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Section 1: Composition and structure of ZAB: “the title could have been 1-2-3!”

While performing an ensemble piece by Boivin, Jean-Pierre Robert, who was then a fellow student of Boivin, caught the glimpse of a promising talented composer and approached him to ask if he would write a solo piece for the bass. Boivin was captivated by the idea and took on the task. During the summer of 1981 the two worked together every day, exploring the instrument and finding new sounds. Boivin remembers the working sessions as being particularly creative and evolving for both of them, keeping a very open attitude of mutual interaction. During the sessions, Boivin was documenting the sounds by recording, and drawing sketches in order to remember the movements. By the end of the summer, Boivin began to reflect on the collected material, to generalise and categorise it, to extend it and explore all possibilities. His experience with concrete music had taught him to organise the material in categories; an approach that shared many similarities with composing methods used by a pioneer in musical and instrumental theatre, Mauricio Kagel. For Kagel, the compositional process would often begin with a systematic exploration and cataloguing of the available resources, researching the instrument as if it had not been employed before (Heile, 2006).

The main categories of sounds in ZAB were divided into the sound of bass, the sound of percussion and the sound of speech. This triangular structure led to an overall organisation of the material in groups of three. The same organisation also found its way down to the micro-levels, for example in defining three general positions for the bow (Sul Tasto, Position Ordinaire, Sul Ponticello) and then another three positions within the Sul Ponticello, depending on the presence of harmonics in the sound.

Ex. 1.1. Sul Tasto, poco Sul Tasto and Position Ordinaire. Three positions of Sul Ponticello. ZAB, page 15, line 3.

The overall structural concepts of ZAB, originating from the basic three distinct sound complexes, were a way for the composer to logically organise his material in time. Although Iannis Xenakis’ piece Nomos Alpha (1966) served as a model in creating the structure, Boivin also recalls being close to Karlheinz Stockhausen’s calculative ideas of structuring the material, as opposed to the explosante fixe of Pierre Boulez, where the material gradually develops from smaller, individual cells.

Example 1.2 shows the first page of the original sketches for the basic structure of ZAB. The three sound complexes are named v (voice), c (double bass) and p (percussion), and Boivin lists seven possible combinations of these complexes. Further, the complexes will be introduced successively in sequences of three. He determines three possible ways of introducing a new element in the sequence:

1. By an overlapping technique, where the previous element is repeated when being attached to a new element:

2. By a successive order of the elements:

3. By a doubling of the element, to create groups:

As in Xenakis’ Nomos Alpha, the order of the three group complexes in a sequence is governed by group transformations (a term borrowed from Jan Vriend: 'Nomos alpha” for violoncello solo (Xenakis 1966) analysis and comments', 1981). These transformations are found by turning the triangle (shown in example 1.2) around its symmetrical axis, which creates six different sequences from the three sound complexes. The order of the sequences is derived from a table (shown at the bottom of example 1.2) that shows all the transformations to be obtained from all possible rotations of the triangle. Boivin was careful to avoid repetitions of the same patterns throughout the piece. The resulting grid of circular permutations of the six transformations is shown in example 1.3.

Ex. 1.2. Page 1 of Boivin’s sketches of the structure of ZAB. The sound complexes and possible combinations are shown at the top, followed by the three possible ways of introducing a new element in a sequence and group transformations by turning a triangle around its symmetrical axis.

Ex. 1.3. Page 16 of Boivin’s sketches of the structure of ZAB. A grid showing the resulting permutations of the six transformations of the three sound complexes. In each row we can see that once a sequence of three numbers is used it returns to the second number in the pattern, which marks the beginning of a new sequence.

The creation of the proportions of the piece can be seen in example 1.4. Boivin chose the sequence of 2-1-3 to be the main proportion of the movements. The decision was taken based upon his preference for the rhythmical pattern that is shown in the top of example 1.4, and its natural proportional balance. He also formulates a verbal distinction of the movements:

2: Appeal
1: Break
3: Achievement

In point II of example 1.4, “Sette cellule peut proliferer 4 fois”, translated to “Each cell can proliferate 4 times”, we can see how Boivin exemplifies the creation of sections and sub-sections within a movement:

a) Divide the piece in 3 movements
b) Divide each movement in 3 parts
c) Divide each movement in 9 sections
d) Divide each movement in 27 sub-sections

Some early attempts of making proportion classes, and calculating the duration of the movements are shown in point III of example 1.4:

C3 = 2’42 (duration of the 2.movement)
C4 = 5’24 (duration of the 1.movement)
C5 = 8’06 (duration of the 3.movement)

However, these durations were abandoned for the final durations of 6, 3 and 9 minutes for the respective movements.

Ex. 1.4. Page 8 of Boivin’s sketches of the structure of ZAB. Displaying the creation of the proportions of the piece.

As a method to created new and unexpected playing techniques and sounds, Boivin organized the v (voice), p (percussion) and c (double bass) in pairs. The process he used is shown in example 1.5, and the resulting grid of couples is shown in example 1.6 (original sketches from the composer). Another interesting detail is that the overlapping techniques, which Boivin used to link sequences, for example as seen in example 1.2;

are displayed further down in example 1.5, being combined with the couples:

Ex. 1.5. Page 17 of Boivin’s sketches of the structure of ZAB. The generation of pairs.

Ex. 1.6. Page 18 of Boivin’s sketches to the structure of ZAB. Grid showing the resulting permutations of the pairs.

The original idea of the piece was to highlight the individual sound complexes in the separate movements. The first movement would highlight the voice, the second movement should concentrate on the percussive possibilities while the third movement should focus on the traditional sounds of the double bass. Eventually, the final result became a much more multifaceted story, where the blend of voice, percussion and bass (and the added movement/gesture) creates unique narratives within each movement. Figure 1.7 illustrates what Boivin himself regards as the central features of each movement. Generally, the voice received less attention in the final result, as it does not occur as much as the percussion and bass sounds. Further, the voice is integrated into the other parts for most of the time and does not receive an individual scoring. The true focus in ZAB is on the percussive techniques, and the new discoveries of sounds on the double bass in the context of the exploration of gesture. In addition, the gesture is eventually separated from its interaction with the instrument, and develops into theatre in some sections towards the end of the piece.

Fig. 1.7. Schematic representation of the central features in each movement.

Original idea for each movement: Final result:
1. Voice Introduction (where all three main elements of sound, plus gesture are introduced). Discovery of the bass, and a new proposition to play the instrument.
2. Percussion Enlarge the space, the relationship between the player and the instrument. The performer goes forward in his instrumental discoveries.
3. Bass We begin to see the rather full sound of the bass. Gesture becomes an independent part and is separated from the instrument, occupying the gradually wider sections. To enlarge the musical discourse by gesture and to enlarge time without writing more music.

For Boivin, structure is a denotation for the organisation of the chosen material, within time and a certain logic. He claims the structure to be an absolute necessary skeleton, which, when finding the right parameters and variation techniques, founds the musical innovation that also allows freely composed parts. Boivin stresses the fact that the structure is not the music! The music has to move away from the formal structure, and, ultimately, be used freely. This becomes an important principle both in the compositional and interpretative processes.