Monday, September 1, 2014


Krzysztof Kostrzewa
ANUL / YEAR IV / NR. 14 / 2014. 07.-09.
Muzică / Music
Rubrica / Box: Articole - Studii / Articles - Studies
2014.09.01. Luni / Monday
Sesiunea de comunicări științifice a Facultății de Arte - Universitatea din Oradea

Autor / Author: Krzysztof Kostrzewa
University of Rzeszów

Redactor / Editor: Anca Spătar
Lect.univ. Dr. Universitatea din Oradea - Facultatea de Arte
Redactor / Editor: Mirela Mercean Țârc
Conf.univ. Dr. Universitatea din Oradea - Facultatea de Arte



mature serializm, sophisticated counterpoint of serial polyphony, developed serial technique, derivatives series, polyphony of series of many parameters, technique of 12-pitch fields, technique of "hidden polyphony", technique of organization according to ending of sounds, technique of division of series on segments


Le marteau sans maître (1953-55) by Pierre Boulez is a masterpiece of middle, mature period of serialism. Serialism was iniciated in 1949 by Olivier Messiaen with his piece Mode de valeurs et d’intensités. In the works of its three greatest representatives: Pierre Boulez, Karlheinz Stockhausen, Luigi Nono, serialism existed to about 1960. These twelve years can be divided into three phases:

·         1949-1952: early serialism (pointillism); it is sometimes called total or integral serialism,
·         1953-1957: middle, mature serialism,
·         1957-1960: late serialism, influenced by Cage’s aleatorism.
In the phase of mature serialism the disadvantages of the early phase (being the result of the pointillistic texture dominating at that time): atomisation of musical narration, static effect, fluctual form and in some cases lack of expression, were finally overcome. Boulez in Le marteau… did it by using developed serial technique. In that piece it is only the pitch series that has constantly 12 elements while the series of dynamics and rhythmics have usually 1, 2, 3, 4 or 6 elements. Therefore Boulez applied the division of the number 12 as categories of serial composition. In this way he created a kind of serial "instrument", which breaks the schematicism of the permanent repetition of 12 elements in all serial organized parameters.

In this paper there are presented five types of Boulez’ sophisticated serial technique: (1) polyphony of series of many parameters, (2) the technique of 12-pitch fields, (3) the technique of "hidden polyphony", (4) the technique of organization according to ending of sounds, (5) the technique of division of series on segments.

The paper includes examples from the score with the series pointed out and a diagram of form of the eighth movement of Le marteau.

In the end of the paper there is recalled the statement of a Polish musicologist, Tadeusz Andrzej Zieliński. In 1960 – a few years after the creation of Le marteau sans maître he expressed his admiration for this piece, which he called „the source of the separate and irreplaceable emotion which Bach, Chopin, Schönberg cannot give”. And he added: „Le marteau by Boulez is remarkably subtle and ethereal music, almost "immaterial". It seems to be more delicate than anything. This work does not shock and it does not electrify; it influences the aural nerve in the way, as the feeling of soft silk influences the touch.”


1. Introduction
Serialism was iniciated by the piece by Olivier Messiaen Mode de valeurs et d’intensités, one of Four rythmic studies (1949). It was followed by Sonate for two pianos op. 1 (1950) by Karel Goeyvaerts, the Belgique disciple of Messiaen. Both these pieces, presented in the summer 1951 in Darmstadt, caused a quick reaction: just in the autumn 1951 Polyphonie X by Boulez and Kontra-Punkte by Stockhausen were composed. To this first phase of serialism we can add also: Structures I for two pianos (1952) by Boulez and two pieces by Stockhausen: Kreuzspiel (1952) and Klavierstücke I-IV (1952/53).
Serialism lasted for about 12 years, from 1949 to about 1960. It can be divided into three periods:

  • Early serialism (1949-52), when there was serialisation of many parameters, technique of pointillism and identity of structure and form;
  • Mature serialism (1953-56), when the form became independent from the structure; Boulez created a sophisticated counterpoint of serial polyphony and Stockhausen introduced the group technique and included statistic laws; he used average values;
  • Late serialism (1957-1960); in Stockhausen’s and Boulez’ creation the aleatory factor became important (introduced under Cage’s influence); Nono developed polyparameter serial technique in vocal compositions.
The serial technique consists in using the series of many parameters, such as: pitch, duration, dynamics, timbre, articulation and others. The direct result of the serial technique at the beginning of its existance was pointillistic texture. This phase of the serialism is sometimes called "integral" or "total" serialism.
Although the pointillistic texture existed already before, in the works of Anton Webern, it was especially its appearance in the early works of serialists (Boulez, Stockhausen, Nono) with the accompaniment of the vanguard theories that caused a shock of the audience and the strong negative opinions from the composers and musicologists not acquainted with the vanguard.
The early serial technique, called also by Bogusław Schaeffer "poliserial" or "polistructural"[1] had indeed at the beginning of the serialism (between 1949 and 1952) many disadventages: atomisation of musical narration, static efect, fluctual form and in some cases lack of expression[2]. Also Theodor Wiesengrund Adorno perceived the automatisation of composing process. He said the composer was becoming a serial engineer and the work - a disertation[3]. However, B. Schaeffer is right to assert that it is true just for the early phase of the serialism, not for the mature one, so the period 1953-1960[4].
Actually, although it is true the puncualism caused static efect, its influence was dissociative and there was a kind of mechanicalism, these were not the essential things for the serialism. It was far more important that punctualism enabled the revolution in the composers' thinking - instead of thinking just about a line (motive, rhythm, melody) and vertical (harmony) and join the timbre, so the instrumentation to these basic elements the composers began to think about a single pitch, as a cross of a diffrent kinds of the sound parameters. In this way punctualism in the early serialism was definitely the opposition towards tradition, also by the elimination of the rest of tonal system, which was still present in the serial (dodecaphonic) work by Schönberg, Berg and Webern, also like motivic thinking.
To be honest, in the case of the typical technique of the early serialism - pointilism - negative critic was right. It is true that it was dissosciative, static, formally amorfical, sometimes it lacked expression. However, these features caused a reaction from the same composers who created their works using pointillistic technique. These drawbacks were overcome in many works composed with group technique, for example in Gruppen by Karlheinz Stockhausen and also in the work which is undoubtedly a masterpiece of serial music - Le marteau sans maître (1953-55).

2. The serial plan. Sketches

In the example of eighth movement of Le marteau sans maître (the piece was composed in 1953-1955) there will be introduced Boulez' advanced technical achievements, which are far from the basic serial technique applied in Polyphony X (1950) or Structures I (1952).

In the piece Le marteau sans maître Boulez uses the text of the French surrealist poet René Char, with the same title.

From 1986 the analysis of Boulez' serial works is easier because of the access to the composer's sketches at Paul Sacher Foundation in Basel. Sketches to Le marteau sans maître were published by Ulrich Mosch in his analysis of the second movement of this work[5].

Boulez prepares a plan of the whole work in two schedules.

The first one (look at the example 1)

Ex. 1

contains 12 twelve-tone series: the initial series and 11 derivatives series, which are marked with Roman numerals since II to XII. Each series contains 12 positions, which are marked with Arabic numerals since 1 to 12. Only the initial series has engaged all 12 positions. The other series (so derivatives series) possess both empty places and places with individual sounds or chords. The method of creating derivatives series from the initial series has been illustrated at the example 2.

Ex. 2

At the beginning there is appointed quantity of half-tones (semitones) in intervals of initial series, together with their direction. First interval, major second up, from E-flat to F, is appointed as + 2 (two half-tones up); next interval, minor third down, from F to D, is appointed as -3 (three half-tones down) etc. In this way we receive the series of numbers, which are closely connected with initial series:

+ 2 -3 -1 -3 + 1 -2 + 3 -4 -4 + 3 -1 -3

In the example 2 there is presented “wander” of the first sound of initial series, E-flat.

Every sound of initial series goes in turn through all verses since II to XII, according to mentioned numerical series, in accordance with rule: if it is + 2, then in next verse sound moves two positions to the right, if it is -3 then three positions to the left etc.

Finally Boulez receives table from which we can read twelve-tone series in each verse (reading horizontally) and in each column (reading vertically). In II, IV and VIII movement of Le marteau Boulez uses series read only horizontally. The empty places are provided for percussion instruments with undefined pitch.

Boulez comments that moment of constructing work as follows:

"In Bourreaux de solitude (movements II, IV, VI, VIII) percussion measures time. (...) When different instruments play, percussion keeps silent; however if only pause appears in instrumental complex, percussion fills it - in dependence from its length - by one or several beats. Percussion creates « supplement » of different instruments; it fills the vacuum, formed among definite heights of sounds - it is a kind of architectural game with time"[6].

Chords in derivatives series (from II to XII) are realized in score either as chords, or successively - then the order of sounds is free. This is an example of local liberty of choice within a framework of close global serial plan, according to the composer's statement. Each derivatives series can begin from any place (also empty one - realized by percussion) and it can be transposed as well.

Among the sketches there is one more schedule, treating to Le marteau sans maître which contains 11 series set in five groups (look at the Ex. 3: Sketch containing modules).

Ex. 3 - Sketch containing modules (“modulo” = module)[7]


[U/UK] V et IX              modulo de 4         1 2 3 4                            êê          combin[aison] tierce

                                         modulo de 3         4 5 6                               êê          combin. seconde majeure

                                         modulo de 6         1 2 3 4 5 6                     êê          combin. quarte et seconde mineure

                                         modulo de 1         3 / 5

                                         modulo de 2         1 2 / 5 6


[U/UK] VII et XII         modulo de 3         1 2 3                               êê          comb. VII et XII 2 à 2

                                         modulo de 4         5 6 7 8                            êê          --- ê XII ê --- ê VII ê ---

                                         modulo de 2         5 6 / 3 4                         êê          VII ê ou VII ê XII ê ou XII ê VII

                                         modulo de 6         1 2 3 4 5 6                                  [ --- means illegible]

                                         modulo de 1         2 / 7                                            


[U/UK] III                      modulo de 1         1                                      êê

                                         modulo de 6         1 2 3 4 5 6                     êê          2 à 2 réciproques (² ® 3 3 ® ²)

                                         modulo de 3         4 5 6                               êê

                                         modulo de 2         7 8

                                         modulo de 4         1 2 3 4

                                                                         5 6 7 8


[U/UK] XI, VIII, X       modulo de 2         1 2                                  êê

                                         modulo de 1         3 / 4 / 7                          êê          combinaison 3 à 3

                                         modulo de 4         1234/1234/5678         êê

                                         modulo de 3         123/123/456

                                         modulo de 6         1 2 3 4 5 6


[U/UK] IV, VI, II          modulo de 6         1 2 3 4 5 6                     êê

                                         modulo de 2         5 6 / 1 2 / 3 4                êê          combinaisons        

                                         modulo de 1         8 / 5 / 2                          êê          horisontales

                                         modulo de 4         5678/5678/1234

                                         modulo de 3         456/123/123

Schedule contains 5 groups with 5 "modulo" in each one. Boulez' term "modulo" means module. They are series of dynamics and rhythmics, which have usually - differently from series of pitch - less than 12 elements. The series of dynamics and rhythmics have either 1 or 2 or 3 or 4 or 6 elements. The quantity of elements of dynamics and rhythmics series takes into account all mathematical possibilities of division of number 12 (the number 12 is divisible by 1, 2, 3, 4, 6), so all modules can be subordinated to every pitch series (these series are always 12 elements). The rhythmics module 6 is precisely fixed (duration from 1 to 6 sixteenths). The other modules have several possibilities of realization, e.g. module 4 can have either from 1 to 4 sixteenths or from 5 to 8 sixteenths. Boulez applies also rhythmical series consisting of 12 elements (rhythmical values from 1 to 12 sixteenths).

The series of dynamics are constructed similarly like rhythmical series. Except series of 12 elements (ff" ff f" f mf" mf mp" mp p" p pp" pp) Boulez more often uses shorter series: of 6-, 4-, 3- and 2 - elements, which are a part of full series of 12 elements. The module 6 can for example look as follows: ff' ff f' f mf' mf (vibraphone, measure from 1 to 4, 4-8, 84-90). The module 4 can look as follows: mf' mf mp' mp (vibraphone, measure 14-20, 109-112). Boulez sets dynamics signs differing with nuances, not contrasting; nowhere appears for example module: ff mf p pp. The nuance dynamics predominates distinctly over contrasting one (characteristic for early phase of serial music).

There is also a module 1, which means, that all 12 pitches possesses the same dynamics or duration (or both of them), for example in vibraphone, measure from 1 to 4: ff.

In Le marteau sans maître only the pitch series has constantly 12 elements. The series of dynamics and rhythmics have usually 1, 2, 3, 4 or 6 elements, and very rarely 12 elements. Therefore Boulez applies the division of the number 12 (and so the whole set of modules) as categories of serial composition. He creates in this way some kind of serial "instrument". He breaks the schematism of permanent repetition of 12 elements in all serial organized parameters.

3. Analysis
In the 8. movement of Le marteau, which has 138 measures, we can distinguish 3 principal sections, in which there are applied different serial methods:
·         section one (I), measures from 1 to 20, where appears (1) polyphony of series of many parameters;
·         section two (II), measures from 21 to 71, where decoding of series procures many difficulties; this section is probably the field of decomposition; this section is not analyzed here.
·         section three (III), measures from 71 to 138, where the decoding of series is easier again, but the serial technique, more elastic than in section one, appears in four new forms:

o   (2) the technique of 12-pitch fields, in which there is the module 12 in range of rhythm, as well as module 3, 4 or 6 in range of dynamics;
o   (3) the technique of "hidden polyphony";
o   (4) the technique of organization according to ending of sounds;
o   (5) the technique of division of series on segments.

In present analysis there is represented 5 types of sophisticated serial technique, applied in sections I and III.

3.1 Polyphony of series of many parameters
At the beginning of part VIII of Le marteau it is difficult to find 12-pitches series, because in vibraphone and xilorimba the pitches repeat already in the first measure. First 12-pitches course is in flute in measure 3-10 (look at the example 4;
Ex. 4

flute transposes quart down, because there is an alto flute). This form of series we can mark as U III 4­, 1, which means, that it is the series III from table of eleven series according to series in inversion ("U" from Germ. Umkehrung = inversion), transposed major third up (4 half-tones), begun from first position (from hitting of percussion) - look at example 1. If we observe this series in flute, we can see, that there are sixteenth pauses among some sounds of flute and exactly in these pauses the hitting of claves appear. Moreover the hitting of claves has the same range of dynamics as the flute: mp ' / mp. Therefore these hitting of claves belong to 12-pitches flute series, according to Boulez' statement about supplement of instrumental sounds by the hitting of percussion. Percussion action makes easier the decision, which of 11 form of series we are talking about: in that series the claves has four single hitting (for easier identification, at the example 1, next to every 11 series from II to XII there has been noted a model of percussion hitting, that belongs to it. It has been fixed on the basis of empty places; there is also important to distinguish single and group hitting). This percussive model exists in fact in three series: III, VI and X, but empty places and single sounds including six positions, like in this flute part, are only in the III. series. In this moment we can easily establish, that it is series III, transposed 4 half-tones up, begun from the first (empty) position. Therefore the connection between rhythmics and pitch in this flute series, measures 3-10, looks as follows:


1      2       3       4       5       6       7       7       8       9      10     11     11     12     12     12       position

e      F       e       D       e      C#     B     D#      C       e       A     A#    F#     G#     E       G       


        7                 8                 7     4 +     3       8                 7     4 +     4               1 +     7        real rhythmical value

                                                            7                                             8                          8             sum of rythmical values

in chords

We can notice here in the dynamics and rhytmics module 2 (2-element series), after setting sounds of series and their dynamic signs with chromatic scale from C to B:


C       C#         D        D#         E          F         F#         G        G#         A        A#         B                   

            >                       >                       >                       >                       >                       >                                    >

mp   mp      mp      mp       mp       mp       mp       mp      mp       mp       mp       mp          module 2 (mp mp)

8         7          8          3          1          7          4          7                       7          4          4           real rhythmical value 

                                     7          8                       8                       8                       8          7           sum of rhytmical values

                                                                                                                                                       in chords

8         7          8          7          8          7          8          7          8          7          8          7           module 2 (7 , 8)

Evident dynamic module 2 (mp mp) is a clue, that also rhythmical module should consist of two elements, according to Ulrich Mosch' assumption, which has been confirmed in his analysis of the second movement of Le marteau[8]. Serial plan contained in schedule of module (example 3) provides, that for series [U/UK] III rhythmical values for module 2 should be 7 and 8. Many sounds have really exactly this duration (e.g. C - 8 sixteenths, C-sharp - 7 sixteenths) whereas as many as six sounds have different duration:

D-sharp lasts 3 sixteenth; B, A-sharp and F-sharp - each of them lasts four sixteenths, moreover G-sharp is a grace-note (acciaccatura), so it lasts even shorter than 1 sixteenth.

Problem is solved, if we add together duration in the chords: in this way B and D-sharp have 7 sixteenths (3 + 4), A-sharp and F-sharp - 8 sixteenths (4 + 4), E - also 8 sixteenths (1 + 7). G-sharp lasts actually shorter than 1 sixteenth, so it could receive value zero. However G-sharp should have value 8, according to value of module; G-sharp can receive this value, if we add together rhythmical values of the whole chord G + E + G-sharp (7 + 1 + 0 = 8). Anyway sound E has in reality considerably shorter rhythmical value - 1 sixteenth, though module 2 in the sketch gives it 8 sixteenths.

Presented way of procedure of composer, which is applied with the purpose of receiving values provided in the serial plan might be called at one side as pure speculation. However from the other side we can perceive in it practical realization of that local liberty of choice, demonstration of "local non discipline" while global, principal tendency remains.

Construction of whole first section (measures 1-20) is based on the polyphonic beams of series; each series is realized as described above series in the measures 3-10, performed by flute and claves. With the help of both of schedules (series and module ones), taking into account rhythmical models of particular series, we can identify all series: this section is constructed very closely. In the example 5 there is presented, with the help of different lines, course of series in section I, without precise analysis already. In this section there are all derivated series (from II to XII), creating some kind of exposition of this part (look at the formal plan of whole part VIII, ex. 11).
Ex. 5

3.2 Technique of 12-sound fields
In section III (measures 71-138) looks of score changes in comparison with section I. At first, series are not arranged horyzontally but vertically, so "harmonically" and they are usually played by all instruments performing this movement (flute, xilorimba, vibraphone). In the score there are therefore 12-sound fields. This fields are quite easily recognizable, because of separate rhythmical and dynamic modules, which are in every field. At second, rhythmical module is not directly correlated with dynamic one, like in I section, but it becomes independent: there is only one rhythmical module everywhere - module 12 (that means the sounds of series receive duration from 1 to 12 sixteenths). Dynamic module, not correlated with rhythmical, has 3, 4 or 6 elements in the III section (module 3, 4 or 6), because the sketch sais so: in the eight movement of Le marteau there are used modules of two last verses from each of five groups only, while in section III (measures 71-138) there are only series VIII, X, XI and II, IV, VI .

Owing to analysis we can notice some deviations in applying rhythmical and dynamic modules. In the example 10 there is in measures 74-76 series UK VIII 5¯, 12 (series VIII retrograded, translated 5 half-tones down, begun from 12th position), in which rhythmical module 12 is realized closely, whereas dynamic module shows two deviations (they are underlined):

C  C#     D      D#      E       F      F#      G      G#      A      A#       B

      >                          >                          >                          >        >               

pp pp     pp       p       pp      pp       p      pp      pp       p       pp        pp   sign of dynamics

p                                                                                                    pp   module 3 (p pp' pp)

3 4 5 6 7          8 9       10       11       12        1 2       rhythmical module 12

Such case of strict realization of rhythmical module 12 is rather rare in whole section III: deviations predominate, though principal tendency (module 12) is obvious. In the fragment of score presented in the example 10 there are also another series, in which module show some deviations from ideal exactness:

·         measures 71-74, UK XI 3 ¯, 12. There is rhythmical module 12, but F-sharp lasts one sixteen instead of two; dynamic module 3 (p pp' pp), but sound F has dynamics p' instead of pp'.

·         measures 77-79, UK VIII 5­, 9. There is rhythmical module 12, but D lasts 8 sixteenths instead of 7; dynamic module 3 (p pp' pp), but C has dynamics pp instead of p. Showed deviations from exactness can be also treat as demonstration of liberty in forming details in the framework of appointed direction.

3.3 Technique of hidden polyphony
In section III we can observe very often some factural transformation which might be called "hidden polyphony". It is situation, when the duration of sound is marked at the beginning and at the end only, in the same register (often by means of grace-notes), therefore the sound does not appear constantly lasting (tenuto); the sign of dynamics of beginning and end of that sound are identical. It is the example of developed serial technique.
The technique of "hidden polyphony" is visible exactly in vibraphone, measures 86-87 - look at the example 6. In this technique both the beginning and the end of a sound can be written/recorded as regular rhythmical values or as grace-notes. During "virtual" duration of sound there can also appear the additional grace-notes on the same pitch, as it takes place in mentioned example 6.
Ex. 6

Series in vibraphone, measure 86-87; U VIII 3¯, 6:


 6    7        8 9       10        10     10  10     11     12      1       3       2       3       3       4        5          5              position

                                A#         A     G#  C                         G       E       F      F#     D#    C#       B         D            

                                            11     10   9       1                          7       6       5       7       3        2          12           2              real rhythmical value       

After setting sounds of series and their dynamic signs with chromatic scale from C to B we can notice here module 6 in the dynamics (6-element series) and module 12 in the rhytmics (12-element series):

C    C#        D        D#         E          F         F#         G        G#         A        A#          B

        >                       >                       >                       >                       >                        >

f     mf       mf        ff         ff          f           f         mf       mf        ff         ff           f       module 6 (ff' ff f' f mf' mf)

1      2          2          3          6          5          7          7          9         10        11          12    real rhythmical value

1      2          3          4          5          6          7          8          9         10        11          12    rhythmical module 12
In this series we see close module 6 in the range of dynamics (ff' ff f' f mf' mf). However, rhythmical module shows some inaccuracies: sounds E and F have inverted rhythmical values. This inaccuracy can be interpreted also in another way: the sounds D, E-flat, F, G have as though transposed scale of rhythmical values a unit down (2 instead of 3, 3 instead of 4 etc.). Another inaccuracy is the case of sound G, which end is an octave higher than the beginning. Inaccuracy of this type appears almost in every series, not only in this technique. Most likely it is not oversight or "mistake", but the next examples of conscious "local non discipline".
3.4 Technique of organization according to ends of sounds.
In analysis of section I (measures 1-20) beginnings of sounds fix their order. In section III (measures 71-138) there exist some series, in which sounds begin a chord successively but they finish simultaneously - look at the example 7:
Ex. 7
vibraphone, measures 95-97. This common end of several sounds could mean that just the end has some meaning. This assumption is confirmed in analysis, but there should be studied not only end of chord, but also end of singular sounds. The technique of organization according to ends of sounds is showed in example 8:
Ex. 8
the order of sounds can be truly coordinated with the sketch (ex. 1), when we take into account moments of ends of sounds.
We are talking here (measures 93-96, compare with ex. 7) about series U XI 4 ­, 10 (series XI, transposed major third up, begun from 10th position). The sounds of chords C + B-flat and F + E-flat + D-flat end simultaneously. Because this time the schedule of series fix the order of ends of sounds (and not beginnings), the suitable hitting of percussion appear directly after sounding out the sounds and not before their attack, like in the section I, measures 1-20. Example 7 includes also another fragments of the piece composed with the help of this technique, marked "TE" (germ. Tonende = the end of sound): measures 96-97 and measures 99-102.
3.5 Technique of division of series on segments
In some fragments of section III, within 12-pitches fields, series can be decoded, only when we read out different instrumental voices separately. Each instrument has some appropriate segment of series, it creates something like polyphonic beams of its segments. In the fragment of score presented in example 9, measures 107-109.
Ex. 9
there is series UK IV 4¯, 1 (series IV, the retrograde transposed major third down, begun from the first position). Series is begun, by hitting of bongos, a little delayed here (ff in measure 107); it is then position 1. Vibraphone realizes in measures 107-108 positions 12 and 11 (B-flat + A and B) then follows directly position 10: hitting of bongos (measure 108, mp). A little later than in vibraphone, in measures 107-109 the next segment of series appears in flute: positions 9-8-7 (E-flat + C, D, E + F-sharp + C-sharp). Positions 6-5-4 are realized by bongos (measure 107) as group of three sixteenths; in accordance with the sketch they precede directly an action of xilorimba. Sounds of position 3-2 (A-flat + G, F) are in xilorimba, they create something like the third polyphonic voice. The sound D-sharp in xilorimba in measure 108 and the hitting in bongos belong to the preceded series.
The sounds of chord-complexes are played in this place successively. The series is divided in this way, that - when we read it vertically - we have completely different order of sounds than the sketch provides for series IV. Great letters at the signing of the series in score example define the order of realizing the segments of series, e.g. in this series: V (= vibraphone), F (= flute), X (= xilorimba).
Ex. 10
In the example 11 there is presented the form of the eight movement – it can be seen as a kind of sonata form. Section I (measures 1-20) functions as an exposition because all the series, from II to XII, are presented here (see example 1). Section II (measures 21-71) functions as development section – the identification of series is very difficult so probably they are transformed in a way. Section III (measures 72-138) is a kind of recapitulation because almost all series from the exposition come back (there is no series III, V, VII, IX).
Ex. 11
The present analysis of part VIII of Le marteau sans maître shows, as far Boulez walked away from pointillist technique applied in Structures I for two pianos (1952). In Structures I he has applied 12-element series in range of pitch of sound, rhythmics, dynamics and the articulation, unifying sometimes some parameter, and so resigning from its serializing (e.g. he has applied constant dynamics for whole series, constant value rhythmical etc.). The result of such technique was music which influences on listener dissociatively, quite "explosive" in expression. In Le marteau Boulez has overcome constant, exactly serial number 12, he has introduced 2-, 3-, 4- and 6-element series (modules). In this way he has prepared serial instrument, and with its help he has composed new forms of serial complexity. The analysis shows, that we have here virtuously treated structural complexity, reached by break of serial "twelve" and by serial of varriattive technique.
Serial technique, described here fragmentarily, but with the smallest details, caused rise of work, which we can call without exaggeration, the masterpiece of serial music. Le marteau, in several years after its rise, awaked real enchantment of polish musicologist, Tadeusz Andrzej Zieliński:
"I remember, that my first emotion with new music occurred in moment of completely not intellectual perception. I was listening to the Boulez' work Le marteau sans maître and I discovered suddenly, that this sound-set gives me some special pleasure, that I didn't know earlier. Important was, that these sounds in sum are the source of separate and irreplaceable emotion which Bach, Chopin, Schönberg cannot give. The work appeared as an independent value, which does not require any external argumentation. (…)
Le marteau by Boulez is remarkably subtle and ethereal music, almost "immaterial". It seems to be more delicate than anything. This work does not shock and it does not electrify; it influences the aural nerve in the way, as the feeling of soft silk influences the touch.”[9]

[1] Bogusław Schaeffer, Nowa muzyka. Problemy współczesnej techniki kompozytorskiej. Kraków 1969, p. 397, 406.
[2] B. Schaeffer, op. cit., p. 397, 484.
[3] T. W. Adorno, Das Altern der neuen Musik, in: „Der Monat” No. 7 (May 1955) p. 150-158.
[4] B. Schaeffer, op. cit., p. 27.
[5] Ulrich Mosch, Disziplin und Indisziplin. Zum seriellen Komponieren im 2. Satz des Marteau sans maître von Pierre Boulez. Musiktheorie. Peter Cahn and others eds. Laaber Verlag 1990 No. 1, p. 43-46, 58.
[6] P. Boulez, Sprechen, Singen, Spielen. In: P. Boulez, Werkstatt-Texte, Translation from French: Josef Häusler, Berlin 1972, p. 137; Translation into English: K. K.
[7] The sketch have been published by Ulrich Mosch, op. cit., p. 58.
[8] Ulrich Mosch discovered that both rhythmical and dynamic values are organised on the basis of the same module; U. Mosch, op. cit., p. 50.
[9] Tadeusz A. Zieliński, Piękno nadal aktualne „Ruch Muzyczny” 1960 No. 15 p. 4. The title of the article means „The Beauty still live”.