2. “Tombeau”: Harmonic Form
As the preceding blog entry has shown, the means that Boulez created for organizing pitch in Pli selon pli is an immensely intricate and original technique for harmonic organization in a non-tonal context. Despite its theoretical complexity, this technique is unarguably less complex from an audible standpoint, for the ear can come to appreciate the harmonic logic in the music, due to the nature of the frequency-multiplication technique of interval associations. What is also appreciable in “Tombeau” is the incredible sensation of forward motion in the first 500 measures and the way in which this motion drives inexorably to the structural climax in m. 517, both of which are audibly clear events in the music. This part of the analysis of “Tombeau” illustrates how pitch, instrumentation and tempo promote these sensations and how pitch, in particular, defines musical form: “Serial harmony,” in essence, becomes “harmonic form.”
The roles of instrumentation and tempo in the musical form are relatively straightforward. “Tombeau” is composed of three distinct sections: Section I extends from mm. 1 to 257, Section II from mm. 258 to 517 and Section II from mm. 518 to 548. In Section I, Boulez divides the orchestra into five principal instrumental groupings (labeled as groupe principal, the vertical ordering of instruments in the score corresponding to these groupings), and each group is introduced successively. Section I is also organized around five different tempos. In this way, instrumentation and tempo contribute to the design of Section I as five distinct sub-sections:
As the preceding blog entry has shown, the means that Boulez created for organizing pitch in Pli selon pli is an immensely intricate and original technique for harmonic organization in a non-tonal context. Despite its theoretical complexity, this technique is unarguably less complex from an audible standpoint, for the ear can come to appreciate the harmonic logic in the music, due to the nature of the frequency-multiplication technique of interval associations. What is also appreciable in “Tombeau” is the incredible sensation of forward motion in the first 500 measures and the way in which this motion drives inexorably to the structural climax in m. 517, both of which are audibly clear events in the music. This part of the analysis of “Tombeau” illustrates how pitch, instrumentation and tempo promote these sensations and how pitch, in particular, defines musical form: “Serial harmony,” in essence, becomes “harmonic form.”
The roles of instrumentation and tempo in the musical form are relatively straightforward. “Tombeau” is composed of three distinct sections: Section I extends from mm. 1 to 257, Section II from mm. 258 to 517 and Section II from mm. 518 to 548. In Section I, Boulez divides the orchestra into five principal instrumental groupings (labeled as groupe principal, the vertical ordering of instruments in the score corresponding to these groupings), and each group is introduced successively. Section I is also organized around five different tempos. In this way, instrumentation and tempo contribute to the design of Section I as five distinct sub-sections:
Each sub-section concludes with a rallentando that “modulates” seamlessly to the following tempo. The principal instrumental groups, introduced by the piano in the opening thirty measures, are maintained throughout the entire work. Example 16 also shows that the brass section of the orchestra is not given a principal role in this section. Rather, the brass instruments generally double the pitches of other instrumental groups, thus establishing bonds between the different groups. In Section II, however, the brass is treated more as an independent instrumental group.
Despite an exact correspondence between changes in instrumentation and tempo in Section I, these changes occur inversely; that is, the number of principal instruments increases, while the tempos decelerate. However, this is reversed in the fifth sub-section: here, the number of principal instruments is reduced, and the tempo accelerates. Also of importance is that the length in the number of measures of each sub-section increases (39, 40, 46, 46, 82 measures, respectively) and thus the duration of each sub-section.
Pitch (specifically, the array of sets reproduced in Example 10) assumes a more substantive role in this formal scheme. The principal instruments in each of the five sub-sections perform harmonic units from the five basic sets (sets x-00 from Example 10), beginning with sets 1-00, 2-00 and 3-00 in the piano in sub-section 1. Sub-section 2, featuring the xylophone, timpani and tubular bells as the principal instruments, continues with sets 4-00, 5-00, 1-00 and an incomplete 2-00. The seven winds of sub-section 3 resume with the third unit of set 2-00, the first two units of which are performed at the end of sub-section 2. Each of the five sub-sections continues with this methodology, resulting in five statements of each of the five sets in Section I. This is reproduced in Example 17. Note the significance of the number five in organizing the differing parameters of the piece.
Despite an exact correspondence between changes in instrumentation and tempo in Section I, these changes occur inversely; that is, the number of principal instruments increases, while the tempos decelerate. However, this is reversed in the fifth sub-section: here, the number of principal instruments is reduced, and the tempo accelerates. Also of importance is that the length in the number of measures of each sub-section increases (39, 40, 46, 46, 82 measures, respectively) and thus the duration of each sub-section.
Pitch (specifically, the array of sets reproduced in Example 10) assumes a more substantive role in this formal scheme. The principal instruments in each of the five sub-sections perform harmonic units from the five basic sets (sets x-00 from Example 10), beginning with sets 1-00, 2-00 and 3-00 in the piano in sub-section 1. Sub-section 2, featuring the xylophone, timpani and tubular bells as the principal instruments, continues with sets 4-00, 5-00, 1-00 and an incomplete 2-00. The seven winds of sub-section 3 resume with the third unit of set 2-00, the first two units of which are performed at the end of sub-section 2. Each of the five sub-sections continues with this methodology, resulting in five statements of each of the five sets in Section I. This is reproduced in Example 17. Note the significance of the number five in organizing the differing parameters of the piece.
Incomplete sets between sub-sections 2, 3, 4 and 5 are means of establishing links between these sub-sections. Thus, these harmonic links are elisions between formal units.
By contrast, frequency-multiplication sets are distributed to the instrumental group that no longer functions as a principal group. The first of these sets is given to the piano in m. 43 (sub-section 2) with the appearance of the second instrumental group (xylophone, timpani and tubular bells) in m. 41. Here, the piano becomes background, at which point frequency-multiplication sets (sets x-22) appear for the first time. At m. 81 (sub-section 3), with the appearance of the third principal group, frequency-multiplication sets are distributed to the piano (x-33) and to the xylophone, timpani and tubular bells (x-22, those sets previously performed by the piano). In essence, each instrumental group moves deeper into the array of sets as Section I progresses:
By contrast, frequency-multiplication sets are distributed to the instrumental group that no longer functions as a principal group. The first of these sets is given to the piano in m. 43 (sub-section 2) with the appearance of the second instrumental group (xylophone, timpani and tubular bells) in m. 41. Here, the piano becomes background, at which point frequency-multiplication sets (sets x-22) appear for the first time. At m. 81 (sub-section 3), with the appearance of the third principal group, frequency-multiplication sets are distributed to the piano (x-33) and to the xylophone, timpani and tubular bells (x-22, those sets previously performed by the piano). In essence, each instrumental group moves deeper into the array of sets as Section I progresses:
Inevitably, as Section I progresses and the number of instrumental groups increases, the number of distinct pitch layers increases as well. Whereas the first sub-section of Section I contains just units of the twelve-note sets performed by one principal group, the fifth sub-section comprises all five levels of the array, performed by one principal group and four non-principal groups. To co-ordinate these various layers, Boulez establishes a unique registral fixation for each pitch, defined by units of the twelve-note sets that are performed by the principal groups, as reproduced in Example 17.
Boulez’s strategy for selecting sets in “Tombeau,” one that is similarly used in cummings ist der dichter from 1970, is determined by a diagonal progression through the array of harmonic units, matching the diagonal pattern of Example 18. The following example charts the sets performed by the piano in Section I:
Boulez’s strategy for selecting sets in “Tombeau,” one that is similarly used in cummings ist der dichter from 1970, is determined by a diagonal progression through the array of harmonic units, matching the diagonal pattern of Example 18. The following example charts the sets performed by the piano in Section I:
When the piano is the principal instrument, it begins, expectedly, with the parent set and moves successively to the following sets on the same level. When it is no longer principal (beginning in sub-section 2), it moves to the second level of the array, yet rather than beginning with the first set of this level, it moves to the set that is diagonally to the right of the parent set (i.e., set 2-22). It then continues reading the second level of sets successively, until a new principal group appears. At this point (sub-section 3), it moves to the third level of the array, again diagonally to the right of the first set performed on the second level (i.e., set 3-33) and continues on the third level.
When an instrumental group succeeds another group on a level of the array, the former begins with the same set, occasionally the following set, performed by the latter. Example 20 lists the sets performed by each instrumental group in Section I. Sets in parentheses represent incomplete sets.
When an instrumental group succeeds another group on a level of the array, the former begins with the same set, occasionally the following set, performed by the latter. Example 20 lists the sets performed by each instrumental group in Section I. Sets in parentheses represent incomplete sets.
The incomplete sets in Example 20 are means for establishing links between instrumental groups and formal units, as with the incomplete sets in Example 17. For example, the piano performs only the first four units of set 4-22 in sub-section 2. The final unit of this set is then given to the xylophone, timpani and tubular bells, as this group moves to the second level of the array in sub-section 3. This is done in nearly every instance when an instrumental group changes levels in the array and is also done between Sections I and II and between Sections II and III. Additionally, sets on each level of the array appear a unique number of times: There are twenty-five x-00 sets, eighteen x-22 sets, twelve x-33 sets, fourteen x-44 sets and eight x-55 sets.
The justification for classifying mm. 258–517 as Section II is that these measures, with a length approximating that of Section I—Section I is 257 measures; Section II is 259 measures—represent another formal unit, one that continues and expands on ideas introduced in Section I. However, while Section I comprises five sub-sections, determined by unique tempo markings, principal instrumental groups and levels from the array of sets, Section II comprises a single irreducible section, defined by one tempo indication, no principal instrumental group and one set-array level for each group for the duration of this section. At the beginning of Section II, each instrumental group advances one level deeper into the array and retains these positions for all of this section. The brass group, now an independent instrumental group, performs the five basic sets (sets x-00), rather than doubling other instrumental groups. The piano, having reached the fifth and final level in the array (sets x-55) at the conclusion of Section I, returns to the first level, with the brass, although in a different manner. Example 21 shows the initial set performed by each instrumental group in Section II:
The justification for classifying mm. 258–517 as Section II is that these measures, with a length approximating that of Section I—Section I is 257 measures; Section II is 259 measures—represent another formal unit, one that continues and expands on ideas introduced in Section I. However, while Section I comprises five sub-sections, determined by unique tempo markings, principal instrumental groups and levels from the array of sets, Section II comprises a single irreducible section, defined by one tempo indication, no principal instrumental group and one set-array level for each group for the duration of this section. At the beginning of Section II, each instrumental group advances one level deeper into the array and retains these positions for all of this section. The brass group, now an independent instrumental group, performs the five basic sets (sets x-00), rather than doubling other instrumental groups. The piano, having reached the fifth and final level in the array (sets x-55) at the conclusion of Section I, returns to the first level, with the brass, although in a different manner. Example 21 shows the initial set performed by each instrumental group in Section II:
Sections I and II feature a variety of similarities, in addition to an approximate correspondence in length. Both sections open with a piano solo, the only instances in these sections in which the piano, or any instrument, assumes such prominence. In both cases, the piano introduces the other instrumental groups by pitch doublings. Further, both sections show a dramatic unfolding of textural density and motion, that of Section II, continuing where Section I left off, being far greater. Lastly, each section concludes with an extended rallentando, by far the two largest modifications in tempo in the entire piece (largest in terms of range of metronome values). In fact, the metronome marking of Section II takes the reduction introduced in Section I one additional step and completes it:
Additionally, Section II could be regarded as a formal expansion, equivalent to the length of Section I, of the third sub-section (mm. 81–127) of Section I. For example, both share the same metronome marking, and both feature six statements of the twelve-note sets by the respective principal instrumental groups.
In contrast to Section I, however, Boulez does not categorize a principal instrumental group in the score in Section II. This may be interpreted in one of two ways. One, the brass section, performing the five basic twelve-note sets, is now the principal group, inasmuch as the principal group invariably performs these sets in Section I (although the piano likewise performs these sets). Two, none of the groups is principal, whereby each would be considered equivalent. Also of distinction in this section is the structuring of pitch. Registral fixation continues to be used in this section, but whereas each of the twenty-five twelve-note sets in Section I works with a different fixation, that of Section II is defined by the parent set (set 1-00) performed by the piano at the beginning of this section (mm. 258–274). Example 23 illustrates the registers of the notes of this set:
In contrast to Section I, however, Boulez does not categorize a principal instrumental group in the score in Section II. This may be interpreted in one of two ways. One, the brass section, performing the five basic twelve-note sets, is now the principal group, inasmuch as the principal group invariably performs these sets in Section I (although the piano likewise performs these sets). Two, none of the groups is principal, whereby each would be considered equivalent. Also of distinction in this section is the structuring of pitch. Registral fixation continues to be used in this section, but whereas each of the twenty-five twelve-note sets in Section I works with a different fixation, that of Section II is defined by the parent set (set 1-00) performed by the piano at the beginning of this section (mm. 258–274). Example 23 illustrates the registers of the notes of this set:
Most of the pitches in Section II conform to this scheme, although certain pitches stray somewhat and do not appear to adhere to any system. Section II, thus, becomes a massive instance of harmonic stasis.
As noted previously, each instrumental group moves one level deeper into the array and maintains this level for the entire section. Example 24 lists all of the sets performed by each of the instrumental groups in Section II:
As noted previously, each instrumental group moves one level deeper into the array and maintains this level for the entire section. Example 24 lists all of the sets performed by each of the instrumental groups in Section II:
As in Section I, the number of sets performed by each instrumental group in Section II differs.
As Example 20 shows, certain sets are left incomplete at the conclusion of Section I. Boulez transfers the units of the incomplete sets to the instrumental group that occupies the new level in the array in Section II (compare Examples 20 and 24). In m. 280, the harps, vibraphone, celesta and guitar are given the fifth unit of set 4-22, left unperformed by the strings at the end of Section I. In m. 283, the strings, somewhat more meticulously, take the one note, C-sharp, that is not included in the second unit of set 4-33 of the winds (mm. 254–55) and remain on this level. In m. 276 the winds open with the third unit of set 2-44, left unperformed by the xylophone, timpani and tubular bells in m. 257. This group, in turn, begins with set 3-55 in m. 287, following the piano’s conclusion on this level with the fourth unit of set 2-55 (the fifth unit of set 2-55 is seemingly disregarded). Again, harmonic units act as elisions between formal components.
Section II and Section III, mm. 518–548, the final section of “Tombeau,” are separated by a general pause, being, in fact, the first complete silence until this point in the piece. Unquestionably, the greatest distinction between Section III and the previous two sections is the absence of metrical rhythmic notation. Section III is grouped into time fields, designated as “senza tempo,” the durations of which are left to the discretion of the conductor on the basis of prescribed cues. Curiously, this aspect of the piece was not subsequently rewritten by the composer, as similar passages in the opening movement, “Don,” were subjected to drastic revisions in the 1980s.
This dual temporal construction, strictness versus freedom, is a pivotal feature in the music of Boulez’s mature period. He has noted, “I regard the two categories—smooth and striated time—as capable of reciprocal interaction…I can say that my whole formal time system is based on them and them alone.” (Pierre Boulez, Orientations, p. 87) His terminology is based on a division of musical time into two categories: pulsed time (i.e., metrical time) and amorphous time (i.e., proportional time). He has observed that in pulsed time, durations are related to chronometric time; this constitutes a pulsation, of either the smallest unit of the system of a simple integral multiple of the system (such as 2 or 3). Amorphous time, however, is related to chronometric time only in a global sense: Durations, either with or without designated proportions (i.e., unfixed time values), occur within a prescribed time field. However, only pulsed time is susceptible to temporal modifications, i.e., acceleration and deceleration; amorphous time can do this only by deviating in density according to a number of events that occur within a chronometric time field (i.e., events occurring more slowly or more quickly). Amorphous time, for Boulez, is comparable to a smooth surface, pulsed time to a striated surface; hence, the terms smooth and striated time. (Pierre Boulez, Boulez on Music Today, pp. 88–89)
The introduction of smooth time in Section III can be understood in terms of the objective of Sections I and II. Since temporal deceleration and the drive to the structural climax in m. 517 are important factors in the first two sections, an application of an amorphous time system would be impractical. However, once the process of deceleration has been completed, as after the climax in m. 517, an amorphous temporal system may be incorporated, as Section III appropriately does. The five movements of Pli selon pli are pivotal in Boulez’s output, in the sense that they are virtually the first works to exploit the reciprocal interactions of these two temporal systems, although this was prefigured in the second book of Structures. In fact, most works after Pli selon pli, in their original, unrevised forms, combine both temporal systems in various ways.
Section III is composed of three sub-sections, each of which is distinguished by differences in texture. The first sub-section, mm. 518–529, is composed entirely around a homophonic (or chordal) texture; the second sub-section, mm. 530–535, is predominantly polyphonic with two brief insertions of the homophonic texture of the first sub-section; the third sub-section, mm. 536–548, recapitulates and concludes with the homophonic texture of the first sub-section. Section III, as this organization suggests, complements the design of Section II. Whereas Section II expands on the micro-structure of a sub-section of Section I, Section III duplicates the three-part macro-structure of “Tombeau” in general, by presenting in miniature (thirty-one measures) the three-part form of the work. Thus, in a structural sense, Section II elaborates on a formal unit of Section I, while Section III summarizes what takes place in the entire work.
Section III maintains the six-part instrumental grouping of the previous section, yet the six groups are aggregated to form two larger groups (piano, xylophone, gongs, bells, harps, vibraphone, celesta, guitar and winds, brass, strings). In the first sub-section these groups are differentiated by the way harmonic units are performed. The first group performs these units with differing attacks and simultaneous decays; conversely, the second group performs units with simultaneous attacks and differing decays. The array of sets likewise contributes to defining this two-part orchestral structuring. The piano, xylophone, gongs, bells, harps, vibraphone, celesta and guitar perform harmonic units from the basic twelve-note sets (sets x-00), while the strings, winds and brass perform units from the frequency-multiplication sets:
As Example 20 shows, certain sets are left incomplete at the conclusion of Section I. Boulez transfers the units of the incomplete sets to the instrumental group that occupies the new level in the array in Section II (compare Examples 20 and 24). In m. 280, the harps, vibraphone, celesta and guitar are given the fifth unit of set 4-22, left unperformed by the strings at the end of Section I. In m. 283, the strings, somewhat more meticulously, take the one note, C-sharp, that is not included in the second unit of set 4-33 of the winds (mm. 254–55) and remain on this level. In m. 276 the winds open with the third unit of set 2-44, left unperformed by the xylophone, timpani and tubular bells in m. 257. This group, in turn, begins with set 3-55 in m. 287, following the piano’s conclusion on this level with the fourth unit of set 2-55 (the fifth unit of set 2-55 is seemingly disregarded). Again, harmonic units act as elisions between formal components.
Section II and Section III, mm. 518–548, the final section of “Tombeau,” are separated by a general pause, being, in fact, the first complete silence until this point in the piece. Unquestionably, the greatest distinction between Section III and the previous two sections is the absence of metrical rhythmic notation. Section III is grouped into time fields, designated as “senza tempo,” the durations of which are left to the discretion of the conductor on the basis of prescribed cues. Curiously, this aspect of the piece was not subsequently rewritten by the composer, as similar passages in the opening movement, “Don,” were subjected to drastic revisions in the 1980s.
This dual temporal construction, strictness versus freedom, is a pivotal feature in the music of Boulez’s mature period. He has noted, “I regard the two categories—smooth and striated time—as capable of reciprocal interaction…I can say that my whole formal time system is based on them and them alone.” (Pierre Boulez, Orientations, p. 87) His terminology is based on a division of musical time into two categories: pulsed time (i.e., metrical time) and amorphous time (i.e., proportional time). He has observed that in pulsed time, durations are related to chronometric time; this constitutes a pulsation, of either the smallest unit of the system of a simple integral multiple of the system (such as 2 or 3). Amorphous time, however, is related to chronometric time only in a global sense: Durations, either with or without designated proportions (i.e., unfixed time values), occur within a prescribed time field. However, only pulsed time is susceptible to temporal modifications, i.e., acceleration and deceleration; amorphous time can do this only by deviating in density according to a number of events that occur within a chronometric time field (i.e., events occurring more slowly or more quickly). Amorphous time, for Boulez, is comparable to a smooth surface, pulsed time to a striated surface; hence, the terms smooth and striated time. (Pierre Boulez, Boulez on Music Today, pp. 88–89)
The introduction of smooth time in Section III can be understood in terms of the objective of Sections I and II. Since temporal deceleration and the drive to the structural climax in m. 517 are important factors in the first two sections, an application of an amorphous time system would be impractical. However, once the process of deceleration has been completed, as after the climax in m. 517, an amorphous temporal system may be incorporated, as Section III appropriately does. The five movements of Pli selon pli are pivotal in Boulez’s output, in the sense that they are virtually the first works to exploit the reciprocal interactions of these two temporal systems, although this was prefigured in the second book of Structures. In fact, most works after Pli selon pli, in their original, unrevised forms, combine both temporal systems in various ways.
Section III is composed of three sub-sections, each of which is distinguished by differences in texture. The first sub-section, mm. 518–529, is composed entirely around a homophonic (or chordal) texture; the second sub-section, mm. 530–535, is predominantly polyphonic with two brief insertions of the homophonic texture of the first sub-section; the third sub-section, mm. 536–548, recapitulates and concludes with the homophonic texture of the first sub-section. Section III, as this organization suggests, complements the design of Section II. Whereas Section II expands on the micro-structure of a sub-section of Section I, Section III duplicates the three-part macro-structure of “Tombeau” in general, by presenting in miniature (thirty-one measures) the three-part form of the work. Thus, in a structural sense, Section II elaborates on a formal unit of Section I, while Section III summarizes what takes place in the entire work.
Section III maintains the six-part instrumental grouping of the previous section, yet the six groups are aggregated to form two larger groups (piano, xylophone, gongs, bells, harps, vibraphone, celesta, guitar and winds, brass, strings). In the first sub-section these groups are differentiated by the way harmonic units are performed. The first group performs these units with differing attacks and simultaneous decays; conversely, the second group performs units with simultaneous attacks and differing decays. The array of sets likewise contributes to defining this two-part orchestral structuring. The piano, xylophone, gongs, bells, harps, vibraphone, celesta and guitar perform harmonic units from the basic twelve-note sets (sets x-00), while the strings, winds and brass perform units from the frequency-multiplication sets:
The sole exception to this is the harmonic unit that opens Section III in m. 519, performed by the harps, vibraphone, celesta and guitar (notated at sounding pitch):
Remarkably, this eight-note harmonic unit is a collection of the units left unperformed by each instrumental group (except for the strings) at the conclusion of Section II. F-sharp of the piano (unit 5 of unit 5-00), G, E, F-sharp of the brass (unit 5 of set 1-00), and B, A, B-flat of the xylophone, vibraphone 2 and bells (units 4 and 5 of set 5-55), A of the harps, vibraphone 1, celesta and guitar (from unit 4 of set 2-22), and C and E of the winds (from unit 5 of set 4-44) are combined to form this harmonic unit. As in Sections I and II, pitch is a significant ingredient for linking Sections II and III.
In the second sub-section of Section III, mm. 530–535, the soprano appears for the first time in the work with the final line of Mallarmé’s sonnet Le tombeau de Paul Verlaine, accompanied by horn and guitar (i.e., one instrument from each of the two instrumental groups). However, as a consequence of the virtuosic writing for the voice, featuring wide leaps and a demanding tessitura, the five words, “Un peu profond ruisseau calomnié…” (“A shallow stream and slandered…”) are virtually unintelligible, much like the vocal writing in the preceding “Improvisation III sur Mallarmé.” The conclusion of this sub-section features a different approach. In mm. 546–548, the soprano performs the two closing words of the sonnet, “la mort” (“death”), set to the pitches F-sharp and D; the performance of the latter is to be “…spoken without timbre, solely on the breath.” Contrary to the unintelligibility of the first five words of the text, these two words are entirely comprehensible, perhaps as a means of highlighting the significance of death in this portrait of Mallarmé.
In mm. 531–32, the soprano is interrupted by two harmonic units, the first performed by xylophone, gongs, bells and strings, the second by harps, vibraphone, guitar and winds. The two-part orchestral structure is still evident here on the basis of performance; the strings and winds perform their units as trills, while the harps, vibraphone, guitar and winds do not. What is especially noteworthy is that these are units 4 and 5 from set 3-33, the two units left unperformed by the strings in m. 517 (see Example 24):
In the second sub-section of Section III, mm. 530–535, the soprano appears for the first time in the work with the final line of Mallarmé’s sonnet Le tombeau de Paul Verlaine, accompanied by horn and guitar (i.e., one instrument from each of the two instrumental groups). However, as a consequence of the virtuosic writing for the voice, featuring wide leaps and a demanding tessitura, the five words, “Un peu profond ruisseau calomnié…” (“A shallow stream and slandered…”) are virtually unintelligible, much like the vocal writing in the preceding “Improvisation III sur Mallarmé.” The conclusion of this sub-section features a different approach. In mm. 546–548, the soprano performs the two closing words of the sonnet, “la mort” (“death”), set to the pitches F-sharp and D; the performance of the latter is to be “…spoken without timbre, solely on the breath.” Contrary to the unintelligibility of the first five words of the text, these two words are entirely comprehensible, perhaps as a means of highlighting the significance of death in this portrait of Mallarmé.
In mm. 531–32, the soprano is interrupted by two harmonic units, the first performed by xylophone, gongs, bells and strings, the second by harps, vibraphone, guitar and winds. The two-part orchestral structure is still evident here on the basis of performance; the strings and winds perform their units as trills, while the harps, vibraphone, guitar and winds do not. What is especially noteworthy is that these are units 4 and 5 from set 3-33, the two units left unperformed by the strings in m. 517 (see Example 24):
The third and final sub-section of Section III, mm. 536–548, serves as a preparation for the final twelve-note unit that concludes the work, the same unit that opens the first movement, “Don.” Moreover, this sub-section preserves the two-part instrumental grouping presented at the beginning of Section III. All harmonic units in these measures are taken from the fifth column of sets in Example 10, as illustrated in the following example:
Note from Example 28 that the order of entry of instruments adheres to the two-part orchestral grouping: The strings and winds perform first, followed by the bells, harps, celesta, piano, vibraphone and guitar.
The twelve-note unit that concludes “Tombeau” in m. 548 likewise concludes the motion generated in the first two sections and, in a sense, in Pli selon pli as a whole. The pitches of this unit and their registral positions are identical to the unit that opens “Don,” yet the instrumentation of each is different. Contrary to the explicit structuring of instrumentation in the preceding measures, all instruments of the orchestra, as well as all pitches, act as one in this unit:
The twelve-note unit that concludes “Tombeau” in m. 548 likewise concludes the motion generated in the first two sections and, in a sense, in Pli selon pli as a whole. The pitches of this unit and their registral positions are identical to the unit that opens “Don,” yet the instrumentation of each is different. Contrary to the explicit structuring of instrumentation in the preceding measures, all instruments of the orchestra, as well as all pitches, act as one in this unit:
The voicing of this twelve-note unit is the key to its configuration. Observe, for example, the notes given to the piano:
This six-note unit is the second hexachord of the parent set (units 3, 4 and 5 from set 1-00) from Example 1. The first hexachord of this set (units 1 and 2) is positioned between the innermost notes of this unit:
The complementary hexachordal make-up of this unit is also represented in each hexachord. The four inner pitches of the first unit in Example 31, B-flat, B, D and C-sharp, are unit 2 of set 1-00, and the two outer notes, E-flat and F, are unit 1 of this set. In the second hexachord of Example 31, units three and four of set 1-00, plus the G of unit 5, are placed in the treble range, while the E and F-sharp of unit 5 are placed in the bass.
Section III of “Tombeau” is a remarkable and an audibly explicit conclusion to the two large-scale evolutions that have taken place throughout the entire piece. The first is that of the orchestra. In Section I, each of the five instrumental groups is successively designated as principal. In Section II, the five orchestral groups are maintained, joined by the brass section as a sixth group. Section III then reduces this six-part division to two parts, reduced further to one part in the final measure, where all groups merge on the final twelve-note unit. Nowhere in the piece prior to this is there an event in which all instruments of the orchestra perform the same gesture. Consequently, this evolution is organized around a gradual aggregation of the independent instrumental groups, from six groups in Sections I and II, to two groups in Section III, and finally to a single group in the last measure. In fact, it is an evolution from an ensemble of ensembles to a single ensemble.
The second evolution, independent of the first, yet following a similar course, is that of pitch. In Section I each instrumental group is assigned different levels from the array of sets that alternate over the course of this section. Section II continues this procedure, yet each group is fixed on a specific level for the duration of this section. In Section III, corresponding to the orchestral structure, individual set levels are disregarded—Section III, in a sense, recycles and completes those sets left incomplete in Section II—and lastly it is the final unit in m. 548 in which all pitches are joined. As there is no simultaneity of performance until this unit, there is similarly no single event in the music prior to this that is built on all twelve pitches.
Elaborate objectives require elaborate means to realize them. More importantly, practically all conclusions made in this analysis can be explained in terms of the musical and poetic correspondence, as the third and final part of this blog entry will show.
Section III of “Tombeau” is a remarkable and an audibly explicit conclusion to the two large-scale evolutions that have taken place throughout the entire piece. The first is that of the orchestra. In Section I, each of the five instrumental groups is successively designated as principal. In Section II, the five orchestral groups are maintained, joined by the brass section as a sixth group. Section III then reduces this six-part division to two parts, reduced further to one part in the final measure, where all groups merge on the final twelve-note unit. Nowhere in the piece prior to this is there an event in which all instruments of the orchestra perform the same gesture. Consequently, this evolution is organized around a gradual aggregation of the independent instrumental groups, from six groups in Sections I and II, to two groups in Section III, and finally to a single group in the last measure. In fact, it is an evolution from an ensemble of ensembles to a single ensemble.
The second evolution, independent of the first, yet following a similar course, is that of pitch. In Section I each instrumental group is assigned different levels from the array of sets that alternate over the course of this section. Section II continues this procedure, yet each group is fixed on a specific level for the duration of this section. In Section III, corresponding to the orchestral structure, individual set levels are disregarded—Section III, in a sense, recycles and completes those sets left incomplete in Section II—and lastly it is the final unit in m. 548 in which all pitches are joined. As there is no simultaneity of performance until this unit, there is similarly no single event in the music prior to this that is built on all twelve pitches.
Elaborate objectives require elaborate means to realize them. More importantly, practically all conclusions made in this analysis can be explained in terms of the musical and poetic correspondence, as the third and final part of this blog entry will show.
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