Reality, Destruction, and Acceptance

An analysis of the Berceuse, from Quatre Chants por Franchir Le Seuil, Mvt. IV “D’après L’épopée de Gilgamesh”

Kevin Baldwin

MUS 577: Composers of the Twentieth Century, Seminar: Gerard Grisey

June 6, 2016 2

Gerard Grisey is known most notably for his works Prologue, Periodes, Partiels, and Modulations, and developed numerous spectral tools for himself in his earlier years writing these works. In Grisey’s later years, he expanded on his spectral techniques and began creating more elaborate, poetic structures. By conducting a metric, orchestral, and spectral pitch analysis, I will show that the Berceuse from Gerard Grisey’s Quatre Chants por Franchir Le Suiel, Mvt. IV “D’apres L’epopee de Gilgamesh” uses two corresponding sound objects, while also poetically corresponding to the text.

The structure of the Berceuse is based around thirteen phrases - certainly an ominous number in a movement about the destruction of mankind. The metric system laid out over the thirteen phrases is in constant fluctuation (with the exception of the

10/8’s repeated at the beginning of the first to phrases), creating an expansion and contraction of beats per phrase. While the number of measures per phrase changes, this is a secondary factor. The intrigue of the structure stems primarily from the cyclical changing of the meters and the length per phrase.

The cyclical nature of the meters is not necessarily always contained by phrase markers. While the first two phrases begin with 10/8, the first contracts and expands out to an 11/8, and the second contracts to a 9/8. Each phrase continues this pattern, though moves further away from the original 10/8. One may note the structural importance of the

10/8 metric marking due to two reasons. First, the repetition of the 10/8 three times in phrase one and twice in phrase two creates a strong identification of the metric duration.

Second, through all the phrases, the 10/8 always appears, yet never ends a phrase. The avoidance of the 10/8 in such a manner reinforces its structural importance just as a constant usage may. 3

Figure 1 shows the metric structure cycle and its continual motion between 8/8 and 13/8. Each phrase begins in the middle of this cycle with a meter ranging from 9/8 to

11/8. While phrases one and two hint at the contraction and expansion of the metric cycle, the repetition of the 10/8 gives the two phrases the sense of being introductory.

From here, a constant cyclical motion is established with no repetition of meter. While phrase three already establishes the 8/8, the lower threshold for the metric cycle, phrases four, six, and eight show a constant expansion ending with 11/8, 12/8, and 13/8 respectively. This cycle resets and repeats itself, expanding from 11/8 to 12/8 and 13/8 in phrases nine, eleven, and thirteen. Overall, the concept of expansion and contraction, as well as the cyclical ideal of moving away from and back to a given point will prove important to numerous aspects of this section.

Another important point is that each phrase ends on a meter that has not yet been in the phrase, and includes a tempo change faster or slower. Any time the phrase ends with an 8/8 or a 9/8, the tempo increases; any time the phrase ends with an 11/8, 12/8, or

13/8 the tempo slows. The exception to this is phrase twelve, as it ends on a repeated 9/8 and does not contain a tempo change. It should be noted again that the 10/8 never concludes a phrase, reinforcing its importance.

The length of a phrase in beats outlines its own interesting structure when paired with the harmonic structure. Two different sound objects can be identified according to the bass note: Sound Object One has a bass note of C, Sound Object Two has a bass note of any other pitch. This places phrase one, three, six, and nine through thirteen as part of

Sound Object One, and phrases two, four, five, seven, and eight as part of Sound Object

Two. This creates two separate lines for each sound object. In figure 2, note the near 4 merger of Sound Object One and Sound Object Two, as Sound Object One begins at sixty beats in the phrase, and Sound Object Two begins at twenty-nine. These two lines continue to meet towards the middle, with the exception of phrase eight as the outlier. In the section about pitch, I will attempt to show phrase eight as the point of maximum dissonance between the two sound objects, and phrase nine as the merging point of both.

With forty-five beats per phrase as the median, both phrases come together to hover around this line, removing the extreme dissonance in phrase length. The concept of the two separate sound objects is reinforced with an orchestration analysis.

Each sound object, mainly through the first eight phrases, has a distinct orchestration, as seen in figure 3. This is visible in that the gong, pitched at C1 and giving the bass C of Sound Object One, is only played in phrases one, three, and six of the first eight phrases. While the cello plays in every phrase, the rest of group II (alto sax, tenor sax, cello, crotales) never plays in Sound Object One, but only in Sound Object Two.

While it can be argued that the saxophones are unused due to their rich overtone spectrum and could dilute the spectrum used in Sound Object One, it still reinforces the two sound object theory.

Phrases nine through thirteen take on a slightly different orchestration and direction. While it was previously presented that phrase nine functions as a meeting point between the two sound objects, the orchestration from phrase nine through thirteen reinforces this idea. Phrases nine through thirteen largely use the same orchestration as

Sound Object One, but with the addition of vibraphone (and later the crotales) and the removal of the clarinet two. The addition of the vibraphone and crotales coincides with the pitch movement of partials above the C bass note in the gong, allowing the pitch to 5 continue rising. In order to understand the function of the pitch material of phrase nine through thirteen, it is first necessary to look at the pitch in the two sound objects before the meeting point.

In Grisey’s earlier works, his focus for pitch organization and orchestration revolved around instrumental additive synthesis. Francois Rose explains,

“For the beginning of Partiels (1975), Grisey was stimulated by a sonogram analysis of a pedal low E1 (41.2 Hz) on the trombone. He selected some component frequencies and orchestrated them. That is why this technique can be metaphorically referred to as ‘instrumental additive 1 synthesis.’” It does not seem apparent that Grisey is using this instrumental additive synthesis, although he developed techniques during this time such as harmonicity and inharmonicity, which are noticeable in this piece.

To create a partial analysis of a spectrum, it is important to identify the fundamental. While in Partiels, for example, the trombone plays the pedal low E1 fundamental, Berceuse offers a unique challenge. A cursory glance at the pitch material per phrase, or the pitch reduction in figure 4, exposes a sizeable interval above the fundamental of each pitch set. All the pitches in a phrase may be grouped together due to the blurred texture combining the undulating gestures of all the instrumental parts. With each phrase beginning with a low pitch from the gong, harp, or double bass, which is not repeated for the continuation of the phrase, pitch material in higher octaves in the blurred texture may be considered a resonance of the bass note played. Where the Berceuse becomes more complicated to analyze than older works such as Partiels is in the

1 Francois Rose, Introduction to the Pitch Organization of French Spectral Music. Perspectives of New Music, Vol. 34, No. 2 (Summer, 1996) pp. 8 6 compositional and poetic choices Grisey uses; in this moment this complication exists in trying to decide which pitch to consider the fundamental.

With C2 (65.4 Hz.) as a recurring pitch, as previously established as the fundamental of Sound Object One, one may consider this the fundamental over which to create a partial analysis. With Sound Object Two consisting of bass notes that are not the

C1, one could consider the bass pitch of each pitch collection as the fundamental.

Considering the partials of Sound Object One with C1 as the fundamental, in its entirety

(from phrase one to thirteen), the partials would move from:

Phrase one: 1, 2.25, 3.5, 4.5, 5.25, 6.25, 8.25, 9.75, 20 Phrase thirteen: 1, 4.5, 5.25, 6.25, 9.75, 10, 11, 13, 21, 24, 26, 29, 32, 34, 36 Only these two phrases are shown as an example to highlight the motion of partials from the beginning to end of Sound Object One. One could argue using C1 as the fundamental, as phrase one has six of eight inharmonic pitches, and phrase thirteen having four of fourteen inharmonic pitches. Converting these proportions to percentages, phrase one is seventy-five percent inharmonic and phrase thirteen is twenty-nine percent inharmonic.

Three of the inharmonic partials (4.5, 5.25, 6.25) carry over from the first phrase to the last. This motion from inharmonicity to harmonicity could be appropriate as it applies to the text and ethos of the lullaby; with a mood of acceptance to the destruction of mankind, the combination of a progression towards harmonicity and the upwards direction of the partials would properly color the concept.

Another option is to use C1 (32.7 Hz) as the fundamental, despite the actual pitch not sounding. This is possible especially consider that Grisey does not seem to attempt to 7 use instrumental additive synthesis to reproduce the sound of an instrument in the ensemble. Using C1 as the fundamental, the partials spanning Sound Object One include:

Phrase one: 2, 4.5, 7, 9, 10.5, 13.5, 16.5, 19.5, 40 Phrase thirteen: 2, 9, 10.5, 13.5, 19.5, 20, 22, 26, 42, 48, 52, 58, 64, 68, 72

With C1 as the fundamental, phrase one has five of eight inharmonic pitches (63%) while phrase thirteen has three of fourteen inharmonic pitches (23%). This option retains the movement from inharmonicty to harmonicity; however, it raises the partials to remove inharmonic partials with an ending of .25. The numbers ending with .25 would mean that a pitch is three octaves below a harmonic tone in the overtone series. While this is surely a possibility, a partial number ending in .25 would imply a greater sense of inharmonicity than a partial number ending in .50. Since C2 has three partials carry from the first to last pitch collection with partials ending in .25 or .75, this would imply a greater inharmonicity for all of Sound Object One. Both are feasible options, as this is a technique Grisey is known to use often.

“Inharmonicity is achieved in stages through a downward octave shifting. For instance, [Figure 6] shows that the first inharmonic tone occurs in the third statement when the fifty-seventh partial of the low E (D7 = 2348.6 Hz) is presented one octave too low [at partial 26.5] (D6 = 1174.3 Hz), by the percussion. In the sixth repetition, the fifty-first partial of the low E follows the same pattern (C7 = 2101.5 Hz, shifted down to C6 = 1050.8 Hz), while the octave-lowered fifty-seventh partial is lowered an additional octave to D5 (587.2 Hz). The same process is carried on until the eleventh statement where only two harmonic components remain, the E3 and the B3 (the fourth and sixth partials, respectively, of the low E1).”2 The last foreseeable option is to use C0 (16.35 Hz) as the fundamental. This may seem unlikely since C0 is below the audible threshold. Using C0 would provide partials:

2 Francois Rose, Introduction to the Pitch Organization of French Spectral Music. Perspectives of New Music, Vol. 34, No. 2 (Summer, 1996) pp. 8-9 8

Phrase one: 4, 9, 14, 18, 21, 27, 33, 39, 80 Phrase thirteen: 4, 18, 21, 27, 39, 40, 44, 52, 82, 96, 104, 116, 128, 136, 144

Poetically speaking, using C0 as the fundamental could act as ‘non-existence’ because the frequency is inaudible and the work is about the destruction of mankind – a return to

‘non-existence’. The issue with C0 as a fundamental is a lack of inharmonic to harmonic motion, as all the partials in Sound Object One then become harmonic. This creates a stronger focus on partial range and motion higher or lower, but removes the structural element of inharmonicty and harmonicty Grisey developed.

In order to preserve a progression of inharmonicty to harmonicty, (to match the poetic acceptance of the lyrics of the destruction of mankind) as well as the quality of

‘non-existence’, C1 (32.7 Hz) functions as the optimum fundamental. While C1 is still an audible frequency, the fact that it never sounds in the work still can be used as a metaphor for ‘non-existence’. As a consequence, Sound Object Two will operate as if the bass note sounding is always the second partial of the spectrum, meaning the spectrum fundamental will be one octave below the bass.

While Sound Object One keeps C1 as a consistent fundamental, Sound Object

Two constantly changes fundamentals. With only five pitch collections, the fundamental moves between E1, Ab0, F0, Ab0, D0, through phrases two, four, five, seven, and eight respectively. It is true that considering the C1 as a pivot point for the first eight phrases

(thus, pivoting at phrase one, three, and six) creates an alternate phrase structure. In figure 7, Timothy Sullivan outlines this alternate structure, stating:

“Note the continuing phenomenon of bass motion by thirds, though now oscillating above and below a central note, C. With the initial bass progression C—E, followed by C—A-flat, we see yet 9

another variation on the fundamental progression from the first song. While the form of the first song suggested the division of a tritone progression from E—B-flat (a symmetrical division of the octave), and then the final step to A-flat, the Berceuse presents another symmetrical division, but now of the entire progression from E—A-flat. However, note still the prominent tritone motion from A-flat—D at the most harmonically distorted point of the Berceuse—also the most melismatic section of the voice part—reinforcing the importance of that intervallic distance throughout the four songs.”3

While Sullivan is correct in applying the intervallic divisions of symmetry from the first movement to the Berceuse, this argument does not take into consideration the constant directional movement of the sounding spectrum above the moving fundamentals, nor does it take into consideration the break from the oscillating structure Sullivan presents in phrase nine. The beginning of the fundamental movement is much like the metric oscillations previously detailed, though the metric structure continues through the final measure of the piece. The pitch structure Sullivan details does not. Differentiating between the two sound objects is important to pitch structure, as reinforced by the phrase length (see figures 1 & 2) and the orchestration (see figure 3).

As noted previously, movement of partials as well as spectrum density should be considered in determining the larger pitch structure. As the pitch reduction in figure 4 shows, there is a constant increase of density between phrases one and eight as well as an overall movement towards higher partials. This is reinforced by the logarithmic graph in figure 6. While this graph does not show the movement of frequencies played, it does show the movement of partials above the given fundamental of each individual pitch collection. In terms of actual pitches played, while phrase one actually contains a higher pitch than phrase eight, phrase eight has, on average, higher frequencies. With the fundamental of phrase eight being a minor seventh below the prominent C1, the space

3 Timothy Sullivan, Gérard Grisey's Quatre Chants pour franchir le seuil: Spectral Music on the Threshold. ProQuest LLC, 2009. P. 113

10 between the fundamental D0 and its highest pitch, D6, creates a spectrum up to the sixty- forth partial. This creates a larger spectrum than the space between C1 and E6 in phrase one, which creates a spectrum up to the fortieth partial. Immediately following the largest and densest spectrum in phrase eight, the spectrum returns to the original size of forty partials, spanning between C1 and E6. With the prominence and important of C1 as a fundamental, Sound Object Two pitch collections act as a textural coloring.

As stated previously, the importance of inharmonicty and harmonicty is an important element for progression. In Partiels, pitches were displaced by an octave or more in order to move from harmonicty to inharmonicty. In the Berceuse, there does not seem to be a progression of harmonicty to inharmonicty or visa versa. One could count the number of inharmonic pitches per pitch collection and come up with: five, one, four, five, four, three, three, three for measures one to eight respectively. What is important in the Berceuse is not the progression from one to another, but the acceptance of inharmonicty as a constant.

On top of the return to the original spectrum and fundamental, phrases nine through thirteen begin a different process. Figure 5 shows the partials of the pitch reduction per phrase above the fundamental. Phrasea nine through thirteen cease to change fundamentals, and remain on C1. Each pitch collection during this section creates a larger spectrum, rising from forty, to forty-six, forty-eight, fifty-eight, then seventy- two, in phrases nine through thirteen respectively. Not only is the top pitch rising, but the density of pitches as a whole continues to rise as well. This is seen in both figures 5 and

6, as well as the space between the fundamental and the next partial continuing to increase. 11

While it has been established that the first eight phrases consist of two sound objects, it is important to understand why this is and why Sound Object Two gives way to

Sound Object One. To do so, first consider the text.

I opened a window And the day fell on my cheek I fell [to my knees]* motionless I looked to the horizon of the sea, The world…

*The bracketed portion was removed from the front of the score to the Berceuse lyrics.

The entire fourth movement stems from the Epic of Gilgamesh, the earliest surviving work of great literature. The story is about the destruction of mankind, and the Berceuse is the lullaby that closes off the movement. The text of the Berceuse can be interpreted as an acceptance of the destruction from the standpoint of an individual’s last moments.

From the Berceuse analysis presented, the larger question to be answered is the necessity for two sound objects and their necessity to be characterized as separate. The text clearly paints two separate images from an individual’s perspective: the coming destruction, and the enjoyment of a final moment. It is feasible to state that Sound Object

One is the enjoyment of the final moment, constantly returning to its fundamental pitch to reestablish its prolonged reality. Sound Object Two is the destruction, the corrosion of the C1 fundamental constantly descending further as it approaches the end of the audible threshold. It was at phrase eight where the two sound objects meet, and in phrase nine the individual falls to his/her knees and accepts that this is his/her final moment. Musically, this is established by a return to the C1 fundamental and the constant upward motion of partials.

As stated previously, the movement from harmonicty to inharmonicity is absent, but what is important is the constant inharmonicity. It is unique for Grisey not to use 12 harmonicity to inharmonicity as a structural elemement, but in the Berceuse it works poetically. Another element of mankind is constant imperfection, reflected by inharmonicity. While the final phrase consists only of three inharmonic pitches, which is less than the five in phrase nine, it is unclear that if more phrases were added there would have been a moment of harmonicity. The text used to conclude the work, “The world…” is only a fragment of a sentence, creating the imagery that the individual speaking was abruptly cut off. This leaves the idea open that harmonicty may have come if the

Berceuse were prolonged. What is clear is that in the Berceuse, as well as the entirety of

Gerard Grisey’s final work Quatre Chants por Franchir Le Suiel, Grisey took more poetic liberties while using the spectral tools he had developed in his earlier years. 13

Figure 1: Metric Structure of the 13 phrases, length of phrase by beats, and corresponding lyrics. 14

60

55

50

45

40

35

30 Beats per Phrase 25

20

15

10

5

0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 Phrases

Figure 2: Phrase length in beats of Sound Object I & II

Sound Object I / Sound Object II

Figure 3: Orchestration chart per phrase. (x – instrument plays all the way through, 0 – plays only the

downbeat of the phrase)

15

Figure 4: Pitch reduction in the 13 phrases

16 41 39 9 41 26 16.5 15 24 36 5 10 20.33 9.5 2 4.2 13 2 8 7 27 42 32.5 46 40 10.5 30 19.5 4.5 13.5 mm. 18-21 mm. 39-43 8 8 8 8 & & ? ? & & ? ? 9 40 7 22 13.5 34 9.75 9 4 2 6.5 4.25 27 18 15 12.33 9.5 2 37 26 16.5 6.75 4.5 10.5 mm. 15-17 mm. 35-38 8 8 8 8 & & ? ? & & ? ? 20 42 42 39 29 68 48 22 10.5 32 26 16.5 10.5 51 46 37 27 21 17.5 31 30 13 72 64 58 52 3 2 26 19.5 13.5 9 8 29 48 41 9 7 2 4.5 22 40 8.5 64 4.05 2 25 13.5 34 20 15 mm. 53-56 mm. 10-14 28 mm. 30-34 27 8 8 8 8 8 8 26 & & ? ? & & ? ? & & ? ? 25 24 25 32 23 22 21 21 29 13 17.5 25 14 58 37 20 9 19 7 18 2 12.5 40 32 18 2 7 2 8 26 10.5 30 19.5 13.5 42 20 27 37 15 10.75 3.9 17 2 12 mm. 26-29 mm. 7-9 16 mm. 48-52 15 14 8 8 8 8 8 8 & & ? ? & & ? ? & & ? ? 13 12 11 10 9 8 7 6 37 36 29 52 19.5 26 10.5 5 16.5 10.5 4 3 6 2 7 2 11 7 1 30 9 48 22 16.5 10.5 9 2 7 2 22 4.5 33 40 13.25 40 19.5 13.5 27 1 mm. 1-6 mm. 22-25 mm. 44-47 8 8 8 8 8 8 8 8 & & ? ? & & ? ? & & ? ? & & ? ? C1 - Overtone Spectrum

Figure 5: Partial Analysis of the pitch material in the 13 phrases 17 13 12 11 10 9 8 7 Phrase 6 5 4 3 2 1 0 5 4 3 2 1 80 50 40 30 20 10

Partials above Fundamental above Partials

Figure 6: Logarithmic Partial Graph, partials above the fundamental.

Sound Object I / Sound Object II 18

Figure 7: Progression from harmonicty to inharmonicity in Partiels4

4 Francois Rose, Introduction to the Pitch Organization of French Spectral Music. Perspectives of New Music, Vol. 34, No. 2 (Summer, 1996) p. 10 19

Figure 8: Analysis of the first eight phrases of the Berceuse by Timothy Sullivan5

5 Timothy Sullivan, Gérard Grisey's Quatre Chants pour franchir le seuil: Spectral Music on the Threshold. ProQuest LLC, 2009. P. 114