The unified colour and the division of orchestral phrases in Kaija Saariaho’s “Laterna Magica”: the modelling process as a guideline for compositional decisions

Rodrigo Meine – [email protected]
  Universidade Estadual do Rio Grande do Sul

This work investigates the use of the horns in Kaija Saariaho’s orchestral work Laterna Magica (2008). Initially, the concept of compositional modelling is elaborated taking as a point of departure the program note available at the composers official site. Then this concept is used to investigate the function of the horns, which Saariaho associates to the red color used in the transitions between scenes in Ingmar Bergmans movie Cries and Whispers (1972). The two aspects attributed to the horns by the composer are addressed separately: the unified color and the division of the orchestral phrases. Finally, some additional considerations regarding compositional modelling are elaborated in orded to constitue possible routes for future research.


Kaija Saariaho’s Laterna Magica (2008) was commissioned by Stiftung Berliner Philarmoniker and Lucerne Festival. This orchestral work lasts approximately 20 minutes and received its world premiere at the Berliner Philarmonie by the Berliner Philarmoniker on August 28 2009, with a second performance taking place just a few days later – September 2 2009 – at the Lucerne Festival, also by the Berliner Philarmonie under the conducting of Sir Simon Rattle. It received more than 20 further performances, including the United Kingdom premiere at Royal Albert Hall on July 17 2012 during the BBC Proms by the BBC Philarmonic Orquestra conducted by Juanjo Mena, and the Spain premiere on January 19 2013 at Teatro Cnovas by the Mlaga Philarmonic Orchestra under the conducting of Jos Ramn Encimar.1

In her program notes, Saariaho states that the title of the piece has its origins in the reading of Ingmar Bergman’s homonym autobiography. The following can be read at the composer’s official website:

In time, as I read the book, the variation of musical motifs at different tempos emerged as one of the basic ideas behind the orchestral piece on which I was beginning to work. Symbolising this was the Laterna Magica, the first machine to create the illusion of a moving image: as the handle turns faster and faster, the individual images disappear and instead the eye sees continuous movement.

Musically speaking, different tempos underline different parameters: the rhythmic continuity is accentuated at relatively fast tempos, whereas delicate shades require more time and space for the ear to interpret and appreciate them.

While I was working with tempos, rhythms with different characters became a major part of the piece’s identity: a fiery dance-rhythm inspired by flamenco, a shifting, asymmetrical rhythm provided by speech and an accelerating ostinato that ultimately loses its rhythmic character and becomes a texture. In contrast to this, there emerged music without a clear rhythm or pulse. This material is dominated by strongly-sensed colourful planes and airy textures, such as the unified colour of six horns, which divides the orchestral phrases. This use of horns points to Bergman’s film Cries and Whispers, in which the scenes are often changing through sequences of plain red colour.

When reading the autobiography I was also touched by the way Bergman described the different lights which his favourite photographer, Sven Nykvist, was able to capture with his camera. Part of the text found its way into the piece in German – for the work was commissioned by the Berlin Philharmonic. The extract, in English, goes as follows:

Gentle, dangerous, dream-like, lively, dead, clear, hazy, hot, strong, naked, sudden, dark, spring-like, penetrating, pressing, direct, oblique, sensuous, overpowering, restricting, poisonous, pacifying, bright light. Light.2

From the program note of Saariaho, the hypothesis that a substantial part of the compositional decisions that engineer Laterna Magica originates from a process of compositional modeling is feasible. Compositional modelling will be understood here as the mapping, intermediated by musical notation, of concepts belonging to a particular domain of origin – possibly, but not necessarily, extramusical – to the sound domain. This paper will investigate the modeling processes that hypothetically guided the compositional decisions pertinent to the use of the horns in Laterna Magica, consisting specifically in the unified color and the division of orchestral phrases, according to the information provided in the program notes and whose domain of origin is the visual/cinematographic one. Preceding an in-depth investigation of how this process of compositional modeling is implemented in the piece, some broad-based observations on the concept here proposed are welcome.

The modelling process as a guideline for compositional decisions

In his article titled Scelsi: De-Composer3, Tristan Murail writes that Music always has a model, whether formal or natural. Even the most abstract art proceeds from models. The question pertaining Scelsi’s music, left unanswered by the author, is what is the object, and what is the model?.

Murail’s rhetorical question finds massive support in the compositional praxis of the twentieth century. The exhaustion of the tonal system, a framework that underpinned a substantial part of the decisions made by composers over more than two centuries, led to a frantic search for new sources susceptible to conversion into musical material. In fact, the specific sources adopted as domain of origin by composers have even been able to characterize their production: Bartók uses folk music frequently in his compositions, idiosyncratically adding the original material to expansive formal plans; Messiaen will use birdsongs, as in Le Merle Noir (1952), Réveil des Oiseaux (1953) and Catalog d’oisaeaux *(1958), among other examples. Xenakis often resorts to the mathematical universe, modelling his compositions after stochastic laws, as in the ST series (1956-1962); after Boolean algebra, as in *Herma (1960-61), or after game theory, as in Duel (1959) and Stratégie (1962); composers associated with the spectralism will study sound phenomena under the microscope in order to transfigure them and reintegrate them into the sound domain, such as the trombone bass whose spectral analysis gives rise to the general structure of the Les Espaces Acoustiques cycle (1974–1985), by Grisey, or the sound of rain falling on a lake in Le Lac (2001), by Murail. Compositional modeling, therefore, is a fertile ground for the stimulation and expansion of creative faculties, an aspect systematically reinforced by twentieth century concert music. The mapping of diverse phenomena into sonorities is certainly not exclusive to the twentieth century. In the common practice period, however, tonalism circumscribes all compositional decisions, constituting a pre-established frame of tacit acceptance. Saariaho recognizes the efficiency of tonalism, at the same time avoiding its adoption, when she writes:

Amongst familiar organizational models concerning pitch the tonal system is, in my own experience, the most effective means of using harmony to construct and control dynamic musical forms. This is illustrated by numerous large-scale, substantial formal structures which emerged during the age of tonal music. It would be difficult to find as dynamic a conception of form amongst other approaches. I think, however, that using tonal functions in such a way is definitely a thing of the past. This is why the tonal system would seem to me to be only a potential model for the creation of tensions through the use of pitches. (1987, p.94)

From this statement, finding descriptions of the modeling processes adopted by the composer for her works in the program notes is acceptable. In Laterna Magica, one of the domains of origin is the visual universe, aspect already highlighted by the title of the piece, homonymous to Ingmar Bergman’s autobiography4. An in-depth investigation of the aspects mentioned by Saariaho may reveal how the process of compositional modeling takes place in this work.

The compositional modelling of the horns in Laterna Magica

The unified colour of the horns, modelling the red colour used for transitions between scenes in Bergman’s Cries and Whispers, is the first object of this research. By unified, it will be understood that the composer intended to construct a sonority whose recurrences throughout the piece can be identified. The investigation will begin with a complete listing of the chords formed by the horns.

The unified colour of the horns

Table 1 shows all entries of the horns in the piece, together with their respective measures and respective Forte set-names. The table only groups chords formed with the exact same position; for this reason, some Forte set-names happen more than once. The two entries marked * are the only ones where polyphonic activity happens, with change of pitches on each horn during the measures. As exceptions, in both entries the pitch with longest duration was considered for the chord. This solution was enough to classify them together with the chords that recur the most.

Analyzing the table, a first finding — which coincides with the hypothesized intention of the composer obtaining a unified sonority — is possible: the chords present a high degree of regularity as to their notational duration, extending themselves between two and four bars with very few exceptions. Thus, the duration of the chords will be proportionally stable along the piece even with the tempo changes, a somewhat relevant parameter according to the program notes that, as a matter of fact, will be frequently modified.5

Table 1

Table 1: Chords played by the horns in Laterna Magica

If a simple solution was used for the unification of sonorities regarding durations, pitches constitute an object of greater organizational complexity. The table clearly shows that the first chords of the piece are also those of greater recurrence. The chords 6-z44, 6-14, 6-z42, 6-z26 and 6-2 will occur respectively 11, 7, 5, 4 and 6 times with the exact same arrangement of each pitch in the horns; to these occurrences, others may be added in which the same Forte set-numbers will be formed, albeit with alternate pitch dispositions. The chord whose count will be changed the most is 6-z42, with four more occurrences.

The total amount of chords the piece makes use of is small when compared to the number of possible six-note chords that can be formed with the six horns. A simple count of all combinations, taking as limits the lowest and highest note found on the horns (respectively E3 and B4) along the piece and without doublings would result in astounding values: almost 40,000 possible combinations6. Such a criterion, however, would enable the qualification of essentially any composition as having a unified sonority. Thus, the abstraction of transpositions, intervals and octave inversions, a common procedure in the scope of harmonic analysis and essential for Forte set-numbers, come in useful. Through such an abstraction process, the chord set from table 1 reveals itself compact when compared to the available total: out of 50 six-note chords tipically recognized by post-tonal harmony7, Saariaho uses only 11 — less than a quarter of the total. Similar percentages limit the use of chords of five or fewer notes: none of these have more than four elements of their class among the ones used in Laterna Magica.

Given such a reduced subset of chords, it is feasible to infer that composer is interested in the resulting sonority. Disregarding harmonic progressions that suggest tonal centers, since they are not object of Saariaho’s attention as evidenced in the previous citation, a somewhat reasonable regularity in the characteristics of the chords can be identified when comparing them to each other. The interval vectors indicating the amount of intervals of the second minor to the tritone contained in the three most frequent chords are shown in table 2:

Table 2: Interval vectors of Laterna Magica’s three most recurrent chords
Chord (Forte set-name)Interval Vector

It should be noted that the two chords of greatest recurrence of the piece hold a high degree of similarity, with equal counts of intervals of minor second, minor third, major third and perfect fourth: the only difference is the presence of a tritone interval in the 6-z44 chord which does not exist in the 6-14 chord, being replaced by an extra minor third interval. In fact, the first transition between the two chords [25-26] makes use of such properties for vocal conduction, as shown in figure 1. A brief idiomatic effect available on the instrument - the descending glissando that happens naturally when the hand is inserted inside the bell - closes the first chord, articulated with the following by an eighth note pause. In the second chord, only horns 3, 5 and 6 will have their pitch modified, each by a whole tone relative to the note of the preceding chord. Although voice leadings similar to the one described above connecting horn chords may not constitute a rule throughout the piece, the recurrences of that very same progression, as in [232-233] and [293-294], and the structural similarity of the chords regarding their interval properties are sufficient evidence to denote Saariaho’s interest in constructing an unified sonority.

Figure 1

Figure 1: Laterna Magica, measures 23-26

This finding is reinforced by the five note chords: out of the four used, three feature the following interval vectors: [311221] (5-6), [321121] (5-5) and [322111] (5-4). The third chord listed in Table 2, 6-z42, even if not presenting such a high degree of similarity in its interval content, is almost identical to the previous arrangement of pitches: only horns 6 and 5 present different notes (see table 1). There remains little doubt as to its contribution in creating a sonority that can be understood as featuring an unified color.

Concluding pitch-related considerations, a predilection for chords with exactly three minor seconds can be noted: three, both in the six-note chords and in the five-note chords. This fact is reinforced by the interval vectors previously listed. The adoption of chords with a regular and non-negligible amount of minor seconds appears to match an expressive quality commonly attributed to the minor second. Cooke (1962) states that the minor second is an expression of anguish in a context of finality”, and then “a hopeless anguish” (p. 89). The coincidence with the modelling realized by Bergman in Cries and Whispers is worthy of note. In his book Images, Bergman writes:

All my films can be thought in terms of black and white, except for Cries and Whispers. In the screenplay, I say that I have thought of the color red as the interior of the soul. When I was a child, I saw the soul as a shadowy dragon, blue as smoke, hovering like an enormous winged creature, half bird, half fish. But inside the dragon, everything was red. (1996, p.90)

Synthesizing the findings presented so far, the combination of durations, pitches and interval content of chords formed by the horns in Laterna Magica validate the composer’s statements when she associates them with the red color used in the film Cries and Whispers. The second statement regarding pertinent the horn’s modelling process mentioned in the program note remains to be checked: the division of orchestral phrases, whose phenomenon of origin is the transition between scenes in the same film.

The division of orchestral phrases

Laterna Magica’s score allows the proposition of three distinct categories for usage of the horns. The first one occurs when the entrance of the horns precedes changes in orchestral activity, such as tempo, timbre, introduction of new materials or combinations of these possibilities. The initial bars [1-3] exemplify this category, hereafter referred to as A: punctuations. After the diminuendo of the horns, the only remaining sonority is the pianissimo glissando of the second timpani, concluded soon after in order to close the opening measures of the piece, succeeded by the introduction of new materials.

Figure 2

Figure 2: Laterna Magica, measures 1-6; category A (strings not shown)

Category B groups moments where the horns are used to articulate events: here, an orchestral behavior will be interrupted at the entrance of the horns, and resumed afterwards. The difference in comparison to category A, therefore, is established by the fact that sections are not closed by the horns, but partially interrupted by them: the juxtaposing of the horns intersects the continuity of the event. The example reproduced below, between measures [226-229], shows the interruption in the activity of the timpani, who follow in tremolo the decrescendo dynamic curve of the horns, and then resume playing the previously presented materials.

Figure 3

Figure 3: Laterna Magica, measures 226-229: category B (interruptions)

Category C includes all passages in which the horns accompany the orchestral activity, without their homogeneous tone assuming a prominent role. Here, the horns do not articulate or indicate closure of sections or events, so that their presence is not an event susceptible to the framing in the functional description given by Saariaho. The passage between measures [125-130] exemplifies this third and last category.

Figure 4

Figure 4: Laterna Magica, measures 125-130: category C (accompaniment)

The horns, without the simultaneous attacks that characterize most of their behavior throughout the piece, gradually build an homogeneous texture that remains in the background and in the midst of which figurations on the flutes, chordal attacks on the piano and contrapontistic movement with increasing dynamics in the strings take place. The same orchestral behavior is held through the next measures, without the horns bringing any sort of perceptible change.

Table 3 shows the categories in which each entry of the horns has been classified, along with its respective measures.

Table 3: classification of each entry of the horns into category A, B or C
A[001-003][023-025] [026-030][052-056] [057-060] [076-079] [095-096] [102-106][122-124][136-139] [233-235] [254-259] [291] [405-407][418-420] [442-445] [452-456] [471-472] [494-495] [516-517] [521-523][525-527] [537-540]23
B[156-158] [227-228] [293-294] [295-296] [299-301] [303-305][313-314] [367-368] [379-280] [385-386] [390-392] [394-395] [400-402][411-412] [413-414] [415-416] [504-506]17
C[066-068][072-074][089-092][125-130][131-133][134-135][166-171] [186-189][212-214][231-232][286-290][308-310][362-365][417] [508-510][513-515]16

Considering categories A and B as representative of the division of orchestral phrases mentioned in the program note, it is possible to state that a substantial portion of the horn entries — more than 70% — match the procedure, here understood as compositional modeling, performed by Saariaho.

Considerations on the results

Interpretation of the results leads up to two conclusions: the first one is the fact that the modelling briefly described by Kaija Saariaho in his program note is, in fact, subject to scrutiny in the score; the second conclusion is that this same modelling does not manifest itself systematically throughout the piece: in other words, the color of the horns is not always unified, but unification is a predominant feature, and the function of the horns is not always, but mostly, that of dividing the orchestral phrases.

Expecting a perfect match between the source phenomenon and the model as presented in its target domain, however, is unreasonable. The very concept of modelling, as elaborated by its related literature found in the Philosophy of Science, nullifies this possibility when the fact that the model is not the phenomenon itself, but an abstract representation, is taken into account. Statistician George Box writes:

Since all models are wrong the scientist cannot obtain a “correct” one by excessive elaboration. On the contrary following William of Occam he should seek an economical description of natural phenomena. Just as the ability to devise simple but evocative models is the signature of the great scientist so overelaboration and overparameterization is often the mark of mediocrity. (1976, p. 792)

Similarly, Mary Hesse proposes a tripartition of the existing relations between a model and the object it represents: positive analogies, consisting in shared properties between the phenomenon itself and the model; negative analogies, consisting of properties duly recognized as devoid of similarities; and neutral analogies, being those pending investigation and remaining susceptible to either maturation or discarding of the model as a representation of a certain phenomenon (1963, p.8). Transposing the ideas of Hesse to the compositional modelling in Laterna Magica, the three kinds can be found: the positive analogy with the recurrence of the red color is modeled on the recurrence of chords like 6-Z44 in its many appearances throughout the piece, as shown in table 1 and subsequent discussion; negative analogies occur in sections previously classified as category C, in which there is no evidence that the horns perform any sort of division of the orchestral phrases. An additional example can be obtained in the measures [286-289], reproduced in figure 5, when the horns provide a textural basis for the melody performed by the piccolo and for the fast figurations performed by the celesta. There is no correspondence between the model and the original phenomenon at this moment of the piece. Neutral analogies, in their provisional condition, can be submitted to different understandings: relations found by those that have some sort of contact with the work and that, in the absence of additional information veritably provided by the composer, remain subject to systematic validation or rejection; or, alternatively, relations which the composer may unintentionally establish throughout the compositional process, and which may be recognized ex post facto as positive analogies.

Figure 5

Figure 5: Laterna Magica, measures 286-289: category C (paused instruments omitted)

Adopting the first understanding proposed above as a fertile route for future investigations, measures [471-472] can be interpreted as a modelling of the function of the horns expanded to a larger orchestral scale: to the six sounds already contained in the horns and orchestrated in a fortississimo the note F1 is added, played by contrabassoons, tuba and basses. The orchestral tutti, with its feroce indication, acts as a climatic divisor of orchestral phrases in the formal scope of the piece, which would not be possible only with horns due to the dynamic range of the orchestral tutti and to the presence of the F1 note, unavailable in the horns. Thus, a process of metamodeling takes place: the horns, whose unified color models the red color and whose function of dividing the orchestral phrases models the transition between scenes of Cries and Whispers, are modeled by the whole orchestra, expanding both the intensity assigned to the red color by Ingmar Bergman and the delimitation of orchestral phrases.

The realization that the modeling process is fed back, with previous models continually giving rise to new models, is particularly appropriate in the context of Laterna Magica, since Bergman reportedly and often appeals to the musical universe in his cinematographic production. In the filmmaker’s own words, found in Persona’s script, ” I didn’t write a film script in the usual sense of the word. What I wrote seems to me to be more like a music score that I will conduct during the filming”. Even more consistent with the proposal of this paper is the origin of the title of the film: the description of Mozart’s Concerto for Piano K449 given by music critic Yngve Flyckt: music that sounds like screams and whispers.

Just like scientific modeling, compositional modeling is a creative and decision-making process. Which aspects of the original phenomenon can be transposed to the sound domain, which elements will be left out, which ones will be represented and which parameters will be used for modeling are questions that the composer - as well as the scientist - must ask himself continuously. Reassessing the previous quote from George Box, this Laterna Magica investigation leads us to conclude that the ability to elaborate evocative models — and the adjective ‘simple’ is purposely left out — is the signature of the composer whose ideas have focus and clarity.

Figure 6

Figure 6: Laterna Magica, measures [471-472]: extension of the function of the horns to the orchestral tutti


BERGMAN, Ingmar. Images: My Life in Film. New York: Arcade. 1990.

BERGMAN, Ingmar. The Magic Lantern: An Autobiography. Chicago: University of Chicago Press. 2007.

BOX, George E. P. Science and Statistics. Journal of the American Statistical Association, v.71, n.356, pp. 791-799. 1976.

COOKE, Deryck. The Language of Music. London: Oxford Paperbacks, 1962.

FORTE, Allen. The Structure of Atonal Music. New Haven: Yale University Press, 1973.

HESSE, Mary B. Models and Analogies in Science. London and New York: Sheed and Ward. 1963.

MATTHESON, Johann; REIMANN, Margarete. Der Vollkommene Capellmeister, 1739. Kassel: Bärenreiter, 1954.

MURAIL, Tristan. Scelsi, De-composer. Contemporary Music Review, v.24, n.2, p.173-80. 2005.

SAARIAHO, Kaija. Timbre and Harmony: Interpolations of timbral structures. Contemporary Music Review, v.2, n.1, pp.93-133. 1987.

SAARIAHO, Kaija. Laterna Magica for Orchestra. Partitura. London: Chester Music. 2008.

CARTER, Elliot. Harmony Book. Edited by Nicholas Hopkins and John F. Link. New York: Carl Fischer. 2002.

PERLE, George. Serial Composition and Atonality: An Introduction to the Music of Schoenberg, Berg, and Webern. Berkeley: University of California Press, 1962.


3 Murail, Tristan. Scelsi: De-Composer. Translation by Robert Hasegawa. Contemporary Music Review, 24(2/3):173-80.

4 Laterna Magica is a device whose origins date back to the seventeenth century, being considered by numerous authors as the grandfather of modern image projectors.

5 The score has 45 metronomical tempo changes, plus many others without metronomical numbers.

6 This value is obtained by simple combination of 20 pitches grouped by 6. The result is 38.760.

7 Besides Forte, George Perle (1962, p.110) and Elliot Carter (2002, p.40) also quantify all possible different six-note chords as 50.