Compared to many of the elements of Messiaen’s musical language, the rhythmic pedal lacks the scope for potential development. At least a survey of the technique in the works examined suggests a tacit admission of this on the composer’s part, since by the late 1940s it loses favour and other rhythmic features come to prominence.
The Visions de l’Amen nevertheless rely on pedals to provide a rhythmic base over some quite extended passages. And even in the very first appearance of a pedal at the start of the work, Messiaen is seeking to meld this apparently rather traditional notion with more original elements of his thinking. The upper stave of the first piano has a pedal of three rhythmic cells. The first is non-retrogradable, and the second and third are based on the Hindu Dhenkî and Greek amphimacer (Table 6.1).
Table 6.1 Rhythmic pedal in the opening bars of Visions de l’Amen Cell Value in semiquavers
1 6, 3, 6 2 2, 1, 2
3 2, 2, 2, 2, 2, 2, 2, 2, 2, 2
The pedal contains subtle alterations that demonstrate how Messiaen manipulated and developed both his sources and rhythmic labels. As the composer remarks, the non-retrogradable rhythm is followed by the same rhythm with a diminution by two-thirds that is (in this diminished form) Dhenkî. However, the non-retrogradable and Dhenkî rhythms are identical in terms of their inner rhythmic relationships, and the second rhythm could clearly also be labelled as non- retrogradable. The amphimacer has been reinterpreted according his conception of ‘monnayage’.1 A similar procedure may be observed in the second pedal located on
the second stave of the first piano, but here the idea is less developed as Messiaen simply adds a quarter to each value at its first repetition. It may be argued that the
succession of cells adumbrates personnages rythmiques, since the first rhythmic unit is merely presented, the second (Dhenkî) has values retracted from each value, and the final rhythm (amphimacer) has values added. Messiaen also tries to obviate excessive laboured repetition by introducing irrational rhythms (2/7–8), which facilitate the subtle manipulation of metre within the pedal. We may therefore perceive in these opening two pages of Visions de l’Amen a tension between the fixed, repetitive nature of an ostinato and the need for rhythmic invention and delicate variety.
Example 6.1 Râgavardhana, Candrakalâ and Lakskmîça at 14/4 in Visions de l’Amen (Reproduced by kind permission of Editions Alphonse Leduc, Paris/United Music Publishers Ltd, England)
The rhythmic pedal commencing at 14/4 (lower stave of the first piano) contains one of Messiaen’s favourite combinations of Hindu Deçî-tâlas during the 1940s: Râgavardhana, Candrakalâ and Lakskmîça (Example 6.1). Certain of the Hindu rhythms were utilised far more frequently than others, and the purely musical reasons are not always clear. Some fascinated Messiaen due to a particular rhythmic quirk which reflected his own thought-processes, such as non- retrogradability or augmentation/diminution. Here the pedal is constructed from altered Hindu Deçî-tâlas, and Messiaen extends the principle in comparison to the previous example by altering many aspects of the three rhythmic cells. However, once the pedal has been established, Messiaen refrains from the type of rhythmic additions and tinkering highlighted above.
The identical rhythmic pedal returns at 29/7 (lower stave of the first piano before transferring to the second piano at 30/4), and on this occasion the rigidity of the ostinato disintegrates towards its conclusion. During the first three appearances of the pedal, the altered Deçî-tâlas are restated without change, but in its fourth (and final complete) appearance the final value of Lakskmîça is contracted (31/7) and all traces of Hindu rhythms are eroded by the concluding continuous semiquavers. The manner of the employment of the pedal in this instance raises the question of whether such manipulations of the original Hindu rhythms destroy their perceptible characteristics. A similar tension between rigidity and freedom may be observed in the passage commencing at 40/1, where a double rhythmic pedal is introduced to combine with a restatement of the movement’s passionate theme. Again, Hindu, Greek and non-retrogradable rhythms form the basis of the pedals before they give way (at 42/10) to a mix of rational and (simple) irrational
patterns, then to uniform quavers, and finally semiquavers prepare the way for the climactic moment (from an emotional rather than technical point of view) at 45/2.
The pedal present throughout the twelfth of the Vingt regards is fixed for the entirety of the piece, apart from the final value being interrupted at the conclusion. The rhythm is perfectly non-retrogradable (it has values of 3, 5, 8, 5, 3 semiquavers) and a rest of seven semiquavers follows. It would be entirely appropriate to associate extra-musical images with the theoretical purity of the pedal, as Messiaen had already employed technical procedures in earlier Regards to represent the different manifestations of God (for instance the depiction of the Three Persons of the Trinity in ‘L’échange’). On this occasion the pedal is unchanging and permits no elaboration or manipulation – an ideal rhythmic metaphor for the timelessness and immutability of ‘The All-Powerful Word’.
Evidence of the lack of evolution in Messiaen’s deployment of the rhythmic pedal may be found in the technique’s employment in the Turangalîla-symphonie. Despite the potential for new explorations in this work, we again find pedals constructed from the same sequence of Hindu rhythms as highlighted above: Râgavardhana, Candrakalâ and Lakskmîça (at 16/1, 111/5 and 272/3). To place such technical stasis in context, comparison may be made with the progression during the 1940s of other aspects of Messiaen’s burgeoning musical language. For example, while the notion of personnages is already integrated into his compositional thinking in the Vingt regards, the Turangalîla-symphonie takes this technique to its summit of complexity. Rhythmic pedals lost out to new ways of thinking, and they were to re-surface only intermittently after 1948.
6.2: Rhythmic Canon
Rhythmic canons usually function in a similar capacity to rhythmic pedals, providing a substructure over which the primary element may be added. Although Messiaen occasionally utilises ‘normal’ canons (a simple two-part ‘normal’ canon at the distance of a semiquaver operates in ‘Par Lui tout a été fait’ (42/10–43/2)), his preference is for purely rhythmic canons.
There are a number of ways in which Messiaen develops purely rhythmic canons, but the concept can be observed in a moderately uncomplicated form in ‘Regard du Fils sur le Fils’ (18/1–24/8). This canon is notable for the amalgamation of elements of Messiaen’s musical language (a factor that would become more frequent in later years) constructed from the often-used combination of Hindu Deçî-tâlas (as noted in the discussion above of rhythmic pedals), Râgavardhana, Candrakalâ and Lakskmîça, with the simple addition of a dot to the lower part. Messiaen returns to the same concept the following year with a slight variation of this type of canon being located at the start of ‘Dans le noir’ (Harawi, 94/5), where the lower stave of the piano adds a quarter to each value of the upper stave. Example 6.2 below illustrates the start of the procedure.
Example 6.2 Canon in ‘Dans le noir’ (Reproduced by kind permission of Editions Alphonse Leduc, Paris/United Music Publishers Ltd, England)
All the cases cited so far have been two-part canons, and the first three-part rhythmic canon makes its appearance in ‘Amen des anges, des saints, du chant des oiseaux’ (Visions de l’Amen, 51/6). The canon is once again not functioning without being combined with other rhythmic ideas, as the three-part canon is constructed from two non-retrogradable rhythms, and this idea is observable again in ‘Par Lui tout a été fait’, ‘Regard du Temps’ (Vingt regards, 26/1 and 55/2) and ‘Adieu’ (Harawi, 52/1). In a similar vein, there are more canons assembled from Hindu rhythms – specifically Râgavardhana, Candrakalâ and Lakskmîça – which surface in the Vingt regards sur l’Enfant-Jésus (26/14, 98/9) and Harawi (23/6, 41/1) and are therefore limited to the one-year time span of 1944–45.
The next stage of the technique makes its debut in Harawi, with a marked shift towards retrograde rhythmic canons. A clear distinction needs to be drawn at this point between a retrograde rhythmic canon, and a rhythmic canon within a retrograde section. The former is a canon in which the lower part is an exact reversal of the upper, whereas the latter is a normal rhythmic canon that has merely been reversed by retrogradation on a larger scale. To clarify these differences see ‘Montagnes’ (Harawi, 13/5) and the lengthy retrograde reprise in ‘Joie du sang des étoiles’ (Turangalîla-symphonie, 203/1) respectively. The Harawi canon uses the rhythm shown in Example 6.3.
Example 6.3 Canon rhythm in Harawi (Reproduced by kind permission of Editions Alphonse Leduc, Paris/United Music Publishers Ltd, England)
The bracket indicates the Hindu Dhenkî rhythm, although ‘non-retrogradable’ is an equally viable label. The forward part of the canon, on the upper stave of the piano, commences on the central value of Dhenkî. Its retrograde, on the lower stave, begins on the last value of this rhythm. Another example of a retrograde
rhythmic canon in the simplest form of the technique occurs in the Turangalîla- symphonie at 99/1, where a 12-bar rhythm is performed simultaneously forward on the flute/clarinet and retrograde on the oboe. The technique may be observed here in a ‘textbook’ form: the oboe’s rhythm is an exact mirror of that of the flute and clarinet. The device reappears in Livre d’orgue and Sept haïkaï, although it is on each occasion aggregated with another rhythmic technique (chromatic durations and Hindu rhythms).
The passage at 203/1 in the Turangalîla-symphonie is, as stated above, a normal rhythmic canon that has merely been reversed by retrogradation on a larger scale; Messiaen takes the section starting at 188/1 and retrogrades it in its entirety. The retrogradation is combined with the technique of personnages. The influence of Messiaen’s wide-ranging analytical interests may be felt in this type of procedure; his enthusiasm for the work of Machaut in particular is clearly reflected here.
It should also be noted that rhythmic canons could function with occasional punctuations without, from Messiaen’s perspective, the integrity of the canon being compromised. A prime example of this approach is found in the Visions de l’Amen, starting at 78/1 with a canon based on the typical combination of Râgavardhana, Candrakalâ and Lakskmîça:
78/1: A double rhythmic pedal in canon on the first piano concludes at 80/1. The distance of the canon is a minim.
80/3: The canon restarts at the distance of a crotchet and finishes at 82/6. 82/8: The canon restarts once more at the distance of a quaver and finishes at 84/6.
This flexibility of thinking is not especially momentous here, but similar technical elasticity surfaces elsewhere in the rhythmic aspect of Messiaen’s music and perhaps more significantly in his harmonic language.
6.3: Non-Retrogradable Rhythms
Non-retrogradable rhythms appear most extensively in the mid- to late 1940s, although the technique is employed across a wide range of Messiaen’s output. The relatively simple notion of a palindromic rhythm is developed to some extent, but the limitations of the concept seemingly impeded any comprehensive elaboration.
The composer observes a link between non-retrogradability and Hindu rhythms in the first bar of the Quatre études, where the palindromic properties of the Vijaya Deçi-tâla are noted. There would appear to be little more to this connection other than a happy coincidence between source material and Messiaen’s own technical thinking, and it illustrates an attempt at integrating aspects of his rhythmic thinking (however debatable the point of view might be).
The principal way in which this device is expanded first surfaces in the final Regard (158/2), with the addition of cells to the left and right of the original rhythm
which retain the integrity of the technique. These extra rhythms may be added and subsequently removed in a fairly free manner to alleviate the inherent rigidity of the concept, as long as the overall rhythm remains non-retrogradable.
The technique remains a small-scale compositional device which, for the most part, functions on a secondary level as support for a more complex rhythmic or harmonic scheme. However, the general idea was also applied to the structural domain where Messiaen constructed palindromic formal designs (see Chapter 9). 6.4: Anacrusis, Accent, Termination
The conception of anacrusis, accent and termination appears early in Messiaen’s output but it never attained a central position in his technical arsenal. It surfaces from time to time (mostly in the 1940s) without ever becoming more than an intriguing aside compared to other rhythmic devices.
The Visions de l’Amen have both extended and more concise instances. At 25/13ff. on the second piano, a lengthy anacrusis of almost two bars leads to an accent fff followed by the termination. Messiaen then extends the idea at 28/14ff. by augmenting the anacrusis and adding a second accent. A more compact occurrence surfaces at 50/1, where the first period of ‘Amen des anges, des saints, du chant des oiseaux’ is formed by an anacrusis, accent, mute which is supplemented by an arsis (but not a thesis).
Further examples may be observed in the Vingt regards sur l’Enfant-Jésus (where it plays a central role in ‘Regard de la Croix’), the Turangalîla-symphonie (124/1) and the Quatre études (2/1). The underlying principle remains the same, regardless of specific implementation and any real sense of development during the life of the technique is absent.
6.5: Chromatic Durations
The most common type of chromatic duration is a straightforward presentation, such as 1, 2, 3 and so on. The technique plays a meaningful role in the majority of pieces, and Messiaen develops the presentations of chromatic series to produce wide-ranging results. A familiar form is the simple exposition of a series, which can be examined in ‘Regard des prophètes, des bergers et des mages’ (Vingt regards sur l’Enfant-Jésus, 122/1–123/3). This instance is notable for the fact that when the series has completed its journey from 16 semiquavers to 1, the final value is repeated – thus slightly distorting the purity of the process. When the repetition of a value is located within a chromatic series, the distortion assumes greater significance – an effect observable in the Turangalîla-symphonie at 11/1–4. The values of the durations (in semiquavers) are as follows:
It could be argued this sequence is not chromatic in the strictest sense: the extra values of 2 and 1 destroy the true chromaticism. This Turangalîla example is, however, a step towards more complex distributions of a chromatic series.
Messiaen occasionally ‘interpenetrates’ chromatic durations to form an interlocking sequence that is no longer truly chromatic but is nevertheless a derivation of the technique. In the Turangalîla-symphonie (96/1), two series of chromatic semiquavers (1–8 and 5–12) are ‘interpenetrated’:
1 2 3 4 5 6 7 8
5 6 7 8 9 10 11 12
The final value is reduced to 10 semiquavers in the score (rather than the 12 indicated above, which would theoretically complete the process) due to the commencement of the next section.2
A stage further in intricacy can be detected later in the Turangalîla-symphonie (266/2; Table 6.2).
Table 6.2 ‘Interpenetrated’ chromatic durations at 266/2 in the Turangalîla- symphonie
Instrument Durations in semiquavers Triangle 15, 13, 3, 4, 15, 13, 3, 4, 15, 13 Wood blocks 12, 14, 1, 2, 7, 8, 16, 12, 14, 1, 2, 7 Turkish cymbal 5, 6, 9, 11, 10, 5, 6, 9, 11, 10, 5, 6, 9 Maracas 4, 3, 13, 15, 4, 3, 13, 15, 4, 3, 13, 15 Chinese cymbal 10, 11, 9, 6, 5, 10, 11, 9, 6, 5, 10, 11 Bass drum 16, 8, 7, 2, 1, 14, 12, 16, 8, 7, 2, 1, 14
The interpenetration is here less rigid than in the example cited above, and it is combined with a scattered distribution of the values of 1–16 semiquavers across three layers of the texture. A willingness subtly to manipulate self-imposed rules is in evidence here, suggesting a possible dissatisfaction with results of an excessively intractably mechanical nature.
2 An analogous passage occurs in the Vingt regards sur l’Enfant-Jésus (81/13), with
series of 1–13 and 3–15 being superimposed to form an interlocking structure. As indicated in the score, the first series progresses from 1 to 13 semiquavers, while the second increases from 3 to 15 semiquavers.
Another concept applied to chromatic durations is that of ‘disperse order’. The passage commencing at 267/9 of the Turangalîla-symphonie, in which values of 1–7 semiquavers are seemingly arbitrarily re-ordered, is a prime example:
1, 4, 7, 6, 5, 3, 2, 8, 11, 14, 13, 12, 10, 9, 15, 18, 21, 9
Messiaen does not provide any reasoning behind the results obtained, and it is possibly only coincidental that there is a noticeable movement from the extremes to centre when ascending numerically.
Chromatic durations can be melded with other rhythmic devices, as in Cantéyodjayâ 13/4 (with a retrograde rhythmic canon) the Quatre études de rythme (interversions) and Livre d’orgue 33/1 (interversions and retrograde rhythmic canon). The already noted potential malleability of the technique makes it suitable for these technical mergers.
6.6: Interversions
Interversions do not appear until the Quatre études de rythme of 1949–50, but they play a role in subsequent works. There is a clear distinction between the type of interversion utilised in the ‘Experimental period’ (1949–51) and the compositions of the early 1960s. The interversions of Cantéyodjayâ, the Quatre études de rythme, Messe de la Pentecôte and Livre d’orgue are all one of the alternative methods listed in Appendix 1, while those in Chronochromie and Sept haïkaï are taken exclusively from the table given by Messiaen in the third volume of his Traité de rythme, de couleur, et d’ornithologie (pp. 16–66).
Interversions can be both melodic and rhythmic, although Messiaen favoured the rhythmic form of the technique. Melodic interversions appear in Cantéyodjayâ; one of the sections in the work’s mosaic structure (19/11–20/6) contains nothing else. Example 6.4 illustrates the start of the procedure. The lower stave has permutations of the four-note motif which is treated as an ostinato above.
The ‘Interversion in a triple line’ appears in ‘Neumes rythmiques’, exactly as outlined in the explanation in Appendix 1 (Example 6.5). The three ‘lines’ (1–5, 6–10, 11–15) are spread across the five phrases.
Example 6.5 Interversion in a ‘triple line’ (Reproduced by kind permission of Editions Alphonse Leduc, Paris/United Music Publishers Ltd, England)
Later in the same work (‘Île de feu 2’) Messiaen favours the ‘interversion in open scissors’. These examples demonstrate the significance of the omission of the final value in the explanation of the method, as the symmetry of the 12 durations does not pivot around a central value (a favoured feature of Messiaen’s techniques).
The problem of a superfluity of results when interverting durational series led Messiaen, at times, to choose only a selection from the total of theoretically possible interversions. This kind of decision-making is an alternative, and logically less satisfactory, means of reducing the results to manageable proportions than the ‘limited symmetrical re-interversions’. An instance occurs in Messe de la Pentecôte (5/5), in which only 10 of a possible 24 interversions are used.
Interversions of Hindu rhythms combined with personnages rythmiques are a prominent feature of Messe de la Pentecôte and Livre d’orgue. On each occasion three Hindu rhythms are interverted, giving the maximum of six interversions.
The table of 36 interversions in the Traité, together with the superposition in groups of three, sums up the favoured form of the technique in use from the time of Chronochromie onwards. The number of interversions selected from these tables is extremely limited, and Messiaen does not discuss his reasons for choosing so few. In Chronochromie and Sept haïkaï only three of the single interversions are seen: 4, 5 and 35. A larger number of superpositions are present (1–3, 7–9, 13–15, 19–21, 22–24, 28–30), but this again is only a percentage of the total available.
6.7: Rhythmic metamorphosis
The first movement of the Sept haïkaï contains the only occurrence of this technique. The process lasts for the duration of the movement and is located on the xylophone and marimba. The metamorphosis involves the gradual modulation from Simhavikrama into Miçra varna, after the latter has been presented at 2/2. Both rhythms are given in Example 6.6 below. The process begins at 4/1 with
the initial presentation of Simhavikrama. The first metamorphosis of this rhythm occurs at 5/1, and is shown in Example 6.7. The values marked A have decreased