Iconic Lexicons of 20th-Century Music: Varèse’s Density 21.5, Babbitt’s Du, and Messian’s Colors of the Celestial City

If one thing could be said to have unified the 20th century, it must be the quality and intensity of the varieties of its disjunction. Nowhere is this more true than in the disparate languages which developed in the wake of atonal music: like bits of cooling matter scattered throughout an ever-increasing universe in the microseconds following the Big Bang (a theory first proposed in 1927), composers soon found themselves in charge of creating their own systems. This solipsism, in which each composer’s language is its own beginning and end, finds its parallel in the increasing individualism prized in the nations from which the three works represented here hail. These three compositions, composed within a span of fewer than thirty years, are not easily made to fit into that paradigm of artificially assembled history: progress! This line of thought, in which Haydn is seen a natural and more perfectly evolved form of CPE Bach, the two bearing the relationship that some bird which nature has bestowed generations of survival does to archaeopteryx (a necessary but eventually discarded stepping stone), fails to cling to composers whose works are detailed below. As such, it is those differences between the composers, rather than their similarities, which will be highlighted. Presented in chronological order, the values displayed within these works differ so wildly that any serious attempt to unite them under any other banner is at best spurious.

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Density 21.5

Edgard Varèse’s Density 21.5, the title of which reflects the density of platinum, was written in 1936 for the inauguration of Georges Barrère’s platinum flute. Because the work is for a rather condensed and limited medium— the solo flute— Varèse makes use of the full range of the instrument in terms of pitch, articulation, and expressive capacity. The work embodies its main compositional elements of symmetry and expansion at foreground and background levels. Tone color, as would be expected with such a composer, is used to highlight and accentuate these elements. 

Varèse begins with work with a 3-note figure as condensed as the medium for which he writes; its trichord, with the notes [F E F#] is [012]. It is in the symmetry that the overall form of the work is also to be found in measure 2, the lower and upper bounds of this cluster are immediately pulled apart, expanded to that most symmetrical of intervals, the tritone [C#-G]. The pivoting note between C# and G is E; the pitch, a minor third from each, is equidistant. These [012] and tritone elements are developed through dynamics and rhythm through measure 6, at which point the upper voice begins its ascent to C at the end of measure 8. It should be noted that the means by which the ascent takes place is through the stacking of minor thirds: the lowest pitch of C# is bound to its G tritone relationship through E; an additional minor third is found when Bb is included in measure 6. This progresses even further: a minor third above this Bb is Db— this note begins the [012] phrase all over again stating in measure 9. The largest interval of these first eight expositional measures (C#-C, unfolded over the course of mm. 6-8) is one which will make a much more expansive display at the end of the work. Thus, symmetry is found is in the germinating element of the [012] trichord and in the means of expansion to the tritone via the minor third; this symmetry is projected on to the ABA structure of the work as a whole. 

Measures 9-11 present another [012] trichord, now in the guise of the pitches [Db C D]. As before, in the case of [C#-G], a tritone is introduced with [D-G#], and is quickly positioned, in measure 12, next to its adjacent [A-D#] tritone neighbor. Thus, from the opening until measure 14, a series of expanding, ascending tritone relationships can be seen:


m.                   Tritone
1-10               [C# G Db]
11-12             [D G#]
12-13             [A D# A]
13-14             [Bb E]


Measures 15 to 17 present two neighboring [012] collections back-to-back in the pitches [E D# F] and [F# E# G]. This last G is separated from the other members of its trichord by more than 2 octaves, and is further highlighted by its extreme dynamic and duration. Similar attributes have been applied to other notes in the preceding measures, and in drawing attention to these notes, another prolonged ascent—this time scalar— can be observed:

m.                  pitch 
1                     F# 
2-3                  G
6-7                 A-Bb
8                    C
9                    Db
11                   D
13-14             E
15                   F
16                  F#
17                  G


It is upon this ascent around which other unifying elements of minor 3rd, tritone, and [012] relationships are festooned for the first section of the work. 

Measures 18-21 present a further minor third relationship of [B G#], and a two further [012] trichords, bound together by the spanning interval of the minor third ([B D]), in [B B# C#] and [B# C# D]. A tritone, [G# D] forms the outer bounds of these measures; measures 21-23 further saturate the texture with yet another [012] in [A A# B].

A second section begins in measure 24 with the addition of key-percussion. Here, the two defining elements of minor third and tritone ([E C#] and [G# D]) are developed through timbre and rhythm. At the tempo change in measure 29, the pitch collections of various [012] sets, ascending through pitch class, are displayed in a variety of both overlapping and disparate registers:


m.        pitch
29        [E# F# G]
31        [F# G G#] / [G G# A]/ [G# A Bb]


Measures 32-40 represent something of a “pedal” point. As the tempo returns to its original marking, a harmony close to a B dominant chord (with extensions) is repeated for several bars. The harmony is eventually revealed as [B F# A C Eb D Db]. 
From 41 on all of the elements encountered in the first section are brought back with slight variation: the opening [012] remains, but is a half-step up from its opening form, now at [E# F# G]. This G’s tritone of C# is still there as it was in the opening measures, but is now in a higher register; this reflects the continued expansion of intervals as the work progresses. The work ends with the flute ascending from its lowest pitch to one its highest (C-B). This framing interval is the product of the projection of the same minor seventh (C#-C) found in the opening 8 measures; these ascents form the bookends to a work for which bookends seem to appear as often as books.


“Wankelmut” and “Begegnung” from Du


Throughout the course of both of these songs, each of the four distinct parts—one voice and three parts on the piano differentiated by register— put forth four tone rows each, and it is through these rows and their trichords that formal elements are established with the song cycle. Although chromatic saturation is constant throughout the work, achieved by the vertical secondary rows assembled by the composer, the predominant aural affect of certain sections within each song is differentiated by variance of trichord variety. In this aspect, Babbitt aligns himself with composers like Bartok or Takemitsu, whose formal elements are often defined and differentiated by a dominating harmony or distinct trichord. When it comes to the works of Babbitt, a discussion is often had on whether or not the painstaking effort with which his pieces are assembled can be heard by even skilled listeners. As will be shown, these efforts result in astonishing levels of relationship between Babbitt’s pitch material; it is more difficult to show or explain the affect of this on a listener. It is through the use of predominating trichords which Babbitt assigns to sections—his “harmony”— those elements which might be called “musical” are experienced by listener, rather than the horizontal lines whose efforts are un-hearable, academic pedantry. 

In the second song of Du, “Wankelmut,” Babbitt assigns four rows to each of the four distinct parts (the voice, high piano, mid piano, and low piano). The first iteration results in the following. 


Voice: 512 6A9  784 0B3 
HP:     340 87B  956 A12
MP:     6A9 512  0B3 784
LP:      87B 340  A21 956


Each horizontal 12-note row can be divide into its two constituent hexachords and likewise, its four constituent trichords. The hexachords of each member’s row in this case has its prime form in [014589], which Martino labels as E4 or all-combinatorial row. This particular hexachord has many options with which its aggregate can be achieved, and this allows Babbitt to establish cross relationships within each hexachord. The dominating “harmony” of this first set of rows is defined not only by its E4 hexachord, but also by the [014] of each of its trichords. In short, each row is made up of two [014589] hexachords and each hexachord is thus made of two [014] trichords. Trichords are maintained in vertical relationships as well. For example, consider the secondary row resulting from the combination of the first trichord of each part:


[512] [340] [6A9] [87B]


When compared with the row made up from the second trichord of the primary rows of each of the members:


[6A9] [87B] [512] [340]


It is seen that trichords are maintained in their original spelling and are related in that the first trichord of the voice is the second trichord of the mid piano; the first trichord of the high piano is the second trichord of the low piano. Likewise, the first trichord of the mid piano is the second trichord of the voice, while the first trichord of the low piano is the second trichord of the high piano. This relationship is maintained throughout the movement: each and every trichord of the piece is related in the same way. Consider the second series:


Voice: A59 162  483 B70
HP:     807 3B4  651 92A
MP:    162 A59  B70 483
LP:      3B4 807  92A 651


These trichords are still defined by their [014] quality, and are related to one another in the same manner as those in the first series. It is not until the third series that the harmonic landscape is changed:

Voice: 431 B02  865  79A
HP:     865 79A  431 B02
MP:     B02 431  79A 865
LP:      79A 865  B02 431


The prime form of these hexachords here changes to A1, [012345]. Accordingly, its constituent trichord changes to [013]. Upon closer inspection it may seem that Babbitt has increased the number of cross relationships— not only are immediately adjacent trichords related in the manner of the first two rows, but whole hexachords are maintained. For example, the first hexachord of the voice, [431 B02], is the second hexachord of the high piano. Likewise, the first hexachord of the high piano, [865 79A], is the second hexachord of the voice. The same relationship is true of the bottom two parts. This relationship is reflective of the fact that there are so many fewer options when it comes to achieving the aggregate with this A1 hexachord. Babbitt is here merely alternating through the pitches of only four trichords, [431] [B02] [865] and [79A]. For what reason did Babbitt change his hexachord at this moment? Is this change afforded by the poetry? The third series occurs largely under the lines


Viel tausend Du
Und immer Du
Wirr
Wirren


(Many thousand you
​And always you
Confused
Confusion)


Is Babbitt here displaying his gifts for text-painting? Is there an “always you”-ness about a smaller number of repeated [013] trichords? Or perhaps Babbitt missed his mark: would not a more combinatorial hexachord, such as the E4 hexachord he begins with, be more reflective of the “Many thousand you” yearned for in the text?; the A1 chord of this third row is perhaps better suited to the “seeking” with which the piece begins as it is the one which must surely yearn more strongly for its complement (“My seeking seeks for the aggregate!” seems to be the stronger subtext).


The last series of “Wankelmut” maintains the hexachord [012345] in all parts as well as the cross-relations of the third series, but here Babbitt returns to a pervasive [014] environment:
Voice: 401 B32  895 76A
HP:     895 76A  401 B32
MP:     B32 401  76A 095
LP:     76A 895  B32 401


Does this collision of the two representative pitch elements (the [014] trichord of the first two series and the A1 hexachord of the third) somehow reflect the “More and more confusion” of the text? The “movement” from the defining [014] of the first two series to the [013] of the third and back again to [014] for the fourth seems analogous to aspects of tonal music and hints at form; whether or not this fact is perceivable lies in the ears of the individual.


In the third song of Du, “Begegnung,” Babbitt’s operations vary slightly from those described above. Although it uses the same medium of delivery (four series iterated by four parts), it is in the manipulation of its material that the song differs: whereas a singular trichord variety defined each series in “Wankelmut,” two trichords are combined in different ways in this song. Consider the first series:


Voice: 504 819  372 A6B
HP:     372 A6B   504 819


MP:     96B 472   81A 503
LP:     81A 503  96B 472

Here, the top two parts share the same E4 hexachord; the voice’s first hexachord is the high piano’s second; its constituent trichord is [015]. However, these elements differ from those found in the lower two parts—through half-step adjustments, Babbitt changes each fundamental aspects of the hexachord: the top two parts’ [504] becomes the bottom two parts’ [503], [819] becomes [81A], [372] becomes [472], and [A6B] becomes [96B]. Through this, the bottom two parts propagate the “major scale” C5 hexachord ([024579]) and a [025] trichord environment. This situation is repeated with the second series, although this time the C5 hexachord is carried by the top two parts while the E4 is moved to the bottom two. 


This misalignment is resolved in the third and fourth series, in which the same B2 [023457] hexachord is carried by each part in both series. Of note is the difference of trichord environments existing in these series: the third series’ hexachord is made up of [013] trichords while the fourth’s hexachord is built from [015] trichords. Another analogy to tonality can be drawn here: the disparity or dissonance between disagreeing harmonies of the first two series ([015] vs. [025]) is “resolved” in the last series, in which [015] has won out to become the predominant harmony.


Colors of the Celestial City
Olivier Messiaen’s Colors of the Celestial City provides a clear juxtaposition of those elements in his later technique for which he is best remembered. The highly sectional works presents clear moments of birdsong, plainchant and organum, the rhythms of Indian classical music, and the composer’s color-chords realized through the use of his modes of limited transposition.  The work, composed in 1963 after a twenty-year hiatus from writing explicitly sacred music, illustrates Messiaen’s religious fervor through its use of four plainchant hymns. These hymns— all of the cheerful Alleluia variety—are performed in both polyphonic and homophonic settings, and are spread throughout the diverse ensemble of winds, piano, and percussion utilized. From the beginning until rehearsal no. 32, the work is largely dominated by the Alleluia of the Eighth Sunday after Pentecost, presented both by brass ensemble (seven “trumpet” parts—the lowest of which are actually played by trombones) and in the pseudo-gamelan ensemble of the percussion battery. From rehearsal 33 to 66, the hymn used is the Alleluia of the fourth Sunday after Easter. The hymns of this section are set using the tone-color hocket of klangfarben, in which a single plainchant is spread throughout many different instruments. from rehearsal 66 to the end of the work, the Alleluia for the Eighth Sunday after Pentecost returns to being the dominating hymn, although appearances are made by the Alleluias of Dedication and of Saint Sacrement. Thus, the work is divided into three large sections, with the Alleluia of of the Eighth Sunday after Pentecost serving as something of a “first theme,” presented again starting at section 67:

             
Rehearsal                            Alleluia

  #1-32                                 Eighth Sunday after Pentecost
                                            Saint Sacrement
          
 33-66                                 Fourth Sunday after Easter


67-end                               Eighth Sunday after Pentecost
                                          Dedication
                                          Saint Sacrement

Birdsong plays an important sectional element in the work, and is interspersed freely throughout. The Celestial City seems to privilege southern species: the Bellbird, Yellowhead, White-necked Thrush, Woodcreeper, and Greyish Saltator are some of the birds which make recurring appearances throughout the work. Much of the work is dedicated to expressing the conflict of the defining attributes of one section (be it birdsong, plainchant, or color-chords) upon the other. A clear example of this occurs at rehearsal 42, in which Messiaen continues his exercise in klangfarben but with through the guise of Indian Tâlas. The following are used before being given up on for another twenty rehearsal numbers, thrown back into Messiaen’s bag of tricks as quickly as they were taken out of it:

Tâla Section: Rehearsal 42-47
Tritîya
Gajalîla
pratâpaçekhara 
vijaya
crétique (relating to Greek poetry)
râgavardhana


Timbre is the largest signifier of form in this work, Messiaen’s use of homophonic color-chords make up a significant part of the timbral landscape. The composer does not make the analyst search for the sections in which the chords are present, as he labels the sections and their representative chordal colors explicitly. Take for example rehearsal number 75, in which we are presented with a series of “Sardoine rouge” chords played on the winds, while the percussion battery are carrying out the Alleluia for the Eighth Sunday after Pentecost. Pitch class is revealed to be only one of determining factors for Messiaen when the following exercise, in which the pitch and interval content of the so-called “color-chords” are compared. The first three chords of this rehearsal number are carried homophonically by the members of the brass choir, and their spelling, from low to high, is as follows:
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A Bb B C# D# F# G    
Bb D Ab C F# B C#E
Bb Eb G B F A D 


For the sake of observing interval patterns, and because these are not verticalized forms of any of Messiaen’s modes of limited transpositions, the chords can be translated into their prime forms:
(0134579)
(0123468B)
(012479)


Compared with the three “roge, taché de bleu” chords which follow at rehearsal 74, similarities can be observed:
B E F G A Gb Bb Eb    (01234678)
A E D Gb Bb Eb Gb Ab  (0124678)
Bb Eb G F B Eb G C Gb Ab (0234579)


In most cases, these “reddish” chords share with each other the presence of major seconds, thirds, and fifths, as well as minor seconds. Since the following three chords, at rehearsal 75, are labeled as “bleu violet,” might it be possible to glean what “blueness” is for Messiaen in this work?
Bb D# G Bb A (0137)
A C# E A D#  (0137)


That any relationship exist between this last set of chords and the preceding two must be mere conjecture; the fact is that Messiaen’s synesthesia was the product of several musical dimensions: instrumentation and voicing played just a large a role as interval vector and pitch class for the composer.


The techniques through which Messiaen, Babbit, and Varèse arrived at their materials could hardly share less in common. Of the three, it is Messiaen whose method is most prophetic and reflective of the late 20th- and early 21st- centuries: the consistency and rapidity with which modern society is bombarded with The New—and the intensity with which The New craves its attention—find their clear analog in Messiaen’s score. It seems that what the 20th- and all preceding centuries share in music is their appetite for newness; what the 20th century redefined are those parameters by which progress is to be measured— or even appreciated.