The concept of re-synthesizing instrument spectra has been thoroughly explored

by spectral composers throughout the past three decades. The idea of re-

synthesis is based on sonographic analyses of the spectra of (acoustic)

instruments. A composer studies the characteristics of specific aspects of an

instrument's spectrum, analyzing the overtone structure of a specific pitch. This

includes determining the existing partials and their respective intensities, and

existing formants and their amplitude(s). Since these elements define the timbre

of an instrument, this technique has great potential - apart from the organization

of pitches - in the parameter of orchestration and the composition of timbre. For

example, an orchestra can "imitate" the sound of a cello pizzicato, a pedal-tone

from a horn, or a trumpet tone played with a mute, thereby becoming a "new

instrument" itself.

The technique of re-synthesizing (instrument) spectra has often been used

by French spectral composer Tristan Murail (b. 1947) to form the basis of pitch

organization for a whole work as well as for certain sections of a piece. The

most striking characteristic of Murail' s musical aesthetic is his concept of a

continuum of 'harmony-timbre' 14. For Murail, both parameters are inseparably

linked with each other and thus become hybrid structures that combine the

characteristics and qualities of the two initial concepts. It is for this reason that

Murail makes frequent use of re-synthesis, since such operations provide the

composer with exactly those hybrid structures. Here, the timbral characteristics

of the re-synthesized spectra are mutually conditional to the construction of

I harmony.

A second maj or aspect of Murail' s individual spectral aesthetic is his conviction,

that also harmony and form should be strongly interlinked. In other words,

harmony generates the formal course of a work resulting in further hybrid

structures defined by harmony and form. This idea illustrates Murail' s

connection to the tradition of tonal western art-music, which also shows strong

links between harmony and form, but at the same time it also points out the

composer's disapproving attitude towards atonal composition philosophies. For

Murail, harmony is the reference point for virtually all other musical parameters,

which means that a logic, meaningful and perceivable harmonic language is a

necessity for a successful and valuable composition.

A third aesthetic concept of great importance to the composer is the idea of

continuity. The "permanent" state of flux is a typical characteristic of Murail's

music, since most of his works are predominantly made of processes, which the

composer describes as 'sculpting sonic material'.15 This does not mean that the

music is entirely free of interruptions or irregularities, but the works as a whole

are strongly directional which is owed to the consequent and meaningful

interlinking of the aforementioned musical parameters.

These general observations about Murail' s composition philosophy can be

verified by analyzing his work Desintegrations. Written in 1982/83, the piece is

scored for seventeen instruments (2fl, lob, 2el, 1bsn / Ihm, ltr, ltromb / 2perc,

pno / 2vl, 1vIa, 1vel, 1db) and tape. The title mainly refers to the predominant

musical processes in the work, which are the (mostly gradual) transitions from

harmonious spectra to inharmonious ones and vice versa. The transfer of certain

partials to another octave within a spectrum could therefore be described as the

"disintegration" of pitches. Other techniques of disintegration are the

'exaggeration,16 of particular partials through the means of orchestration, or the

use of other filtering techniques. In addition, the title could also refer to the

15 op.cit, 123160p.cit,141

processes of extracting melodies or melodic fragments from a spectrum, when

overtones are presented horizontally and in different (not "natural") orders.

The work Desintegrations is subdivided into eleven sections, each of them

describing the transition from a harmonious spectrum to an inharmonious or

vice versa. The organization of harmonic progression, however, is based on a

variety of different techniques, as the following analysis will show.

• Re-synthesis

• Ring-modulation

• Frequency shifting (linear and non-linear)

• Frequency modulation (FM)

• Harmonic distortion

The following paragraphs will give detailed analyses of representative passages

to illustrate how and to what effect these techniques are used by Murail in this

particular work.

The harmonic material from the extensive opening section of Des integrations is

entirely based on the results of the spectral analysis of a Cl from the piano. This

sonographic analysis revealed - among other aspects - the formants of the

analyzed sound. In other words, Murail obtained the information on the intensity

of the resonance of each partial within the analyzed spectrum. The composer

was particularly interested in the spectrum's formants (loudest areas of

resonance), since the individual timbre of the low piano sound is defined by the

order and intensity of the formants.

Murail's spectral analysis1? showed the following results: there are six fields of

formants among the first forty partials of the spectrum based on a C 1 of a piano.

• Partials 2-7, with a strong emphasis on 2 and 7

• Partials 9-13, with an emphasis on 11

• Partial 15

• Partials 17-23, with a strong emphasis on 21

• Partials 27-30, with an emphasis on 29

• Partials 35-38

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The composer used this information to re-synthesize the spectrum and timbre of

a low piano sound as the underlying concept for the opening section of

Des integrations .

[§]1312

Example 6 shows the first twelve aggregates18 of section 1. The results of the

sonographic analysis have been applied to two different spectra, one with the

fundamental BflatO and the other with the fundamental Csharp2 through the

means of transposition. This way, the concept of re-synthesis is not only used as

a technique of imitating the instrumental model; in addition it also produced a

unique variant - the timbre of a particular spectrum eCl) transferred to two

different fundamentals at the outset of the piece.

Murail made use of this material by introducing a continuous shuttling back and

forth between the two spectra, a process, which dominates the whole first

section of the piece. An analysis of the overtone structure of each aggregate

shows, that the composer exclusively used partials from the zones of formants of

the analyzed piano spectrum. Each partial located outside the six zones of

formants (partials 8, 14, 16,24-26,31-34, 39,40) is therefore left out. The

example also illustrates, that all twelve aggregates are harmonious.

Over the course of the section, Murail intuitively explores the two different

spectra. Each aggregate reappears in a slightly different form, e.g., partial 11

from aggregate I is left out in aggregate III whilst being reintroduced in

18 The term 'aggregate' describes an excerpt from a spectrum. Such an excerpt is a hybrid structure since it canbe perceived both as a chord (harmony) and as a sonority or a timbre.

aggregate V, where the thirty-sixth partial is left out instead. Notes are

constantly added or removed while the overall structure of each aggregate,

however, remains almost unchanged, which explains the subtlety of change that

the composer applied to the harmonic and timbral progressions.

The fundamentals of the two spectra (BflatO and Csharp2) are introduced with

the first four aggregates, but are then consequently left out only to be imagined

(added) by the listener instead. This phenomenon hints at Murail' s subtle and

sophisticated concepts of perception and his reflection on psycho-acoustics.

Even though the fundamentals of each respective spectrum are left out, the

relationship and the distance between the two spectra remain clearly audible.

This is due to the fact, that the predefined range of each spectrum used for the

aggregates is almost the same for both spectra (Bflat: partials 1 to 36; Csharp:

partials 1 to 28). This means, that the abstract distance from the interval of the

tenth separating the two fundamentals, is constantly apparent, although the

fundamentals are actually not being played.

It is to a great extent the sudden disappearance of the two fundamentals which

strikingly points out the potential of re-synthesizing instrumental sounds: the

tape "extracts" and reconstructs the piano's timbre, which is usually hidden

behind the initial piano note (fundamental), and then heightens the listener's

awareness of it. In other words, the "subsidiary" parameter timbre becomes

harmony without losing its former timbral identity. This phenomenon can serve

as an example for Murail's concept of 'harmony-timbre'.

There are two further layers of differentiation applied to the re-synthesis of the

piano spectrum in section 1. One of them is achieved through the means of

orchestration. The sounds on tape, which contains the complete pitch material of

all aggregates in section I, are supported by the acoustic instruments. These

instruments filter or exaggerate certain partials from each aggregate. In

aggregate I, for instance, partials 7, 20, 29, and 36 are doubled by flute,

clarinets, and percussion, whereas in aggregate III partials 7, 13, 29, and 36 are

doubled. Murail enhances and reinforces certain formants within each aggregate

thereby adding another dimension to the subtle changes of harmony-timbre. A

further heightening of the complexity of sounds is achieved through the

harmonic overlapping of the acoustic instruments. In bar 5, for instance, partials

7and 11 from aggregate II are still sustained by the flutes, although the next

aggregate based on BflatO has already been introduced by tape, clarinets, and

percussIOn.

Another (inevitable) phenomenon of sound-enrichment is created through the

addition of the inherent spectra of each acoustic instrument. These spectra

increase the complexity of the composed sounds, but at the same time they

thwart the concept of an undisturbed instrumental re-synthesis as executed by

the tape, which makes the audible harmonic results ambiguous to a certain

degree. It should also be remarked in this context that due to practical reasons

the microtonal notation for the acoustic instruments has been limited to quarter

tones.19 On the one hand the results obtained contradict and potentially disturb

the originally calculated harmonic structures played by the tape. On the other

hand, however, this compromised notation also generates a variety of complex

sounds that can be of great interest to the composer.

The second layer of differentiating the actual execution of the re-synthesis is the

dynamic distinction between the partials within each aggregate performed by the

tape. The dynamic hierarchy follows the hierarchy of the formants: the strongest

formants (partials 7, 11) are playedfortissimo, the second-strongest (12, 13,21)

forte, the third-strongest (5, 10, 19, 29) mezzo forte etc.20 Here, the electro-

acoustic sounds actually imitate the timbre of the low piano spectrum.

19 Murai1 even abandoned all microtones in section VII due to the fast tempo.20 op.cit, 213

As was mentioned before, there are further techniques used by Murail to

organize harmony in the first section of Des integrations . One moment of great

importance is the superposition of the two spectra in bar 30.

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[§]Bar 38

13

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The first part of Example 7 shows the merging of two aggregates from the

progression described before. The resulting aggregate incorporates excerpts

from the two different spectra whose respective characteristic qualities become

assimilated by the unified outcome. The sound heard in bar 30 is ambiguous in

terms of its structure: an analysis is required to filter out the two components

that form the final aggregate. Therefore, the spectrum cannot be considered to be

a harmonious one any more, so that at this point the previously explored

progression of harmonious aggregates is interrupted by the composer. The final

bars of section I eventually present a quick evolution from harmonicity to

inharmonicity.

The second part of Example 7 shows the final aggregate of section 1. Again, the

sound as a whole is ambiguous, but the analysis shows, that both subordinate

aggregates already contain inharmonious structures. Partials 17 and 21 from the

BflatO spectrum as well as partial 13 from the Csharp2 spectrum have been

transposed down by an octave, while partial 19 from the latter spectrum has

been transposed down by even two octaves.

In summary it can be said, that Murail applied three essential methods to

organize harmony in the first section of Desintegrations:

• Partial re-synthesis of an instrumental spectrum and its transpositions

• Creation of a double-spectrum through the superposition of

aggregates

• Transforming harmonious aggregates into inharmonious ones

There are many examples from Desintegrations or other works by Murail that

could be chosen to discuss this last aspect. The exploration and interaction of

harmonious and inharmonious structures is probably the most frequently used

technique in spectral music. This is not surprising since this concept is strongly

related to that of "consonance and dissonance" in non-spectral music: it is to a

great extent its equivalent.

The second half of section III (bars 169 to 192) introduces a further technique to

generate harmony, which Murail frequently uses in his works: Frequency

shifting. This technique resembles that of traditional transposition since both

concepts describe a shifting of notes into a previously specified direction. The

major difference, however, lies in the fact that transposition is a linear process

whereas frequency shifting is non-linear (transposition refers to the shifting of

intervals, whereas frequency shifting deals with abstract frequencies).

Transposition by a semitone Frequency shift bv 33 Hz

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The example illustrates the difference between transposition and frequency

shifting; the semitone shift from C5 to H4 (33 Hz) was chosen as the reference

point for the frequency shifting.

This phenomenon of "non-linear transposition" can be observed in section III of

Des integrations .

II III IV VEx. 8 Frequency shifting in Section III (bars 169-192)

Example 8 gives an overview of the basic harmonic progression in bars 169 to

192. At the outset Murail introduces a harmonious five-tone aggregate based on

the fundamental Fl. The composer intended to compose a gradual frequency

shift that would take the course of the bass line as the point of reference. This

shift was supposed to cover the distance between the C3 of the first and the

Dflat2 of the final aggregate. Due to considerations of duration and form, this

process had to be divided up into ten steps. The distance between the

frequencies of C3 and Dflat2 amounts to 61.5Hz, so for each step of the

frequency shifting all frequencies of an entire aggregate had to be lowered by

6.8Hz. The results, however, did not please the composer (there was, for

instance, an F-major triad among the resulting aggregates), so Murail decided to

recalculate the whole process.21 This time, 25 steps were calculated (each

aggregate lowered by 2.56Hz per step). Murail then intuitively chose the ten

aggregates from the collection of 25, which would eventually be used in the

This variant of constructing a harmonic progression based on frequency shifting

explains the irregularities of the harmonic progression shown in Example 8.

Aggregates separated by very small frequency shifts (e.g., I to II) alternate with

those separated by much larger shifts (e.g., VIII to IX), which means that a few

aggregates between VIII and IX have been left out. This approach, which could

be described as a merging of system and intuition, is very typical for Murail' s

way of composing, where the composer's ear always controls the results

obtained from technical and mathematical operations.

In addition, this excerpt is a good example for Murail' s conviction, that neither a

'totally predictable nor a totally unpredictable discourse ,22 are desirable for a

composition, and that 'structural predictability needs to be contradicted

constantly by some type of unpredictability within the discourse' .23 By

"filtering" the results he gained from his calculations through his own musical

intuition, Murail created subtle moments of irregularity within the continuity of

the macro-process (here: the frequency shifting), which precisely generate the

effect the composer was interested in.

Other than in section I, where the transformations from harmonious to

inharmonious spectra were deliberately composed, in section III these

transformations are literally inevitable. This is due to the fact, that frequency

shifting is furthermost a mathematical operation (each partial is shifted

individually!), which does not consider the construction of the various spectra.

In other words, the detailed structure of the resulting aggregates is of an entirely

theoretical nature.

Example 9 shows the overtone structure of the first and the last aggregate from

Example 8:

22 op.cit, 21723 op.cit, 216

It becomes obvious, that the non-linear transpositions of the five pitches of each

aggregate have nearly entirely destroyed the previously harmonious structure of

the spectrum, which led to a final aggregate whose structure is almost

completely inharmonious.

A closer look at the score discloses further elements that take place

simultaneously to the frequency shifting described above. The processing of the

harmonic material has become much more complex than in section I, where

there were mainly homophonic structures rather plainly presented by the electro-

acoustic sounds. In this example from section III the material is distributed to

both the whole ensemble and the tape. The partials of each aggregate are

permanently interchanged by the means of orchestration (e.g., the "bass notes"

are shared by bass clarinet, bassoon and trombone), and there is a great amount

of figuration and inner motion (e.g., trills and melodic gestures). Furthermore,

there is an extensive amount of harmonic overlapping between the aggregates, a

concept which Murail had already introduced in section 1. In addition, the

textures are sometimes "filled up" with additional (distorting) pitches that are

not part of the underlying harmonic progression of frequency shifting. This

increasing amount of complexity is mainly due to the conceptions on the macro-

level (the third section serves as part of a larger build-up to the climax in section

VIII). It is on the one hand for this reason that the music gains additional layers,

but on the other hand this is also another way to avoid harmonic and structural

monotony and predictability.