João Rafael

It is not our intention here to exhaustively pursue the most minute details on all the levels. We will do so, perhaps, in some examples which are considered more significant. In general, directive lines and "clues" will be given which could open the road to more extended and deeper analyses. We will show the principal procedures, methods, and stylistic characteristics - "constants" - employed.

To deal here with the electronic part (the ad libitum option furthermore leaves open the possibility of playing the piece without electronics) would be obviously beyond the scope of this work.

Our attention will concentrate on the analysis of the original musical material, created and developed specifically for this piece. Passacaglia 3, having as its base germinal material reworked from another piece, constitutes a special case necessitating an approach to another type of problem, and will not be part of this analysis. A brief reference will be made to it toward the end of this study. Passacaglia 3 can in any case be separated from the rest of the piece and played in concert as a string trio.

The manuscript and preparatory sketches of Wandlungen have been consulted in the elaboration of this analysis.

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Concerning the organization of pitches, one unique chord of five tones is at the origin of the entire piece:

Figure 1

Let us note at the outset that it is composed of two superimposed fifths and a note between the two fifths. As the two extreme notes are in the relationship of a tritone (in fact, the only one present in the chord) we can transpose the chord at this interval in such a way as to maintain the same two pitches (G - C#):

Figure 2

Within the chord, there are three new pitches. If one now inverts each successive interval of the preceding chords, one obtains Figures 3a and 3b:

Figure 3a and 3b

The same tritones are evidently present. More interesting is the fact of having, in Figures 3a and 3b, the same fifths (or fourths) of Figures 2 and 1 respectively. The inversion of each chord has only generated one single new pitch each time: the fifth note (i.e. the note between the two fifths).

These four chords and their reciprocal relationships form a nucleus whose characteristics decisively influenced the succession of developments in the composition of the piece.

First observation: the 4 chords include, in all, 10 different pitches (5+3+1+1), thus leading to the decision of taking exclusively these 10 pitches for the entire piece. The two pitches excluded, the E and the Bb, will never appear in it. In addition, the number 5 will spread throughout, polarizing and unifying the organization of the piece at quite different levels. For example, each attack will admit only a maximum of only 5 simultaneous notes, a principle concomitant with the composer's idea of the "banishment of grey":

However, some exceptions will take place in the case of the superposition of 2 or 3 simultaneous developments, or when certain notes, or certain chords, remain held and are superimposed upon the following events.

The next step: the analysis of chords of 5 notes, which are constituted in two superimposed fifths and a note between the two fifths, which don't contain either E or Bb. In this "universe" of 10 tones, there exist only eight fifths. From their combination, 66 chords have been generated, grouped in 9 families, established according to the structure of the intervallic relations between the five notes which compose them. Each family - from A to I - corresponds to a given interval between the two fifths. Figure 3 on the following page shows the number of chords for each family, the interval between the two fifths, and the intervallic relationships between the 5 notes.

Family A is that of the original chord, of its possible transpositions and inversions. In the 66 chords, the 8 fifths occur according to 22 different combinations of the two fifths.

The 66 chords have then been linked in such a way as to form the progression in Figure 4 on the following page:

The fifth note of each chord is notated as a whole note. The small arrows indicate the chords of family A. The letters designate the families of chords, and the numbers refer to the 22 types of associations of 2 of the 8 existing fifths. The intervallic relation between the two fifths is also indicated here.

The two fifths which are most often associated with each other (10 times) are F#-C# and C-G (type 21). The chords which they form group themselves each time with the two chords which flank them to constitute the groups of 3, indicated in Figure 4 by the horizontal brackets. The sequence segmented according to these groups of 3 chords, reveals a symmetrical structure:

3 5 3 5  3 2 3 2 3  5  3 2 3 2  3  5 3 5 3_______3 

Furthermore, the beginning of the "melody" of the fifth notes (see the succession of whole notes in Figure 4) is equally symmetrical about the eighth note (the A flat). The choice for the concatenation of chords is based especially on criteria of contrasts, in such a way as to avoid the juxtaposition of the same fifths and also to individualize each chord by its disposition in the tessitura. The two exceptional juxtapositions in which the fifths do not change are encompassed within a frame in Figure 4.

The fifth notes have been freely placed in relation to the two fifths. The latter are always more or less spaced out from one another, with some exceptions indicated by an asterisk where the two fifths interlock.

An attentive observation of Figure 4 will still provide further precious data on the way in which the sequence of chords has been composed. The realization of each chord constitutes a particular case which is difficult to generalize.

From this point, the progression of the 66 chords will have a very important role, comparable to that of a cantus firmus, throughout the whole piece.

Let us pursue this. We have already seen that the number five corresponds structurally to the maximal vertical density of the pitches. We can add now that, almost always in the working of the pitches, only one-, two-, four-, or five- "part" (voice) material will be utilized. Several examples will be given of this material, of its derivation and its realization, but to understand them better, it is necessary to make a parenthesis and proceed first to the organization of timbres.

The score of Wandlungen has been composed for 25 instruments:

Figure 5

This ensemble has been organized into 25 homogeneous or heterogeneous groups of which 20 are constituted by 2, 3, 4, or 5 instruments. As exceptions, the other 5 groups are composed of very particular cases of instrumental formation, evident in themselves (see Figure 6 on the following page.)

Very individualized "colors" emanate from each of the instrumental combinations, impregnating the piece firstly with their vertical sonority, but also with the horizontal deployment of the instruments of which they are composed. In several parts of the piece, one of the timbral groups:

- is predominant (for example group 13, Passacaglia 1 from page 19, measure 6),

- conducts the principal action (group 16, from page 13)

- or polarizes and gives form to the development (group 18, page 8 last measure up to the end of page 9). Let us remark that here, and already from the beginning of the piece, group 18 is closely connected to the original chord in compact position (Figure 1). The entire first part of Passacaglia 1 (pages 1 to 6) was also organized around it.

 A sequence of these timbral groups (from 1 to 23 only) was composed next. The sequential choice of groups reveals an intention of contrasting the instrumental combinations, and of creating uncommon progressions of timbres. There are never any instruments common to two consecutive groups.

Several fragments of this original chain of timbres have been successively juxtaposed to it, like fragmented recalls of past events. The entire sequence comprises 66 groups (see Figure 7 below):

The permutability which is possible between the thirteenth and fourteenth members of the chain (groups 18 and 5 indicated by the small arrow in Figure 7) can be understood very easily by comparing Figure 7 with the chain of 66 chords of Figure 4. The fourteenth chord is actually the original chord (from Figure 1). Compare also the sixty-sixth and last member of these two Figures (4 and 7).

Let us now come back to the work of the pitches. The one- two-, four-, and five-"part" material has been almost exclusively derived from the cantus firmus , in terms of the succession of chords, or from the very structure of the chords and of their families. No derivation of three-"part" material has been done. This would be less related to the principal characteristics of the opening material. In addition, the different materials and forms of working in one and five "parts" - the more extreme contrasts - take, without doubt, the most prominent position in the whole piece. (Here again we see the intention to eliminate the intermediate or mediating situations (i.e. the more "grey." situations).

As an example of 5-part material, we have already seen the cantus firmus. Another version of this linking of chords has been composed for the sequence of timbral groups. Here each chord changes its disposition in the tessitura in accordance with its respective instrumental group (see Figure 8 on the following page).

This version of the cantus firmus, metamorphosized by the sequence of timbral groups makes its appearance two consecutive times. In the first time (Passacaglia 2, pages 1 to 3), without the fluctuations of tempo indicated in Figure 8, the rather fluid temporal flow still follows the same articulation and grouping of chords (indicated in Figure 8), but interprets it otherwise (Figure 8b below):

(The numbers refer to timbral groups.)

In its second appearance (Passacaglia 2, pages 4 to 7) this progression of chords becomes more flexible, shaped by the changes of tempo indicated in Figure 8. In addition, it is, this time, "traversed" by melodic interventions whose elaboration can be retraced.

There are some points where the figures belonging to different types start together. The three points which correspond to the simultaneities of (v) and (r) (circled in Figure 8) occasionally generate a single rhythmically periodic figure which utilizes the pitches belonging to the chords in its proximity. The number of notes in each melodic figure, and for each one of the three types (a), (v), and (r), follows the following scheme:

The pitches exposed by these melodic figures have been developed from the first derivations of the original chord. Five different melodic orders using always the 5 notes of this chord, have been composed and arranged in the tessitura. To these five groups four others were added, with 6 notes in each, (respectively on the top and the bottom of Figure 10a below):

 These last 4 groups of 6 notes are constituted respectively by the junction of pitches from:

• fig. 1 and fig. 2 without the tritone G-C#

• fig. 3a and fig. 3b without the tritone G-C#

• fig. 1 and fig. 3b

• fig. 2 and fig. 3a

The transposition of these 9 melodic groups generate only three possible transpositions each, except for the last three, which only configure one of them. See Figure 10b (pitches without placement in the tessitura).

Two different sequences, each utilizing these 30 segments were finally composed, one for (a), and the other for (v) and (r). The order of succession of the 30 groups, for each of the two sequences has been indicated in Figure 10a and 10b by the numbers placed respectively above and below each system.

The cantus firmus only appears in its "bare" form (the sequence of the 66 chords of Figure 4 without any transformation, not even from the electronics) at the beginning of Passacaglia 5, pages 1 to 6. Here, for example, is the first page of it (Figure 11 on the following page).

At this point, the instrumentation of the cantus firmus is not in a direct relation with the 25 timbral groups. Each chord has been "orchestrated" freely but, often, by its timbre, it clarifies the internal structure of the two fifths plus one note (for example, in Figure 11, the chords marked "a"). On other occasions, the harmonic tensions within the chord are reinforced more by the dynamics (b).

One can see again, the intention of contrasting the timbral ensembles in the progression of one chord to another (c), or on the contrary, of linking them via their common tones (d). The function of the dynamics in the interior of a chord in relation to the instrumentation is also that of shaping it in time, that is to say, giving it an individual life, like an acoustic entity, by way of timbral metamorphoses over the course of its duration (e).

As we have just seen in its "instrumentation", the rhythmic exposition of the "bare" cantus firmus - quite irregular and unpredictable in its appearance - similarly does not permit analysis along fixed pre-established schemas. Nevertheless, it is possible to perceive in it a construction in three parts (see Figure 12 on the page 46). This construction is clearly based on the number 5 and on the duration of 8 seconds - as in the whole piece.

In the first part (A) the rhythm of the first line of the example presents 10 chords which can, in spite of appearances, be subdivided into two groups of 5 chords (5 durations). Each group constitutes a different fragment of each of the two halves of the rhythmic pair 17/15:

Figure 12 The three underlined values had already determined the larger-scale durations - of the three parts A, B and C - indicated above in Figure 12. In fact, the juxtaposition of these tw fragments "simulating" a single continuous and coherent fragment creates the sensation of a "false" rhythmic pair, due to the continuity of the pulsation of 15 and the discontinuity of the one of 17. This phenomenon becomes clearly visible if one re-groups the durations, two by two:

The pulsation of 15 functions as a "pivot" assuring the continuity in the linking of the two fragments.

The rhythm of the second line - of the first part (A) - deploys the chords in a more or less sinuous rhythmic flow, based on an alternation of short and long values which leads to 5 periodic chords (5 x 3 = 15 sixteenths), culminating in a final chord of 8 seconds.

The second part (B) begins simultaneously with the rapid line of the glockenspiel - Passacaglia 5, page 3 - which actually plays the notes of the 66 chords melodically, always in the order of the cantus firmus, but of course disposed differently in register. This part can be divided in 5 segments, each one displaying a clearly different way of exposing 5 chords in the same duration of 15 quarter notes: "rallentando", 4 rapid chords and a very long chord, a fragment of a rhythmic pair, five periodic chords, and "accelerando". The numbers in Figure 12 part B correspond to the durations in multiples of quarter notes.

The third part (C) is constructed in a sufficiently clear manner in itself, and finally this appearance of the "bare"cantus firmus ends on the original chord, repeated periodically 5 times by the timbral group 18. The 3 high notes (G#, A, C) in the 3 violins which are here superimposed on this original chord, are the three new pitches in its transposition of the tritone (see Figure 2).

On the other hand, this line in one "voice" does not maintain the same registration of notes as in the cantus firmus. It is disposed differently, each of its notes being played at the unison by the instruments of one of the timbral groups of the sequence of Figure 7. (See Figure 13 on the following page.)

In the score this "melody" can be found two times.

In the rhythm of the first part (from page 19 to page 20, third measure) some quite sinuous and irregular "ritardandi" can be seen which follow the falling movement of each short melodic figure. The durations are indicated in multiples of sixteenths (first system of Figure 13). Conversely, the second part begins with 3 "accelerandi", still in the descending melodic movements, and, after the first pause, takes up the "ritardandi" again. Five other rapid figures take place, intercalated between these events and composed of 3, 2, 10, 3, and 2 notes respectively. The durations are indicated in multiples of quarter notes.

A new element is superimposed on the melody in this second part. It is a kind of harmonic "canvas" composed of all of the pitches of this large line (Figure 13) occupying the same positions in the register. This "canvas" never appears complete; each sustained chord constitutes a filtering of it.

Very important in the composition of this melody, where each note is played at the unison by several instruments, are the dynamics. They metamorphosize "in real time" the global timbre as already indicated in the "bare"cantus firmus (Figure 11, marked by: "e").

The first appearance of the melody was in Passacaglia 2, page 8, third measure, up to the end of the Passacaglia. Its realization was identical to what we have just seen, but it is "crossed" at the same time by an almost continuous melodic intervention in the three brass, giving voice to the unwinding of the chords of the cantus firmus as read melodically. Another example of this type has been given above, but in the glockenspiel (Passacaglia 5, pages 3 and 4).

At the end of Passacaglia 4 (pages 15 to 18) there exists an even more special case of such a melodic reading of the chords. The notes of each chord of the cantus firmus are "difracted" by a grid of sixteenths, but they remain held afterwards; the chord is constructed by the cumulative entry of its components. The position of the pitches in the register remains unchanged here in relation to the original cantus firmus (Figure 4). For each of the chords, a timbral group has been chosen. As each instrument plays one note, the timbre of the group is similarly "refracted" and the ensemble sonority is similarly formed afterwards, by accumulation. There are often more complex harmonies and timbres which appear vertically because the timbres and the pitches of one chord remain prolonged during the following chord(s). Here is the beginning of the order of the timbral groups:

18, 14, 23, 12+1, 17, 7+8, 1+4, 22, 18, 20, 2+10, etc.

Figure 14

Still one more last and very peculiar melodic example (Passacaglia 5, pages 7 and 8) should be presented. It involves a melody, confined to the mid-register, where each note is played at the unison by a combination of different instruments. It is a "melody" of timbres which plays a melody of pitches. At the same time, there is one single timbre (the clarinet) which plays the entire melody. For some of the notes, the register explodes abruptly into several octaves of the same note, sounding simultaneously with it as an additional "acoustic" effect (of timbre). It creates a change in the spectrum of the note, equivalent to those provoked by the different instrumental combinations at the unison.

Immediately after this, in pages 9 and 10, this same idea is taken up again in a different form, more reduced and "simplified". Instead of orchestrating each note, successive small melodic morsels are "doubled" at the unison, each one of them by a different single instrument. Here, a viola replaces the clarinet in the role of the sole conductor of the melodic flux.

The whole Passacaglia 4 (except for the end - pages 15 to 18, already analyzed above) is dedicated to developments in two "voices." We give here a global view of these fourteen pages of the score, especially concerning the unfolding of these developments, and their relationships with the other simultaneous "layers".

There are 3 sequences in 2 "voices". If we call them B1, B2 and B3, we find:

    -B1 in pages 1 and 2,

    -B2 from page 3 to page 7 measure 1,

    -B3 from page 7 measure 4 up to the end of page 14.

    In these 14 pages there exists always an interactive superposition of 3 different developments:

    -in the percussion (repetition, written two times slower, of percussion parts already or not yet, played)

    -melodic interventions (recalled and transformed fragments)

    -in 2 "voices" (linking of harmonic intervals)

 

One could still add to this, as a fourth dimension, the compact "summaries" of the material in 2 "voices":

 

    -B1 in the violin (page 3)

    -B2 in the 4 strings (end of page 5 and beginning of page 6)

During B1 and B2 the percussion part comes originally from that of Passacaglia 1, page 8 last measure, up to page 12.

For the melodic interventions during B1, it is necessary to refer once more to Passacaglia 1 - page 4, measure 5, up to page 6 measure 5 - where they already had as their material a development in 2 "voices" (B2). For those during B2 and B3, see Passacaglia 2, pages 4 to 7.

B2 always unfolds in rhythmic unison with the percussion.

B3 is constituted by a succession of linkings of two fifths in the order of those of the chords of the cantus firmus. B3 allows its appearances in "blocks" to be framed, either by the melodic interventions or by the percussion (originating from Passacaglia 5, pages 24 to 27).

We have already given many examples of repeated parts involving lesser or greater degrees of transformation in relation to the original "object" (an extract from the score, or elements of the "out of time" material). Some more cases should be viewed more closely, as examples of the very different results at which one can arrive by means of the generalization and proliferation of compositonal procedures.

The percussion part in Passacaglia 1, pages 10 to 12 (already referred in relationship to B2), constitutes a reprise of that which goes from page 3, last measure to page 6, measure 5. Between its previously sparse interventions, are now inserted 26 4-part chords (superpositions of 2 fifths) in sustained tremolo. In these three pages, (10 to 12) we witness again the exposition of the original cantus firmus played in the other instruments. Its rhythmic schema is the retrograde of that of the percussion, in this part, beginning from the change of tempo.

The instruments of timbral group 16 share the conducting of this flux of melodic interventions. Short heterophonies echoed in the other instruments often accompany the short lines with minimal rhythmic delays. Each time that 2 consecutive "chords" (melodic lines) have the same number of pitches, a rhythmic "hole" equal to three quarter notes is formed between the two, and a variable number of chords (1 to 5) is inserted into it. These chords are those of the original cantus firmus. Here is the scheme of the number of notes of each melodic fragment, also indicating the number of chords inserted (numbers in parentheses): #9; This large section is repeated two times. #9;

The second reprise of this section (Passacaglia 5, pages 11 to 18) is textual (i.e.exact,) except for the dynamics, the tempi and the order of its subdivisions.

Let us consider in the original, the points where the insertion of a group of 5 chords has taken place, as being particular points which cut the whole in several parts. These points correspond, in the score, to the small measures with tempo change, except for the first group of chords. If one designates the 5 large segments, thus defined, by the letters from A to E, and the 4 small measures, by the numbers from 1 to 4, here is the order of the 9 parts, in the original section and in this second reprise (Figure 16 below).

The very last part of the piece (Passacaglia 5, pages 24 to 27) offers us a very special example. The compositional technique seems "derived" from the usual procedures of electronic manipulation, but it creates here, solely by written means, results which on the one hand are neither mechanical nor automatic and on the other hand, are impossible to obtain even by electronic means. It consists in repeated echoes, but let us see how. The chords of the cantus firmus, adapted to the timbral groups (Figure 8), are first of all presented according to the impulses generated by a succession of rhythmic pairs (of which three are in a rhythmic relationship of a tritone and one in a relationship of a minor third), divided in two halves (the letters A and B designate the two halves of each pair):

Here is the beginning of the rhythm, in multiples of sixteenths, generated by these impulses:

Afterwards, each chord will be repeated four times in written echoes (5 appearances in all with the original chord). The four echoes of one chord can "loosen" themselves from the original by taking different rhythmic forms: ritardando, a fragment of a rhythmic pair, a periodicity, accelerando, or each echo placed in rhythmic unison with the entries of the subsequent chords.

The superposition of different forms of echoes coming from several chords creates quite new and complex results in relation to the other parts of the piece. In addition, the echoes of the same chord often change in instrumentation!

The string trio, which forms the whole Passacaglia 3, is a unique case in the score. Here the composer has utilized melodic and rhythmic material foreign to Wandlungen since it comes from his piece Aura, for solo flute - specifically from its first 4 pages. Nevertheless, this material integrates quite well into the piece, for example, when it is "seen" through the original chord of Figure 1. A confrontation of the materials of the two pieces takes place beginning on page 3b where the 'cello melodically exposes the notes of the cantus firmus. The similarity of character between the coda of this Passacaglia (page 4d) and that of Passacaglia 1(from page 26 measure 5) should still be noted.

Finally, in order to have a global vision of the whole piece, let us attempt to sketch a schema of the entirety which embraces all the parts to which we have been referring in this analysis. The proportions between the large parts of the piece are founded upon the impulses generated by the rhythmic pair 27/20. Each of the 5 passacaglias constitutes a continuous fragment of it. Here is the global form of the piece, the durational values being indicated in multiples of 8 seconds (Figure 19 on the following page):

translation John MacKay

revision: João Rafael

Notes:

1 Wandlungen (1986) Five Passacaglias for 25 instruments and live electronics ad libitum. Duration of approximately 30 minutes. Premiere: Donaueschingen 1986, Ensemble Modern, direction: Ernest Bour, Experimental Studio of Heinrich-Strobel-Stiftung. This analysis was presented in March of 1995 in the author's Final Examination in Composition in the Hochschule für Musik-Freiburg im Breisgau, Germany.

2 See also footnote 6 of this work.

3 (...) "Que l'ensemble du discours harmonique soit d'une luminosité presque éclatante, parfois crue. . Que tout ce qui concerne le temps, les durées, le rythme, soit, de façon prédominante: incarné par des valeurs simples, strié selon des unités de base d'une assez vive mobilité, mais simples, dirigé vers une forte distinction des contours, vers leur pérennité tout au long de l'oeuvre. Que deux contradictions soient bannies: la régularité irrégulière (timide de l'autre), et surtout, l'irrégularité régulière." (...) See the composer's text for the premiere of the work, "Wandlungen - The Banishment of Grey" published in the programme of the Donaueschinger Musiktage 1986, and reprinted in the Festival d'Automne : Paris programme of 1992 where some extracts of the present analysis were also published.

6 In this analysis allusion has only rarely been made to the multiple concrete exceptions and "irregularities" existing between the described objects and the reality of the score - or even between several parts of the material. In a general way, this aspect has already been emphasized in the preliminary remarks, as well as the importance of the careful and comparative study of the score in relation to the "schemas" or of these in relation to one another. It is indispensable to note once more that in this score, the Exception constitutes rather the rule. All the situations, in one way or another, bear a trace of this. Almost elevated to the level of a system, the Exception becomes a constant presence which must have always been considered and integrated into each compositional decision.

In the concrete case of our example, we see a total of 65 notes, and not 66, as was the "custom." It is true that the number 65 establishes many more numerical relationships with the basic numbers of the piece - the 5 and the 8:

65 = 5 x 13 and 13 = 5+8

In addition, the melody analyzed here (Figure 13) is subdivided into 2 parts of 5 + 8 = 13 units of 8 seconds. But the reason is entirely an other one, and we should not think that the last note has been left aside, in such a way as to stop at the number 65.

In fact, in the cantus firmus of Figure 4, the tenth and eleventh chords possess the same fifth note, a B. This note has simply not been repeated in the melody, hence the total of 65 notes. Conversely, the sequence of timbral groups has not undergone any alteration at this point, following its course, which has provoked a shift of one term in one of the two sequences - fifth notes/timbral groups - in relation to the situation of coincidence of the sequences - chords/timbral groups - observed in Figure 8.

Furthermore, Figure 8 already contained a remarkable exception, but in another place. Timbral group 19 has been repeated 4 times for the 4 extremely high chords marked "Adagio" in Figure 8. Consequently, three timbral groups of the sequence should be excluded - however not the 3 last but the 3 groups 10 -1- 4 before the last. In the case of our melody in Figure 13 it is just this last timbral group - the group 18 - which has been removed.

7 The chords which had been used here constitute an exception to the rule given earlier in this analysis (maximum of 5 notes simultaneously). Some of the chords used in this sequence have already been constructed with up to a maximum of 8 pitches.

8 A small parenthesis here to add that in this reprise, other supplementary echoes created by the electronic transformations, are added to to the short echoes (present previously in the way of writing the heterophonies to the lines, but devoid here of their instrumentation as a "distinctive feature", capable of differentiating them) - thus reinforcing the character of insistent repetition.

ex tempore
as published in Vol. VIII/2, Summer 1997