sorrowful message, two of the four foundational rows from the First Object are appropriately used here where the words concern mercy and compassion. (The foundational rows are P-0, R-0, I-0, and, in Threni, RI-6.)

TETH

In TETH (MM. 204-216), rows from two objects are combined symmetrically. The alto soloist sings I-2 (1-4) from the Third Object, followed by the tenor soloist P-9 (5-12) from the First Object. Note that these row segments do not form an aggregate, since C# and F# are in both rows. The clarinets play I-0. The rows and Objects are shared in a similar manner to those shared previously in MM. 182 and 184. Table 73 shows the palindromic symmetrical structure of row presentation.

LAMED

Like TETH, LAMED (MM. 217-230) also employs fragments of rows from two objects, one fragment of four pitches and the other of eight. In the case of LAMED, the bass sings P-7 (1-4), the tenor sings I-11 (5-12), and the instruments play RI-5 with no fourth pitch (G). Here the bass's P-7 is from the Second Object, and the I-11 and RI-5 are from the Third Object.

Most likely, Stravinsky creates the parallel between TETH and LAMED because each of the sets of three verses in these sections begins with the same or similar word. The verses in TETH begin "Bonus est," "Bonum est," and "Bonum est." The verses in LAMED each begin with "Ut." Fittingly, this word repetition is not unusual, because the structure of the text in the third chapter of Lamentations is a triple acrostic, with three successive lines beginning with the first letter of the Hebrew alphabet, and the next three lines beginning with the next letter of the Hebrew alphabet, and so on through the 22 letters. In the cases of TETH and LAMED, Stravinsky capitalized on the similarity of the words in the Latin translation by incorporating them into his form.

NUN

Stravinsky returns to the four foundational rows from the First Object and presents them simultaneously for "return again to the Lord" in NUN (MM. 231-245). Rows are employed identically in the first two verses (MM. 231-234 and 235-238). The chorus soprano and alto 1 parts sing R-0, the alto 2 and tenor parts sing I-0. P-0 begins in the trombones and is passed to the celeste, violas, and cellos. After an initial chord of I-0 (1-3) in the harp and contrabass, the low strings and clarinets play RI-6. The third verse (MM. 239-245), however, is different in that all the vocal parts sing RI-6, as the instruments play I-0 (1-3).

SAMECH

In SAMECH (MM. 246-259), the rows are fragmented into hexachords and obscured in reference to the words from Lamentations: "Thou hast covered thyself." In addition, row statements further fragment into even smaller units for the text "Thou hast made us as the off scouring and refuse in the midst of the people." The section begins (MM. 246-249) with a tenor soloist singing R-0 (1-6) followed by the sopranos and altos in the chorus each singing P-0 (7-12) at a different rate and contour. Note that all three of these voices sing the same six pitches, albeit the chorus parts are in reverse order of the tenor part. The section continues with a bass soloist singing RI-6 (1-6) followed by the sopranos and altos in the chorus each singing RI-0 (7-12) at a different rate and contour. Up to this point, SAMECH has consisted of hexachords from the foundational forms of the First Object. The final part of SAMECH (MM. 252-259), however, employs fragments from all four foundational forms. The tenor soloist begins with RI-6 (1-5), R-0 (1-6), and I-0 (1-8). Then the instruments enter with P-3 rot5, and the bass soloist sings an altered form of P-0, which is mis-ordered (3, 9, 11, 12, 1, 2, 11, 4, 5, 6, 7, 8, 9 in contrabass) and contains all the notes for an aggregate save C (10). This order is close to a P-0 rot9. Possibly the first two pitches were transcribed from the treble clef, and should have been E and C (9 and 10), and the F (11) in M. 258 should have been a G. Nevertheless, the wrong-ordering in the score seems to convey the words about the individual's a lienation from society.

AIN

AIN (MM. 260-281) employs a single row from the First Object, R-9. The row is first sung by the soprano and alto soloists, and the tenor and bass soloists answer with a hexachord made of the outer notes from the row (3, 2, 1, 12, 11, 10). This row use repeats two more times in this section. Note that the direction of the voices and their melodic lines from high to low depicts "till the Lord look down and behold from heaven."

The three letters NUN, SAMECH, and AIN all use rows from the First Object. The compositional procedure in these three letters displays a logical progression. In NUN the full rows are presented in a clear and straightforward manner. In SAMECH the rows are obscured through hexachordal and fragmented presentation. Finally, in AIN a single row is employed for the entire section. It seems as if the First Object hereby is progressively refined from many rows into one in a manner akin with putrefaction in alchemy, where purity is obtained only after decomposition. This row refinement is appropriate for the progression into the depiction of the eye that observes contemporary injustice depicted in the words of AIN.

TSADE

The dramatic narrative shifts to "enemies" and "affliction" in TSADE (MM. 282-309). The subject matter in TSADE is similar to the subject matter in Querimonia, and the presentation in TSADE is again imitative, albeit now as fugal subjects rather than strict canons. In addition, like Querimonia the subsections here are formally additive--the first subsection for two voices, the second for three voices, and the third for four. The first subsection (MM. 282-290) begins with the alto soloist singing RI-6 from the First Object, and the tenor following with R-5 from the Third Object. The second subsection begins with the soprano soloist singing R-0 from the First Object, followed by the tenor singing I-0 from the First Object, and the alto singing P-11 from the Third Object. Thus far, the RI-6 and R-0 (First Object) initial entrances each become mirrored by the following statements of their retrogrades, transposed (degenerated) a whole step down: R-5 and P-11 (Third Object). Perhaps to balance the statements of the First and Third Objects of the first two subsections of TSADE, the third subsection (MM. 301-309) begins with the bass singing I-1 from the Second Object. The other voices sing rows that were already heard in TSADE: the alto sings RI-5, the soprano I-0, and the tenor P-11. Here Stravinsky's row selection seems to portray the lone bass (first hearing of the Second Object in TSADE) over which, according to the poetic text, flows the waters in the other voices, which are singing previously stated forms.

The last measure in TSADE (M. 309) consists of a variety of incomplete row fragments (trichords), depicting the text "I am cut off." The measure contains all the notes of the aggregate except A.

COPH

COPH (MM. 310-321) closes Sensus spei by using rows from the Second Object centered on E. In the first of three subsections (MM. 310-313) the soprano soloist sings R-1, the alto soloist sings I-1, and a cello solo plays P-1. In the second subsection the soprano sings R-1, the alto and tenor both sing I-1 at different rates and contours, and the cello soloist again plays P-1. In the third subsection, the bass sings I-1 alone, as he did at the end of TSADE, forming a formal link between the two final letters of "Sensus spei."

The curious contrabass pizzicati in MM. 317-318, Eb and F, seem to be related to nothing else in Threni and do not double any other rows. Perhaps they portray the "cry" of the text by playing the first notes of rows from the First and Third Objects in contrast with all the other rows used in COPH, which are from the Second Object.

Sensus spei closes in M. 321 with a restatement of the row fragments from M. 309. Here, with the text "fear not," the trichords heard previously are extended by one note into tetrachords, forming a complete aggregate.

Table 74 lists the Objects used for Sensus spei.

Solacium

The final subsection of "De elegia tertia" is Solacium, or "Compensation." As in the previous two subsections of "De elegia tertia," Solacium is structured around three repetitions of the Hebrew letter texts sung by the chorus. In this section, three letters are each repeated three times. Following each letter, the Latin text is sung by soloists as well as the chorus.

Table 75 presents the Latin words and King James English translation of the first part of "De elegia tertia:" Solacium. Stravinsky's alterations of the Latin text are designated with square editorial brackets [].

All of the rows used here for the Hebrew letters are from the First Object. RES(H) employs both P-0 and I-0 forms; SIN uses RI-6; and THAU uses I-0 forms. The rows used for the Latin text are from all three objects, but are employed to create a symmetrical formal structure. Furthermore, Stravinsky depicts the words musically in the permutated rows in SIN, the central part of Solacium.

The rows employed for Solacium as well as the formal structure are shown in Table 76.

The outer two parts of Solacium, RES(H) and THAU, are pseudo-reflections of each other in terms of row use. The rows used are related to each other, but are transformed either by Retrograde or Inversion. The row relationships are shown in Table 77. The rows in the Second Object are connected by solid arrows, and the rows in the Third Object are connected by dashed arrows.

The first and second parts of RES(H) as well as the first and second parts of THAU use rows from the First and Third Objects; the second part of RES(H) and the last part of THAU use rows from the First and Second Objects. Like Querimonia, the ending of THAU includes an additional row that does not formally close the work. In MM. 378 ff. of THAU, the I-10 row in the Bass from the Second Object has no analogous similar Second Object statement in RES(H). Therefore, Solacium finishes incompletely and points forward formally to "De elegia quinta." (Note that in the first part of RES(H) two rows from the Third Object (I-5 and R-5) balance with one row in the first part of THAU (RI-5). In the sense that RES(H) has one more row from the Third Object than THAU, and THAU has one more from the Second than RES(H), the formal parts balance. Even so, RES(H) has no rows balancing I-10.)

In SIN, the central section, rows from the First Object are permutated -- in this case ordered by increasing odd and decreasing even ordinal members (i.e., 1, 3, 5, 7, 9, 11, 12, 10, 8, 6, 4, 2) -- an imaginative device to underscore the "device" mentioned in Lamentations 3:61-62, "Thou hast heard their reproach, O Lord, and all their imaginations against me. The lips of those that rose up against me, and their device against me all the day."

De elegia quinta

The last section of Threni is "De elegia quinta," the fifth chapter of Lamentations. Unlike all the previous sections in Threni, "De elegia quinta" does not contain statements of Hebrew letters. This final part of Threni also is much shorter than either "De elegia prima" or "De elegia tertia."

Table 78 presents the Latin words and King James English translation of the first part of "De elegia quinta." Stravinsky's alterations to the Latin text are designated with square editorial brackets [].

The form and row use of "De elegia quinta" are shown in Table 79.

The "Oratio" in M. 384 recalls the Incipit at the opening of Threni. The P-0 and I-0 rows are sung simultaneously, a return of the foundational rows from the First Object.

In MM. 385-390, the spoken choral text recalls MM. 27 ff. from "De elegia prima." Appropriately, the aural recollection aptly depicts the words "Remember, O Lord, which is come upon us."

In MM. 390-404, the words "You, O Lord, remain for ever. You alone from generation to generation" are depicted both musically and graphically. Beginning in M. 395, the Tenor I soloist sings RI-2 from the Third Object as the Alto and Tenor II soloists, printed and sounding above and below the Tenor I, share members in another statement of the same row. Therefore the pitches of the Tenor I row literally remain with those in the row shared by the Alto and Tenor II. At the same time, beginning in M. 391 the orchestra plays P-6 and P-0 from the First Object, perhaps reflecting the steadfastness and eternal unchangeableness of God.

In M. 405-411 rows are broken up and permutated to depict the words "Turn thou us unto thee, O Lord, and we shall be turned." The Soprano and Tenor parts in the chorus share a chopped up P-0 (Soprano has pitches 1, 11, 3, 4, 8, 6, 7, 9; Tenor has pitches 12, 2, 9, 6, 5, 7). The horns play RI-3 and RI-8 from the First and Third Objects. Perhaps the opening trill in the first horn paints the word "converte," or "turn."

Stravinsky creates a fascinating formal conclusion in the last bars of Threni (MM. 412-419). As might be expected, all the rows are from the First Object. The vocal parts sing rows from the foundational rows, all of which end on either Eb or F#, the first and last notes of the Prime row. The rows played by the horns begin on F# or Eb, but end on A or C. Table 80 shows that the vocal parts sing rows "towards" the Prime row beginning and ending pitches, whereas the horns play rows "away from" the Prime row beginning and ending pitches. In this manner, Stravinsky depicts the final words "renew our days as of old," closing the work conclusively and solidly in the First Object.

    A             A
 I-6
 
 
           F#
     R-0
 
 P-0
    Eb            Eb
 
 
   RI-0
           C
 
 
 
    A             A

    A             A
 
 
   RI-6           P-3
           F#
 
 
 
    Eb            Eb
 I-0                 R-9
  
  
           C
 
 
 
    A             A

Threni: Conclusion

As demonstrated above, Stravinsky experimented with twelve-tone compositional techniques in Threni to a greater degree of complexity and a greater extent than in his shorter twelve-tone works. His row treatment included combinatoriality, set rotation, permutation, incomplete row usage, and large-scale formal row usage. His compositional choices maintained a close relationship with the meaning of the poetic text. In addition, analysis with rows projected onto three-dimensional objects aids in the explanation of many of Stravinsky's row choices for and within the individual formal sections, as well as the distinction of much of the overall structure of Threni. Stravinsky ensures the overall cohesion of this monumental work with the varying forms of, and the compositional usage of, the foundational rows from the First Object. These foundational forms are the structural frame around which the whole work is constructed.

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