121
DOI: 10.4312/mz.58.2.121-153
UDK 781.63:781.5:004
The Role of Orchestration in Shaping Musical 
Form: Theory and Practice of a Methodological 
Proposal and Its Computational Implementation
Charles de Paiva Santana,
a 
Didier Guigue
b
a
Aix-Marseille University, CNRS, PRISM, Marseille
b
Federal University of Paraiba
ABSTRACT
We introduce a method for computer-assisted analysis of orchestration. We also look into the 
role that texture and orchestration have in structuring musical form. The method comprises a 
numerical representation, a hierarchy of ‘textural situations’ and measures for heterogeneity, 
diversity and complexity of orchestral-textural configurations.
Keywords: musical analysis, orchestration, musical texture, computational musicology, audio 
analysis
IZVLEČEK
Predstavimo metodo za računalniško podprto analizo orkestracije. Pregledamo tudi vpliv 
teksture in orkestracije na izgradnjo glasbene oblike. Metoda vključuje številčni prikaz, 
hierarhijo »teksturnih situacij« in merila za heterogenost, raznolikost in kompleksnost or -
kestrsko-teksturnih konfiguracij.
Ključne besede: glasbena analiza, orkestracija, glasbena tekstura, računalniška muzikologija, 
avdio analiza
MZ_2022_2_FINAL.indd   121 MZ_2022_2_FINAL.indd   121 10. 02. 2023   13:52:01 10. 02. 2023   13:52:01

muzikološki zbornik • musicological annual lviii/2
122
1 Orchestration, a Challenge for Musical Analysis
From the end of the nineteenth century, composers began to adopt increas -
ingly systematic orchestration strategies that tended to actively involve this 
dimension in the structuring of the work, and thus in the expression of musical 
thought and its consequent perception.
1
Makis Solomos
2
 observes that Rimsky-Korsakov, in his Treatise on Orches-
tration of 1891, insists on the use of instruments “in relation to the categories 
of écriture.” Solomos cites, for instance, a paragraph in which Rimsky-Korsakov 
discusses “the amplification [...] of sound qualities, a technique by which the 
resonance of two different groups (or the different timbres of a single group) is 
contrasted [...] to transform a simple timbre into a complex timbre.”
3
Our objective is to establish and evaluate, through experimental applica -
tions, a theory and method of analysis that would, by hypothesis, make it pos -
sible to evaluate the impact of these techniques on formal dynamics. Even 
briefly, Walter Piston, in his book on orchestration published in 1955 and now 
a classic, underlines the relevance of such an undertaking:
The objective in analysis of orchestration is to discover how the orchestra is used as a me -
dium to present musical thought. [...] It is a means of studying how instruments are com-
bined to achieve balance of sonority, unity and variety of tone color, clarity, brilliance, 
expressiveness, and other musical values. Ultimately, the analytical process shows the dif-
ferences in orchestral style between various composers and periods.
4
Piston then lists the steps by which he believes a method of orchestration 
analysis should be carried out.
We can also mention the monumental Traité that Charles Koechlin published 
at the same time.
5
 Based exclusively on his immense empirical knowledge, Koech -
lin advances as far as possible in the systematization of the relationships between 
the various acoustic parameters that define the sound of an instrument, in particu -
lar volumes, intensities, and densities, for which he manages to constitute gradual 
“scales” that make it possible to put in a situation of relative comparison various 
instrumental configurations, an approach unprecedented in this field.
6
1 Pioneers preceded them, who formed a genealogy that had not yet been studied extensively, 
which, starting as far back as Rameau, reached Debussy, passing through the Mannheim 
School, Gossec, Haydn, the post-revolutionary musical practices in France (Cherubini, Méhul), 
Beethoven, Berlioz, Meyerbeer and Wagner. The tool we present here aims to help analyze the 
history of the evolution of orchestration as an active dimension of composition.
2 Makis Solomos, De la musique au son: L’émergence du son dans la musique des XXe-XXIème siècles 
(Rennes: Presses Universitaires de Rennes, 2013).
3 Ibid., 31.
4 Walter Piston, Orchestration (New York: Norton, 1955), 355.
5 Charles Koechlin, Traité de l’orchestration en quatre volumes (Paris: Max Eschig, 1954).
6 Ibid., 288.
MZ_2022_2_FINAL.indd   122 MZ_2022_2_FINAL.indd   122 10. 02. 2023   13:52:01 10. 02. 2023   13:52:01

C. de Paiva Santana, D. Guigue: The Role of Orchestration in Shaping Musical Form
123
In 1985, the Editions Moeck published Instrumentation in der Musik des 
20. Jahrhunderts: Akustik – Instrumente by Walter Gieseler, Luca Lombardi 
and Rolf D. Weyer.
7
 Unlike traditional treatises, this book understands and 
approaches instrumentation through the concrete study of the acoustics of 
instrumental and vocal sounds, considering the manipulation and organiza -
tion of the sound material as an integral and interactive part of the composi -
tional process – and not as an isolated activity. The extraction of instrumenta -
tion data from a large number of contemporary representative works is not 
intended to establish a catalogue of empirical prescriptions, but rather to 
provide a basis for understanding the techniques of producing “sound colors” 
(Klangfarben). Instrumentation as a compositional technique is approached 
by conceptual categories of compositional results, such as comprehensibility 
(Fasslichkeit), distinctness ( Deutlichkeit), intention ( Absicht) ..., an approach 
that breaks with the tradition of the genre and which moreover allows the 
incorporation and combining of any sound resources, not only of those pre -
sented in that book.
8
As for the most innovative part of the book Sonic Design,
9
 written about ten 
years earlier, it resides in the project to develop a theory of “sound color” and 
orchestration. The authors’ criticism of the “common practice” of the musical 
analysis of their time is striking and reveals their confidence in the validity of 
their approach:
Analysis of sonic design adds a new dimension to musical understanding. It provides a 
rationale for such features as instrumentation and orchestration, registration
10
 and dy-
namics
11
 – crucial aspects of music, which, until now, have largely escaped analytical un-
derstanding. Sonic design is a mode of analysis that accounts for the complete sound of mu-
sic.
12
[...] Interference phenomena (especially beats), tone modulation, and noise, regarded 
so often in the past as negative or irrelevant properties of sound, are now found to be 
necessary, positive features of sound experience. Indeed, they are fundamental constructive 
elements of music [...]. Ultimately, it must be acknowledged that those modes of analysis 
and understanding that ignore the supranotational elements
13
 and the total sound of music 
are limited and (to say the least) often misleading.
14
7 Walter Gieseler, Luca Lombardi, and Rolf-Dieter Weyer, Instrumentation in der Musik des 20. 
Jahrhunderts: Akustik, Instrumente, Zusammenwirken (Celle: Moeck Verlag, 1985).
8 Ibid., 119.
9 Robert Cogan, and Pozzi Escot, Sonic Design: The Nature of Sound and Music (New Jersey: Pren -
tice-Hall, 1976).
10 I.e. the distribution of sounds between different regions of the instrumental range.
11 In our approach, we prefer to call them intensities.
12 In italics in the original.
13 By this they mean elements that are not explicitly codified in the score but are activated at the 
time of the performance of the work.
14 Cogan, Sonic Design, 397.
MZ_2022_2_FINAL.indd   123 MZ_2022_2_FINAL.indd   123 10. 02. 2023   13:52:02 10. 02. 2023   13:52:02

muzikološki zbornik • musicological annual lviii/2
124
Aware that their undertaking was taking them to the “limits of our present 
knowledge” the difficulties they experienced show how far we have progressed 
on certain technical aspects – for example, in the analysis of the timbre of the 
instruments and the various factors involved in the constitution of their sound 
identity, data that are now widely available, but whose insufficiency was cru -
elly felt by these authors at the time
15
 – although the practice of orchestration 
analysis has not become so widespread as to occupy the space they called for in 
the range of tools that should nowadays be commonly used in musical theory, 
composition or analysis.
In a way, our intentions inherit these insights and pursue a similar ob -
jective. In this article, we present an experimental theory of orchestration 
analysis and a practical method of application, followed by a description of 
our tool to assist in this analysis developed for the SOAL library in Open-
Music. In a way, our intentions inherit these insights and pursue a similar 
objective.
SOAL is intended to be useful for a range of analytic purposes, in situa -
tions where a ‘top bottom’ approach is more or equally pertinent that a ‘bot -
tom-up’ one. The root of SOAL background concept is the compound sonic unit, 
technically defined as the combination and interaction of musical ‘primary’ 
components (a collection of pitches) with ‘secondary’ components – namely 
intensities, ranges, registering, densities, modalities of statistical distribution 
of pitches or other low-level elements, e.g. deviations, entropy and others. Be -
ing modular, any other ad hoc analytic component can be add at any time. The 
idea is to infer musical structures by comparing the relative sonic qualities of 
a sequence of such units, which are ranked onto a ‘relative complexity’ vector. 
As the reader will see, our proposal will present new functions for SOAL that 
are able to integrate the orchestration dimension into the arsenal of analytical 
tools already proposed.
Our method is intended to systematically elucidate how orchestration 
strategies come into play in the formal structure of a work, and what would be 
its impact in all the dimensions of the compositional practice that contribute to 
the construction of a musical form based on sound. The field of application can 
range from the first symphonists to the most recent large-scale productions.
The methodology is based on the information provided by the composer 
in the score. It involves both quantitative and qualitative evaluation of the 
various instrumental configurations by means of which the composer articu -
lates a sound dynamics over time, and the way in which they are organized to 
create more or less dense or complex textures. To do this, we use “Partitional 
Analysis,” which provides the agglomeration and dispersion indices of the in -
strumental parts.
15 Ibid., 365.
MZ_2022_2_FINAL.indd   124 MZ_2022_2_FINAL.indd   124 10. 02. 2023   13:52:02 10. 02. 2023   13:52:02

C. de Paiva Santana, D. Guigue: The Role of Orchestration in Shaping Musical Form
125
In a second stage, if there is one, an audio recording of the work is used, 
which is analyzed in order to assess the concrete effect of the written prescrip -
tions, and to see to what extent their impact on the form reflects it.
Finally, it is suggested how a synthesis of these two approaches could be 
achieved. We are of course aware of the difficulty of addressing a field whose 
“rational and scientific approach is still to be done”, and for which “the obsta -
cles that must be overcome in its analysis and formalization are considerable”, 
especially when dealing with music from the second half of the twentieth cen -
tury, for which “spectral and noisy revolutions have reshaped the relationship 
with traditional orchestration.”
16
To illustrate our approach in concrete terms, we have chosen, for this pub -
lication, to concentrate most of the musical illustrations on Webern’s Variations 
Op. 30 (1940), which as we know mark a fundamental milestone in the consol -
idation of serialism as a composition technique. It is the high level of “timbral 
chromaticism” of its orchestration that seemed to us to provide a privileged 
field for experimentation.
17
 A sound fragmentation pushed to the extreme – 
because it sometimes goes down to the note-for-note – offered us the possibil -
ity to sharpen the tools under development and to test their sensitivity to this 
dimension of the compositional technique. However, we are simultaneously 
experimenting on other corpora, including Beethoven, Berlioz and Rameau, 
as well as, Murail and other contemporary composers closer to us. However, 
in order to save on reading and consulting scores, we have preferred to limit 
ourselves to asking the reader to follow us on an excerpt from this opus 30, in 
this case bars 56 to 82 of the Edition Philharmonia.
The remainder of this document is organized as follows: the following sec -
tion elaborates step by step on the proposed model, illustrating it with real mu -
sical examples; the third section describes the implementation in OpenMusic. 
The fourth section outlines the analytical conclusions that should be possible 
to draw from this method and addresses the question of the future interaction 
between the analysis of written prescriptions and that of the sound recording 
of the work.
2 A Model for Analyzing Orchestration
We conceive this project as being part of a global project of analysis based on 
“sonority,” or, more precisely, on the concept of a compound sonic unit, a term 
that identifies, at a given moment, a certain sound state, a “instantaneous 
16 Yann Maresz, “Pour un traité d’orchestration au XXIe siècle,” L’Etincelle, no. 11 (2006).
17 Jinho Kim, “Représentation et analyse musicale assistée par base de données relationnelle de la 
partition des variations pour orchestre op. 30 d’Anton Webern: Vers un système d’analyse musi -
cale assistée par base de données relationnelle” (Doctoral Dissertation, Université Paris IV, 2006), 
426 and 434.
MZ_2022_2_FINAL.indd   125 MZ_2022_2_FINAL.indd   125 10. 02. 2023   13:52:02 10. 02. 2023   13:52:02

muzikološki zbornik • musicological annual lviii/2
126
synthesis of a certain number of components [of the compositional tech -
nique] that act and interact in complementarity.”
18
 In other words, what we 
call at the bottom of this flowchart the “Orchestration Relative Complexity” 
will have to or will be able to interact with other aspects of the compositional 
technique that we have already modeled and implemented in the SOAL 
library, such as achronic and diachronic relative densities, harmonicity and 
sonance rates, periodicity, relative entropy, etc.
19
 The objective of this data 
set is to systematize the qualification of a compound sound unit in all aspects 
relevant to sound, including that of the orchestration dimension, when it plays 
a structuring role.
The orchestration is evaluated on two levels. First, we identify the prescrip -
tions recorded by the composer in the score. We have formalized them with -
in a hybrid component – LSS Relative Complexity in the flowchart – which 
counts the various instrumental combinations used during the work and quali -
fies them according to the way in which the instruments “agglomerate” or on 
the contrary “disperse” to generate more or less complex textures. In a second 
part – on the right side of the flowchart – the audio files of these same configu -
rations are examined using ad hoc statistical and psychoacoustic descriptors 
in order to assess the concrete effect of the prescriptions, and to see to what 
extent their impact on the form reflects it. The measurement of the interaction 
between symbolic prescriptions and concrete sound results is given by the syn -
thetic component Orchestration Relative Complexity.
In other words, it is a question of approaching the object of study at the 
same time at the abstract/symbolic level of the written code and at the concrete 
level of its effective sound realization, two angles of approach whose conver -
gence and synchrony we feel will not always be the case. The objective is to 
make the model capable of withstanding these possible dichotomies as intrin -
sic to the orchestration dimension, since the endless uncertainties that can arise 
in the performance of a work for orchestra in concert situations have never 
inhibited composers in their desire to fix on paper the smallest details of the 
performance, as if they were as objective and stable as a metronomic indication.
2.1 Score Analysis: Identification of Instrumental Configurations
2.1.1 The Sonic Resources Index
For the first part of the model, the analysis at the symbolic level, the process 
consists in identifying, in the score, all the sound configurations selected 
by the composer. To do this, we first establish a Sonic Resources Index (SRI), 
18 Didier Guigue, Esthétique de la sonorité: L’héritage de Debussy dans la musique pour piano du XXe 
siècle (Paris: L’Harmattan, 2009), 40.
19 Ibid., 52 and 391; Didier Guigue, “Sonic Object Analysis Library: OpenMusic Tools for Analyz -
ing Musical Objects Structure,” Version 5.0. (MacOS, 2016).
MZ_2022_2_FINAL.indd   126 MZ_2022_2_FINAL.indd   126 10. 02. 2023   13:52:02 10. 02. 2023   13:52:02

C. de Paiva Santana, D. Guigue: The Role of Orchestration in Shaping Musical Form
127
which is the non-ordered set of sound resources that are deployed during the 
work. It takes the form of a textual list corresponding to the nomenclature 
of sound producing sources mentioned or described. These are, in most cases, 
and always in the traditional repertoire, the instrumental parts indicated at 
the top of the score ( Orchestral Parts), to which is added a list of all the in -
formation, textual or symbolic, which aims to produce a particular sound 
for a given instrument or desk, and which the composer mentions, either in 
incipit, for a permanent effect, or in the score during play, for specific effects 
- which is probably the most frequent case. This may include, in particular, 
the various modalities of sound modification by mechanical means (mute 
or other), electroacoustic means (distortions, transformations by digital pro -
cesses …), or specific techniques ( flatterzung, col legno battuto, etc.). In some 
circumstances, the solo and divisi indications of a desk may be considered 
sound decisions and are therefore included in the index. In the flowchart, 
this information is defined as Instruments, Timbres & Effects. The listed Sound 
Resources can be constituted, in addition or alternately, by ad hoc groups of 
instruments or objects producing sounds,
20
 or by themes, patterns, motifs.
21
 
For the analysis of Hermeto Pascoal’s Sinfonia em Quadrinhos (1986) made 
by our collaborators,
22
 an enumeration by group and topics proved more 
relevant, since the composer conceived his orchestra by blocks of complex 
sounds, very rarely isolating one or another instrument.
The index therefore encompasses the universe of sounds from which the 
composer will draw the subsets that will mold the sound plastic of the work 
over time. Part of Webern’s SRI list of Variations Op. 30 is shown in the Table 
below. It is noticeable that there are two different Sound Resources for the 
20 In future developments of the model, it will be necessary to be able to systematize the inclusion 
of noninstrumental sounds in the index, whether they have been fixed on a support or whether 
they are produced in real time, from an acoustic or digital source. To do this, it will be necessary 
to group them into distinct sound categories according to their physiognomy. Each of these cat -
egories will be incorporated into the index as an additional resource. For an overview of the pos -
sible techniques for this classification, see Stéphane Roy, L’Analyse des musiques électroacoustiques: 
Modèles et propositions (Paris: L’Harmattan, 2004). However, the reader should keep in mind that, 
in this part of the analysis, knowledge of the concrete sound characteristics of the resources is not 
taken into account.
21 The concept of Sonic Resource is quite close to Tagg’s “participant,” which “refers to the source 
(the oboe, lead vocals, kick drum track, scratch sample, alto voice, etc.) that participates in the 
generation of a strand [...] and/or a layer.” Participant is a useful notion in music semiotics be -
cause it acknowledges the “[...] music as socially constructed activity.” In Tagg’s model, a “strand” 
is a wider and not so euroclassical-connoted substitute for “voice,” while a “layer” roughly matches 
our Local Sonic Setup. See Philip Tagg, Music’s Meanings: A Modern Musicology for Non-Musos 
(New York and Huddersfield: Mass Media Music Scholars’ Press, 2012), 447 and 449.
22 For a first approach to this work see Didier Guigue, and Thiago Cabral, “Entropia e Textura Rít -
mica na Sinfonia em Quadrinhos de Hermeto Pascoal,” abstract, paper presented at XXVI Con-
gresso da Associação Nacional de Pesquisa e Pós-Graduação em Música (22–26 August, 2016), https://
docplayer.com.br/121008799-Entropia-e-textura-ritmica-na-sinfonia-em-quadrinhos-de-her -
meto-pascoal.html .
MZ_2022_2_FINAL.indd   127 MZ_2022_2_FINAL.indd   127 10. 02. 2023   13:52:02 10. 02. 2023   13:52:02

muzikološki zbornik • musicological annual lviii/2
128
flute, depending on whether it is played normally or flatterzung. Also observe 
the two resources for the harp and timbals, and the many differentiated re -
sources for the first violins.
23
2.1.2 The Local Sonic Setups
A Local Sonic Setup
24
 is a particular configuration at a given time. A new setup 
is identified each time the composer changes the previous instrumental con -
figuration or modifies a timbre or playing mode of one or more instruments or 
includes or modifies an electronic intervention. Since, according to our theo -
retical premises, the compound sound unit is the product of the combination 
of a varied number of components, “the rupture in structural continuity of at 
least one of these components implies […] a rupture in sound continuity and, 
consequently, identifies a new structural articulation, that is, a new unit.”
25
 This 
means that each new orchestral setup has the ability to generate a new unity, 
since it causes a break in continuity on the sound level. In other words, a local 
sound setup is both a marker of sound discontinuity and a compound sonic unit 
defined by the orchestration criterion.
26
This reading, which depends only on a careful reading of the score,
27
 pro -
vides the initial database. Figure 1 illustrates the setup tracking process for 
some measures of the selected extract from the Webern’s Variations. In this 
excerpt, the segmentation process uses 8 LSS, respectively: bars 68 and 69 (the 
thicker box indicates the most prominent sound unit in the sequence), 70.3 
(the segmentation is caused here by the break in the continuity of intensity – 
change of “nuance” in violas and cellos), 71.2, 72, 73, 74 and 75. The reader will 
find this sequence in the table in Table 1.
Some scores are more fluid, more progressive than others, manifesting a less 
clear-cut sonic structure. This means that the segmentation process may have 
to deal with sequences where the LSS interlock, link together in tiling, rather 
than by juxtaposition. We show in Figure 2 a page from Akrata (1964–1965) 
by Xenakis with its segmentation.
23 For the sake of space saving, the index in the table is interrupted. It actually contains a total of 78 
Sound Resources.
24 In this text, LSS and setup can be used alternatively as synonymous shortcuts.
25 Didier Guigue, Esthétique de la sonorité: L’héritage de Debussy dans la musique pour piano du XXe 
siècle (Paris: L’Harmattan, 2009), 58.
26 If other criteria were to complete the analysis, they would be subordinate to it, i.e. they would 
not have the ability to re-segment the piece into different and contradictory units from the one 
caused by the orchestration.
27 The implementation of a computer support for this task makes it necessary to encode the score 
into a MIDI file in which each of the sound resources is the subject of an independent track. But 
it is quite possible that this may not be possible in all cases, making human control essential in 
any case.
MZ_2022_2_FINAL.indd   128 MZ_2022_2_FINAL.indd   128 10. 02. 2023   13:52:02 10. 02. 2023   13:52:02

C. de Paiva Santana, D. Guigue: Th e Role of Orchestration in Shaping Musical Form
129
Figure 1: Anton Webern, Variations, Op. 30, bars 68–75: segmentation process by local 
sonic setups.
28
Th is listing is formatted in a table in which the list of all the sound resources 
identifi ed is placed in a column and the setups are arranged in line in sequen-
tial order of appearance, labelled with the bar number where they begin. An 
integer is inserted for each active resource in each setup. Th is integer is equiva-
lent to the maximum number of simultaneous sounds played by the instrument 
in the analyzed setup
29
(1).
28 Copyright: Universal Edition.
29 Th is information has not yet been incorporated into the model. It would function as an additional 
MZ_2022_2_FINAL.indd   129 MZ_2022_2_FINAL.indd   129 10. 02. 2023   13:52:04 10. 02. 2023   13:52:04

muzikološki zbornik • musicological annual lviii/2
130
Figure 2: Iannis Xenakis, Akrata, bars 225–239: segmentation process by local  
sonic setups.
30
This table can be used to map the distribution of instruments during the work 
(from the information provided by the “Recur” column) and to obtain statisti -
cal data on the frequency of their use by the composer. It also allows, using 
pattern recognition algorithms, to identify how many times and which con -
figurations are repeated, to classify LSS according to the number of SRs they 
contain, in order to know the most frequent solutions, etc.
If the number of SRs is not disproportionately high, this table can also 
be displayed as a clock. In this case, each SR is placed on a point on the cir -
cle and each LSS is represented by the junction of the points corresponding 
to the resources used. Figure 3 shows, for example, 4 neighboring LSS in a 
passage from Beethoven’s Trio from the Scherzo of the 3d Symphony, whose 
SRI contains 24 resources.
31
 The instruments are classified from top to bottom 
according to their register, on the left for strings, on the right for winds. This 
representation makes the sound contrasts caused by the composer’s orchestral 
writing very visible.
but “virtual” sound resource (since it does not require a new concrete resource); it also acts, to an 
extent yet to be studied, on the sensation of “agglomeration” of textures (we define this term below).
30 Copyright: Boosey & Hawkes for the score.
31 Namely: woodwinds by two, three horns, two trumpets, timpani, and the string desks that we have 
chosen to separate from the point of view of sound rendering on the basis of the playing technique 
(L=ordinario and/or legato, S=arco staccato).
MZ_2022_2_FINAL.indd   130 MZ_2022_2_FINAL.indd   130 10. 02. 2023   13:52:06 10. 02. 2023   13:52:06

C. de Paiva Santana, D. Guigue: The Role of Orchestration in Shaping Musical Form
131
2.1.3 The W eighted Number of Resources (WNR)
The next step is to weight the setups according to the number of sound re -
sources they contain, assigning them a relative value called Weighted Num-
ber of Resources, or WNR. The basic information is obtained by summing the 
Figure 3: Ludwig van Beethoven, excerpt from the “Trio” from the Symphony No. 3:  
4 LSS in clock representation.
MZ_2022_2_FINAL.indd   131 MZ_2022_2_FINAL.indd   131 10. 02. 2023   13:52:07 10. 02. 2023   13:52:07

muzikološki zbornik • musicological annual lviii/2
132
non-empty cells of the table (line Total Resources).
32
 This must be normalized 
in order to reach the maximum (1) when this sum is equal to the maximum 
number of Sound Resources that can be used in the same setup. The calcula -
tion of this maximum will depend on how the Index is calculated. In general, 
classical symphonic writing induces a selection by desk. The total number of 
possible resources is therefore over. But in the case of works such as Pascoal’s 
symphony, for which the index is composed not of individuals but of sub -
sets of instruments, the potential number of groupings, based on the available 
instrumental complement, is close to infinity because there is practically no 
combinatory impossibility. We are therefore not currently considering a single 
solution for obtaining the standardization paradigm applicable to WNR.
Table 1: Structured data from orchestration and textural analysis of Anton Webern’s 
Variations for Orchestra, Op. 30 
Header column refers to the SRI of the work, while the header row indicates the bar 
numbers. For improved readability, sound resources not employed are hidden. The column 
recurs refers to how much the specific sonic resource is used during the entire piece.
Recur. Sonic Res.Index 
(SRI):   bars >
68 69 70.3 71.2 72 73 74 75
35 Fl 1 1 1 1 1
39 Ob 1 1 1
44 Bb Cl 1 1 1 1 1 1
19 Bass Cl 1 1 1
14 Hn F sord. 1 1
34 Tp C sord. 1 1
18 Tbn sord. 1 1
11 Basstuba sord. 1 1
35 Celesta 4
52 Hp 4 4
14 Vln I   solo   
arco
1
4 Vln I   solo   
pizz.
1
15 Vln I   tutti   
arco
2
9 Vln II   tutti   
arco
2
3 Va   div. 1   arco 1 1
3 Va   div. 2   arco 1 1
32 Also, it is not obtained by summing the values contained in these cells (see note 19).
MZ_2022_2_FINAL.indd   132 MZ_2022_2_FINAL.indd   132 10. 02. 2023   13:52:07 10. 02. 2023   13:52:07

C. de Paiva Santana, D. Guigue: The Role of Orchestration in Shaping Musical Form
133
9 Va   tutti   arco 2
3 Celli   div. 1   
arco
2 Celli   div. 2   
arco
1 1
10 Celli   tutti   
arco.
2
Total resources 8 11 8 8 2 2 1 2
WNR 0,64 0,74 0,64 0,64 0,2 0,21 0,2 0,21
Agglomeration -7 -13 -12 -12 0 0 0 0
Dispersion 21 42 16 16 1 1 1 1
Difference 14 29 4 4 1 1 1 1
Setup Com-
plexity
0,82 1 0,69 0,69 0,2 0,21 0,2 0,21
In the current state of our experiments, and in cases where the SRI is estab -
lished from individual instruments or desks and the timbre effects applied to 
them, we have worked with two normalization values: the first is the simple 
result of the sum of the Sound Resources contained in the index. This calcu -
lation probably satisfies all works, which contain little or no special sound 
effects. But it is very likely that in many cases from the twentieth century 
onwards, this sum will be much higher than the actual number of perform -
ers. In De Natura Sonoris (1966), Penderecki prescribed eight string playing 
modes: sul tasto, sul ponticello, col legno, legno battuto, three unconventional 
bow effects, in addition to ordinario. Moreover, the first two flutes must play 
the piccolo alternately. Besides, several types of vibratos and tremolos are 
described. Finally, the six percussionists must have a very large arsenal of 
instruments and mallets. Thus, there are many distinct sound resources to 
index, resources that cannot be played simultaneously, at the same time. The 
procedure then consists in establishing, on the one hand, the list of the num -
ber of instruments prescribed by the composer, classified by desk, and, on the 
other hand, the total number of sound effects that each instrument is called 
upon to perform. From this double list we extract the minimum value for 
each desk. Indeed, either the number of sound effects is less than the number 
of instruments on the desk, in this case the number of SR corresponds ex -
actly to the number of different timbre effects, or the number of instruments 
is less than the number of effects requested, in which case it is this number 
that imposes its limits. The sum of these minima constitutes the normaliza -
tion paradigm. The Table 2 shows how the De Natura Sonoris
33
index could be 
33 This table is presented for illustrative purposes only and is not intended to be a reference for the 
analysis of this work.
MZ_2022_2_FINAL.indd   133 MZ_2022_2_FINAL.indd   133 10. 02. 2023   13:52:07 10. 02. 2023   13:52:07

muzikološki zbornik • musicological annual lviii/2
134
hypothetically realized. The nomenclature prescribes 86 instruments (Pend -
erecki indicates precisely how many strings he wants for each desk, which is 
not always the case). The sum of the prescribed different sound effects is 60,
34
 
but only 52 different sounds can be played at the most at the same time. It 
is this last value that will be used to normalize the number of resources used 
for each LSS.
Table 2: De Natura Sonoris, no. 1, Sound Resource Index. The score specifies 86 
instruments, including the exact number of string instruments needed for each section. 
The score indicates a total of 60 different sound effects, of which only 52 different sounds 
can be performed simultaneously.
name # instr # sonic res n  max simul  res 
4 fl (2 picc) 4 2 2
ob 3 1 1
eh 1 1 1
cl 2 1 1
bcl 1 1 1
sax 2 1 1
bn 3 1 1
cbn 1 1 1
hn 6 1 1
tpt 4 1 1
tbn 3 1 1
tba 1 1 1
perc 6 24 6
pf 1 1 1
harm 1 1 1
flexatone 1 1 1
vn 24 8 8
vl 8 8 8
vc 8 8 8
db 6 6 6
Total 86 60 52
34 Probably much more if we went into detail about the different playing modes and timbres of the 
percussion.
MZ_2022_2_FINAL.indd   134 MZ_2022_2_FINAL.indd   134 10. 02. 2023   13:52:07 10. 02. 2023   13:52:07

C. de Paiva Santana, D. Guigue: Th e Role of Orchestration in Shaping Musical Form
135
Th e formula we have chosen and implemented in SOAL for the factoring of 
these two values (the number of SRs of each LSS and the constant denomina-
tor) is logarithmic. Indeed, the logarithmic curve introduces a compensatory 
equilibrium, by giving more visibility to Setups with fewer resources – and for 
which we hypothesize that they tend to be, as a general rule, the most used – 
and by bringing as close as possible to (1) those that are close to the maximum. 
So, for each Local Sonic Setup, we have,  
WNR =  (1)
where WNR (Weighted Number of Resources) is the weighting, ρ is the number 
of Sonic Resources in the Setup, and P is the total number of Resources identi-
fi ed according to the methodology adopted.
35
2.2 An Application of Partition Th eory
Th e impact that the manipulation of sound resources can have on the formal 
dynamics over time is directly aff ected by the way the composer organizes 
them into more or less autonomous fl ows. It can be said that from quantita-
tive data, the composer makes qualitative choices, and that these choices have 
an impact on quantitative decisions. Th e distribution in polyphonic fl ows 
characterizes what is known as texture , a dimension that signs a composer’s 
personal style of orchestration, because it refl ects his way of negotiating in-
strumental individualities and more or less stratifi ed sound masses. In his 
classic Structural Functions in Music, Wallace Berry proposes a representation 
of texture according to the degree of independence or interdependence of the 
voices that compose it.
36
 According to him, a texture would be composed, on 
the one hand, of real components, each of which would correspond to a “voice” 
– i.e. a part that individualizes in general polyphony – and of sound compo-
nents that represent the sum of the sound resources used in what I call here a 
setup. It is the measurement of the degree of independence/interdependence 
of a resource that groups it into a real component or leaves it outside as an 
isolated fl ow.
Although he does not mention it, this reasoning, as well as the numerical 
representation it proposes, off er obvious convergences with the classical math-
ematical theory of the partition of integers, initially developed by Euler as early 
35 Th e reader can compare the lines Total Resources and WNR, for a demonstration of the impact 
of the logarithm on the weighting of the number of sound resources: Setup 63, for example (AR 
column), uses only 16 of the 78 Sound Resources indexed.
36 Wallace Berry, Structural Functions in Music (New York: Dover Publications, 1987), 184.
WNR =  (1)
MZ_2022_2_FINAL.indd   135 MZ_2022_2_FINAL.indd   135 10. 02. 2023   13:52:07 10. 02. 2023   13:52:07

muzikološki zbornik • musicological annual lviii/2
136
as 1748.
37 
According to this one, number 5, for example – a setup of five sound 
resources, let’s say, to stay in our field of study – has seven partitions ( p(5) = 7), 
i.e. seven ways by which it can be represented by the sum of other integers, in 
this case: (5 ,4 + 1,3 + 2,3 + 1 + 1,2 + 2 + 1,2 + 1 + 1 + 1,1 + 1 + 1 + 1 + 1). A 
standard form of representing this set in an abbreviated form consists in group -
ing the “real components” into vectors: 5 ,41,32,311,311,221,2111,11111, or 
according to a formula in which the base indicates the part and the exponent 
its multiplicity 5, 1
4
, 2
3
, 1
2
3, 12
2
, 1
3
2, 1
5
.
38
We have adapted the first of these representations so that it can be directly 
read and understood in OpenMusic, which is written in Common Lisp. This is 
how we will write ((5)(4 1)(3 2) … (1 1 1 1 1 1 1 1)). In this case, the scores with 
the most numbers are those with the highest rate of dispersion – Berry speaks of 
independence – hence it follows that representation (1 1 1 1 1 1 1) means that 
each of our five instruments plays an independent part. In Berry’s terminology, 
we have here a texture with five real components. The nominal value of each fig -
ure reflects the agglomeration rate, which corresponds to Berry’s interdependence. 
In this case (4 1) would be the way to represent a texture with two real compo -
nents, a soloist accompanied by a chord played by the other four instruments.
In music, however, the possible number of partitions of a finite set of sound 
resources is much higher than that obtained by partitioning the total, because 
it is necessary to include all possible partitions of subsets that can be consti -
tuted by groups that use only a part of the resources. To use the same scenario, 
the possibilities of partitions, and therefore textural configurations, of five re -
sources, amount to 18.
The complexity of a texture is therefore directly related to the dispersion 
rate of its components, as well as being proportional to the number of them. To 
calculate the rate of agglomeration or dispersion of a given Local Sonic Setup, 
firstly we need to count every combination, or rather every possible relation of 
any two elements of the LSS. We can do it by referring to the general formula 
for finding the number of combinations of p objects from a set of n objects, 
known as n choose p:
37 George Andrews, The Theory of Partitions (Cambridge: Cambridge University Press, 1998); Pauxy 
Gentil-Nunes, “Análise Particional: Uma mediação entre composição musical e teoria das par -
tições,” in Simpósio de cognição e artes musicais (20–26 May, 2009), 343–354; Pauxy Gentil-Nunes, 
“Particiograma e indexograma: Topologia e dinâmica das progressões particionais,” paper pre -
sented at XXI Congresso da Associação Nacional de Pesquisa e Pós-Graduação em Música (22–26 
August, 2011), https://anppom.org.br/anais/anaiscongresso_anppom_2011/ANAIS_do_CON -
GRESSO_ANPPON_2011.pdf. In the field of composition, Milton Babbitt is known to have 
been the first composer to make exhaustive use of the total number of partitions of the number 
12 in serial music, by inventing the all partition table. See Robert Morris, “Mathematics and the 
Twelve-Tone System: Past, Present, and Future,” in Mathematics and Computation in Music, eds. 
Timour Klouche and Thomas Noll (Heidelberg and Berlin: Springer-Verlag, 2009).
38 Gentil-Nunes, “Análise Particional”; Gentil-Nunes, “Particiograma e indexograma”; George An -
drews and Eriksson Kimmo, Integer Partitions (Cambridge: Cambridge University Press, 2004).
MZ_2022_2_FINAL.indd   136 MZ_2022_2_FINAL.indd   136 10. 02. 2023   13:52:07 10. 02. 2023   13:52:07

C. de Paiva Santana, D. Guigue: Th e Role of Orchestration in Shaping Musical Form
137
                                                 .            (2)
For instance, in a setup composed of 4 sonic resources playing agglomerated 
parts, let’s say a woodwind quartet, represented by the singleton list (4), there 
is a total of 6 unique pairs as
C(4,2) = 6, that is
(Fl Ob) (Fl Cl) (Fl Fg) (Ob Cl) (Ob Fg) (Cl Fg)
On the other hand, in a LSS of four soloists playing independent parts, that 
is (1 1 1 1), when we consider any of its individual real-components or instru-
ment, we fi nd a total of zero unique pairs as C(1,2) = 0.
We will refer to the total number of unique pairs of any resource or real 
component of a given setup as T
2 
or simply T. By reworking the equation given 
at (1), we will defi ne it as a function in the following way:
                                 .                                      (3)
Th is way, the sucessive total unique pairs when n is mapped to the fi rst eight 
positive integers, that is T2 * (1 2 3 4 5 6 7 8) = (T2 (1), ... , T2 (8)) is equal to 
(0 1 3 6 10 15 21 28). 
It follows that, in order to calculate the rate of agglomeration of a given lo-
cal setup, we need to sum the T2 value of each of its components. For instance, 
the rate of agglomeration of the setup represented by the list (211) is given by 
(T2 (2) + T2 (1) + T2 (1)) which results in 1. It is formally defi ned by the fol-
lowing function:
                                           ,                            (4)
where the list (a0 ... ar−1) represents an LSS, ai each of its elements, that is, its 
real-components, and r the length of the LSS.
                                                 .            
                                 .                                      (3)
                                           ,                            (4)
MZ_2022_2_FINAL.indd   137 MZ_2022_2_FINAL.indd   137 10. 02. 2023   13:52:08 10. 02. 2023   13:52:08

muzikološki zbornik • musicological annual lviii/2
138
Th e dispersion index (d ) is the result of the diff erence between (a ) and T [9].
D: N
r 
→N
 (a0 ... ar−1) 7→T2(ρ) −A(a0 ... ar−1),                  (5)
where ρ is the sum, the number of sonic resources of the LSS, that 
is,                 .
We then obtain a pair of indices (a, d ) whose visual arrangement in the 
form of an indexogram contributes to the interpretation of the dynamics of 
textural confi gurations on the time axis, by means of a symmetric presentation 
of a and d around zero, made possible by transforming (a) into negative values.
But the negative of (a) has another virtue. When added to (d), it forms the 
sum I, so
I(a0 ...ar−1) = (D−A)(a0 ...ar−1). (6)
Th is produces a synthetic evaluation that shows the trend of the texture, ei-
ther to agglomeration (when the sum is negative) or to dispersion (positive 
sum). And, of course, the values give us the graphic plot of this trend. Th is 
synthesis seemed to us to be of signifi cant interest for our model because, 
intended to weight a quantitative data – the number of instruments or re-
sources used – it has the power to modulate it possibly less, i.e. to weaken its 
qualifi cation, when its agglomeration index weighs more than that of its dis-
persion. In other words, if, as we have argued above, it is the dispersion rate 
that defi nes the complexity of a texture, the integration of the calculation of 
its agglomeration rate allows a more precise calibration. It is therefore this 
synthesis I that we will preferably use.
39
 Th e lower graph in the Figure 4 pro-
vides an example of I for an excerpt from Rameau, the beginning of the aria 
“Un Horizon serein,” from his opera Les Boréades (1764). Th e upper graph 
shows the indexogram of values from which the values for I (the textural 
tendency) originate. Th e analysis will show that the orchestra only produces 
clearly agglomerated textures to characterize certain events related to drama-
turgy. Th e rest of the time, it is the dispersion of the instrumental parts into 
rhythmically independent fl ows that tends to dominate. Th e comparison of 
the two representations shows that each can make a specifi c contribution to 
understanding the texture of the objects analyzed and their relationships in 
the overall form.
39 It is possible that in some contexts, it is the indices (a) or (d) alone that may be more relevant. Th e 
implementation in OpenMusic off ers all the alternatives.
is,                 .
MZ_2022_2_FINAL.indd   138 MZ_2022_2_FINAL.indd   138 10. 02. 2023   13:52:08 10. 02. 2023   13:52:08

C. de Paiva Santana, D. Guigue: The Role of Orchestration in Shaping Musical Form
139
Figure 4: Jean-Phillippe Rameau, “Un Horizon serein” ( Les Boréades, Act I, Scene IV), 
bars 1–105. Top: Indexogram of conjugated indices a (blue) and d (red). Bottom: The 
tendency I of the texture complexity.
2.3 A Qualitative Evaluation of Textures
2.3.1 Relative V oicing Complexity
In order to integrate orchestration into a general model of analysing musical 
morphologies based on the concept of a composite sound unit, it is necessary to 
place the descriptors and measurements on a single axis of “relative complex -
ity.” A solution to obtain a normalization is to divide I by the value T of the 
setup that has the highest ( max) number of Sound Resources; in other words, by 
MZ_2022_2_FINAL.indd   139 MZ_2022_2_FINAL.indd   139 10. 02. 2023   13:52:08 10. 02. 2023   13:52:08

muzikološki zbornik • musicological annual lviii/2
140
the greatest number of binary relationships possible in a given set of setups. 
A confi guration with a dispersion index equal to this number would in fact 
represent the greatest possible complexity in the context. We therefore obtain 
a relative index RVC (Relative Voicing Complexity).
RVC(                                                . (7)
Th e RVC value is scaled through the application of                 , where λ stands 
for (a
0.
..ar−1)
.
Th e partitional analysis, however, is neutral as to the musical criteria that 
would defi ne the agglomeration and dispersion rates. Berry essentially takes 
responsibility for the rhythm, direction of contrapuntal lines and interval con-
tent. It recognizes three categories of interaction identifi ed by the prefi xes 
homo-, hetero- and contra-, the fi rst of which refl ects the “identity” of the parties 
(interdependence or agglomeration), and the other two, two levels of disper-
sion (independence or dispersion), the most pronounced of which is character-
ized by opposing movements.
40
If heterorhythmia seems in many cases to be the most eff ective criterion 
for provoking a dispersion of voices, there are examples for which the textural 
writing requires other parameters and strategies. Below is a list of the criteria 
that we have used to date in our various analytical experiments. We have tried 
to rank them in descending order of eff ectiveness in terms of their ability to 
cause dispersion in LSSs.
41
(1) dominant heterochromy, when the dispersion is caused by the splitting into 
streams of diff erent sounds – e.g. high-pitched woodwinds against low-
pitched brass. It can encapsulate an undetermined number of other criteria 
which have a less eff ective infl uence on complexity; they are placed on a 
lower hierarchical position;
(2) dominant heterorhythmy (divergence of rhythmic structures, phase asyn-
chrony); It can encapsulate an undetermined number of other criteria, 
which operate in a lower hierarchical position;
(3) heterokinesis; (divergence of melodic direction) includes contrary motion stricto 
sensu, to which we do not see the need to assign a diff erent weight as Berry does;
(4) heteroarthria (divergence of articulation, typically legato versus staccato);
(5) heterophony (understood as a homokinetic and homorhythmic texture, but 
with interval divergences).
40 Berry, Structural Functions in Music, 193.
41 Th is eff ectiveness is measured primarily by estimating the impact that the criterion has on listen-
ing. Further studies are needed to make this classifi cation less subjective.
RVC(                                                
Th e RVC value is scaled through the application of                 , where 
MZ_2022_2_FINAL.indd   140 MZ_2022_2_FINAL.indd   140 10. 02. 2023   13:52:09 10. 02. 2023   13:52:09

C. de Paiva Santana, D. Guigue: The Role of Orchestration in Shaping Musical Form
141
We hypothesize that the last three criteria only contribute significantly to the 
qualification of texture complexity in the absence of the first two.
This classification is not static: on the contrary, it is context-sensitive, 
which means that it may be appropriate to modify it according to the music, 
and to add or remove criteria.
42
 It is also not uncommon to find that in some 
cases more than one criterion can be considered equally effective in causing 
dispersion.
43
To implement this hierarchy, the solution adopted consists in “increasing” 
[to weight] by a certain percentage the relative indices according to the crite -
rion by which they will have been evaluated. The musicologist decides to which 
aspect of the texture he will assign each percentage. In the proposed ranking 
above, a minimum percentage of 5% could be established for criterion (5) and 
increased in steps of 5% to 25% for criterion (1).
44
 These rates are applied to 
the RI values to give the overall Relative Voicing Complexity (RVC) rate.
2.3.2 Local Sonic Setups Relative Complexity
As mentioned at the beginning of this text, these two groups of data – the 
weighted number of sound resources used ( WNR), and how they interact to 
modulate the sound texture ( RVC) are closely interdependent. Indeed, the quan -
tity of voices in which a texture can be stratified obviously depends on the num -
ber of resources made available. A setup consisting of a single monophonic in -
strument can only produce a technically “null” texture. On the other hand, it was 
established that the maximum dispersion – which was assumed to configure the 
most complex textures – was produced when each of the sound resources played 
an independent part. But it is quite obvious here too that the complexity effect is 
once again put into perspective by the number of instruments involved. If there 
are only two, it is much more likely that their parts will have a higher degree of 
independence than in a tutti of sixty instruments, which will not prevent the 
texture of our duo from remaining thin despite this greater independence. In 
both logical and algorithmic terms, it is therefore clear that RVC weights only 
make sense as qualitative modulators of setups. Because it is the instrumental 
configurations that, in the first place, determine the possibilities of polyphonic 
composition. In practice, RVC weights multiply those of WNR, in a way as a 
metaphor for the frequency modulation process. More precisely, the result of this 
multiplication is added to the value of WNR. The weight of the modulator can 
also be adjusted, up or down. The result configures what we will call the Local 
Sonic Setup Relative Complexity, a simplified acronym SRC, hence
42 For Webern, we have adopted the hierarchy (1) heterorythmy, (2) heterokinesis, (3) heterophony 
(which rarely occurs); for Xenakis and Pascoal, only heterochromy is considered.
43 In this case, we apply the criterion that gives the most dispersed partition, i.e. returns the highest 
quality of complexity.
44 The steps we are currently adopting in our experiments range from 5 to 12.5.
MZ_2022_2_FINAL.indd   141 MZ_2022_2_FINAL.indd   141 10. 02. 2023   13:52:09 10. 02. 2023   13:52:09

muzikološki zbornik • musicological annual lviii/2
142
SRC = WNR + (WNR × RVC
w
) (8)
where w is a weight (a percentage) of the RVC modulator.
The result of this modulation corresponds to a formalization of the com -
plexity of the orchestral texture that reflects the compensatory play be -
tween the two components of analysis, the quantitative and the qualitative 
balance.
The reader should note that the evaluation does not take into account a 
priori the duration of setups, although this can be included, for visual infor -
mation, in the graphical representations in OpenMusic (see Figure 6), since 
LSSs are segmented according to their sound configuration. They therefore 
last as long as it does not change. This process can generate segments of 
very different duration, from a fraction of a second to several minutes. The 
musicologist may therefore feel the need to refilter the value of SRC accord -
ing to the relative duration of the LSS, following a logic where the longer 
ones should acquire more weight. The information required for this support 
is the intervals between the onsets (starting points of the LSS). The unit of 
evaluation of the size of these intervals can be a beat - this choice is only 
satisfactory if the work has a stable tempo – or absolute time (for example in 
milliseconds). This information can only be extracted from a MIDI or audio 
file of the work.
45 
This file must first have been segmented in accordance with 
the LSSs identified in the partition. It is obviously sensitive to the perform -
ers’ agogic choices.
The relative duration of each LSS is obtained by dividing its individual 
duration, either by the duration of the longest LSS of the work, or by the 
total duration of the work, this second choice generating generally very small 
values.
46
 These values modulate the SRC. If this operator is the multiplica -
tion, the previous formula will be rewritten as follows, where t is the relative 
duration:
47
SRC = WNR + (WNR × RVCw) × tw (9)
45 The MIDI file must contain the tempo data and its variations.
46 This function is available in SOAL under the name of relative span.
47 Like RVC, d can be weighted by a percentage p.
MZ_2022_2_FINAL.indd   142 MZ_2022_2_FINAL.indd   142 10. 02. 2023   13:52:09 10. 02. 2023   13:52:09

C. de Paiva Santana, D. Guigue: The Role of Orchestration in Shaping Musical Form
143
Figure 5: Histograms showing the evolution of SRC weights with or without the inclusion 
of the relative duration or span (Anton Webern, Variations for Orchestra, Op. 30, bars 56–80).
This methodological process therefore emits a final weighting that aims to 
qualify each sound unit on a complexity vector related to the orchestration 
strategies adopted, as they can be identified from the score.
3 Implementation in OpenMusic and Procedure
In the current state of our work, this process is assisted, initially, by a spread -
sheet, in which information of the score is collected. These are then exported to an 
OpenMusic patch. We have implemented a function called soal-texture-complexi -
ty, which is located in the “Partitional Analysis” folder of SOAL. Equation T was 
also made available. The soal-texture-complexity function gathers all the algorithms 
and patches developed for this project. The SOAL library is implemented using 
the Common LISP language and a standalone, python version also exists.
Figure 6 shows the compiled function, in a patch analyzing the Webern 
extract we have chosen for demonstration. The numbers and letters refer re -
spectively to inputs and outputs, as described below. Some steps and secondary 
outputs will not be detailed here.
3.1 Inputs
(1) As a main entry, the list of setups, described by two arguments (encapsu -
lated list), the first of which contains the partition of each setup and the 
second the partition criterion sequence number.
(a) First argument: the sequence of integers in the score corresponds to the 
number of real components, and their value to the number of sound 
resources each contains. The format adopted is that described in section 
on partitional analysis.
48
 Their sum must correspond to the total number 
of resources counted in the setup.
48 By convention, setups with zero resources ( Gran Pause) are identified by the value (0.9) and not 
(0) which would produce a division error.
MZ_2022_2_FINAL.indd   143 MZ_2022_2_FINAL.indd   143 10. 02. 2023   13:52:09 10. 02. 2023   13:52:09

muzikološki zbornik • musicological annual lviii/2
144
(b) Second argument: the order number of the criterion chosen for the score. 
It starts at 1 (the most “eff ective” criterion). Th ere are as many order 
numbers as there are criteria, plus one that will be assigned to the setups 
without any dispersion, i.e. containing only one real component.
49
Figure 6: OpenMusic patch with the soal-texture-complexity function prototype in use to 
analyze bars 56–82 of Anton Webern’s Variations for Orchestra, Op. 30.
3.2 Resources
Th e process is currently done manually, in the same table where the various 
sound resources and setups have been annotated (see Table 1).
Th us, in Figure 6, we can see that the fi rst three setups have the following 
format:
((3 3 3)(2)) ((3 1 1)(2)) ((3)(5))
What it says: the fi rst setup totals 9 sound resources distributed between 3 real 
components each containing 3 of these resources, according to partition criterion 
(2) (in this case, according to our personal choice for Webern, heterokinesis). Th e 
second, 5 resources distributed equally among 3 real components according to 
the same criteria, but of which two components have only one resource each. Th e 
third setup is a chord of 3 sounds (3 agglomerated sound resources); the number 
5 precisely indicates that no partition criteria are applicable – in an analysis where 
in this case we adopted 4 hierarchical partitioning criteria.
49 In the Dispersion Criteria section, we give an example of a hierarchy with 5 criteria. In this case, 6 
order numbers will therefore be required.
0.5
0.37
0.25
0.48
0.16
0.64
3
3
1
2
2
4
9
3
3
12
0
24
27
7
0
16
1
96
18
4
3
4
1
72
0.67
0.39
0.24
0.52
0.16
1.0
Agglomeration Dispersion Difference
Setup
Complexity
LSS’s Sorted
by Complexity
Weighted
Number of
Resources
Number of
Real-Components
soal-texture-complexity
(63 1.0)
(69 0.87)
(56 0.67)
(68 0.61)
(60 0.52)
(65 0.52)
26 5 0.05 2.0
(56 58 59 60 62 63 65 67 68 69 70 
71.2 72 73 74 75 76 78 79 81 82)
Bars
Total Resources
Number of
Criteria Step
(((3 3 3) (2)) ((3 1 1) (2)) ((3) (5)) ((4 4…
LSS and Criteria
Modulation Weight
MZ_2022_2_FINAL.indd   144 MZ_2022_2_FINAL.indd   144 10. 02. 2023   13:52:09 10. 02. 2023   13:52:09

C. de Paiva Santana, D. Guigue: The Role of Orchestration in Shaping Musical Form
145
(2) Here we enter the total number of sound resources indexed in the complete 
work ( Sonic Resources Index) – 78 in this case, for the Variations.
(3) An integer corresponding to the number of criteria chosen, plus one (see 
above, 1b).
(4) The step of progression of the percentages that will be added according to the 
hierarchical weight of the chosen partition criterion; in the figure: 0.05 = 5%.
(5) Receives the list of setup labels (bar numbers).
50
(6) The Modulation weight of WNR output by RVC output, a number (2.0 in 
the figure).
(7) The user’s choice for Partitional Analysis: (1) relative agglomeration index 
(a); (2) relative dispersion index ( d); or (3): index of relative sum of (( a*(-1)) 
+ (d)).
(8) Either remove duplicates or not when calculating the real-components.
3.3 Outputs
(A) WNR: Weighted Number of Resources. This is the quantitative part of the 
orchestration analysis. The figure shows, below the output of the function, 
in the form of a column in a filebox, the results obtained for the Webern 
extract, as well as, at the very bottom, these same values represented in a 
curve ( breakpoint function).
(B) Real Components: number of real components per LSS. Similarly, the val -
ues obtained are shown below.
(C) The T index of the total number of resources (a single integer) – for We -
bern in this case, this index is 120.
(D)Outputs 4, 5 and 6 inform respectively the absolute indices of agglomera -
tion ( a), dispersion ( d), and their sum I. The values referenced to Webern 
are shown in the corresponding boxes below.
 Output 7 returns the sum a*(-1) + d. Outputs 8 to 10 return the same cal -
culations as (D) but in normalized, i. e. relative values (from 0.00 to 1.00).
(E) RVC (Relative Voicing Complexity): the texture (voicing) complexity, ac -
cording to Partitional Analysis user’s option in input 7.
(F) RSC (Relative Setup Complexity): This is the main function’s output. The 
Relative Setup Complexity corresponds to the WNR list (output A) weight -
ed by the RVC list (output E). The figure shows both the list of Webern’s 
RSCs in a filebox and a graphical representation of them (bottom).
(G) orders the setups (labelled by their bar number or string name) according 
to their relative complexity (the F list values): most complex ones at begin -
ning. In our sample, the most complex setup occurs in the bar 63, and the 
simplest is the bar 82’s. These bars are shown in the figure.
50 We have chosen to label the setups with the bar number where they start. But a string of any kind 
(alphabetical list, words ...) can be used.
MZ_2022_2_FINAL.indd   145 MZ_2022_2_FINAL.indd   145 10. 02. 2023   13:52:09 10. 02. 2023   13:52:09

muzikološki zbornik • musicological annual lviii/2
146
(H)  This is not a soal-texture-complexity output, but the combination of that 
two OpenMusic basic tools, x->dx then dx->x, provided the former is fed by 
the sequence of bar numbers, or any other data relative to the position in 
time of the LSSs, can be used as the x-coordinates of a breakpoint function 
curve, thus displaying the points on the horizontal axis according to their 
relative durations. However, we prefer histograms to curves, because the 
former induce a linear progression from one point to another, which does 
not correspond to reality: we are indeed in the presence of configurations 
that change without transition. The build histogram function allows this 
representation, in which the width of the histograms is a function of the 
relative duration of the LSSs.
4 Audio Analysis
4.1 Preparing the Audio Material
The segmentation of the score into units that are coherent from the point 
of view of orchestration, explained above, must be reproduced identically 
for the audio file of the work: these segments are called Local Audio Units. 
LAUs are indeed replicas of LSS in the audio file. The aim is to analyse 
how and to what extent the written prescriptions are implemented, and to 
evaluate the convergences and divergences between them.
51
 The segmenta -
tion task is automated thanks to the Generate Markers function available in 
the Audiosculpt software.
52
 Proper programming of the generator parameters 
requires some testing and depends in any case on the work and its record -
ing. In our experience, Positive Spectral Difference segmentation detects very 
finely the changes in energy, which, as a general rule, correspond to changes 
in sound, i. e. setup. Then we manually adjust the markers that would not be 
placed exactly where we want them to be a written simultaneity on the score 
may not be as synchronous in the real world of its acoustic performance – 
we add the segments that the score has induced but that have passed unseen 
to spectral detection (or we reset the function so that it recognizes them), 
we remove those that do not match the pre-established segmentation – un -
less we prefer to incorporate them into the original cutting (and return to 
the previous step).
The next step, still in Audiosculpt, uses the Chord Sequence Analysis function 
and its method of calculating the average spectrum. For orchestral music, we 
used a maximum number of between 40 and 60 partials, and an amplitude 
threshold of -70 dB or related to the sonogram. The results of the analysis 
51 It is also by this means that comparative analyses of different recordings of the same work can be 
carried out.
52 Audiosculpt is of course not the only software on the market to offer an automatic generation of 
markers. But it is the complementary features we use that make it preferable for our project.
MZ_2022_2_FINAL.indd   146 MZ_2022_2_FINAL.indd   146 10. 02. 2023   13:52:09 10. 02. 2023   13:52:09

C. de Paiva Santana, D. Guigue: The Role of Orchestration in Shaping Musical Form
147
(such as the one shown in Figure 10) are saved on the one hand as a collection 
of small audio files, each of which corresponds to a segment, therefore to a 
LAU, and on the other hand as a single SDIF file. It is this material that will 
be required for the analysis of the orchestration itself, in OpenMusic.
Figure 7: A screenshot of Audiosculpt showing the LAU segmentation and the results of 
the Chord Sequence Analysis by Average Spectrum, for an extract from the same work by 
Webern. The LAUs are identified by the vertical markers, and each horizontal line corre -
sponds to one of the partials preserved by the analytical process.
4.2 The LAU’s for Orchestration Analysis
The main function of setups in their audio format (LAU) is to allow, if the 
musicologist so wishes, to compare the prescriptions set by the composer with 
the work. In particular, as we announced at the beginning of this article, it is 
a question of measuring the real impact of these requirements on the form, 
and of observing how they are perceived in various performance and audience 
contexts. This branch of the theoretical model requires computer tools that 
deal with the sound signal, first and foremost psychoacoustic descriptors. As 
Philippe Lalitte has already clearly shown in his analysis of Sequenza VII de 
Berio, “the extraction of sub-symbolic information operated by psychoacous -
tic descriptors offers the possibility of approaching the perception of several 
musical dimensions such as time […], height (roughness, salience, […], etc.) 
and timbre (brilliance, inharmonicity, envelope, spectral clarity, etc.).”
53
 Many 
53 Philippe Lalitte, “Du son au sens: Vers une approche sub-symbolique de l’analyse musicale 
MZ_2022_2_FINAL.indd   147 MZ_2022_2_FINAL.indd   147 10. 02. 2023   13:52:09 10. 02. 2023   13:52:09

muzikološki zbornik • musicological annual lviii/2
148
of them may be adequate to highlight the area of timbre that is most affected 
by the composer’s orchestration, or the one that offers the most salience to 
perception. The problem lies in the quantity of descriptors available, and the 
heterogeneity of the information produced. Indeed, it is important to keep in 
mind that the basic concept of a descriptor is to “flatten” a multi-dimensional 
component, the stamp, on a single dimension. In other words, it makes a ge -
neric and oriented reduction of the signal, depending on the information they 
are supposed to return. Therefore, relying on them alone would not provide 
the analysis we need. The idea is therefore to constitute a modular network of 
descriptors that would be used according to contexts, and to standardize their 
results on the same vector of relative complexity to which the other compo -
nents of the model have been subjected. This variable network of descriptors 
is standardized in our model by the LAU Relative Complexity component, ac -
ronym ARC. The advantage of this formatting is that it can produce a more 
synthetic, holistic vision of the behavior of sound configurations over time. 
Indeed, it is not so much a question of qualifying local audio units in absolute 
terms, but rather of evaluating the degree of difference, or distance, between 
one unit and the other in a given field.
However, the development of ad hoc descriptors seems essential and is part 
of the specifications of our future steps. In the meantime, or in parallel, some of 
the statistical analytical tools offered in the SOAL library may be of some help, 
thanks to its ability to read both MIDI and SDIF files and extract data sets, 
all standardized on the simplicity-complexity vector. For audio sources, one 
may speculate that some of the following capabilities of SOAL could be useful 
in our specific context: the calculation of the relative range of the LAU – that 
is, the distance between its lowest and highest extracted partials; the manner 
in which the partials are distributed along the spectrum, giving if necessary 
a statement of the number of partials for each selected frequency band, and 
a weighting of the LAUs according to the register of occupied bands;
54
 how 
harmonically and/or linearly that partials are distributed along the spectrum; 
estimates of the relative average amplitude of each LAU and their relative 
duration.
This last information is already available if you want to weigh the setups 
according to their relative duration. We have mentioned above the possible 
relevance of this factor and how it could be integrated into the model. One 
of its most immediate uses is to compare various recorded versions of a work 
according to the musicians’ interpretations of time and tempo indications. For 
example, we compared the relative durations of two recorded versions of our 
assistée par ordinateur,” Musurgia 18, no. 1 (2011): 116.
54 These frequency bands and weights are user-defined. It may be thought that an analysis may wish 
to weight setups with a majority of very low or very high frequencies more heavily, for example, 
because, in general, they are noisier and have a greater impact on overall sound complexity.
MZ_2022_2_FINAL.indd   148 MZ_2022_2_FINAL.indd   148 10. 02. 2023   13:52:09 10. 02. 2023   13:52:09

C. de Paiva Santana, D. Guigue: The Role of Orchestration in Shaping Musical Form
149
Webern extract with the durations induced by writing time in the score. These 
are the recordings by Pierre Boulez (1969) and Hans Zender (2007).
55
 Figure 
8 shows the data. From top to bottom, the first histogram shows the repre -
sentation of the relative complexity of the LSSs (RSCs) as a function of the 
relative durations deducted from the number of time/measures each occupies. 
Remember that the width of the histograms is a function of the value assigned 
to the durations. The second and third histograms compare these same setups 
according to the relative durations adopted by each of the two conductors in 
the recordings. The last two repeat the comparison, but this time including the 
relative duration as a weighting of complexities in the calculation. Our goal 
here is not to start an analysis of this data, but only to show one of the func -
tionalities of including the analysis of the works’ audio support.
Figure 8: Anton Webern, Variations, Op. 30, bars 56–82: comparative analysis of two re -
corded versions of the work with the relative durations induced by writing.
55 Pierre Boulez (conductor), Variationen für Orchester Op. 30, London Symphony Orchestra (re -
corded live in London, 1969), in Webern Complete Works (Sony Classical, 1991); Hans Zender 
(conductor), Anton Webern: Variations For Orchestra Op. 30 & Franz Schubert: Symphonies No. 1 & 
4, SWR Sinfonieorchester Baden-Baden und Freiburg (SWR Classic, 2007).
MZ_2022_2_FINAL.indd   149 MZ_2022_2_FINAL.indd   149 10. 02. 2023   13:52:09 10. 02. 2023   13:52:09

muzikološki zbornik • musicological annual lviii/2
150
5 Conclusions
The aim of the method, whose theoretical bases and practical procedure we 
have outlined here, is to offer the possibility of evaluating the involvement 
of orchestration in the structuring of the work. To do so, we started from the 
axiom that each local sound configuration (an orchestral configuration in the 
case of symphonic music), or Local Sonic Setup, delimits a sound unit. The 
qualification of these setups according to the number of Sound Resources used 
and the way in which they are distributed to create more or less polyphonic 
complexity is information that comes in addition to the other dimensions 
that contribute to the elaboration of the form through sound. Its formatting, 
a vector on an axis of relative complexity, allows it to be integrated in a way 
that is compatible with the other dimensions that we have already formal -
ized in our previous research. Correlations and other statistical calculations 
can be applied to allow a better understanding of the interaction of all these 
elements in the construction of a musical form based on the articulation of 
sonorities.
Analysis at the symbolic level, which isolates written prescriptions from the 
sound results they are supposed to produce, reveals the orchestral technique, 
style and aesthetics of the composer under study. After all, as we have pointed 
out, it is on paper that composers orchestrate. The analysis of the concrete re -
sults of these prescriptions, based on one or more recorded media of the work, 
then makes it possible to confront them with the real world of performance, a 
dimension that is beyond the absolute control of the composer. The creation of 
a formal flow therefore involves a complex dialectic that this analytical model 
aims to shed light on.
The results, obtained on these Variations by Webern’s well as on the other 
composers in our research program, encourage us to continue our exploration 
of the multi-instrumental or mixed repertoire with the experimental method -
ology presented here, focusing, for the time being, on the development of more 
specific tools for the analysis of the sound carriers of the selected works.
References
Andrews, George. The Theory of Partitions . Cambridge: Cambridge University Press, 1998.
Andrews, George, and Kimmo Eriksson. Integer Partitions. Cambridge: Cambridge Uni -
versity Press, 2004.
Berry, Wallace. Structural Functions in Music. New York: Dover Publications, 1987.
Cogan, Robert, and Pozzi Escot. Sonic Design: The Nature of Sound and Music . New Jersey: 
Prentice-Hall, 1976.
Dolan, Emily. The Orchestral Revolution: Haydn and the Technologies of Timbre . Cambridge: 
Cambridge University Press, 2013.
Gentil-Nunes, Pauxy. “Análise Particional: Uma mediação entre composição musical e teo -
ria das partições.” In Simpósio de cognição e artes musicais (20–26 May, 2009), 343–354.
MZ_2022_2_FINAL.indd   150 MZ_2022_2_FINAL.indd   150 10. 02. 2023   13:52:09 10. 02. 2023   13:52:09

C. de Paiva Santana, D. Guigue: The Role of Orchestration in Shaping Musical Form
151
Gentil-Nunes, Pauxy. “Particiograma e indexograma: topologia e dinâmica das progressões 
particionais.” Paper presented at XXI Congresso da Associação Nacional de Pesquisa e Pós-
Graduação em Música (22–26 August, 2011). https://anppom.org.br/anais/anaiscongres -
so_anppom_2011/ANAIS_do_CONGRESSO_ANPPON_2011.pdf .
Gentil-Nunes, Pauxy, and Alexandre Carvalho. “Densidade e linearidade na configuração 
de texturas musicais.” In IV Colóquio de Pesquisa do Programa de Pós-Graduação da Escola 
de Música da UFRJ (2003).
Gieseler, Walter, Luca Lombardi, and Rolf-Dieter Weyer. Instrumentation in der Musik des 
20. Jahrhunderts: Akustik, Instrumente, Zusammenwirken. Celle: Moeck Verlag, 1985.
Goubault, Christian. Histoire de l’instrumentation et de l’orchestration: Du baroque à 
l’électronique. Collection Musique ouverte. Paris: Minerve, 2009.
Guigue, Didier. Esthétique de la sonorité: L’héritage de Debussy dans la musique pour piano du 
XXe siècle. Paris: L’Harmattan, 2009.
Guigue, Didier. Sonic Object Analysis Library – OpenMusic Tools for Analyzing Musical Objects 
Structure. Version 5.0. MacOS. 2016.
Guigue, Didier, and Thiago Cabral. “Entropia e Textura Rítmica na Sinfonia em Quadrin -
hos de Hermeto Pascoal.” Abstract. Paper presented at XXVI Congresso da Associação 
Nacional de Pesquisa e Pós-Graduação em Música (22–26 August, 2016). https://anppom.
org.br/anais/anaiscongresso_anppom_2016/3998/public/3998-13999-2-PB.pdf .
Kim, Jinho. “Représentation et analyse musicale assistée par base de données relationnelle 
de la partition des variations pour orchestre op. 30 d’Anton Webern: Vers un système 
d’analyse musicale assistée par base de données relationnelle.” Doctoral Dissertation, 
Université Paris IV, 2006.
Koechlin, Charles. Traité de l’orchestration en quatre volumes. Paris: Max Eschig, 1954.
Lalitte, Philippe. “Du son au sens: Vers une approche sub-symbolique de l’analyse musicale 
assistée par ordinateur.” Musurgia 18, no. 1 (2011): 99–116.
Maresz, Yann. “Pour un traité d’orchestration au XXIe siècle.” L’Etincelle: Le journal de la 
creation à l’Ircam, no. 11 (2006). http://etincelle.ircam.fr/652.html .
Morris, Robert. “Mathematics and the Twelve-Tone System: Past, Present, and Future.” In 
Mathematics and Computation in Music, edited by Timour Klouche and Thomas Noll, 
266–288. Heidelberg and Berlin: Springer-Verlag, 2009.
Piston, Walter. Orchestration. New York: Norton, 1955.
Roy, Stéphane. L’Analyse des musiques électroacoustiques: Modèles et propositions. Paris: 
L’Harmattan, 2004. 
Solomos, Makis. De la musique au son: L’émergence du son dans la musique des XXe-XXIème 
siècles. Rennes: Presses Universitaires de Rennes, 2013.
Tagg, Philip. Music’s Meanings: A Modern Musicology for Non-Musos. New York and Hud -
dersfield: Mass Media Music Scholars’ Press, 2012.
Tucker, Alan. Applied Combinatorics. New Jersey: John Wiley & Sons, 2012.
MZ_2022_2_FINAL.indd   151 MZ_2022_2_FINAL.indd   151 10. 02. 2023   13:52:09 10. 02. 2023   13:52:09

muzikološki zbornik • musicological annual lviii/2
152
POVZETEK
Vloga orkestracije pri oblikovanju glasbene oblike: Teorija in 
praksa metodološkega predloga ter računalniške  
implementacije le-tega
Predstavimo metodo za računalniško podprto analizo orkestracije. Naš cilj je vzpostaviti 
formalno razumevanje teh simbolnih dimenzij, ki bi lahko bile enakovredne obstoječim 
računalniškim pristopom k ritmu in tonski višini. Prav tako poskušamo raziskati vlogo, ki jo 
ima kontrola teksture in orkestracije pri izgradnji glasbene oblike. Naša raziskava je osnovana 
na teoretičnih opažanjih o glasbeni teksturi, ki jih je predstavil Wallace Berry v klasičnem 
delu Strukturne funkcije v glasbi (Structural Functions in Music), in posledičnem številčnem 
prikazu ter kombinatorični manipulaciji, osnovani na matematični teoriji razčlenitve naravnih 
števil (integer partititions), ki jo je opredelil Pauxy Gentil-Nunes.
Metoda vključuje: 1) splošni številčni prikaz ki omogoča abstrakcijo in posledično raču -
nalniško obdelavo teksturnih konfiguracij; 2) hierarhijo ‘kriterijev disperzije’ ali ‘teksturnih 
situacij,’ ki omogočajo stratifikacijo glasbene površine v različne realne komponente; 3) me -
rilo, ki omogoča kvantifikacijo heterogenosti odnosov v teksturnih konfiguracijah; 4) merilo, 
ki ocenjuje, kako so različni zvočni viri uporabljeni pri realizaciji teksturnih konfiguracij; 5) 
model relativne teksturne kompleksnosti, osnovan na diverziteti orkestracije in komple -
ksnosti alokacije realnih komponent v določenem glasbenem delu. Računalniški postopki so 
bili implementirani v programskih jezikih Common Lisp (Open Music) in Python. Da bi 
opredelili vlogo orkestracije v glasbeni obliki, smo predpostavljali, da vsaka zvočna konfigu -
racija (oz. orkestrska konfiguracija v primeru simfonične glasbe), lokalna zvočna postavitev, 
predstavlja formalno enoto. Kvalifikacije teh postavitev glede na število uporabljenih zvoč -
nih virov ter načinov njihove razporeditve, s katerimi ustvarjajo večjo ali manjšo polifonično 
kompleksnost, potem pretehtamo skupaj z ostalimi dejavniki, ki pripomorejo k formiranju 
glasbene oblike skozi zvok.
MZ_2022_2_FINAL.indd   152 MZ_2022_2_FINAL.indd   152 10. 02. 2023   13:52:09 10. 02. 2023   13:52:09

C. de Paiva Santana, D. Guigue: The Role of Orchestration in Shaping Musical Form
153
ABOUT THE AUTHORS
CHARLES DE P AIV A SANT ANA (charles@prism.cnrs.fr ) holds a PhD in music from the 
University of Campinas and in computer science from the University Pierre-et-Marie-Curie. 
His research focuses on the analysis, modeling and computer simulation of compositional 
strategies of contemporary repertoire, as well as their impact on perception. He teaches 20th 
century music and computer music at the Aix Marseille University.
DIDIER GUIGUE (didier.guigue@gmail.com ) was born in France and lives in Joao Pessoa, 
Brazil, since 1982. As a Senior Researcher at the Brazilian National Council for Scientific 
and Technological Development (CNPq) and Tenured Senior Teacher at the Universidade 
Federal da Paraiba, his academic production and lecturing activities are mainly in the fields 
of 20th and 21st century Music Theory, History & Aesthetics, and Computational 
musicology. PhD in musicology by the E.H.E.S.S., Paris (France) under the direction of 
philosopher and composer Hugues Dufourt, he is since 1997 the founder and director of the 
Mus3 Research Group, a IRCAM associated partner, and member of other research groups 
and laboratories in Brazil and France. Among his publications we find the book Esthetique 
de la sonorité (Paris: L’Harmattan, 2009). His concerns as a composer is about digital music 
and multimedia art.
O AVTORJIH
CHARLES DE P AIV A SANT ANA (charles@prism.cnrs.fr ) je doktoriral iz glasbe na Uni -
verzi v Campinasu in iz računalništva na Univerzi Pierre-et-Marie-Curie, njegove raziskave 
pa se osredotočajo na analizo, modeliranje in računalniško simulacijo kompozicijskih strategij 
sodobnega repertoarja ter vpliva teh na recepcijo. Glasbo 20. stoletja in računalniško glasbo 
poučuje na Univerzi Aix Marseille.
DIDIER GUIGUE (didier.guigue@gmail.com ) je rojen v Franciji, od leta 1982 pa živi 
v kraju Joao Pessoa v Braziliji. Iz muzikologije je doktoriral na E.H.E.S.S. v Parizu pod 
mentorstvom filozofa in skladatelja Huguesa Duforta. Deluje kot raziskovalec v Brazilskem 
narodnem svetu za znanstveni in tehnološki razvoj in je redni profesor na Zvezni univerzi 
v Paraibi. Ukvarja se predvsem s teorijo in zgodovino glasbe 20. in 21. stoletja, estetiko in 
računalniško muzikologijo. Od leta 1997 je ustanovni član in direktor raziskovalne skupine 
Mus3 (IRCAM partner) ter je član drugih raziskovalnih skupin in laboratorijev v Braziliji 
in Franciji. Med drugim je izdal knjigo Esthetique de la Sonorité (Paris: L’Harmattan, 2009). 
Kot skladatelj se ukvarja predvsem z digitalno glasbo in multimedijsko umetnostjo.
MZ_2022_2_FINAL.indd   153 MZ_2022_2_FINAL.indd   153 10. 02. 2023   13:52:09 10. 02. 2023   13:52:09