Time, eternity and the problem of minimal music’s alleged non-linearity in Louis Andriessen’s De Tijd


This article explores contrasts between time and eternity in Louis Andriessen’s De Tijd from 1981. The music, although inspired by the experience of “complete tranquility”, appears to establish a dialectical opposition between musical elements signifying timelessness and measured time. Robert Adlington argues that this piece succeeds in establishing experiences of musical change that do not necessarily comply with Western cultural models of (linear) time, but rather with an “extended present”, or, as Jonathan Kramer famously called it, “vertical time”. Whilst this is entirely in keeping with the minimalist characteristics of De Tijd, a close analysis of the music reveals a more ambiguous situation, wherein the focus is on the opposition between stasis/eternity and progress/time. Remarkably, both aspects of this opposition become symbolized through paradigmatic minimalist tropes, which are commonly presumed to be associated with the realm of ‘vertical time’. If minimalist techniques can represent both ‘vertical’ and undeniably linear aspects, then this would call for a reconsideration of the nature of minimalism’s idiosyncratic relation to time.


Taking a text from St. Augustine dealing with the distinctions between time (characterised as continuous motion) and eternity (characterised as immobility), the Dutch composer Louis Andriessen composed De Tijd (‘Time’), a monumental work for female chorus and large ensemble. Music, being a time-based art, unfolds in time and the listening experience can only take place over the same time-span it takes to make the music sound. This implies an essential connection between time and music, which is presupposed for any piece of music. Andriessen’s piece does not deal with time only because it is a setting of a text on this subject, but more fundamentally because it attempts to provide a sounding musical means of considering time and its nature. If music is indeed so dependent on its temporal features, then a piece of music can be construed to explore or reveal the phenomenon of time itself. In that respect, De Tijd has a lot in common with De Snelheid (1982-83), where the nature of speed is similarly made tangible in the musical material itself. Both pieces might even be considered as each other’s antithesis, represented by the static representation of time as eternity in De Tijd versus the dynamic accumulation of speed - time as acceleration - in De Snelheid. 

The following discussion of De Tijd will deal with the particular combination of musical aspects denoting both ‘time’ as well as ‘eternity’, and thus constituting a fascinating musical dialectic between both modes of temporality. More importantly, Andriessen’s work will be discussed against the background of minimal music (De Tijd, after all, features one of the most stringent uses of minimalist composition techniques in Andriessen’s output), for minimalism has often been taken to aspire for the prevalence of stasis over dynamic elements, of non-linearity over linearity, of the absence of teleological direction, indeed, of the establishing of what Jonathan Kramer famously called: ‘vertical time’ as opposed to linear time (1988, pp.54-57, 62-65, 375-393). Of these ‘vertical compositions’ as Kramer calls them, minimal music is the most explicit (though not the only) example. 

Theoretically, eternity is the opposite of time. One of the fundamental concerns of St. Augustine’s text (as used in Andriessen’s composition) is to explain the nature of eternity “which is for ever still” as contrasting with time which “is never all present at once” (as it is, in Augustine’s words, a sequence of movements “constantly following each other into the past”). The present is understood in correlation to its past and its future, while the course of time involves the incessant movement between those: the present moving into the past and the future hovering beyond the present. “But in eternity, nothing moves into the past: all is present,” as Augustine argues. The fundamental difference between time and eternity is the question of movement: the present as something fleeting, continually moving into the past, whereas the eternal present involves stillness. In other words: time can be considered as a dynamic process, whilst eternity would be completely static. 

These concepts of time and eternity find a very interesting parallel in musical principles of teleology and ateleology, of musical movement versus stasis or of ‘horizontal’ versus ‘vertical’ temporalities. Virtually all Western music is characterised by a teleological or goal-directed motion. This teleology works on several levels: a dissonance is first prepared and then resolved, a build-up of tension culminates in a perfect cadence, a development section leads to the recapitulation, etc. These musical processes are essentially linear: they lead from somewhere to somewhere else. This linear mode of musical thought is reflected in the listener’s active involvement of memory: the recollection of what went before and the anticipation (often actually the predictability) of what is to come are intrinsically involved in how any ‘present’ musical element is understood. 

Jonathan Kramer identifies linearity and nonlinearity as two ‘structural forces’ whose interaction governs most Western music. He defines linearity as “the determination of some characteristics of music in accordance with implications that arise from earlier events in the piece” (1988, p.20). Nonlinearity, for him, is not the absence or negation of linearity, but rather what he calls a ‘nonprocessive’ principle set against the ‘processive’ function of linearity: “the determination of some characteristics of music in accordance with implications that arise from from principles or tendencies governing an entire piece or section” (1988, p.20). Given the fact that music is an essentially temporal art form and only exists in and through time as mentioned above, this linear concept of music should not be so surprising. Nevertheless, in the second half of the twentieth century, a tendency can be discerned which strove to avoid that musical linearity. Several composers and compositional styles from that period have in one way or another introduced approaches where stasis prevails, or -employing Kramer’s terminology -where the nonprocessive aspects have a comparatively larger impact than the processive ones (e.g. all music determined a single serial prime form, rather than one musical element being determined by a preceding musical element). Thus, the dynamic, linear drive with its inherent teleological motion becomes less evident or, in some cases, is pushed to the point of breaking. 

Quite possibly, no musical style has been so emphatically associated with eliminating linearity and hence teleology as minimal music. The claim that minimal music would be essentially ateleological was introduced in some of the earliest scholarly writings on minimalism. Wim Mertens describes how the basic minimalist techniques of sustaining sounds for a remarkably long period of time, or excessive repetition (or near-repetition) can be easily explained as thwarting any teleological directionality. The listening experience is altered accordingly:

The listener will therefore need a different approach to listening, without the traditional concepts of recollection and anticipation. Music must be listened to as a pure sound-event, an act without any dramatic structure (Mertens, 1988, p. 20). 

When, in extensively repetitive structures, the ‘present’ music is so much similar to what preceded it and to what will follow it -the past and future -then, indeed, the schemata of linear unfolding and the listener’s sense of teleological direction would no longer comply with traditional concepts of linearity, sequence, tension and, possibly, climax. It was not an explosive, passionate feeling. It was an experience that we probably all have lived through or will live through once or twice in life: an experience of the stopping of time, of complete tranquillity. This, of course, has to do with loveThis altered perception of music which no longer follows a certain (dynamic) course, but rather remains within a continuum (stasis) also has a profound impact on the experience of time. The lack of differentiation between musical events that came before and those that are about to follow may lead to a sense of time being suspended, and of prevalence of the present (Augustine having already described eternity as a situation in which “all is present”). The most famous and often-quoted concept that addresses this unusual relationship with time is Jonathan Kramer’s term ‘vertical time’, which on first reading closely corresponds with the remarks made by Andriessen. Louis Andriessen has mentioned that a personal experience lay at the basis of conceiving this piece. 

It was not an explosive, passionate feeling. It was an experience that we probably all have lived through or will live through once or twice in life: an experience of the stopping of time, of complete tranquillity. This, of course, has to do with love. When I experienced this feeling it was so strong that I decided to write a piece about it. (Andriessen, 2002a, p.138) 
The experience of time stopping - which is nothing less than an instance of ecstasy[1] - strongly resonates with Kramer’s description of vertical time as “a single present stretched out into an enormous duration, a potentially infinite “now” that nonetheless feels like an instant.”(1988, p.55) Among Kramer’s many models of temporality, this is the one that invokes eternity, or, as Kramer points out with a sense of paradox, timelessness rather than stopped time: “timelessness does not, despite its etymology, imply that time has ceased to exist, but rather that ordinary time has become frozen in an eternal now.”(1988, p.377) The extreme lack of linear direction, phrase structure and large-scale closure means that such music, in spite of the presence of gradual evolution (perhaps even towards goals) “allows the listener to make contact with his or her own subjective temporality, it is music of subjectivity and individuality.”(1988, p.57) 

Andriessen’s De Tijd 

But at the centre of De Tijd stands Augustine’s fundamental question, ‘What, then, is time’. And so, transferred onto the musical plane, the work manipulates our perception of musical time by means of its structural organisation and technical detail, and engages us by the poetry that these generate. (Wright, 1993 p.10) 

The tendency to make compositions as a means of reflection upon a well-defined extra-musical subject is one of the most prominent features of Louis Andriessen’s oeuvre, and in that respect, De Tijd is no exception. However, in comparison to pieces dealing with political issues (De Volharding (1972), Il Duce (1973), De Staat (1972-6), Mausoleum (1979 rev. 1981)) and the relationship between spirit and matter (De Materie (1984-8)), De Tijd stands apart because of the strong identification between (extra-musical) subject and (musical) realisation. That De Tijd is, in the first place, a conceptual piece appears from the approach of Andriessen to his material. 

At the centre of the work stands the choral part, set for a chorus of female voices singing a setting of the text by St. Augustine. However, the long drawn-out setting of each syllable makes it hard to follow the meaning of the Latin text, forcing the listeners to concentrate instead on the sound of the held notes. 

The slow tempo combined with the long durations grant this piece an ascetic quality and a sense of extreme stasis. With a tempo marked crotchet = 48 and almost entirely in a time signature of 8/4 in which each chord (covering one syllable of the text) lasts for an entire bar, an unprecedented level of stasis in Andriessen’s music is reached. It takes 10 seconds to complete such a bar, which means that it takes an entire minute before we get to the end of the first page of the full score. 

The large ensemble uses instruments from all sections of the orchestra, recombined into a non-standard configuration, as is characteristic of Andriessen’s work. De Tijd’s ensemble consists of six concert flutes, two alto flutes, three bass clarinets, one double bass clarinet, six trumpets, two harps, Hammond organ, two bass guitars and a small string section where the cellos are omitted (six violins, two violas and four double basses). In addition to this, three percussive quartets, arranged left, right and centre stage are given a structurally important function. The stage centre quartet of xylophone, log drums, gongs and tam-tam is in between the two antiphonal quartets of vibraphone, crotales, tubular bells and piano (stage left), with the same line-up stage right but for a cimbalom replacing the tubular bells. 

After the almost-tutti first chord, the female voices sing (in what in fact is a hocket, albeit lacking the antiphonal drive of the high-energy hockets in Andriessen’s Hoketus (1975-6) or De Staat) the text that is stretched out over the long held notes, much in the manner of a renaissance cantus firmus. However, as opposed to a true cantus firmus, the long notes do not establish the basis for new (and faster) musical activity imposed on top of it: Instead, these held tones are accompanied by the Hammond organ, the strings and the harps providing a harmonisation of this vocal part. Supported by the binary rhythm, the resulting music most resembles a chorale, albeit an extremely slow one. The female voices mostly sing monody that occasionally gives way to two-part writing, wherein the voices sing at an interval of a major or minor second. The vocal part is embedded in a chordal accompaniment that consists mainly of (up to eight-part) dissonant chords within a harmonic progression that still possesses recognisable traces of functional harmony and modulations, such that the work displays a remarkable combination of diatonic and chromatic elements. The fact that the vocal part for the first 72 bars[2] circles around the central a’ further enhances a sense of stasis. 

In bar 10 the stage right antiphonal percussion group introduces the first of a long series of ringing bell-like chords, the clarity of which contrasts with the subdued sound of the chorus, harps, organ and strings. The impulses of the radiant percussion continue to form an independent layer against the sustained chords at irregular time-intervals. Only gradually will a listener become aware of the fact that the irregular distances between the impulses from the percussion ensemble are not irregular at all, but correspond to mathematical proportions, always making up an iambic rhythm (short¬long) with systematically shortening note values, which results in an acceleration against the fixed sustainment of the other parts. This shortening of the notes in this ‘iambic’ layer follows the pattern in figure 1, with the lengths of notes given as the number of crotchets they occupy. 

In this first segment of the piece (bars 15-86), the composer starts his iambic system with the ratio of 12-24, in order to arrive by a process of gradual shortening at the ratio of 2-4 (always expressed in crotchets). There are a few exceptions to the strict logical evolution of this process, as can be seen in figure 1. The reason is not very clear, but it helps to make the process smoother: the progression from 12-24 to 11-22, for instance, is realised in two steps. In spite of the slight irregularities, it is clear that each iambic ratio is stated three times. The progression continues into the next section, where the stage left antiphonal percussion ensemble enters and a hocket ensues between the two near-identical groups. This leads to the statement of the iamb in its most primary form, the ratio 1:2, which appears from bar 87 onwards (see figure 2). This ‘Urgestalt’ of the rhythmic pattern is the result of the interplay of the two antiphonal hocketing ensembles. 

Figure 2: Louis Andriessen De Tijd bars 85-90 (strings, chorus and percussion only)
Copyright 1994 by Boosey & Hawkes Publishers Ltd.
Reproduced with permission

The fact that the arrival at the shortest realisation of the iambic pattern coincides with the beginning of the first hocket-section adds to the dramatic impact of this moment. This is the first moment (about 15 minutes into the piece) that the instrumentation changes, and the chorus with its instrumental accompaniment momentarily drops out. The stern compositional logic of the time-proportions, the extremely slow pace and the static quality of the music heighten the impact of every sudden change in the texture. Andriessen takes advantage of this by employing an instrumentation that gradually becomes more dense, with the most dramatic effect at the beginning of the third choral section in bar 161, where the trumpets herald the moment of highest musical intensity of the composition. 

At this point, Andriessen introduces a third compositional technique, in the form of three superimposed rhythmic cycles (bars 97-123) played by the centre stage group of percussionists. This consists of a log drum playing a beat every six quavers, a gong striking every seven quavers and a xylophone playing one beat at irregular time intervals, but at an average of every twelve beats. The mechanical character of this composite 6-7-12-quaver cycle is reinforced by the dry percussive sound of the instruments, which enhances the association with clockwork mechanisms. The appearance of the ‘clockwork’-type cyclic material completes the representation of time in this piece. The situation in the first large section of the piece with subjective, measured time in the accelerating iambs versus eternal time in the binary sustained chords now becomes complemented by the inclusion of artificial (clockwork) time in the rhythmic cycles. The first two types of musical material may be taken to symbolise particular types of temporality through the associations between their musical characteristics: slow, regular, chorale-like for the stillness of eternity, and the accelerating, irregular iambic material for the dynamic time ‘always in motion’. The association between the ‘ticking’ sound of the interlocking cycles and the clock time/ clockwork they represent is of a more literal order. 

The text is divided into nine segments (referred to in figure 3 as ‘phrases’ and numbered P1 to P9). These are distributed over the composition with interludes and overlaps from the other instrumental ensembles playing hockets and superimposed rhythmic cycles, so that the entire work can be divided into several distinct sections according to the scheme shown in figure 3. 

Whilst the first hocket section (bars 87-97) clearly serves to separate the two choral sections, the subsequent appearances of a hocket between the two antiphonal ‘percussion’ quartets are integrated in respectively the preceding (bars 151-161) or following (bars 205-244) choral section. The third hocket section does appear to start as an autonomous section, but soon becomes overlapping when at bar 219 the chorus enters again. Notice how from Chorus II onwards the organisation corresponds to a mirror-symmetrical outline: (Chorus + Hocket) - (Chorus) - (Hocket + Chorus). 

After the introduction of the three basic elements of long held cords, (accelerating), iambic patterns and the clockwork-like multiple cycles, the rest of the composition is an intensification of these elements and processes as they become increasingly superposed, and the thickening of the texture adds to the sense of acceleration. 

The idea of rhythmic cycles remains an almost constant presence from then on, although it does not always appear in this reasonably fast clockwork-like presentation. Instead, there are rhythmic cycles (bars 126-161) in both the bass guitars and the bass clarinets at regular intervals of 13 quavers; another cycle in the violins and violas, also with one (pizzicato) beat at every interval of 13 quavers, begins in a different metric position than that of bass guitars. Both 13-beat cycles are placed against the regular cycle of chorus (and flutes) that has a length of 14 quavers. Towards the end of this section, a second hocket-section is superposed, which leads to the entry of the third choral section (bars 161-204). 

At bar 161, the moment of the composition’s golden section,[3] the texture is thickened to the maximum when the last instrumental group (the trumpets) has joined the ensemble. Even more striking than the expanding orchestration is the tessitura of the voices. Having started at a’ in bar 1, they suddenly enter here in a considerably higher register reaching their highest pitch (g#’’) in bar 193. The harmonic material, which has so far been constant, is replaced by new chords and the roles are reversed: In the second phrase of this choral section (bars 185-204) the regular, binary nature of the material of the chorus develops into its opposite, the ‘iambic’ short-long pattern, within a complex combination of cycles, summed up in figure 4. 

The reversal of regular and iambic rhythmic identities is one of the most crucial elements in the interpretation of the notions of time, timelessness and linearity, as will be discussed below. In the final section the corresponding shift of symbolic functions happens, as the stage left percussion quartet starts playing in regular chords (rather than the iambic rhythm), and are soon joined by the chorus which returns to the material from the beginning. The result of the chorus briefly adopting an iambic pattern (or more precisely, a vague approximation of an iambic pattern, as the 4:5 ratio is a far removed from the ternary basic 1:2 pattern) and the percussion quartet suddenly playing in regular binary rhythms has a large impact in a composition that relies to such an extent on strict processes, and on the meticulous distribution of musical elements among the chorus and instrumental subsections. 

The final section opens with a hocket in which the two antiphonal percussion quartets are joined by the main ensemble (without the choir). The stage left percussion quartet states the chords over 8-beat bars like those featured at the beginning of the piece, taking over the role that was initially reserved for the chorus. This proves an interesting exchange of functions, as the joining of the chorus to the iambic scheme in the previous section is now reciprocated by the originally ‘iambic’ percussion quartet taking over the regular binary function. The stage right percussion quartet[4] answers this part with impulses every 7 beats, bringing about a hocketing process to which a third part is added by the rest of the ensemble (strings, flutes, organ, bass guitars, bass clarinets, occasionally joined by the gong). This third hocketing part is not conceived as a static cycle with notes of equal length, but corresponds to the iambic type of material, which includes a fast process of diminution, and arrives at a 4:8 ratio in bar 218. Additionally, the stage right percussion group shows some irregularities concerning the note-lengths, so that any predictability is avoided and the hocketing character is foregrounded. 

The entrance of the chorus in bar 219 does not bring further rhythmic complexities, since the female voices join the regular 8-beat chords of the stage left percussion quartet. Whilst the hocketing process continues, the chorus returns to the material of the opening section. The obvious difference lies in the fact that the opposition between the soft, fragile sound of the chorus (doubled and accompanied by sections of the orchestra - mostly strings, flutes and Hammond organ) versus the clashes of the bells is now synthesised. The chorus and the stage left percussion quartet play together, so that the radiant sound of the bells (with its hocketing echo from the stage right percussion quartet) pervades the closing minutes of the piece. There is, however, one remaining surprise at the end of the piece. As the last syllable and bell-stroke fade out, the log drum plays three bars of fast semiquaver-quintuplets, suggesting a pulse that for about 42 minutes had been remarkably absent from the sounding music. It is the most clockwork-like musical gesture that rounds off the piece. The fast speed of time quite literally ‘ticking away’ in those final bars offers an intriguing contrast with the stillness of the slow chorale-type material, as well as with the monolithic chords that mark the iambic patterns. 

Shaping Time 

Holy time in eternity
Holy eternity in time
(Allen Ginsberg, Footnote to Howl) 

De Tijd establishes a set of binary oppositions, from which it derives its musical tension and its ability to address the paradoxical nature of time itself. Regular (binary) and iambic rhythmic elements are contrasted, static regularity is combined with an accelerating motion through the shortening of note values, the opposition of different types of material gives way to an integration of musical characteristics, and the vertical orientation - representing eternity - becomes drawn into time’s linearity. All these oppositions gradually strive towards some level of integration, so that the fundamental opposition between time and eternity turns out to be a far less mutually exclusive matter than might have been expected. The simultaneous presence of time and eternity, the mystical essence of which is hinted at in the verses by the poet Allen Ginsberg (more than 1500 years after St. Augustine) quoted above, is what lies at the core of De Tijd

The tendency to lay down a strong opposition between two mutually exclusive concepts from which nonetheless a synthesis is suggested, is typical for Andriessen’s approach. Particularly in terms of his political ideas, Andriessen has often referred to the dialectic tradition of Hegel (Andriessen, 2002b, pp.140-141). But this brings us back to the fundamental question: how is an integration of time and timelessness possible, and how can such a thing be achieved by the alleged minimalist characteristic use of ‘vertical time’? 

From the analytical description above, it is clear that the two basic types of musical material and the way they are developed in De Tijd are crucial to the interpretation of the abstract subject matter that underlies the musical elements. The juxtaposition between the regular binary sustainment and the irregular iambic figure is asserted by the composer to be “the most important aspect of the whole composition” (Trochimczyk, 2002b, p.140), and we can consider these as identifying the paradoxical coexistence of static eternity with dynamic (‘always moving’) time. Both concepts are also dependent on one another, because the (relative) immobility of the fixed ‘cantus firmus’ layer of sustained chords is experienced as such because of the contrast with the diminishing time-proportions of the other. The second layer thus deals with measuring time. The mathematical 1:2 proportion defines shorter and longer values and symbolically creates the units with which to measure time. 

There is a strong tendency in music analysis to conceptualise larger-scale temporal organisation in music in terms of proportions. Indeed, the considerable weight given to proportions - particularly the iambic ratios - in De Tijd makes it worthwhile to make some critical observations about this phenomenon. However, although a substantial number of compositions throughout music history display a refined use of temporal proportions - mostly in the ratio between the respective durations of segments or sections - there might be cause to doubt the relevance of these proportions. Jonathan Kramer (although himself relying on comparison of respective durations of musical sections as an analytical method) criticised any exclusive emphasis on proportions on the basis of the problematic identification of such proportions in the listening experience. The ‘beauty’ of mathematical ratios to the music analyst - so easily identifiable in the score - is far less easy to identify by a listener. Not only are music analysts sometimes too eager to search for certain ratios in a given piece of music (the golden section and the Fibonacci series certainly rank highest in this respect), the perceptibility of such ratios is a problem of a far more fundamental nature. As Kramer states: “How can we reconcile analysis based on measurement of absolute time with experienced musical time that is influenced by the continually changing contexts of most compositions?”(1988, pp.324-325) 

The question whether listeners are capable of perceiving, understanding and remembering proportions is an important one to be asked, because, unlike in the visual domain, the listener has no immediate perception of proportions. Memory plays an important role in this process, as it is involved in comparing a given duration with another. The highly complicated processes of music perception may indeed make it difficult to accurately perceive lager-scale durational proportions as such, but Kramer is quick to admit that those proportions may still have a relevance to the listening experience. “Although the proportional systems…may not be heard directly, they may well be perceived subconsciously, just as atonal sets, twelve-tone rows, and tonal Urlinien are. The music is the way it is in part because of its proportions.”(1988, p.329) 

Although Andriessen does use the golden section as a means of organising the shape of the composition as a whole (a feature that is very common in Andriessen’s music), his manipulation of durational proportions in the application of the iambic ratios is carried out in such a way that takes the listener’s perception of it clearly into account. By giving the iambic material to the two antiphonal percussion quartets, it immediately stands out from the ‘chorale-like’ musical texture. Whilst the exact ratios of the durations of the intervals between two successive struck chords may be somewhat unclear to the listener, the process-driven shortening of those time-intervals and its related perception of an increasing rate of musical activity would be very hard to miss. The symbolical meaning attached to the 1:2 iambic ratio (as will be explained below) is an important element underlying the concept of the piece. Appropriately, the composer made sure to highlight this feature in the musical foreground. 

The “narrative of time and timelessness”, as Adlington describes this piece (2002, p.16) involves a remarkably linear direction when considered in its totality. Accumulation, acceleration, textural expansion, intensification and ultimately the integration of material are all organised in clear, directional processes and combined in a broad crescendo movement over the course of the piece. On the local level, in the listening experience, this directionality is far less evident, which is symptomatic for the high degree of ambiguity in the piece. The superposition of distinct layers with different material and the simultaneous unfolding of different musical processes already accounts for a significant amount of such ambiguity, as it tends to make it harder for the listener to identify the material and processes that are at work. More importantly, however, the ambiguity is also present within the basic musical material itself, notably in the extreme duration combined with the music’s slow pace and in the design of the harmonic material. 

The sustained chords encompass such an extensive time-span that it is most unlikely for a listener to be able to measure it: each chord lasts long enough to assume at least some sense of eternity. The same can be said of the initial large ratios of the iambic patterns (12:24, 11:22, etc.). From cognitive musicological research, we learn that the human mind is only capable of identifying successive musical elements as a rhythmic pattern if they occur within a time span of around three seconds (Fraisse, 1982, pp.149-180). Two impulses that occur at less than 50 milliseconds apart cannot be perceived as separate identities and elements that are more than three seconds apart tend to be perceived as isolated, unrelated entities.[5] Because of this phenomenon, it takes a long time before the music reaches a point where the listener can identify the ‘iambic’ impulses as a rhythmic figure. Only at around the ratio of 2:4 (which appears only at the end of the fourth phrase in the first choral section -somewhere between 12 and 15 minutes into the piece), will the listener grow aware of the exact ‘Gestalt’ of the iambic rhythm, which is confirmed when the proportion of 1:2 is reached and the iamb falls more or less within the three-second frame. This means that the first section of the piece only gradually reveals the coexistence of an eternal time, with the measured time contained in the iambic pattern of the percussion. 

A similar ambiguity is present at the harmonic level. Andriessen has managed to conceive a large-scale harmonic homogeneity which, in spite of the frequent chord changes and modulations (such as the sudden move back to the A major of the opening, at the start of the second choral section in bar 97 (Andriessen and Schönberger, 2002, p. 169)), succeeds in establishing some sense of sustenance on a larger scale. The high level of continuity in the registration of the chords, and even more forcefully present in the way in which the chorus rarely strays far from a central pitch, is summed up in figure 5. Nikolaus A. Huber has remarked how Andriessen tends to organise his progressions from one given chord to the next by choosing chords with multiple notes in common. For instance, the first five chords from the piece are conceived in such a way that respectively 5, 3, 6 and 3 tones are shared between every two neighbouring chords (Huber, 1985, p.26). However, it should not come as a surprise that with the heavy eight-or-more-part harmonies he uses throughout, Andriessen is bound to have a substantial number of common pitch classes between any two adjacent chords The sense of harmonic continuity - or of harmonic stasis, even - does not depend on the selection of common pitches alone, however, but also on the registration and instrumentation of these chords. Even in places where the harmonic material is less continuous (after all, two adjacent eight-part chords with three pitches in common have a greater number of different pitches between them than common ones), the impression of homogeneity in the listening experience is surprisingly high. 

The fact that the sense of harmonic drive or evolution is not so strongly present in the listening experience is above all the result of the type of chords employed by Andriessen to help create a musical continuity. Voice leading and harmonic movement are present, but their effect is limited due largely to the slow tempo, but also due to their harmonic properties. The composer mentioned how the harmony developed from the idea to write a piece ‘about’ a dominant seventh chord (Andriessen and Schönberger, 2002, pp.165-166) which led him to develop a particular type of altered dominant seventh chords. The basic type of harmony used in De Tijd is a combination of two superimposed dominant seventh chords, a fifth apart (shown in figure 6).  

This merges tonic and dominant functionality within the same harmony: a dissonant dominant chord that carries its own resolution within it. From this basic superimposed dominant seventh chord, notes may be omitted and other notes can be added (for instance, the B in the upper system in the example from bar 4 can be seen as a way of extending the lower dominant seventh chord on A to a dominant ninth chord) and indeed Andriessen makes use of various ways of devising minute variations of his basic type of harmony. The V-I relationship of the two constituent dominant seventh chords, however, remains constant throughout. Andriessen remarked that: 

[i]t depends on the context whether the thesis-like character of the chord (the resolved chord) or its arsis-like character (the chord demanding resolution) predominates. Technically speaking, you could call De Tijd a succession of dominants: an endless suspension of which the resolution is always present. (Andriessen and Schönberger, 2002, p.166) 

The tendency to combine a dominant chord together with its resolution is reminiscent of the (single) dominant eleventh chord on E, used by Steve Reich in Four Organs (1970), of which Reich also remarked that the eleventh note (A) is in fact the ground note of the tonic (1974, p.50). Reich’s voicing of that chord (with the ground note of the dominant as affirmative bass note and the tonic strategically cast as top note) is a clever way of exploiting this inherent tonic-dominant tension. 

By placing the arsis-thesis tension (or the dominant-tonic resolution) within one and the same harmony, Andriessen weakens the impact of the harmonic progressions present in the chord-to-chord movement. However, much harmonic directionality can be identified in the score, including many dominant-tonic progressions between successive chords; again, they are subverted by the particular design of the chords, and the many progressions establish what Robert Adlington so aptly described as a ‘saturatedness of progression’: 

It is precisely this saturatedness…that prevents the construction of a single syntactical sequence. And every new chord has a sufficiently complex harmonic content to command immediate and full attention: a listener is given little opportunity to dwell on the multiple progressions formed between chords. (2002, p.28) 

This way of (partly) neutralising the harmonic functionality adds to the stillness of the composition and the sense of fascinating immobility that succeeds in evoking the impression of eternity. This is an eternity that is juxtaposed by the measuring of time contained in the iambic patterns, the ‘clockwork’ cycles, and even the log drum of the coda - the most immediate representation of time ticking away. 

Verticality and linearity 

In general, minimal music has often been seen as rejecting the conventional linear conception of time. Wim Mertens associated it with the notion of ateleology, with severe implications for the time-based listening experience: 

Since there is no absolute point of reference, a host of interpretive perspectives are possible. So that goal-directed listening, based as it is on recollection and anticipation, is no longer suitable….traditional recollection of the past being replaced by something akin to a ‘recollection into the future’, actualisation, rather than reconstruction. This ‘forward recollection’ removes memory from its privileged position. (1983, p. 90) 

The ‘vertical music’ that Kramer, like Mertens, characterises, depends on all archetypal minimalist compositional techniques: those based on sustenance (drones), as well as those grounded in repetition (including multiple rhythmic cycles) and repetitive processes that gradually evolve. The association of cyclic or even linear direction of processes with the vertical or non-goal-directed character is taken into account by Kramer: 

One might think of such works as purely linear, but listening to them is not a linear experience, despite their internal motion. Because in such works the motion is unceasing and its rate gradual and constant, and because there is no hierarchy of phrase structure, the temporality is more vertical than linear. (1988, p.57) 

The view of minimal music as quintessentially ‘vertical’, as Jonathan Kramer so influentially introduced, can indeed to some extent apply to the music of De Tijd. Especially in the first half of the piece, the predominant listening impression is one of utter stasis, of chords suspended in time, of sudden bell-like strokes appearing at irregular moments and finally of a clockwork-like percussive pattern joining the texture. It isn’t until the final stages of the composition that the process-driven unfolding of the piece (one process starting as early as bar 10, but only gradually experienced as such by the listener) becomes clearly apparent and -with the support of the large sense of intensification (texturally, as well as through the gradual crescendo and expansion of the tessitura and instrumentation) -may even become the focus of the piece. There is no denying that a narrative of time and eternity is present, moving from symbolic juxtaposition towards synthetic integration. Likewise, the inexorable linear unfolding of that process (or, the interplay of superposed processes within the multi-layered texture) is a clear and important feature of De Tijd. However, according to Kramer’s theory, the point would be that such linearity does not prevent the minimalist work from being essentially ‘vertical’, i.e. from establishing a time experience that addresses the extended present, rather than articulating time as ‘always in motion’. 

The fact that such an extended present lies at the core of De Tijd is what Robert Adlington argues (2002, pp.22-35), thereby corroborating the composer’s own intention, quoted at the beginning of this article, to write a piece about his experience of the ‘stopping of time’. Crucial in Adlington’s argumentation is that the differentiation between the layers representing ‘time’ and ‘timelessness’ is intangible in the audible result: “[w]hile successive sections of the score do indeed have different characteristics, the principal impression is one of continuity rather than contrast.” The very gradual pace in the music’s unfolding only adds to this impression, which leads Adlington to the observation that “[i]n important respects De Tijd presents changing music that never changes” (2002, p.31). This is symptomatic of the ambiguity involved, which is so characteristic for this piece. However, the same sense of ambiguity can also be found in the position towards minimalist composition techniques. 

One of the curious aspects of De Tijd is that it succeeds in taking different paradigmatic compositional techniques from American minimalism to denote the opposition between stasis/eternity (drones, sustenance, the avoidance of harmonic resolution) and progress/time (pulse, rhythmic cycles, hockets, process-like acceleration). Remarkably, both aspects of the time/eternity or verticality/linearity opposition become symbolised through paradigmatic minimalist tropes, which were in Kramer’s theory supposed to be associated only with the realm of ‘vertical time’. Moreover, the linear elements in De Tijd are rather clearly goal-directed. The goal in question is the obviously climactic conclusion of the piece, where the culmination point of the process-driven material coincides with the dialectic synthesis of the regular/ eternal versus iambic/evolving categories of musical material. The material, which at the beginning of the piece was still so clearly distinct and strictly juxtaposed, has by the end of the work become somehow integrated. The choral cantus firmus accelerates throughout the piece, from 8 beats at the beginning, over 7 beats at Phrase 5 to 6 beats in Phrase 7. It has been mentioned previously how, at the end of Phrase 8 (the second segment of Chorus III), the acceleration arrives at its culmination and the voices no longer sing in equal lengths, but in steady alternation of notes of 4 and 5 crotchets long. This unequal pattern is not written in the 1:2 ratio of the iambic patterns, but is nevertheless transformed into at least a sense of iambic rhythm. Similarly, the ‘bells’ of the stage left percussion quartet play the regular 8-beat chords with the chorus in the final section. The cantus firmus-like layer may represent eternity, but this eternity is not as immobile as one would think and becomes deeply affected by the measuring of time. The integration on a musical level between these two paradigmatic elements (the ‘cantus firmus’ and the ‘iambic’ types of material) also implies that the two temporal concepts they symbolise - time and eternity - that were supposed to be mutually exclusive become integrated. 

One little detail from De Tijd may illustrate how, on a fundamental level, the piece itself subverts the sense of the infinite, the static sense of eternity. In bar 81, Andriessen has added one note written as a triplet for the gong, piano 1 and bass guitars that stands out because it is a sudden fortissimo interruption in a musical context which until then had been very quiet (cf. figure 7). This is the only triplet in the entire work. According to the composer, this is some kind of “Augenmusik”, the number 3 of the triplet revealing that this moment marks one third of the length of the entire composition.[6] This means that this enigmatic signal divides the work into 1+2 thirds: an iambic pattern, exactly in the 1:2 ratio. The microstructure dominated by iambic proportions is then reflected in the macrostructure of the entire work: De Tijd may offer a glimpse of eternity, but in a finite, tightly organised and accurately measured time-span covering the entirety of the composition. 

Figure 7: De Tijd, bars 80-82 (strings and winds omitted)
Copyright 1994 by Boosey & Hawkes Music Publishers Ltd.
Reproduced with permission.

Due to the slowness and difficult perceptibility of the linear elements, De Tijd may offer an image of eternity in time (or, as Adlinton argues, an essentially vertical experience that challenges the culturally conventional models of time (2002, p. 2)). However, the opposite is also true. In De Tijd, on a hermeneutic level at least, a strict use of minimalist compositional techniques represents the subjective experience of time as ‘continually in motion’. This implies that minimalist tropes are used and can be used precisely for their linear qualities -for their potential to denote time’s progress -although in the listening experience this sense of progress can be rather ambiguous (ambiguity is, after all, a quality that Andriessen actively explores in this composition). That Andriessen achieves this by only using quintessentially minimalist techniques implies that within minimal music the process-driven techniques can create a strong resistance against the alleged overall static, vertical character. The linear potential of minimalism is, in other words, stronger than often assumed, even from the perspective of the listener. Robert Fink coined the term ‘recombinant teleology’ as a means of recognising the strong effect of larger-scale directionality within a strongly repetitive musical language (2005, p.9). Likewise, in some respects De Tijd reaches beyond the immediate experience of time as extended present. Given Andriessen’s predilection towards Hegelian dialectics, a dominance of the ‘eternal’ quality over the directionality of time would be surprising. Rather, a synthesis between both concepts involves a position that would embrace the many paradoxes it encounters. Not the verticality in spite of linear direction, but the paradoxical coexistence of both concepts at once is what occurs. The equally paradoxical assumption that minimalist compositional techniques may serve at once to establish and represent both oppositional concepts is then a logical consequence. A consequence that also implies that linear and non-linear aspects are far from mutually exclusive and can be fundamentally and perhaps simultaneously present in minimal music. 


Adlington, R. (2002) Counting Time, Countering Time. Indiana Theory Review, 22(1).
Andriessen, L. (2002a) The Art of Stealing Time. Todmorden: Arc Music.
Andriessen, L. (2002b) Lectures for Young Composers. In: Trochimczyk, M. (ed.) The Music of Louis Andriessen (New York: Routledge.
Andriessen, L. And Schönberger, E. (2002) On the conceiving of De Tijd, in Andriessen, L. (2002) The Art of Stealing Time, p. 169.
Fink, R. (2005) Repeating Ourselves. American Minimal Music as Cultural Practice. Los Angeles: University of California Press.
Fraisse, P. (1982) Rhythm and Tempo. In: Deutsh, D. (ed.) The Psychology of Music. New York: Academic Press.
Ginsberg, A. (1996) Selected Poems 1947-1995. New York: Harper Collins.
Huber, N. A. (1985) Erlebniswanderung auf schmalem Grat. MusikTexte, 2(9), p. 26.
Kramer, J. (1988) The Time of Music. New Meanings, New Temporalities, New Listening Strategies. New York: Schirmer Books.
Mertens, W. (1983) American Minimal Music. London: Kahn and Averill: London (Kahn & Averill).
Reich, S. (1974) Writings on Music (New York: New York University Press).
Wright, D. (1993) Louis Andriessen: Polity, Time, Speed, Substance. Tempo, 187, p. 10. 


[1] Ecstasy, from the Greek ek-stasis, literally means ‘standing outside’ and generally refers to the experience of briefly losing touch with the physical realities of living: awareness of bodily presence and of time passing. Mostly associated with religious or -as in Andriessen’s case -love-related experiences, ecstasy usually involves a heightened experience of the moment itself (the present) isolated from past or future. Hence the experience of ‘time stopping’ (Andriessen) or ‘timelessness’ (Kramer) the ecstatic focus on the now is of such power that the permanent flux of time may appear to have been lifted.

[2] Given the slow tempo, 72 bars equals 12 minutes, but is actually even slightly longer because Andriessen has included some bars in 9/4 and 10/4 instead of the uniform 8/4 metre.

[3] The composition has a length of 2247 crotchets (at a constant tempo). The ‘golden section’ moment comes at 1371 crotchets, which is not the exact mathematical point of a golden section (that would be 1388) but is nevertheless a very close approximation.

[4] Each of the percussion groups is joined by one of the harps in this section.

[5] An interesting discussion of the implication of this phenomenon of rhythm perception applied to works by Morton Feldman, can be found in: Moelants, D. (2003) Feldman, Memory, and Perception of Slowness. Tijdschrift voor Muziektheorie/Dutch Journal of Music Theory, 8(3), pp. 215-240. The slowness of the music in De Tijd, and even the use of harmony show some similarity to works by Feldman from the 1970s and 80s, such as Rothko Chapel (1971).

[6] Andriessen, L., private conversation with the author (Amsterdam, 11 December 2003). 

About the author:

Maarten Beirens studied musicology at the Catholic University of Leuven (KU Leuven), where he also received his Ph. D. with a thesis on European minimal music: He published articles on the music of Michael Finnissy, Karel Goeyvaerts, Louis Andriessen, Michael Nyman, and analytical strategies for minimal music, that appeared in a.o. Tempo, The Belgian Review of Musicology, The Dutch Journal of Music Theory, and the Journal of the Royal Dutch Society for Music History. Further publications include many articles about new music in Flanders, as well as the New Grove Online entries on composers Wim Mertens and Jean-Paul Dessy. In addition to his academic work, he is a music critic for the Flemish newspaper "De Standaard", as well as the Flemish Classical Radio Channel. He was the holder of a postdoctoral fellowship of the FWO Flanders at the KU Leuven, conducting research on the music of Steve Reich. He is currently a lecturer in musicology at the University of Amsterdam.