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Prestimagination: Interactions between Performance,
Compositional Design, and Aesthetic Priority in Kaija Saariaho's Sept Papillons
Christopher Gainey
University of British Columbia
[email protected]
Abstract. "Harmony," writes Saariaho, "provides the impetus for movement, whilst timbre
constitutes the matter which follows this movement. On the other hand, when timbre is used to
create musical form it is precisely the timbre which takes the place of harmony as the progressive
element in music." This statement implies that timbre and harmony are conceptually separate
domains—a useful guideline for composers who explore the possibilities of timbre as a formbearing element in their music. From an analytical perspective, however, the notion that timbre
may "take the place of" harmony glosses over the flexibility with which listeners cognitively
process incoming auditory information according to musical context.
In this paper, I begin by detailing how the physical and cognitive challenges facing the
performer inform compositional design in the first two pieces from Saariaho's Sept Papillons. I
then discuss how the structures revealed through this analytical perspective reflect Saariaho's
aesthetic preoccupation with timbre and harmony and suggest the appropriateness of "holistic"
versus "atomistic" listening in these works. My analytical approach to these pieces reflects what I
imagine to be an important aspect of Saariaho's compositional process—a careful consideration of
how practical concerns of instrumental technique might align with her aesthetic priorities. Said
another way, the prestidigitation that performers use to access the timbral diversity of their
instrument may be a lens through which Saariaho is able to focus her musical imagination towards
an exploration of what Gérard Grisey refers to as the "liminal" zone between timbre and harmony.
All harmonics are not created equal. Although I, for one, hold this truth to be self evident, most
orchestration texts do not directly address the issue. There is evidence, however, that the authors of these
texts are at least aware of the differing qualities of harmonics1 but one can imagine that a more complete
characterization of this phenomenon is not a priority. The qualitative difference between harmonics is,
more often than not, too subtle to be a salient factor in orchestral textures. Considering that the work
under discussion in this paper is for solo cello, however, the subtle differences between harmonics are
more easily perceived and are thus, potentially, of greater structural significance. In an effort to more
directly experience the qualitative differences between harmonics before fully exploring Kaija Saariaho's
Sept Papillons, I spent some time attempting to reproduce the most common natural harmonics on various
string instruments: banjo, guitar, banjolele, violin, and, most appropriately, an obliging acquaintance's
cello. I found, not surprisingly, that the extent to which a stable and clear pitch is produced at a particular
harmonic node is related to its overtone rank in a way that is commensurate with the general notion that
the intensity of partials tends to be weaker the further they are from the fundamental. The "further"2 a
For example, Samuel Adler characterizes the "touch M6" harmonic as somewhat unsuitable for use in orchestral
contexts, while the "touch M3" harmonic, which produces the same pitch is more "secure." Samuel Adler, 1989, The
Study of Orchestration, 2nd Ed. (New York: W.W. Norton and Co.), 48.
"Further" in the sense of the harmonic series as a single dimension. If (like me, to some extent depending on
musical context or analytical perspective) one prefers the notion that sounds with more harmonics have (in general
and with many caveats) more timbral "depth" or "richness," then one might prefer a way to conceive of the harmonic
harmonic is from the fundamental3 the more difficult4 it is to produce at a desired dynamic. Furthermore,
noisy artifacts5—more prominent in the more difficult harmonics—obfuscate the clarity and stability of
the resultant pitch. Eventually, based on subjective aesthetic assessments of my first-hand observations, I
began to conceive of the six most commonly used natural harmonics on a given string as points along an
axis of "purity" as shown in the lower stave of Figure 1.
Figure 1: A conception of harmonics as points along an axis of "purity"
When extended to include all four strings of the cello, all harmonics produced in the same way—
at least with regard to left-hand technique—may be considered members of a harmonic class since they
feature similarly prominent inharmonic artifacts and produce a pitch that is similar in clarity and stability.
"Artificial" harmonics, produced by touching nodes above stopped notes, may be considered part of the
harmonic class wherein the relationship between the node and the stopped note is the same as the
series as a dimension along these lines. At the very least, the issue is conceptually problematic. Consider, for
example, a sine wave. Since a sine wave (theoretically) has no overtones, it could be considered maximally "close"
to the fundamental, but also, speaking in more qualitative terms, the "shallowest" and "poorest" of timbres—an
evaluation that might not ring true in all musical contexts. Since, however, I have arranged harmonics along an
"axis" (see Figure 1) for use as an analytical tool in this project, a conception of the harmonic series itself as a
measure of "distance" is, for the moment, most appropriate.
i.e., the pitch, or, more appropriately, the frequency of the stopped or open string
"Depending on the skill of the performer and quality of the string and bow, the acoustical properties of the
instrument, and the sound environment in the room of performance, it is possible to produce harmonics through the
seventh, eighth, and even ninth partials. In situations where it is necessary to produce a specific, audible pitch, it is
wise to limit the natural harmonic to, at most, the fifth partial. When purely coloristic, filigree types of effects are
desired, natural harmonics through the eighth partial may be called for." Alfred Blatter, 1997, Instrumentation and
Orchestration (Boston: Schirmer), 34.
e.g., the susurrus of bow hair scraping against the strings
relationship between the node and the open string in a natural harmonic.6 Although the left hand stretch
required to produce artificial harmonics is a significant practical issue, the qualitative difference between
artificial and natural harmonics of the same harmonic class is negligible. Taken together, these factors
contribute to an analytical perspective in which members of a harmonic class have a similar overall
timbral quality and are thus—at least in the context of a piece like "Papillon I" which is made up almost
entirely of harmonics—functionally equivalent on some level.
"Papillon I" is easily parsed into five distinct gestures and these gestures are renotated according
to harmonic class in Figure 2. All notes correspond to the sounding pitch and are placed on staves labeled
with numbers that correspond to the harmonic classes identified in Figure 1. Although an exhaustive
account of the intriguing details that become evident through this renotation of "Papillon I" is beyond the
scope of this paper, I would like to briefly consider the sounds which, to my ear at least, are the most
focal over the course of the work. A detailed guide to the analytical symbols used in Figure 2 is available
in Table 1.
Table 1: Key to symbols used in Figure 2
"Artificial harmonics are not really artificial at all" since the stopped note essentially creates a shorter string.
Blatter, Instrumentation and Orchestration, 35.
Figure 2: An analytical representation of the five component gestures of "Papillon I"
Focal sounds, identified in Figure 2 with three different kinds of boxes, are almost all members of
harmonic class four—a harmonic class that results in a relatively clear pitch and is considered to be the
most practical means of producing artificial harmonics on most bowed string instruments. The exception
to this tendency comes near the end of gesture 4 where a B4 of harmonic class 5a draws the ear's focus
before a harmonic glissando leads towards the rather ambiguous emphasis on a D5 of harmonic class 4.
The focalness7 of this D5 is undermined by its involvement in a fingered tremolo with the relatively
"purer" A4 of harmonic class 3. Although an argument can be made for a preference for either A4 or B4
as the most focal sound in measure 11, my ear leans towards an interpretation in which D5 is most
focal—a preference that may be due to the focalness of D5 throughout the preceding gestures. Regardless
of one's analytical interpretation of this moment in the music, I feel confident in stating that, in contrast to
the introduction of a G4 of harmonic class 4 in measures 6 and 7 which convincingly wrests focus away
from D5, the B4 and A4 in the fourth gesture introduce a dramatic amount of ambiguity just before the
incorporation of the more spectrally complex stopped notes of gesture 5 and the "resolution" of D to C# in
measure 14.
I use the term "resolution" here with some trepidation. While I do feel that the piece eventually
settles on C#, I am left wondering how best to interpret this sensation in relation to what I believe to be
Saariaho's aesthetic priorities—specifically her preoccupation with the conceptual and perceptual gray
area between timbre and harmony. To that end, Figure 3 shows two possible interpretations of the
harmonic domain in this movement. The first is a "tonal" interpretation—a conception that is seemingly at
odds with Saariaho's aesthetic priorities considering her stated opinions that tonality as a means of
organizing pitch structures is "out-dated" and "a thing of the past."8 I do not believe, however, that a
consideration of tonal implications in this music is inherently inappropriate.
In a 1987 article for Contemporary Music Review, Saariaho describes her aesthetic priorities in
relation to some of her preferred compositional procedures. She writes of an aversion to tonality, but,
intriguingly, this aversion is juxtaposed with statements that may be read as either reluctant
acknowledgements of the affective power of an unfashionable practice or subtle yearnings for the
dynamism of tonal functions tinged with late-twentieth century avante-garde guilt. After all, in the same
article Saariaho alludes to the "exciting domain of ritual, monotonous and hypnotic musics, [and]
minimalism" without explicitly mentioning that some music in this domain employs the very tonal
functions she eschews in the creation of a general affect of which she apparently approves. It is my
"Focalness" is not, technically speaking, a word as far as I can tell. I have been able to find uses of the word
"focality," but the connotation of the -ity suffix (expressing state or condition) seems less appropriate to this analysis
than that of the -ness suffix (denoting state or quality).
Kaija Saariaho, 1987, “Timbre and harmony: interpolations of timbral structures,” trans. S. Welbourn,
Contemporary Music Review 2(1): 94, 132.
considered opinion that by the time Saariaho composed Sept Papillons, thirteen years later, her aversion
to tonal function was overshadowed by an increased focus on the perceptual overlap of timbre and
harmony. I do not mean to imply, however, that the "tonal" interpretation detailed in Figure 3 necessarily
reflects a conscious compositional choice. It is more likely that, as Saariaho worked out the timbrally
vibrant texture of "Papillon I," a subtle and somewhat imperfect evocation of tonal function arose
organically and was not rejected by the composer's ear as necessarily antithetical to her aesthetic goals.
Figure 3: "Harmonic" analyses of "Papillon I"
If a "tonal" interpretation provides one possible harmonically-focused listening strategy for
"Papillon I" and we assume that Saariaho's twenty-first century aesthetic preoccupations continue to be
guided by the functional elision of timbre and harmony, then it seems wise to consider a more timbrally
focused account. Since this piece consists almost entirely of harmonics, one's mind might turn toward a
conception of these sounds as an imperfect microcosm of a larger organizing principle. Robert
Hasegawa's analytical technique of "tone representation"9 is especially suited to this perspective and the
second interpretation in Figure 3 details a way in which the sounds of "Papillon I" may be conceived and
heard as partials whose relationships may be summarized in relation to a virtual bass line.10
A hearing of this music that aligns with Hasegawa's notions of tone representation is intriguingly
similar to a "tonal" interpretation of this music. For example, the move from a D fundamental to a G
fundamental and back again over the course of the first three gestures resonates with a tonal interpretation
of this passage as a tonic expansion—a move to and from a subdominant sonority. However, the fourth
Robert Hasegawa, 2009, "Gérard Grisey and the 'Nature' of Harmony," Music Analysis 28: 349-371 and 2006,
"Tone Representation and Just Intervals in Contemporary Music," Contemporary Music Review 25(3): 263-281.
"Virtual bass line" is, psychoacoustically speaking, not quite accurate—a mixture of the harmonic and timbral
metaphors. In this case, however, a conception of the series of "virtual fundamentals" (a.k.a., "phantom
fundamentals," "virtual pitches," and "residue pitches") as indicative of a timbral/harmonic progression resonates
with the "liminal" (to borrow a term from Gérard Grisey) preoccupations of Saariaho and other composers with
similar "attitudes" (to borrow a term from Tristan Murail) towards composition.
gesture, a passage I characterized earlier as dramatically ambiguous, assumes a rather different character
in a more timbrally oriented hearing. The B4 of measure 9, rather than drawing the ear's focus, is heard as
a component of an underlying D fundamental. In the sense that the timbre of a sound can be said to relate
to its spectral content, the introduction of B4 in the fourth gesture is a dramatic re-coloration of the
sonority that opens the second gesture. Most intriguingly, however, an interpretation of the harmony
according to Hasegawa's notion of "tone representation" suggests a timbral solution to a logistical
question posed by Saariaho in her 1987 essay: "how can a chord or a pitch suddenly assume a new
function and thus give rise to utterly different relationships amongst the same, previously known
Although the two analytical interpretations in Figure 3 may form the basis for different but not
necessarily contradictory modes of listening to this music, it is unlikely that either reflects considerations
that are essential to Saariaho's compositional process. Perhaps a more general expository timbral
narrative—a characterization of "form and content" as "organically contained" within an "idea" of overall
form12—is more appropriate. Saariaho, not alone among composers influenced by the aesthetics of
spectral music, alludes to the idea that observations of the internal features of sound, features she refers to
as "microphenomena,"13 are especially provocative as models for the conception of musical form.
Imagine, if you will, that the idea of the overall form of "Papillon I" is that of an evocation of the cello as
a sonorous sound object. The move from less spectrally complex harmonics to the full-bodied sound of
stopped pitches could be heard as a gradual exposition of the full richness of the cello's timbre—a
richness that peaks with the noisy increase in bow pressure between measures 13 and 14. From this
perspective, harmonic interpretations such as those detailed in Figure 3 can be considered structures that
emerge organically through the exploration of a more general formal idea. Although I cannot say for sure
what formal conception guided Saariaho's ear in the creation of this piece, this general expository timbral
narrative resonates with Saariaho's affinity for the ideas of Kandinsky—specifically that "Form is the
external manifestation of inner meaning."14
In "Papillon II," a constant and rapid stream of attacks may be divided into two timbral
categories—harmonics and stopped notes—and no two consecutive attacks occur on the same string. This
excitingly vibrant and active texture makes significant physical and cognitive demands of the performer.
Saariaho, "Timbre and Harmony," 131.
ibid., 105.
ibid., 130.
ibid., 93; Saariaho is quoting here from Kandinsky's Concerning The Spiritual in Art (1912/1969).
In light of these challenges, I have chosen to apply a different analytical perspective15 that stems from
ways in which difficulties facing the performer are mitigated by identifiable patterns of instrumental
Three bowing modules—boxed and labeled as X, Y, and Z in Figure 4—organize the constant
stream of attacks and create groups of unequal size. To demonstrate this, I have re-notated the piece in
Figure 4 to show the sounding pitch of harmonics on the top staff, stopped notes on the middle staff, and
the string on which the harmonic or stopped note is played on the bottom staff. Before discussing the
deployment of these bowing modules in "Papillon II," however, it is worth noting that, as identified in
Figure 2, only three bowing patterns are repeated in "Papillon I." Although these patterns are not
prominent features of "Papillon I," their similarity to the structurally significant bowing modules of
"Papillon II" suggest a conception of "Papillon II" as a developmental elaboration of an ancillary feature
of "Papillon I."
Figure 4: Bowing patterns and the establishment of foreground
and background layers in "Papillon II"
I first undertook an analysis of "Papillon II" alongside analyses of works by Thomas Adès and Elliott Carter in a
2014 paper entitled "Play This, Hear That: Three Approaches to Modularity in Contemporary Music" presented at
the 2014 meeting of Music Theory MidWest in Appleton, Wisconsin. I had originally planned to include my
analysis of "Papillon I" in this project, but it didn't quite fit with the modular analytical approach detailed in the
paper. However, after finishing the "Play This, Hear That" project, I revisited my analysis of both "Papillon I" and
"Papillon II" and found that, taken together, they can be heard (as I will discuss later in this paper) as two different
manifestations of Saariaho's preoccupation with timbre and harmony.
Figure 4: (continued)
Some bowing patterns, as reflected in Figure 4, are conceived as hybridizations and/or
transformations of the fundamental bowing modules. Descriptions of these patterns in relation to the three
fundamental bowing modules are a matter of analytical interpretation—suggested groupings based on a
comparison between instrumental technique, the composer's notational choices, and audible pitch
patterns. In the interest of being concise, Figure 4 shows only those points at which either the bowing
patterns or pitch content changes and does not include immediate repetitions. While it is possible that the
relationship between bowing pattern and pitch content as reflected in Figure 4 will provide a useful guide
for cellists interested in performing "Papillon II," it is more likely that, since I am not a cellist, the
analytical strategy behind these groupings demonstrates an approach to developing an embodiment of this
work that effectively communicates an interpretation of its structure.
Intermittent internal periodicities can be heard throughout "Papillon II" as a result of the
succession of bowing modules and the establishment of foreground and background layers by a timbral
difference between stopped notes and harmonics. In a passage that seems to foreshadow this aspect of
"Papillon II" a sensation of increasing forward momentum is created by a steadily shrinking interval
between C#6s in measure 12 of "Papillon I" (see Fig. 2). Again, it seems that an ancillary feature of
"Papillon I" has been elevated to prominence in "Papillon II."
Figure 5: Pulse streams and rhythmic grouping in "Papillon II"
The pulse streams that emerge from the texture in "Papillon II" are the result of the periodic
occurrence of stopped notes within the active texture. Figure 5 reflects my analytical interpretation of
these pulse streams in a way that reflects my hearing of "Papillon II" as a polyphony of displaced internal
periodicities which are differentially predictable. Consider, for example, the predictability of the pulse
streams of measures 6-8 which are realized by a single bowing pattern, in relation to the combination of
many bowing patterrns in measures 11-15 which creates the sensation of transient pulse streams that
emerge intermittently from a rather chaotic texture.
Although the bowing modules help the performer organize the constant stream of attacks in
"Papillon II" and the ear is drawn to pulse streams that emerge from the active texture, a listener's
perception of the overall shape of the piece is likely to be tied more closely to a pitch structure that
realizes what I have identified in Figure 6 as the harmonic background of the work.
Figure 6: Harmonic analyses of "Papillon II"
The foreground analysis of Figure 6 represents the arpeggiated sonorities of "Papillon II" as
simultaneous chords and serves as a preliminary step in the description of the overall harmonic structure.
A transfer between textural layers created by a distinction between harmonics and stopped notes—a sort
of textural voice exchange—is indicated by arrows that show different notes in successive harmonies
played on the same string. When a harmonic is replaced by a stopped note on the same string it is as if the
harmonic has emerged from the background of the texture and changed pitch in the process. Conversely,
when a stopped note is replaced by a harmonic on the same string, it seems as if the sound has faded into
the background. Dashed arrows in the middleground harmonic analysis of Figure 6 reflect this layered
aspect of the texture and I have added slur lines to reflect what I hear as the most salient voice leading
traversing the background harmonic outline of the work.
The progression between sonorities in "Papillon II" is quite smooth and the music gradually
moves from one pole to the other tracing the intermediate stages between harmonic goals featured as
significant formal articulations in the music. The fluidity of the harmonic structure relies on the
performer's ability to confidently realize an active texture of rapid pulsations while moving smoothly
between physical patterns. Rather unexpectedly, an exploration of this aspect of the structure of "Papillon
II" results in a narrative of Saariaho's compositional process that seems to have more in common with the
juxtaposition of a limited number of finger rolls in "Scruggs-style" banjo playing than with the usual
characterization of her music in relation to the music of "spectral" composers. More importantly,
however—since it is doubtful that Earl Scruggs has had much of an influence on Saariaho's music—my
approach to the analysis of "Papillon II" suggests that a compositional design based on instrumental
technique has allowed Saariaho to realize the sort of timbrally diverse texture that is a priority of her
personal style.
In closing, I would like to briefly consider "Papillon I" and "Papillon II" as two different
manifestations of Saariaho's preoccupation with timbre and harmony. "Harmony," writes Saariaho,
"provides the impetus for movement, whilst timbre constitutes the matter which follows this movement.
On the other hand, when timbre is used to create musical form it is precisely the timbre which takes the
place of harmony as the progressive element in music."16 In "Papillon I," I would argue that timbre is the
more progressive element while in "Papillon II" timbrally diverse resources are deployed in a way that
realizes a background harmonic progression. The prevalence of harmonics in "Papillon I" allows the
listener perceptual access to their subtle timbral differences and guides the ear towards a holistic
evaluation of their roles within the texture. Furthermore, a sense of the unequal "purity" of the pitches
produced by the harmonics is analagous to the unequal roles of partials within a complex tone—a factor
that is, psychoacoustically speaking, essential to our gestalt perception of timbre. Conversely, in "Papillon
II," the relative quality of different harmonic classes is overshadowed by a more obvious dichotomy
Saariaho, "Timbre and Harmony," 94.
between harmonics and stopped notes—an aspect that suggests the need for an atomistic listening strategy
that allows the listener to parse the active texture into a timbrally distinct foreground and background and
a polyphony of internal periodicities.
My "way in" to both of these portions of Sept Papillons has been through an exploration of
challenges that face the performer. After all, this is not a sight-readable score and I was curious to see
how an attempt to make sense of the sleight of hand necessary to perform this music might lead towards
the identification of analytically significant features. Although I cannot say for sure, I imagine that an
important aspect of Saariaho's compositional process is careful consideration of the ways in which the
practical considerations of instrumental technique might align with her aesthetic priorities. In other words,
the prestidigitation that performers use to access the timbral diversity of their instrument may be a lens
through which Saariaho focuses her musical imagination.
Adler, Samuel. 1989. The Study of Orchestration. Second Edition. New York: W.W. Norton and Co.
Blatter, Alfred. 1997. Instrumentation and Orchestration. Boston: Schirmer, Cengage Learning.
Gainey, Christopher. 2014. “Play This, Hear That: Three Approaches to Modularity in Contemporary
Music.” Paper presented at the annual meeting of Music Theory MidWest, Appleton, Wisconsin,
April 25-26.
Hasegawa, Robert. 2009. "Gérard Grisey and the 'Nature' of Harmony." Music Analysis 28: 349-371.
———. 2006. "Tone Representation and Just Intervals in Contemporary Music." Contemporary Music
Review 25(3): 263-281.
Saariaho, Kaija. 1987. “Timbre and harmony: interpolations of timbral structures.” Translated by S.
Welbourn. Contemporary Music Review 2(1): 93-133.