felixpastor ethers (1)

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Tristan Murail’s Ethers ( 1978)

by Felix Pastor [email protected]

Brooklyn, July 2007



Index

I. Introduction 1

a. Waves 2

b. Attention manipulation 4 c. Sound masses and lters 4

II. About the Form I 5

III. Analysis I 6

a. Unit I

i. Section A 6

ii. Section B 14

iii. Section C 19

iv. Section D 22

IV. About the Form II 25

V. Analysis II 29

a. Unit II

i. Section E 29

ii. Section F 32 iii. Section G 36

iv. Section H 40

b. Unit III

i. Section I 43

c. Coda

i. Section J 50

VI. About the Form III 54

VII. Bibliography 58



I. Introduction

“Ethers is a piece by Tristan Murail from 1978 for ute (piccolo, in C, in G

and bass ute), trombone, violin, viola, cello, double bass, maracas and live sound

processing and spatialization. His exact description is: for ute, ve instruments and

maraca continuum. This in fact tells us two important things about the construction

of the piece. First of all, there is a separation of the instruments in three layers. The

second observation is the maraca continuum. In his performance notes he species

that the maracas must maintain a steady layer of sound except where notated (a

handful of slight crescendos towards the end). His intention is that their audibility

depend on the other layer’s activity and on the listeners capacity to focus. With this, I

believe he is already hinting at one of the important characteristics of the piece: one

thread can temporarily mask another only to later reveal it in its new and evolved

form. This points us to the spectral component of the piece.

As Gerard Grisey said in an interview, spectral music is an attitude1. It is

through this attitude that we can group certain pieces as spectral beyond their pitch

collections being derived from one or several spectra (natural or synthetic). In other

words, while this particular piece uses collections derived from different spectra, its

spectral speculation is less in the realm of pitches as it is in the fundamental departure

point of spectral music: music as the exploration of sound (in all its parameters as well

as its phases of production, generation, manipulation and unfolding) from a physical

as well as a psychoacoustic point of view. This exploration shows itself through severalelements and techniques that fall, in terms of their extraction, into three categories:

natural phenomena (breath patterns, waves, heartbeats, etc.), psychoacoustic models

(mostly Gestalt psychology) and sonic properties (sound imaging, audio processing

techniques, etc.) Three of these elements become the building blocks of “Ethers”:

waves, attention manipulation and sound masses/lters.

1 Interview with David Bündler in Los Angeles on January 18th, 1996. 20th -Century Music. March 1996issue.

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a. Waves

In the performance notes for “Ethers”, Murail refers to the opening as a

sequence of waves that get shorter and shorter 2. This shows us the importance of

these waves in the conception of the piece. There are two ways in which waves are

used.

The rst is essentially structural: waves take the place of themes and phrases.

The nature of a wave is to move between two opposing states or poles3. There are

several pairs of such opposing poles in sound: loud/soft, thin timbre/rich timbre,

homophonic/polyphonic, fundamental/nth partial, etc. In this piece, Murail describes

waves between many of these pairs at the same time. Sometimes the nodes of

different simultaneous waves coincide and other times they don’t thus implying the

possibility of different periods or temporal scales. For example, while the initial

section of the piece is made by waves between the poles partial and fundamental, as

we will see, the entire section is just the beginning of a wave between noise and pitch

that spans the length of the whole piece.

The second way in which waves are used in this piece has to do with how

they are manipulated. The waves are, in substance, a collection of sound events that

we regard as one. We know from research in musical streaming that the temporal

distance between two events is one of the most determining factors in our hearing

2 “Suite de vagues, toujours plus courtes”.

3 According to the Oxford American Dictionaries, waves are “a periodic disturbance of the particles

of a substance that may be propagated without net movement of the particles such as in the passage

of undulating motion, heat or sound; a single curve in the course of this motion”. A wave is also “a

ridge of water between two depressions in open water” and “a gesture or signal made by moving

one’s hand to and fro”. What all these denitions have in common is that a wave implies two different

poles (a high and a low, left and right, etc.) and is actually the movement from one pole to the other

and back.

From now on, and since we’re dealing with sound and a metaphor for sound, I’ll take the acousticsmodel of a sine wave as reference where the zero crossings are called nodes and the distance be-

tween two nodes is half the period.

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them as separate or as one4. In “Ethers”, Murail is constantly experimenting with this

by using the wave structure. For example, a sequence of events describes a curve

that we hear as a unit5. As this sequence is compressed, we start to hear it as one

event. As it is compressed even more, we start to hear it as one event in a “sequence

of events that describes a curve that we hear as a unit”. We get the opposite effectwhen the time within the event is dilated. In this case, the result is that of observing

an object under a microscope: all of a sudden, what seemed like a smooth surface is

really an intricate mesh of diverse particles.

Both of these ways of using waves spring from the ways in which we encounter

sound (and almost anything) in our world. Using waves as the units in a piece

comes from the fact that our rst experience of producing sound is through breath.

Breath is a wave between the poles full and empty with two distinct, yet parallel,

paths corresponding to each direction: inhalation or expansion, and exhalation orcompression. At a more technical level, sound is a wave between the positive and

negative poles.

The coexistence of different scales and the movement between them, implied by

these two uses of waves, is something inherent in almost anything physical. It could

be understood as the simple action of zooming in and out of an object. In other

words, anything cyclic has a period that corresponds to the distance between two

occurrences of the same thing. This has the potential of dening a scale. In such

a movement (cyclic), at a very low frequency we perceive movement: planetaryrotation, tides, expansion/collapse of lungs, etc. At a higher frequency, we perceive

pulse: beating, tempo, heartbeat, etc. As we speed up the periodic occurrences

(increase the frequency), we move into the realm of audible pitch, then inaudible

pitch (for humans of course), and nally, light (theoretically). All of these different

periods are present simultaneously in most pieces of music and our own lives.

However, perception is in the ear of the beholder.

4 McAdams, Stephen. Psychological constraints on Form-bearing Dimensions in Music. ContemporaryMusic Review, 1989.London, Justin. How to Talk About Musical Meter.Albert S. Bregman, Auditory Scene Analysis: The Perceptual Organization of Sound.Cambridge, Massachusetts: MIT Press, 1990.5 For more information on how this grouping and encoding procedure works, refer to the aforemen-tioned Stephen McAdams article.

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b. Attention manipulation

This is probably the most abstract element of the piece and at the same time

the most apparent. Using the phenomenon that anything periodic tends to recede in

our awareness while new events always come forward, Murail shapes our experience

of the piece by focusing our attention in different directions. His intention to do so

is already clear, again, in the program notes. Referring to the maracas he says that

they should remain as continuous as possible and at a level where the listener can

forget their presence6. In other words, the maracas must move from the foreground

to the background not by themselves but by a change in the attention of the listener.

As we will see, by introducing new events (or building on existing ones), Murail,

manages to mask the slow evolution of certain layers. These layers are then shown in

their new form once the distraction is gone.

c. Sound masses and flters

This element refers to the translation of electronic processes into compositional

techniques. This is something found in many spectral compositions since the

development of the “attitude” is closely related to the advances in the eld of audio

technology7. “Ethers” is about a very specic process: ltering.

Throughout the piece, using the aforementioned elements, we are presented

with events that become a mass (texture) that is then ltered to produce another

event. This second event is then turned into another mass that is ltered again to

produce ye another event. Though this scheme of event1mass 1 ltering

event2 mass 2 etc. might seem similar to the traditional development in that all

events are derived from one another, it is radically different in that events aren’t used

to construct other events: both events are present simultaneously and through ltering

we become aware of one or the other. Another way of seeing this is that the same

event can be presented in different ways that bring forth different facets of itself.

6 “[…] ils doivent produire un bruit de fond très discret et aussi continu que possible, de telle sorte queles auditeurs oublient leur presence”.

7

One mustn’t forget that audio technology has allowed us to record, archive, manipulate and repro -duce sound as an object. Thanks to audio technology we are now capable of measuring signals andcreating images for them in a way that permits us to “enter” the sonic entity; one of the pillars of thespectral attitude.

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II. About the Form I

As in many spectral pieces, the form is derived from the sound itself. It is a

constant process of feedback; sound generating itself. Therefore, though there are

some clear interruptions and formal markers, form is mostly dened by process and

formal rhymes rather than by more traditional returns, developments, etc. I must

reiterate that for the spectral attitude, sound is an object and therefore, the piece is

the unveiling of an object before us. In presenting this analysis I will make an effort to

bring forth how this difference at the conception stage is found in the music8.

Also, as I mentioned earlier, more emphasis is placed on the perception

of the piece. As we will see, even though the different techniques might be very

complex and derived from intricate systems, the systems are meant to be kept at an

operational level; what counts is the perception of their result as sound. This intention,

which is at the base of the spectral attitude, will transpire to the form. In other words,

however intricate the structural form may be, the actual form (the perceptual one) is

the one constructed by the listener.

Obviously, different listeners will hear slightly different large scale forms.

However, at a local and medium level, the discrepancies between different forms will

be smaller. It is for this that I will discuss my understanding of the form at different

stages or scales at the end of the rst large unit (About the Form II) and the end of

the piece (About the Form III).

For clarity in following the score, I have chosen to follow the rehearsal letters

as markers even though at times the formal markers might not correspond with them.

Large sections are labeled I and II while measures are indicated as C23 being the

twenty-third measure of rehearsal letter C (also called section C).

8 In other words, instead of talking about themes (which are of course absent here), I will talk aboutsnapshots of the object from one position. Similarly, what could be seen as a transition from one themeto the next in a traditional form, I will present as the movement between two observation points.

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III. Analysis I - a. Unit I

i. Section A

This section contains most of the information of the piece: it introduces the

wave as the movement between two poles (pitch/noise or fundamental/partial in thissection mostly), it takes the wave unit and constructs a texture with it, and it gives us

the rst example of masking.

It starts out with the maraca continuum; essentially noise. From this cushion,

string harmonics begin to emerge. These are all partials of C#19 and most of them

are in the right place (except for the F# in the cello). These discrepancies with

the harmonic series seem to result from the way in which the harmonics are being

produced. In other words, what is important is not the pitch itself but its becoming

from noise by applying different degrees of pressure on the string at a given node.

As we can see, starting at measure 1 (gure 1), the violin is ngering a fth

harmonic that produces a D7. As more pressure is applied to the node at D6, the

audible pitch ceases to be a harmonic and becomes a D610. Physically, we have

moved from the 68th partial of C#1 (D7) to the 34th (D6). Musically we are moving

from noise to pitch and closer to the fundamental.

In gure 1 we see the rst 15 beats of the violin. Notice how this change in

pressure described above happens in two different pitches simultaneously.

Fig.1

9 C4 is middle C.

10 String harmonics are produced by lightly touching the strings (without pressing on the ngerboard)at points where there is a node. Nodes are the zero crossings of waves; those points of the wave thatdon’t move. To produce a fth harmonic, the string player shortens the string with one nger and thenngers a node with another. For more on string harmonics you can consult any orchestration book likethe Samuel Adler or the Walter Piston.

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There are several things worth noting about this beginning. The rst is that,

both in dynamics and pitch content, we end up where we started. This clearly

describes a wave from “upper partials and soft dynamic” to “lower partials and

louder dynamics” and back. The placement of the bow describes another wave

(ordinario to sul ponticello and back to ordinario) that seems to even out the effectslightly11. However, this change in position also brings with it a change in the richness

of timbre which suggests another pair of poles that might be more appropriate for

this wave12: thin timbre and rich timbre. This effect is augmented by a footnote in the

score that instructs the player to add a little vibrato on his/her arrival at the stopped

notes but to revert to no vibrato on the harmonics13.

All of this contributes to the establishment of our basic unit. Throughout this rst

section, different qualities of this entity are brought forth, distorted or elaborated on

to the point where the original wave becomes unrecognizable.

The rst of these transformations is the addition of accelerations and

decelerations during the third instance of the wave (A11). These respond to the

crescendos and diminuendos and in fact coincide with them. This gives direction to

our original wave and does little more than augment its natural inertia. Figure 2

presents a reduction of the next stage of development of the wave that includes the

acceleration/deceleration wave and a slightly more complex pitch space.

11

Playing “sul ponticello” (on or near the bridge) tends to bring out the higher partials since the bowforces an anti-node at a position on the string that only higher frequencies can accommodate.12 String harmonics are the thinnest possible timbre that you can produce on a string. On the otherhand, a stopped pitch has all of its partials. Playing sul ponticello brings out the higher partials thatwould otherwise be hidden and therefore the resulting timbre is richer in its high register.13 “vibrer un peu en arrivant sur les notes appuyées. Revenir au non vibrato sur les harmoniques.”

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Fig.2

Taking a closer look at the reduction we see that the wave is asymmetrical: the

acceleration lasts for approximately 10 beats while the deceleration lasts for a mere

6 beats. Also, after the deceleration our tempo is 60 bpm as opposed to 40 bpm.

This indicates an overall acceleration. At the same time, we now have more events

than before since our pitch space has also grown bigger. In other words, our wave is

being compressed as it gets more complex.

This process will continue to happen in the following waves in very much the

same way: each new wave expands the pitch space towards the fundamental as it

accelerates and decelerates to a slightly faster tempo than it started with. This is the

mechanism by which the rst mass will be created.

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By the end of the sixth wave (m.A26), the pitch space has nally reached

the C#2 (in the bass) and therefore our movement from partials to fundamental is

complete14. We are then ready for a new element: a complex ute sound.

This sound is executed by playing one pitch while singing another. The

theoretical result (or at least what Murail is counting on) is that the complex sound

will be a mix of the played pitch, the sung pitch and the sum and difference tones of

the two pitches15. The sound is perceived as a rough multi-phonic. Figure 3 illustrates

this procedure as found in the rst instance of this complex sound.

Fig.3

While this may seem a purely mathematical process, since both the played and

the sung pitch belong to the spectrum of C#1 (8th and 27th partials respectively), so

do the sum and difference pitches16. Therefore, the complex sound only brings forthcertain pitches that were already present.

The way in which this new event integrates with what has happened until now

is most interesting. We started with an undulating movement between thin timbre

and rich timbre, or noise and pitch, or soft and loud. As this movement has been

14 The reader might recall that I took C#1 as the fundamental for the spectrum and therefore C#2 isthe rst partial. However, it is common practice in spectral music to be quite exible with the position-ing of certain partials. Given the resonance of the C#2 in the bass and its distance from everything

else, I’m inclined to consider the C#2 as enough of an establishment of the fundamental.I must also add that the F#, which is the only pitch that is really misplaced in its current octave, isn’tpresent from here on (the rst F# in the C#1 spectrum is the 43rd partial F#6). This further reinforces theassumption that the fundamental, at least from this point on, is C#1.15 This effect is known as ring modulation.16 Algebra 101: given a pitch, its harmonic series is calculated by multiplying the frequency of thefundamental (F) by integers. Therefore, the frequency of the nth partial (n) is n*F. Given two partials rand s of the harmonic series with fundamental frequency F, the sum frequency will be r*F+s*F(r+s)*Fwhere the partial (r+s) obviously belongs to the spectrum of F. The same applies to the differencefrequency.

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compressed it has gained momentum and it has slowly developed what resembles a

crest. The complex sound is this crest: the release of the acceleration. And as such, it

is followed by a moment of stasis that engenders the next build. In less poetic terms,

let us examine this wave more closely.

Figure 4 presents a reduction of a full wave as found in m.A28-A38.

Fig.4

The rst thing that is clearly visible from the reduction is the alternation and

cross-fade between the strings and the ute. Both streams (ute and strings) describe

an asymmetrical curve in dynamics and timbre complexity. The latter refers to theamount of partials present in the sound. In other words, the strings start the wave

with two pitches and, towards the latter third of their curve, expand to more than ve.

Similarly, the ute starts with a played pitch, adds a unison sung pitch (resulting in

multiple octaves) and climaxes with four pitches (the sung pitch, the played pitch and

the sum and difference pitches of both).

The wave in the strings is also emphasized by an increase in rhythmic density

right before each ute entrance. The top part of gure 4 indicates the distance

between attacks given the tempo and an approximate count of attacks in a pulse.It is worth noting that there is also a difference between the attacks (hence the

“approximate” count): the attacks start by being swells from niente during the

less dense portions of the curve and end up being fully articulated just before the

ute sound. This increase in density, heightened by the change in articulation, will

become important in the later instances of the wave since it brings out the inherent

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directionality of this breaking wave curve.

The last thing that is interesting about gure 4 is that it shows the mechanism

by which the pitch collections evolve. You may recall that at the beginning of A the

pitches were generated by following a given spectrum and by the mechanics involved

in the process of producing the pitches (nodes were depressed in different degrees

to produce harmonics and stopped pitches). These are all factors that determine the

production of sound from noise (or silence) and therefore can be used, as we have

seen, to metaphorically represent the becoming of sound. Similarly, as I showed

earlier when discussing the complex ute sound, ring modulation can be seen as the

exploration of the relationship between two sounds (or actually four) and its context:

the spectrum. In other words, this is the composer’s way of saying “now that I have

sound(s), let me show you how they belong together”.

As seen in gure 4, at A28 the strings start playing pitches from the C#1

spectrum17. The timbre gets more complex (more pitches) and thins out to a C#4, E5

and D6. Notice how these pitches are picked up by the ute: the C#4 is the base

of the complex sound and the E5 and D6 are the sum and difference tones18. The

companion pitch to these three pitches is A#5 which is very prominent throughout the

wave. After the ute makes its complex sound, notice how its pitches are picked up by

the strings. You can see that the translation of the pitches from the ute to the strings

isn’t literal: the B+419 becomes a B4. Furthermore, the G5 which is now incorporated

into the string wave doesn’t belong to the C#1 spectrum. However, F%5 and G+5 do.This reinterpretation of pitches is a direct consequence of spectral music being music

as opposed to physical modeling.

The elements present in Fig.4 are what constitute the nal evolution of

our initial wave. As we have seen, they can all be deduced either physically or

metaphorically from the basic movement from noise to pitch. As I shall discuss later

17 The only pitch that is out of place is an F#4 harmonic that turns into an F#2 by stopping the stringat the node (not shown in the chart). The rst F# in the C#1 spectrum is F#6 (43 rd partial). However,

the fact that both of these pitches are extremely short and played piano (the second is even played sulponticello) gives the impression that Murail intended to diffuse them as much as possible. Furthermore,the relationship between them corresponds to the sound production pattern of the beginning of this sec-tion (node to stopped pitch).18 The D6 in the ute is about 1/6 th of a tone sharp so I think it’s safe even for a physical model, whichas we will see this is not, to assume they are the same pitch.19 Since many of the pitches discussed in this paper are quarter tones, I’ll be using the following con -vention:C+ is a C quarter tone sharp (between C and C#)C% is a C three quarters sharp (between C# and D)

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on, this is a moment of stasis; the moment when we have accomplished something that

we can see.

The mechanism by which Murail has generated his pitches could continue

and thus our object would continue to evolve as far as pitches go. However, Murail

chooses to freeze the pitches by repeating the same complex ute sound from m.A51

onwards. There are two consequences to this. The rst is that our wave is rounded

off as unit that is repeated: every ute entrance is no longer a motor of change but

rather a marker of the beginning or end of a cycle. The second is that this unit, with

its inherent directionality (emphasized by a collection of musical parameters) has a

dened peak: the ute sound. All of this is used to take our wave to a new level by

simple compression.

As described in research on musical streaming20, given a set of sonic events,

the temporal distance between them determines, to a great extent, whether we

perceive them as separate events, parts of one event, a pattern or simply one event.

This is the rst time we clearly see this facet of sound at play.

By compressing an object (our wave), we go from perceiving it as an extended

unit with cross-fades and three distinct sections, to grouping it all together as a single

event with a ute sound at its core.

At m.A60, this single event, that is now perceived as the pulse, suffers a slight

transformation: the density of attacks in the strings has augmented to the point where

they are no longer bowed notes but rather ricochets. Again, this is an outgrowth of

something that was present already. However, it is not until this point that we are

aware of the potential of a simple re-articulation of a pitch. This transformation of the

mass into ricochets has been masked by the foreground transformation of the wave

into a pulse.

This new texture is further accelerated starting at m.A64 and released (sudden

drop in tempo) at m.A71 leaving us at another moment of stasis that begins section B.

Before moving on, here is a recapitulation of the important elements of this

section since, as we will see, they are reinterpreted again and again throughout the

piece.

20 See footnote 4.

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We started with harmonics that came out of noise.1.

These harmonics were structured into waves; a unit to hold on to.2.

The unit grew as it brought forth its different elements (increase in density and3.

timbre complexity).

The unit was compressed thus transferring our attention from elements of the4.

unit to the unit itself (micro to macro).

While focusing on the macro level we took micro elements for granted and5.

missed their transformation (from distinct bowed attacks to ricochet clouds).

The change in the micro level became apparent as soon as the foreground6.

disappeared. In other words, our attention, lacking the macro element that

it had focused on (the ute outbursts) struggles to nd a new element: the

ricochets.

The elegance of this rst ripple in the form is that each transformation is made

to seem inevitable. Our attention is manipulated so that each change is revealed as

a new element even though all elements are the result of stretching or exaggerating

something that was already present. We have only been hearing facets of the same

thing.

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ii. Section B

This section is a re-composition of A. Both have in common that they start at

a moment of relative stasis and build a texture by exaggerating certain elements

that are present but hidden in the sound. Again, we have a local unit shaped like a

wave. At a larger scale, the sequence of waves describes, like in A, another wave in

dynamics and event density. At an even larger scale, some transformations continue

uninterrupted over the section line. For example, as we will see, the transformation

from unarticulated bows, to articulated attacks, to rhythm, to ricochets (that serve

as the background texture in this section), will eventually turn into a texture of trills.

These different simultaneous periodicities help avoid the feeling of nality we might

get from the sudden drop in density and intensity between A and B.

The pitch material in this section is also slightly more complex. While in the

A section we could argue that the fundamental was C#1, this section has several

possible fundamentals that develop into a hybrid spectrum or spectral mass. Let us

take a look at two of the most obvious fundamentals.

The rst option is F#1. Most pitches conform to its spectrum and both the

complex ute sound at m.B1 and the violin guration at m.B20 (preceded by an F#2

in the trombone not shown in the chart) reinforce this21.

Fig.5

21

The pitches that are not in the F#1 spectrum are D#4 and B+5. The former isn’t far from the D%4(7th partial) and the latter could be B+5 which is also found in the ute complex sound.

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Further supporting the F#1 hypothesis is its fth relationship with the previous

fundamental C#122. However, there is another spectrum that accommodates the pitch

collections at m.B1-B10: D#.

As you can see in gure 5, there are two pitches being emphasized in this

section: C#5 and D#4 (notice the cello and the ute gure at m.B2). The F#1

spectrum contains all these pitches in the same octave except for the D#4 which

should be a D#6 (27th partial). On the other hand, a D#2 spectrum accounts for all

the pitches23 except one: the B5 in the violin.

Notice that the complex ute sound at m.B4 (gure 5) contains a B+5 that

has been clashing with a B5 in the violin. Eventually (m.B4) the ute adds a B5 that

agrees with the violin and nally delivers a multi-phonic at m.B10 that contains the

emphasized pitches (D#4 and C#5) and a B5. This multi-phonic serves to mark the

end of a nal adjustment before continuing ahead; a delayed cadence approached

by acceleration and resolved with a sudden tempo drop.

Another thing that makes this moment signicant has to do with the production

of the pitches. As I mentioned earlier, the ute substitutes a B+5 that clashes with the

violin for a B5 that doesn’t. What makes this substitution unique and also takes this

moment beyond the technical domain and into the realm of the spectral metaphor is

that the rst pitch is obtained by amplitude modulation while the second is part of a

multi-phonic. These two techniques represent the two ways in which a monophonicinstrument such as the ute can become polyphonic.

After the multi-phonic at m.B10, there is a diminuendo and a tempo drop to 60

b.p.m. This is another moment of stasis in which the background texture emerges once

again (the richochet strings). The ute recedes to the back after echoing itself and

settles on a very quiet but rough C3 (mostly breath and played with utter tounge). It

will not dene itself until m. B22.

22 Obviously, this relationship is not functional in any tonal way but it is worth pointing out that, sincetonality is at times modeled to conform to the harmonic series, many tonal relationships have parallelsin the spectral domain. We nd an example of this crossover when classifying chords by function in atonality (tonic, subdominant and dominant). Tonic chords are the most stable and, curiously enough,are the ones that don’t contain the perfect fourth degree of the scale. The perfect fourth is the 43 rd partial and is therefore “barely” in the spectrum of the “tonic”.

23

I’m taking the liberty of considering C#5 to be lling in for a more precise C#5 a sixth of a toneat.

15



(Fig.6 continued )

Notice how the glissandi are virtually imperceptible but at the same time have

a clear goal: an F# spectrum. As I pointed out earlier, both the multi-phonic at m.

B10 and the violin guration at m. B.20 support this. In gure 6 you can also see that

the arrival of the last glissando on the double bass is an F#3. Also, the trombone

enters at m. B19 with an F#2. Aside from the C3 in ute, the only pitches that don’t

belong in the F#1 spectrum (taking it in favor of the less inclusive F#2) are the C3 in

the viola and the B3 in the cello24. These pitches are dropped at m. B22 when the

establishment of F# is complete.

Taking a nal look at gure 6 we see that two things happen as we approach

m. B20: the ute is strengthening its low C3 and pitches begin to accumulate on

top of the F#2. The way in which the ute is gaining strength, as you can see in the

24 I’m taking the liberty of considering E4 as the seventh partial in place of the more accurate E quarterat.

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reduction, is in swells of breath: the familiar wave design from the previous section.

Notice how the trombone enters to punctuate the peak of these swells (starting at

m.B19). The ute is dening a unit (swell) with a center (peak) around which events

begin to cluster. As in section A, the foreground provides a structural element

that fullls the function of an absent melody, while it masks the evolution of thebackground.

The second thing that happens (the accumulation of pitches above F#2) is

preparing the canvas for the next “lesson” in sound. It is actually the continuation of

the process of creating a sound mass that started at A. At A we started by focusing

a pitch. Then many pitches were put together to form a mass. This mass was then

focused into a spectrum. Now, the spectra are superimposed to form a spectral

mass25.

As I mentioned earlier, the ute has established a unit in the shape of a wave

around which other events are clustered. Before moving on to section C, the ute

swell incorporates a harmonic sweep based on C3. This could be understood as

the beginning of the establishment of the lter metaphor by way of introducing a

frequency sweep and resonance. This unit incorporates fast glissandi rst in the viola

and then in the violin that echo the frequency sweep.

After a slight accelerando that compresses the swell and a subsequent

rallentando that lets the sweep recede to the background, the background textureemerges as mass of trills. This is the nal stage of the creation of a mass initiated at A.

Section C, with the sweeps introduced at B, will be an exploration of this mass.

25 A closer examination of the spectra resulting from the low cluster seen at m. B31 in gure 7 isbeyond the scope of this paper. However, below I present a chart that shows the rst common pitchbetween some of the resulting spectra and their position in the partial series to give the reader an indi-cation of the complexity of the spectral mass:

G1, G#1 and A1 (bass and trombone) G#5 17th, 16th and 15th partialsF#2, G2 and A2 (cello) G#6 18th, 17th and 15th partials

18



iii. Section C

Murail, in his Performance Notes, says that this section is a game (or play)

on the spectrum of the low C of the ute26. There are two elements throughout this

section: a mass of trills and a harmonic sweep.

The rst, as we saw in the previous section, is made by the low instruments

(trombone, cello and bass) and results in a homogenous canvas of sound. The

second was also introduced at the end of B and plays one of the roles played by

the complex ute sound in section A: it provides a sense of pulse and directionality.

Additionally it serves as a metaphorical spotlight on the mass showing us that the

background isn’t really as homogenous as it seems.

While the mass changes very little until section D, the sweeping element

becomes more complex: it is initially a harmonic sweep from the C3 in the ute, itthen incorporates a harmonic glissando in the viola, and nally the violin joins in with

another harmonic sweep.

Figure 7 shows the basic sweeping unit in the ute, violin and viola and their potential

pitch content:

Fig.7

The ute is instructed to bring out the fundamental (C3) and the rst 2

overtones (C4 and G4) between sweeps. The violin sweep is an E5 spectrum while

the viola could be a G3 or a C3 spectrum depending on the string its played on.

26 “Jeu sur le spectre du do grave de la ute.”

19



Since E5 and C3 are both partials in the utes C3 spectrum, the overlap is

almost seamless. However, in the case of the possible G3 spectrum in the viola, since

G4 is the rst G in the C3 spectrum, the result is the introduction of inharmonicity into

the ute’s C3 spectrum27.

One nal element worth mentioning about the texture of section C is the

transferring of the two control pitches C#4 and G5 between instruments28. Figure 8

shows this transferring of control pitches between instruments as heard in m. C3-C4.

Fig.8

The rst time they appear (in the trombone and cello) they are the echo of the

ute’s sweep at m. C3. As the trombone stops, the ute and the cello maintain the

two pitches. Finally, the viola picks both pitches up as the tail end of the sweep and

27 Harmonicity is a way of classifying a spectrum in terms of the relationship between the frequenciesof its partials and the frequency of its fundamental. A purely harmonic spectrum has all its partials asinteger multiples of the fundamental frequency. An inharmonic spectrum has non-integer multiples ofthe fundamental frequency. The movement between each pole can be achieved in several ways oneof which is folding over partials (harmonic partials are displaced down by octaves until they are nolonger an integer multiple).28 While many interesting reasons can be given for the choice of these two particular pitches, I aminclined to think that what is really important is the choice of the interval. As we will see, the entire lastsection is constructed around the diminished fth.

20



the preparation for the new ute wave. Murail’s mention of the need for this diad to

remain as balanced as possible despite the change in timbre implies that it should act

as a thread of continuity between the sweeps.

As I mentioned earlier, the texture changes very little throughout this section.

Eventually, however, the glissandi in the strings dissipate as the instruments slowly

become part of the texture. On the other hand, the ute sweep remains the same but

its occurrences start to group together: they start to create larger phrases. A way of

describing it would be to say that at the beginning of C each sweep is its own event.

By the last third of C, sweeps start to take on the role of announcing “the big one”.

Murail achieves this by compressing the sweeps (acceleration), and grouping several

of them under an envelope of dynamics and duration shaped like a wave. This also

serves the purpose of solidifying the metaphor of the lter 29; with each sweep, we can

now visualize the knob on the lter being turned up and down.

After m. C30, Murail takes the metaphor one step further and turns the knob of

the lter too far 30. The knob in question would be the resonance control which creates

a feedback loop at the center frequency thus boosting the given frequency and giving

it a ring. This overload provides the necessary energy to transform the texture into a

shimmering chord of trills; the nal form of the sonic mass that has been forming since

the beginning of the piece.

29 In order to clarify the lter metaphor I’ll be working with for this section (and in fact the wholepiece), following is brief description of the basic properties of a lter. Filters essentially sift signals. Todo this, they have frequency bands around what are called center frequencies. The range (or size)of these bands is called the bandwidth (or Q). Some lters have a resonance setting that activates afeedback loop around the center frequency. This causes the frequency to ring.

30 “effet semblable à un “accrochage” électronique (accrochage de ltre poussé trop loin).”

21



iv. Section D

This section starts with a homogenous sound mass in the strings that has taken

three sections to build: from noise, to spectrum, to several spectra. You might recall

how in the rst section we started with a set of partials in the strings that “triggered”

a complex ute sound. The pitches resulting from the ute were picked up by the

strings as the new set of partials. Essentially, the process was one of transformation

through ltering, or combing, of the initial string partials. Section D is the same

process at a larger scale: by ltering a sound mass we obtain a new texture and

pitch collection. This ltering is done in several stages each of which demonstrates

a different facet of a physical lter unit. Also, the ltering is applied to both the

frequency and time domains.

Figure 9a shows the initial mass as found in m. D1-D2.

Fig.9a

A couple of things are worth noting about this mass. The rst is the presence

of C#4 and G4 (the pitches that were being transferred between instruments in the

previous section). The second is the A#5 (or Bb5) that has also carried over from

the previous section. The third important thing is the distribution of the mass into four

distinct frequency bands31. The spacing between the bands is, from the bottom up, a

minor ninth, an octave and a major seventh (minor seventh once the ute enters). We

have a four band lter being applied to a signal. Throughout this section we’ll see

how this application is modied in time; a performance the lter.

The rst thing that happens Is that the bands begin to expand in range starting

at m.D3. Figure 9b shows the expansion of the violin band in stages: (1) initial stage

31 These roughly correspond to 98-130.8 Hz for the bass and trombone, 277-392 Hz for the cello,784-987.7 Hz for the viola and ute, and 1760-1975.5 Hz for the violin.

22



(m. D1), (2) initial expansion(m.D3), (3) center frequency shift (m.D12-13) and (4)

nal expansion (m.D16).

Fig.9b

The next type of ltering is called quantizing. This one starts to be perceptible

around m. D20. While the effect is that of a deceleration, what is actually happeningis that pitches are being dropped from the pitch collection as beats get further apart.

In other words, imagine we establish a grid of 10 beats per second and map a 10

note pitch collection on it. If we expand the grid, the beats are longer (our unit is

more than a second) and we still have a 10 note pitch collection. However, if instead

of expanding the unit we eliminate certain sections of the grid, the beats get longer

(deceleration) but we start omitting pitches from the pitch collection. This is called

quantizing and it is what is happening in this nal stage of ltering. It’s interesting

to note that in this case (as in most quantizing done by sequencing software), some

pitches aren’t actually dropped but rather are moved to the closest beat. It can also

be seen as verticalization of horizontal structures.

23



While this is happening, the bandwidths are compressing and their center

frequencies are also converging so the overall bandwidth is compressed by the end of

the deceleration. Figure 10 shows the nal stage of this compression and quantization

as found on m. D26-28.

Fig.10

This ends section D and leaves us at a moment of stasis. This is the end of the

rst of three cycles of mass creation mass ltering.

24



IV. About the Form II

In the previous section, I called the end of rehearsal D a moment of stasis.

This refers to its relative periodicity or predictability. The basis for this is a scale

(admittedly arbitrary) presented by Gerard Grisey that proposes a way of classifying

intervals, rhythms and sound masses in terms of their predictability32. In this scale, or

continuum as he calls it, there are two opposing poles that correspond to absolute

predictability and absolute un-predictability. Neither of these is necessarily desirable

but they correspond to two extremes with a musical representation: predictability is

periodic and un-predictability is statistical. Another advantage of this scale is that it is

on the side of the listener as opposed to that of the score reader.

Without going into the details of this classication, between these two poles

that correspond to what we may call the perception of chronometric time, there are

two types of dynamism. Each of these types acts differently on our perception of

the musical time. Predictable acceleration and deceleration (acceleration curves for

example) have the effect of compressing or dilating time respectively. The second

type inserts discontinuities in these otherwise predictable curves causing a skip in

time or a compression of the acceleration. If the discontinuities are taken too far,

our perception is forced to focus on the moment thus stopping time. Therefore, we

can say that aperiodicity has the effect of accelerating, decelerating or stopping

(compressing, dilating or skipping) time while periodicity allows time to unfold. The

two poles of perception of time translate musically into dynamic and static moments;static (periodic) moments allow us to survey where we are and hear time unfold while

dynamic moments direct our perception towards the “now”.

One nal distinction is relevant to the scale: the difference between

acceleration and deceleration. Acceleration presents us with more and more

information. Conversely, deceleration reduces the density of information. Therefore,

even though both are dynamic processes, the former has greater potential for

unpredictability while the latter tends to become static much quicker.

Looking back at rehearsal letters A through D, we can establish certain

moments of relative periodicity and others of dynamism. Below is a description of the

static moments found thus far in the piece.

32 For a more detailed description of the scale refer to Gerard Grisey’s article Tempus ex Machina: acomposer’s refection on musical time.

25



Rehearsal A starts with the maraca continuum with very soft and unfocused-

glassy harmonics in the strings.

Rehearsal B starts with a ricochet texture that contains a nearly imperceptible-

drift on the low end.

Rehearsal C is a sequence of pseudo-periodic harmonic sweeps supported by-

the strings.

Rehearsal D ends with a periodic asymmetrical gure in the strings.-

These moments of stasis are connected by dynamic processes like the ones

mentioned in Grisey’s scale. The connection between A and B is a continuous

acceleration followed by a sudden deceleration. The connection between B and C

is smoother partly due to the fact that both these sections contain slight continuouscompressions and dilations within and are therefore mostly static in themselves.

The connection between C and D is done by an acceleration at the end of C and a

deceleration throughout D.

Figure 11 presents rehearsal letters A through D with the aforementioned

static/dynamic mapping. The gradient indicates the dynamic moments and the lighter

shading indicates the static moments.

Fig.11

Looking at gure 11, we see that there are essentially three waves of movementthat have their crests at the end of A, the second half of B and the end of C. D is

mostly a continuous deceleration and is therefore less dynamic (unpredictable). We

could also create a gradient that engulfs this whole section and has its peak at the

end of C (the over-blowing of the ute). Similarly, we can apply this classication to

the smaller individual sections.

26



Figure 12 consists of three bands of information. The top gradient is taken from

the same time span in gure 11. The middle chart is a symbolic representation of the

various gestures in relation to time (i.e. the curves indicate the expansion of range;

the rectangles are the complex ute sounds; the dots are the ricochets). The lower

band is a sequence of gradients that represent the unpredictability like in gure 11.

Fig.12

Looking at gure 12 before the rst ute sound (rst two minutes), we have a

sequence of static pitches that are destabilized by movements away from them. In

other words, two static moments (i.e. 1’06’’ and 1’39’’) are connected by a dynamic

moment (i.e. 1’10’’-1’30’’). At the entrance of the ute we have the same structure

even though our static moment has now become more complex.

As time compresses starting at 3’, the unpredictability of each individual ute

utterance becomes less important in favor of a general unpredictability of the mass.

Therefore, I have grouped ~3’20’’-3’40’’ under one gradient. The importance of this

is that we have moved down in the scale of magnication. In other words, the top and

bottom gradients of gure 12 agree at this point showing that the alternation between

static and dynamic states is present in all temporal scales.

27



This illustrates the basic formal model of early spectral pieces: X and Y are two

sounds or sound masses (or a sound and silence) that are connected by a dynamic

process. Another way of saying it is that X and Y are snapshots connected by

interpolation33.

As we have seen until now, rehearsal letters A and B have been the creation of

a sound mass. Rehearsal letter C was the exploration and distortion of this mass and,

nally, rehearsal D was the ltering of this mass into a simpler and more periodic

(static) texture. The rest of the piece operates in very much the same way two more

times: E through H and I through J. Rehearsal E through F create a mass, G explores

it and H lters it. Rehearsal I creates a mass, explores it and starts to lter it. J

concludes the ltering and returns to the maraca continuum thus delivering us where

we started at A.

Since the process is the same for the rest of the piece, I will continue by

describing the highlights and particularities of each section of the remaining two

waves/units.

33 One nal metaphor is drawn from animation. In the early days of animation, a master artist woulddraw important frames of the picture. This done, a team of illustrators would draw the hundreds andhundreds of frames in between the master frames. This process was called tweening (in between between ‘tween). This is similar in that X and Y are master frames and the connection is the ‘tween.

28



V. Analysis II - a. Unit II

i. Section E

Rehearsal letter E is the beginning of the second big wave of mass creation/

ltering. Its similarities with rehearsal A reinforce the assumption that they occupy asimilar place in the aforementioned process.

E starts with a moment of stasis formed by quiet string chords played with the

periodic though asymmetrical rhythmic gure found at m.D28 (gure 10). The ute

joins the strings with multi-phonics and plays the same gure at the beginning of E.

A slight acceleration (from MM=20 to MM 60) which equates the 5/8 gure to the

quarter note. Also, the ute and strings are out of phase thus evoking the owing

waves of rehearsal A.

At m. E17 the trombone leads the strings into a decelerating sequence of beats

shown in Figure 13.

Fig.13 m.E16-18

29



Notice how at the beginning of the beats there is a sudden change in dynamics

(forte) and a tempo change (form MM=60 to MM=100). The leap in dynamics is

self-explanatory. However, the tempo change demonstrates the use of tempo as a

compositional tool at the micro level. In other words, instead of writing smaller note

values that get longer (what is usually used in these cases for its exibility), Murailchooses to control the whole time of the mass with the tempo markings. This also

shows how the mass is being treated as a malleable object.

At the end of the deceleration, the ute plays a multi-phonic and the strings

echo it as they dissolve into a sustained texture. The maracas are also indicated to

crescendo slightly as the strings disappear.

Figure 14 shows m.E22-24 where we can see the end of the beats, the ute multi-

phonic and the beginning of the crescendo in the maracas.

Fig.14

30



This describes a wave that goes from pitch with high rhythmic density (entrance

of the trombone) to multi-phonic to echo with low pitch density. In order to point out

the similarities with A that I mentioned earlier, gure 15 shows a schematic reduction

of the waves in A and E. Notice how both have the same shape in dynamics, rhythmic

density, time perception and even content.

Fig.15

Waves at A:

Waves at E:

The evolution of both these waves and therefore the way in which they create

a mass is slightly different. At A, the waves were compressed (accelerated) in a fairly

linear manner until the mass was created. At E, however, the waves are warped: the

initial beating section gets progressively shorter while the sustained echo gets longer.

Also, the ute begins to move forward so the beating coincides with the multi-phonic.

The longer portion of the sustained echo incorporates a crescendo so the wave is

smoothening out.

At m.E50, the length of the crescendo is taken to the extreme and it ends

suddenly with what would have been its rst beat of the next wave. Instead, the ute

is left to play its multi-phonic (triple forte) alone. And this marks the beginning of F

and a new (or reinterpreted) process of mass creation. Notice how the sudden burst

and projection to the next section resembles the connection between A and B.

31



ii. Section F

This section is the beginning of a big accelerando that brings us to the climax

of “Ethers”. The basic unit is, once again, a wave. Each of these units starts with a

pitch collection (a diade played on the ute) and, after a given process modeled

after an acoustical property of string instruments, ends with a new pitch collection.

At rehearsal A we had a pitch collection in the strings that went from partials to

fundamental. When the fundamental was reached, the ute sang the fundamental

and played different pitches thus producing a new pitch collection resulting from ring

modulation (an acoustical property of the ute). So from this point of view, A and

F are the same process. However, at F, the elements are reversed: the ute gives

the initial pitch collection and the strings produce the new pitches by playing sub-

harmonics34. Figure 16 shows the rst of the units from m.F1-5.

Fig.16

Taking a look at g 16, we see that the ute starts with two pitches (multi-phonic34 The production of sub-harmonics on string instruments, like the production of multi-phonics on theute, is a fairly controversial one: as with multi-phonics, the clarity of the pitches involved is sometimesobscured by the noise the process generates. The basic principle of the technique is that by apply-ing great pressure on the bow, you force an anti-node that corresponds to a longer string double thelength than the one you have. Two basic problems arise. The rst is that this “virtual” string is actu -ally slightly shorter so instead of hearing an octave below it is closer to a major seventh. The secondproblem is that the process of crushing the bow against the string produces a dry scratching sound thatmakes any pitch difcult to hear even though it might show up in a spectrogram.

32



stage). These pitches are picked up by the violin. Then they are crushed theoretically

producing the same two pitches transposed down a major seventh. This new pair is

picked up by the viola and crushed again with the same effect as before (crushing

stage). This process continues until the bass is reached. At that point, the note in the

bass is taken as a fundamental (or some octave transposition of it) and partials of itbegin to appear in the strings from low to high.

This wave follows a similar transformation as the wave in A: by way of an

acceleration, the unit is compressed until it is no longer a sequence of waves but

rather a sound mass.

Figure 17 shows m.F20-22.

Fig.17

33



You can see in this score excerpt that the wave has collapsed into a pseudo-

statistical texture where each instrument preserves some trace of the initial features of

the unit. From this point until m.F37, each instrument derives towards a simple gure

of its own. In other words, similar to the quantizing process we saw at D, each line

becomes sparser. However, at the same time, two things happen that.

The rst is that the tempo accelerates progressively (though rapidly) from

MM =50 to MM = 92. This is exaggerated by the fact that smallest durational unit

goes from a quarter note at 50 to 16th notes at 92. In other words, from roughly 1.2

seconds to .16 seconds.

The second is that the different simplied rhythmic gures start to sync up. Both

are tied since as the durational unit gets smaller rhythmic subtlety is lost35. The result is

shown in gure 18 which is a score excerpt of m.F37-39.

Fig.18

35

In his article How to Talk About Musical Metre, Justin London proposes a range of durations inwhich we can hear rhythm clearly. The range is from 100ms to 2s. Above and below this range wehave difculty perceiving acceleration and deceleration. Additionally, for durations below 100ms westart having trouble perceiving order.

34



Here you can see how all the instruments (except for the trombone) are now in

concerted rhythm and still the acceleration continues until its nal stage: the trill. With

the sound mass newly transformed into a mass of trills, we arrive at G.

Before moving on to the next section, I would like to point out the resemblance

the whole process from E to F has with what we’ve encountered at A-C. First of all,

in both cases we have gone from static sparse textures to dense masses and in both

cases this has involved different stages corresponding to different smaller sections.

Second, the relationship between these smaller section pairs (A and B, E and F) is

also similar in that they are connected by an elision.

35



iii. Section G

Rehearsal G is the climax of “Ethers” in terms of dynamics and range: all the

instruments are instructed to play triple forte and the range spans from an F#7 in

the piccolo to a G1 in the trombone. The space in between is lled, very unevenly,

by a mass of string tremolos with different accents that become more prominent as

the section advances. The result is that we hear a sequence of eight pairs of notes

in the piccolo and the trombone, and a homogenous mass between them. The eight

pairs are attacked together and each attack is accompanied by a change in the pitch

collection of the mass.

Figure 19 shows a reduction of the pitches in section G. In each chord there

are three white note-heads. The top and bottom ones correspond to the piccolo and

the trombone. The middle one is an A4 which is sustained throughout. The rst pair

is preceded (though it’s not shown in the reduction) by a glissando to the highest

possible note on the cello and bass, and the rst note of the chord on the ute and

violin. This glissando lasts only about one second.

Fig.19

The rst thing we notice from gure 19 is that the initial chord ts a harmonic

spectrum with the exception of the A3 (the numbers to the left of the rst chord

indicate the partial number in relation to the fundamental 1). This A3 is actually part

of an oscillation between A3 and A4 that by the third chord has thinned out to just

A4.

36



The second thing to point out is the movement between the three white note-

heads: the A4, the piccolo and the trombone. Notice how the A4 remains stable

while the piccolo and the trombone move closer and closer together.

In the performance notes for this piece, Murail gives two indications that

are helpful in understanding the technique he is using here. The rst one is that

the short and dramatic glissandi that precede the rst chord should sound like

the glissando of an oscillator 36. The second indication is that the trombone should

sound like a granular difference tone37. In reference to the earlier discussion of

amplitude modulation (of which ring modulation is an extreme), I mentioned that

when modulating the amplitude of a carrier signal by a modulating signal (another

oscillator) we obtain two additional pitches that correspond to the sum and difference

frequencies38. The following chart shows the four different possible tendencies of the

sum and difference frequencies in relation to a static pitch (sFrq) and a modulatingfrequency that is above sFrq (xFrq) or below sFrq (yFrq) and either ascending or

descending:

36 “Glissando initial (Fl, Vn, Vc, Cb) semblable à un glissando rapide de générateur.”37 “Le Tbn apparait comme un différentiel grave et granuleux.”

38 In frequency modulation we get a similar effect but the spectrum is more complex. The resultingsidebands are F

c±F

m, F

c±2F

m, F

c±3F

m,…, F

c±nF

m. Even though frequency modulation may very well be

the process emulated in this section, given the similarities between the resulting frequencies in bothmethods, I will use the amplitude modulation model since it reduces the amount of frequencies presentand thus makes the explanation clearer.

37



Looking back at gure 19 we see that if we assign the piccolo to the sumFrq,

the trombone to the difFrq and the sustained A4 to the sFrq, their relative movements

reect those of case 4. In other words, the A4 (carrier frequency) remains xed,

the piccolo descends (sum frequency) and the trombone ascends (difference

frequency). In order to get the pitches found in the trombone, the frequency of themodulator needs to descend from a G4 (slightly at) to a D%4 (slightly at). Given

that a different glissando is needed to account for the descending piccolo, the

process is either more complex than simple ring modulation, or it is being applied

metaphorically.

Two things are worth pointing out about this section before moving on. The rst

is the ascending trombone line in measures 5-8 of gure 19. Notice how it describes

a diminished chord D-F-G#-B. In measures 1-4 of the same gure, the intervals are

much smaller. In order to have these last four resulting pitches, the glissando in themodulator would have to be a curve (acceleration)39.

The second refers to the progressive inharmonicity of the spectra. Taking the

lowest note as a hypothetical fundamental, gure 20 shows the partial numbers of

each pitch. Numbers preceded by “-“ mean that the partial is displaced down by as

many octaves as “-“ precede it.

Fig.20

39

Pitches in the lower register are separated by fewer Hz. Therefore, to have a bigger differencefrequency, the modulator needs to drop by a bigger interval.

38



Notice how the rst chord is harmonic (every partial is in its place) and most

partials are odd numbered (new partials and not just octave doublings). The second

and third chords have a similar conguration but this time most of them are displaced

by an octave. In other words, if the fundamental were an octave lower they would be

harmonic. Starting at the fth chord through the 7, most partials are displaced by atleast an octave making the spectra more and more inharmonic.

The nal chord is slightly more harmonic in a different way. The partial

numbers in the gure are in relation to the B2 of the trombone. However, notice how

there is a D major triad starting at D4. So different sections of the chord conform to

different spectra. It could be understood as an upper structure triad40.

This nal chord brings us to the end of G where we have explored the initial

chord and its transformation, and Murail has developed the amplitude (or frequency)

modulation metaphor he used to create the mass at the beginning of the piece

(remember the complex ute sound relied on this very same principle).

40 I’m referring to what is also known as a polychord where two different structuresare superimposed and, because of their individual consistency, we are capable ofhearing the resulting structure as a whole.

39



iv. Section H

This section describes two general movements of the mass. The rst of these

movements, and the most obvious, is a ritardando from 70 to 60 at the beginning,

and an accelerando from 60 to 80 at the end; a wave. Again, like with most tempo

operations in this piece, the effect is felt in the density of the mass and not in the

change of pulse. Tempo acts as the hand that shapes a piece of clay.

In section G I mentioned that the string mass was made up of string tremolos

with accents that became more prominent as the section progressed. The effect of

this increase in density of the accents is that the mass starts to break up into smaller

units. By creating sequences of accents in the different instruments or threads, the

threads start to gain individuality and the mass begins to break apart41. By the end of

G, each instrument is no longer playing a double stop but rather a pattern of double

stops. Figure 21 is an excerpt of the score m. G13-15.

Fig.21

41 You could also refer to this as the process of “granulizing” the mass.

40



As the tempo drops to 60 and each thread starts playing longer values

(decelerates), we hear the different patterns of each instrument and therefore, for

a brief moment, we get a closer view of what the make up of our mass is. This is

another instance of our change in scale: from mass to grains.

Conversely, the acceleration at the end of H re-creates the mass from fast gures, to

trills to tremolos. Figure 22 shows an excerpt of the score corresponding to m.H13-17

that illustrates the acceleration.

Fig.22

41



The other type of movement that this section describes is a compression in

register. Figure 23 shows the reduction of three snapshots of section H corresponding

to the beginning (m.H3), the middle (m.H7) and the end (rst beat of m.H17). In

the gure, whole notes indicate pitches that are being played by more than one

instrument and therefore the pitches that have a greater probability of comingthrough.

Fig.23

Notice how the nal pitch collection slowly clusters around A4 and nally A4

ends up being the lowest note. This of course is a one direction process in contrast to

the wave of deceleration/acceleration. As we will see, roughly the rst half of section

I is an expansion in register that balances this process thus describing a larger wave

in this parameter.

Also worth pointing out is the fact that the pitch content of H doesn’t change

dramatically in these three stages. However, the pitches being emphasized (played

by more than one instrument) does. Looking back at gure 23, we see how at m.

H3 the whole the whole notes outline a D major triad and two more notes (D#5 and

C#6). In the second snapshot, the C#6 is no longer being emphasized but is rather

being blurred by the C+6. In the last pitch collection (m. H17) the only pitch that

is being played by more than one instrument (more specically, by the bass and

trombone) is the A4.

The nal state of the mass at the end of H is a sustaining four note chord in

shimmering tremolos. There is no pulse and no change so it gives us a moment to

survey where we are. Also, we have cycled through our process of mass creation (A

and B, E and F), mass exploration (C, G and H) and mass ltering (D, H) once more.

This brings me to group E-H as our second big unit, or wave, of the piece.

42



b. Unit III

i. Section I

This section begins, therefore, with a moment of stasis. It is the beginning of

the last unit of the piece. This nality is supported by two things: it has a cadenza-likecharacter, and it is a condensed and smoother version of the process that underlay

the previous two units (a sort of winding down).

The cadenza quality of the beginning of I is self explanatory: the strings

provide a static support for the ute’s gures. According to Murail’s performance

notes, the strings represent a reverberation mass. As such, they react to, and slowly

incorporate, the pitches of the ute.

As the ute expands its gure with more pitches, the string chord becomesdenser. Figure 24 shows the process of mass creation for this nal wave in a reduction

of m.I1, 3 and 7.

Fig.24

43



By m.I15, the full mass is formed and the process of exploration begins. Figure

25 is an excerpt of m.I15-18.

Fig.25

This is done by expanding the trills into patterns (or gurations) and then

decelerating the gurations; the mass is disintegrating before us letting us, once

again, see its internal make up. This process of disintegration is illustrated in the

following excerpt that corresponds to m. I27-30.

44



F i g .2 6

45



Notice how each instrument is structured in the form of a wave either in

dynamics (trombone and bass), in density (ute, violin, viola and cello) or in register

(ute, violin and viola). These waves have different periods: their crests don’t

necessarily coincide.

Figure 27 shows the pitch content of m.I27-30 and the partial numbers in a C#1

spectrum.

Fig.27

Except for the bass, all the instruments are playing some section or all of this

collection. Taking a closer look at the pitches we see that they more or less form a

C#1 spectrum but not quite. However, the sound of this mass is clearly of a harmonic

spectrum. The reason for this is that the spacing is like the one in a harmonic

spectrum42.

It is also worth pointing out that the acceleration and deceleration of each

wave corresponds to this exploration of the spectrum. As the waves ascend to the

denser regions of the spectrum, the gure accelerates. As it descends, it decelerates.

From this point (m.I28) to the end of I, these separate streams go through thesame two dimensional ltering process we saw at section D. In the frequency domain

the bandwidth narrows and the center frequency establishes itself around F4 (though

no F4 is being played). In the time domain, notes get further apart (values get longer

as in a ritardando) by dropping pitches from the guration. The result is a reduction in

42 The spacing between the partials in a harmonic spectrum gets closer as we rise in register. In thiscase, the pitch collection follows the same design.

46



pitch content and the dissolution of the individual waves.

While this is happening, the next element (or next transformation of the waves)

is developing in the background: a quiet glissando in the trombone and cello starts to

take shape. Figure 28 shows the origin at m.I32.

Fig.28

47



Figure 29 shows how it starts to lock into an aperiodic repetition at m.I37-39.

Fig.29

48



And nally, gure 30 shows its nal periodic state as seen in m.I48-52.

Fig.30

This, with the exception of the ute and trombone that fade out before J, is

the texture that forms the basis for J. This marks another static moment in the piece

and the end of another cycle through the process. Section I started by creating a

mass by emulating a reverb unit. Then it “turned the unit loose” creating those waves

(or threads) of partials that echoed each other. Finally, it ltered them in a way that

resembles the decay of a reverb or an echo unit leaving us with a four note pitchcollection. As you can see in gure 30, this pitch collection has internal movement

supplied by the glissandi in the violin and the cello. Murail refers to this internal

motion as phasing (another acoustical phenomenon).

49



c. Coda

i. Section J

Having nished another cycle through our mass-creation/mass-ltering process,

J assumes the role of a coda. In other words, nothing remains to be done from theprevious cycle and J isn’t a full cycle in itself. However, as codas usually do, it closes

the larger cycle of the piece and addresses loose ends that might remain. Both of

these are made clear by the same event: the stopping of the maracas.

The maracas started out the piece with the instruction of playing continuously

until this moment. They represented the canvas of noise from which pitch emerged.

As pitch has occupied our attention until now, naturally the maracas recede from our

awareness. With their sudden stop we realize they were there. Furthermore, in their

absence, what is left is pitch. You might recall that the rst halves of the waves at Awere from noise (upper partials) to pitch (fundamental). With this arrival to nothing-

but-pitch, the same half cycle has arrived at a larger scale.

The maracas enter again with a slow crescendo from niente at m.J9.

This initiates our journey back to noise thus completing the remaining half cycle

summarized in the initial waves at A.

The way in which this second part of the cycle is done is illustrated in gure 31

which is a score excerpt of m. J10-14.

Fig.31

50



As seen in the gure, the glissandi that gave the effect of phasing, slowly

transform into discrete pitches. Each instrument extracts a pattern from these pitches

and repeats it as shown in gure 32 (m.J18-20).

Fig.32

151



Another connection with the beginning of the piece is made by the entrance

of the complex ute sounds (ring modulation) and their subtle transformation of the

pitches in the string texture. Figure 33 shows the rst of these ute sounds at m.J21-

23.

Fig.33

With each ute sound (12 in total), the strings become less and less active and

closer to assuming the role of a mere echo of the ute. Figure 34 shows the last of

these ute utterances and the end of the piece.

52



Fig.34

Notice how the end of the piece resembles the beginning in reverse. The strings

fade away and then the maracas stop. We are where we started off: noise and then

silence. This points to an arch or wave that spans the whole piece and that I will

discuss in the next section.

53



VI. About the Form III

As I mentioned in the Introduction, from the origins of Spectral Music, great

emphasis is placed on perception. It follows that all elements of the piece, including

the form, are to be understood in terms of their perception rather than their

construction. From this point of view, our rst perception of the form is at a very local

level; in other words, our grouping tends to be more by proximity.

In About the Form II, I explained how the rst unit (sections A through D)

connected two moments of stasis. Also, we saw how this big unit could be divided into

smaller sections that were also the connections between moments of relative stasis. In

other words, similarly to tonality, form in this piece is constructed by the alternation of

stasis (tonic), movement away from stasis (dominant) and stasis again (tonic).

Taking a step back after analyzing each of the three units separately, Ipropose the following form based on grouping by similarity.

As you can see in gure 35 (following page), the piece is divided into three

large units (A-D, E-H and I) that correspond to bigger moments of stasis and also to

completions of a process. This process, that metaphorically emulates a lter, involves

creating a sound mass, exploring the sound mass and, nally, ltering it. Figure 35

shows the process in these three steps and where in each unit this happens.

The similarities between the units are clear. A, E and I create a mass by similarmechanisms: A by ring modulation, E with multi-phonics and I with echoes. B and F

solidify the mass and are both connected to their previous section by elision. C, G

and the middle of I explore the mass in ways that emulate a lter. Finally, D, H and

the end of I lter the sound mass in both the frequency and time domains.

54



F i g . 3 5

55



All that remains is J. When discussing it in the previous section, I mentioned that

J was connected to A. You may recall that J brings up the maracas (by omitting them

and then bringing them in again), repeats the wave design of A (with complex ute

sound included) and nally nishes with the maracas alone (exactly how A started).

The obvious conclusion is that the piece has an arch (or wave) form from noise tosomething-else and back to noise.

When discussing section A, I showed how the smaller waves went from

noise to pitch to noise. They also went from upper partials (metaphorical noise) to

fundamental to upper partials. At the largest scale we are focusing on now, these

two poles hardly apply since our arrival to pitch at A and our return to noise at J are

extremely quick in comparison to the overall length of the piece. However, since our

perception of denite pitch is a function of the harmonicity of a spectrum43, we can

take harmonic and inharmonic spectra as metaphors for pitch and noise respectively.

Looking back at section A, we see that the pitch content conformed to a C#1

(each wave descended further in the overtone series bringing us closer to C#1).

When discussing I, a reduction of the pitch content of m.27-30 (gure 27), showed the

undulating threads were also exploring a C#1 spectrum. The rest of the sections were

spectrally ambiguous except for G. As seen in gure 19, section G is the only section

that has block structures that change in all instruments at once; as in a showcase of

pitch collections that are to be understood in a purely vertical sense. The reduction

of the same section seen in gure 20 shows how the pitch collections move fromharmonic, to very inharmonic and back to almost harmonic. In a way, it is a summary

of the entire movement to point our attention in this direction.

In the same way that B through F got progressively more inharmonic (or

noisier), H and the rst part of I get progressively more harmonic. Figure 36

shows two bands in terms of harmonicity: the top one represents the timbre of

the instruments (how noisy the sound is) and the bottom one represents the pitch

collections.

43 A harmonic spectrum (i.e. spectrum where all the partials are integer multiples of the fundamentalfrequency) reinforces the perception of the fundamental pitch. An inharmonic spectrum obscures theperception of a single fundamental pitch.

56



Fig.36

A G I JB C D E F H

maracas maracasensemble

C#1 inharmonic C#1

noise noisepitch

pitch noise pitch

timbre

collections

From this point of view, the piece describes two out of phase oscillations between

noise and pitch: one at the level of individual instrumental timbres and the other

at the level of sound masses. The rst one is real while the second is metaphorical.

This brings forth one of spectral music’s greatest ambiguities and challenges: is it a

physical model or a metaphor?

57



VII. Bibliography

Bayer, Tildy. “Music Inside Out: Spectral Music’s Chords of Nature.” Found at: http://www.byz.org/~tildy/spectral.html

Bündler, David. “Gerard Grisey” [Interview], 1996/rev.2001. Found at: http://www.angelre.com/music2/davidbundler/grisey.html

Castanet, P.A. “Gérard Grisey and the Foliation of Time.” Trans. Joshua Fineberg.Contemporary Music Review Vol. 19, Part 3 (2000), pp. 29-40.

Fineberg, Joshua. “Guide to the Basic Concepts and Techniques of Spectral Music.” [ApendixI] Contemporary Music Review Vol.19, Part 2 (2000), pp.81-113.

Grisey, Gérard. “Tempus es Machina: a composer’s reections on musical time.”Contemporary Music Review Vol. 2, Part 1(1987), pp. 239-275.

Huron, David. “Review of Albert S. Bregman’s Auditory Scene Analysis: The PerceptualOrganization of Sound.” Psychology of Music Vol. 19, No.1 (1991), pp.77-82.

Kane, Brian. “L’Objet Sonore Maintenant: Reections on the Philosophical Origins ofMusique Concrète.” Spark , February 18th (2005), pp. 58-60.

London, Justin. “How to Talk About Musical Metre.” (2006) Found at: http://www.people.carleton.edu/~jlondon/UK%20PPT/HTTAM%20Web%20Version.ht m

McAdams, Stephen. “Psychological Constraints on Form Bearing Dimensions in Music.”Contemporary Music Review (1989). Found at: http://mediatheque.ircam.fr/articles/textes/McAdams89a/

McAdams, Stephen and Albert Bregman. “Hearing Musical Streams.” Computer Music Journal Vol. 3, No.4 (1979), pp.26-43.

Murail, Tristan. “The Revolution of Complex Sounds.” Trans. Joshua Cody. ContemporaryMusic Review Vol.24, No. 2/3, April/June 2005, pp.121-135.

Murail, Tristan. “Scelsi and L’Itineraire: The Exploration of Sound.” Trans. Robert Hasegawa.Contemporary Music Review Vol. 24, No. 2/3, April/June 2005, pp.181-185.

Presnitzer, Daniel and Stephen McAdams. “Acoustics, Psychoacoustics and Spectral Music.”Found at: http://www.zainea.com/psymusic.htm

Rose François “Introduction to the Pitch Organization of French Spectral Music ”

felixpastor ethers (1)

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