Proc. of the 15th International Symposium on CMMR, Online, Nov. 15-19, 2021

A psychoacoustic-based methodology for sound mass
music analysis
Micael Antunes1 , Guilherme Feulo do Espirito Santo2 , Jônatas Manzolli1 , andMarcelo Queiroz2
1

NICS - Interdisciplinary Nucleus for Sound Studies, University of Campinas
2Computer Science Department, University of São Paulomicael.antunes@nics.unicamp.br

Abstract. A sound mass is a specific state of the musical texture corresponding
to a large number of sound events concentrated within a short time and/or frequency interval. Conceptually, it is associated with the work of György Ligeti,
Krzysztof Penderecki, and Iannis Xenakis, among others. Recent studies have investigated sound masses via perceptual models, such as Gestalt models of perception and auditory scene analysis, and also from a more acoustic and psychoacoustic perspective obtained through audio recordings. The main goal of this paper isto propose a methodology for the musical analysis of sound mass music throughaudio recordings. We apply this method in the analysis of a performance of thefirst movement of Ligeti’s Ten Pieces for Wind Quintet (1968), and explore relationships between the obtained audio descriptors and Ligeti’s concepts of timbreof movement and permeability, in order to reveal Ligeti’s strategies when dealing
with musical texture and sound masses.
Keywords: sound mass music, musical analysis, audio descriptors, psychoacoustics

1

Introduction

This paper introduces a computer aided musical analysis methodology anchored on audio descriptors. Specifically, psychoacoustic models are applied to study sound masscomposition. Sound mass composition emerges in the context of discussions about perception and 20th century serial music [19]. Noticeably, these discussions were part of
the Darmstädter Ferienkurse, where composers attended classes and lectures on psychoacoustics, phonetics, information theory, and sound synthesis [5]. Some well-known
examples of sound mass compositions are the large number of attacks in Ligeti’s Continuum (1968), the micropolyphony and cluster techniques in his Chamber Concerto(1961), and the mass created by glissandi and extended techniques of the string orchestra in Xenakis’ Aroura (1971).
The central idea in sound mass composition is to emphasize perceptual features ofsound, by exploring the continuum of time and frequency domains to produce sound

Micael Antunes is supported by FAPESP Grant 2019/09734-3. Jônatas Manzolli is supportedby CNPq Grant 304431/2018-4 and 429620/2018-7. Marcelo Queiroz is supported by CNPq
Grant 307389/2019-7.

135Proc. of the 15th International Symposium on CMMR, Online, Nov. 15-19, 2021

textures with a high level of fusion and inner movement. Perception of sound masses
is often linked with the limits of sound integration by the ear [19] and microtime perception [3]. Sound mass music is also associated with Huron’s perceptual principlesof minimum masking, pitch proximity and limited density, which are anchored in thecritical bandwidth psychoacoustic model [17, 26].
Previous works have studied Ligeti’s sound mass composition from a perceptual
perspective, mainly through the symbolic analysis of the score. Clendinning exploredsuch a perceptual approach in the study of Ligeti’s compositional techniques such as
pattern-meccanico [10] and micropolyphony [9]. Cambouropoulos [8] used Gestalt theory to investigate links between Ligeti’s techniques and their perceptual outcomes, anapproach already explored by Ferraz [14]. More recently, Douglas et al. [12] investigated Continuum (1968) within the context of Bregman’s auditory scene analysis [6].
Methodologies anchored in audio descriptors with a psychoacoustic approach,which emerged in the context of computational and systematic musicology [23, 36, 21],
have also been used to study Ligeti’s works [21, 2, 1]. In this paper, we propose amethodology for musical analysis [36] focused on perceptual concepts that motivate
sound mass music composition, associating them with descriptors derived from audio recordings. Specifically, we study Ligeti’s viewpoint on sound mass composition
through the concept of timbre of movement [19], associating it with loudness [13] androughness [31]. Due to the correlation between spectral information and the perceptionof pitches and individual voices [17], we also investigate the use of spectral entropy [25]and spectral irregularity [7], associating them with Ligeti’s concept of permeability [19,2, 1, 3]. We present an musical analysis of the first movement of Ligeti’s Ten Pieces forWind Quintet (1968), using score-based information alongside the audio signal of aparticular performance of this piece. We also derive representations based on audio descriptors that allow us to discuss Ligeti’s compositional strategies and their perceptual
aspects, as well as the formal development of the piece from the viewpoints of timbreof movement and permeability.
In Section 2, we lay out the theoretical background for this study, starting withan exposition of the concepts of timbre of movement and permeability. Then, we givean overview of the first movement of the Ten Pieces for Wind Quintet, followed by areview of the audio descriptors used in this work. In Section 3, we outline the analyticalmethodology proposed, and in Section 4 we present and discuss the results of our study.
Finally, in Section 5, we present our conclusions.

2

Theoretical background

2.1

Ligeti’s concepts of Timbre of Movement and Permeability

Two relevant György Ligeti’s concepts associated with sound mass music composition
are timbre of movement and permeability.
The concept of timbre of movement3 refers to the achievement of fusion in musicaltexture by mixing a large number of sound events [19, p. 169]. Ligeti associates this3

In the original, Ligeti uses timbre du mouvement in French and Bewegungsfarbe in German [19, p. 169].

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Proc. of the 15th International Symposium on CMMR, Online, Nov. 15-19, 2021

concept with his collaboration with Gottfried Michael Koenig in the electronic studioof the Westdeutscher Rundfunk (WDR) in Cologne [19]. To him, the most meaningfulknowledge acquired in the studio was the observation that sound samples or synthesis
components merge into a single texture when the number of sounds surpasses a certain
threshold of our perception. This occurs when our auditory system can no longer discern the individual components of a musical texture, leading our attention to the globalfeatures and inner movements of sound masses [19, p. 169]. Ligeti used this conceptof timbre of movement in his instrumental compositions with the micropoliphony technique [9], which allows achieving dense textures by overlapping a large number of
melodies with short notes.
The concept of permeability refers to a state in which we are unable to distinguishpitches and individual voices. According to Ligeti: “The loss of sensitivity to intervals
is at the source of a state that could be called permeability” [19, p. 123]. This concept
is mainly associated with the use of tone clusters in his works, such as Lux Aeterna(1966). According to Ligeti, the tone cluster “is somewhere between sound and noiseand consists of several voices stratified and interwoven in semitones, which thereby giveup their individuality and become completely dissolved into the resultant overriding
complex” [20, p. 165].
2.2

First movement of the Ten Pieces for Wind Quintet

Ten Pieces for Wind Quintet was composed in 1968, and dedicated to the Wind Quintetof the Royal Stockholm Philharmonic Orchestra. Each movement was conceived as a
micro concerto with tutti odd movements and solo even movements, each solo being
dedicated to one of the performers [33]. We choose as analytical corpus, for all feature
extraction and section division, the version of the piece performed by London Winds inthe album Ligeti Edition 7: Chamber Music, recorded in 1998.
Vitale [33] presents a thorough score-based analysis of this work, and highlights
the gradual processes appearing in the piece, based on micropolyphonic strategies togenerate the musical texture, where the musical material is articulated with slow modifications in pitch, timbre, density, and rhythm [33, p. 2]. Using as criteria pitch registerand dynamics, this author proposes a division of the score of the first movement of theTen Pieces for Wind Quintet (1968) in two main sections (Section 1: measures 1 - 16;
Section 2: measures 16 - 22) followed by an appendix (measures 22 - 25). This corresponds respectively to the following time segments in the London Winds recording:
0:00.000 - 1:32.367 (Section 1), 1:32.367 - 1:58.390 (Section 2), 1:58.390 - 2:17.048(Appendix).
2.3

Audio descriptors

The use of audio descriptors in the context of musical analysis is a multidisciplinary
task [36] which admits a multiplicity of approaches depending on the context in which
it is applied [21, 23, 36]. In this work, we design the analytical methodology anchoredin audio descriptors for two main reasons: 1. audio descriptors provide a perspective(in our case, a perceptual perspective) on the musical sound data, allowing a better
understanding of the musical composition [23]; 2. graphical representations of audio

137Proc. of the 15th International Symposium on CMMR, Online, Nov. 15-19, 2021

descriptors guide the listening throughout the analysis and facilitates the observation ofrelated perceptual concepts [11]. As detailed in Section 3, we associate the concepts oftimbre of movement and permeability with four audio descriptors: loudness, roughness,
spectral irregularity and spectral entropy.
Loudness - Loudness is a psychoacoustic measure of sound intensity, usually associated with the perception of dynamics [3] in musical analysis. The total loudnessof a time frame (segment of an audio signal) is based on Zwicker’s critical bandwidthmodel [37, 7]. The specific loudness of each Bark4 band can be computed by a simplification of the original equation [27] asLoudness =NE(z)0.23 ,z=1

where E(z) is the energy in the z-th bark band for the time frame considered.
Roughness - According to Vassilakis [31], roughness is a perceptual feature related with the sense of very fast amplitude variations in the sound and it is partiallyconditioned by both the sound stimulus and the properties of the basilar membrane.
The roughness value of a time frame is based on an approximation, proposed in [30],of the Plomp & Levelt experimental dissonance curve5 [28]. For complex sounds, theroughness value can be computed using a formulation by Vassilakis, which embodies
the physical and psychoacoustic mechanisms involved in its perception, as
Roughness =3.11 0.84|f −f |N N
1.38|fj −fi |

j
i
2aj
(ai ∗ aj )0.1
e 0.0207fi +18.96 − e 0.0207fi +18.96 ,2
ai + aj
i=1 j=iwhere fi is the i-th partial of the sound and ai its corresponding amplitude.
Spectral Irregularity - The spectral irregularity feature used in this work was proposed by Krimphoff et al. [18] as a measure of the noise content of the spectrum [7, p.
60]. It is usually computed for each time frame in the magnitude spectrum as
Irregularity =ak − ak−1 + ak + ak+1  ,


3

N
−1 

k=2

where ak is the value in the k-th magnitude coefficient and N is the total number of
frequency bins in the spectrum.
A low irregularity value denotes a spectrum whose energy is concentrated in few
frequency bins, associated with distinguishable components in the sound. In contrast, ahigh irregularity value implies a more regular energy distribution across all frequencies,
associated with a more noisy content [7].
Spectral Entropy - Spectral entropy is an audio feature used for estimating signal
information and complexity in the Time-Frequency Plane [15]. Higher entropy values
are usually associated with higher spectral activity along all frequencies, and lower
values are related to a concentration of spectral energy on few components.
4
5

Bark is the unit of Zwicker’s critical bandwidth model [37].
For a full revision on roughness curves, see [31].

138Proc. of the 15th International Symposium on CMMR, Online, Nov. 15-19, 2021

The Spectral Entropy descriptor is derived from Shannon’s information theory equation through an analogy between signal energy densities and probability densities [34],asNP (Ek ) ln(P (Ek )),Entropy = −k=1

where P (Ek ) denotes the relative frequency of the energy present in the k-th bin.

3

Methodology

Sound mass music, as already pointed, is intrinsically related to the perceptual outcomeof the musical events [26, 12, 3]. Therefore, any musical analysis focused only on thescore would not provide all relevant information for the understanding of sound mass
features [3]. It is our aim to devise an appropriate approach to sound mass music analysis, based on information extracted from a musical performance through derived audio
features. In order to do that, we propose a methodology for sound mass music analysis
using audio descriptors and psychoacoustic features associated with Ligeti’s musicalconcepts, aligned with score-based information.
The concept of timbre of movement is associated with the dynamic perception of the
global behavior of musical texture and its microtime manifestation [29, 1]. The loudness
descriptor is used as a measure for global perceptual dynamics [3] and the roughness
descriptor was used to describe the microtime behavior of sound masses [1, 31].
According to the principles of minimum masking and limited density [17], the higher
the level of spectral information in the auditory nerves, the lower our ability to perceive
musical pitches and intervals. Therefore, the concept of permeability is represented by
the textural information level of the sound mass, associated with spectral entropy [4],and the noise content, associated with spectral irregularity [7].
Based on the above concepts and their interrelationships, the analysis was conductedin 3 steps: 1. Manual segmentation of the audio signal according to the score, as described in Section 2.2; 2. Computation of the selected time-varying audio descriptors(Section 2.3), their corresponding graphical representations, mean and standard deviation values, as well as scatter plots to illustrate their correlations; 3. Musicological(human conducted) analysis of the piece to establish the relationships between musicalcontent of the different sections and the obtained descriptors values.
Feature extraction was done using Python6 and the Jupyter7 environment. Loudness,
irregularity and entropy were computed from the magnitude spectrogram obtained using Librosa [24], with a window size of 4096 samples and hop length of 1024 samples.
The roughness descriptor was obtained from the reassigned spectrogram [16] (with thesame parameters described above), as it depends on precise frequency and amplitude
values. All the code used to extract and plot the audio features is available at a Gitlab
repository8 .
6https://www.python.org/
https://jupyter.org/
8
https://gitlab.com/Feulo/ligetis-wind-quintet-analysis
7139Proc. of the 15th International Symposium on CMMR, Online, Nov. 15-19, 2021

4

Results and Discussion

Figure 1 corresponds to the graphical representations of the descriptors obtained fromthe audio analysis as functions of time. Each different color represents one of the three
sections of the score: blue is the first section, orange the second section and green the
appendix. Mean and standard deviation values for each descriptor and section are presented in Table 1. The analysis was conducted in 2 stages: first we explore the characteristics associated with timbre of movement, followed by the behavior associated withpermeability.
Timbre of movement - According to the methodology proposed (Section 3), thepsychoacoustic descriptors of loudness and roughness are associated with the conceptof timbre of movement. Each section of the piece displays a different behavior in termsof this concept.
The first section displays a somewhat regular fluctuation of loudness values (blueline in the upper left corner of Figure 1). Within the same section, roughness (blueline in the upper right corner of Figure 1) displays low values with low variation. The
corresponding statistics can be seen in Table 1.
In evident contrast with the first section, the second section of the piece displays thehighest values of loudness. We highlight that, although the standard deviation values
for these two sections are not very different, by inspection of the loudness curve, we
can see that the first section has an oscillatory behavior while the second section displays an ascending pattern. Also, in the second section we observe the highest values ofroughness with a complex oscillatory pattern, with spikes that go upwards towards theend of this section. Finally, the appendix presents low values and low variation for bothloudness and roughness.
Section Loudness
Roughness
Irregularity
Entropy
141.87 ± 14.49 9.96 ± 5.86 63.54 ± 40.72 0.42 ± 0.13
266.36 ± 12.52 103.12 ± 62.44 171.63 ± 58.37 0.74 ± 0.15
313.36 ± 5.29 0.55 ± 0.56
9.98 ± 6.58 0.10 ± 0.03

Table 1. Mean and standard deviation values for loudness and roughness on each section.

Permeability - Ligeti’s concept of permeability is linked to the audio descriptorsof spectral irregularity and spectral entropy. By observing the two curves at the lower
half of Figure 1, we can also observe a distinct profile within each one of the sectionsof the piece.
In the first section, a regular fluctuation of the values is observed in both descriptors,
but entropy displays a lower range of variation relative to the mean (σ/µ = 0.64 forirregularity and σ/µ = 0.31 for entropy, according to the values in Table 1). In the second section, we can observe an ascending pattern in both features, similarly to what wasobserved for loudness and roughness, with increasing spikes in the spectral entropy profile. The same observation can be made here for the relative variation of both features,with σ/µ = 0.34 for irregularity and σ/µ = 0.20 for entropy. Finally, the appendix
displays once again the lowest values in both descriptors, as observed with loudness
and roughness, with smaller relative entropy variation (σ/µ = 0.30) with respect toirregularity (σ/µ = 0.66).

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Proc. of the 15th International Symposium on CMMR, Online, Nov. 15-19, 2021

Fig. 1. Roughness (upper left), Loudness (upper right), Spectral Irregularity (lower left) and Spectral Entropy (lower right) for the 3 sections of the piece.

By observing all descriptors taken together, we see that the three sections of thepiece have very different behaviors from the perspective of their perceptual features.
The psychoacoustic difference between the sections is illustrated in the first plot of
Figure 2, which represents the relationship between loudness and roughness, and in thecorrespondence between spectral irregularity and spectral entropy, shown in the second
plot of Figure 2. In both graphs, the spatial placement of the three section clusters, aswell as their geometrical arrangement, make the exploration of timbre of movement
and permeability relatively explicit, allowing us to observe a link between the formal
division of the composition and the different perceptual feature aspects of the soundmaterial.
Section 1 has a focus on the global behavior of the musical texture in terms of timbre of movement, with a high variation of permeability. Section 2 emphasizes timbre of
movement with a focus on the microtime behavior, while at the same time reaching thehighest levels of permeability. The appendix displays a low level of activity in terms ofboth timbre of movement and permeability. It is interesting to observe that, with respect
to the first section, we see the blue cluster lying horizontally on the scatter plot, where
the large variations in loudness emphasize the global dynamic perception. In contrast,
the second section (orange) corresponds to a highly scattered cluster in both roughness
and loudness axes, but concentrating on high values of loudness, thus bringing the mi-141Proc. of the 15th International Symposium on CMMR, Online, Nov. 15-19, 2021

crotime behavior (variation of roughness) to the forefront. In terms of permeability, weFig. 2. Scatter plot with the loudness (x-axis) and roughness (y-axis) values (left). Scatter plot
with the spectral irregularity (x-axis) and spectral entropy (y-axis) values (right)

can observe in Figure 2 that the spectral irregularity and spectral entropy fluctuations
in all sections are highly correlated, producing a log-like, quasi-diagonal shape in the
scatter plot, which correspond to constant changes of pitch perception in the musicaltexture. This might be associated with the harmonic technique of blurring [8, p. 122],
used by Ligeti to manipulate the musical texture. Especially in the second section (orange), the higher values of loudness and the large variation of the spectral descriptors
obliterate the perception of individual events, turning our attention to the mass behaviorof the composition. Finally, it is interesting to notice that the low level of all descriptors
in the third part (green) could be the reason why Vitale [33] described this section as anappendix of the piece.

5

Conclusion

In this paper we presented a methodology for the musical analysis of sound mass compositions, based on audio descriptors associated with Ligeti’s concepts of timbre of
movement and permeability. In terms of the musicological interest in audio analysis
techniques focused on sound mass composition, the proposed method reinforces theidea that the perceptual features associated with the performance of a musical work
bring important elements that help understanding the formal development of a work,without reducing the importance of symbolic analyses based on the musical score.
By analyzing the psychoacoustic features of each section of this particular piece, we
may argue that the most important perceptual characteristics of the work do not depend
heavily on specific choice of pitches, rhythms or harmonies, but are highly anchoredon the perceptual qualities of the sound masses. Also, audio descriptors could expand
the gradual process approach [32], enriching the symbolic analysis with performative
characteristics of the piece.
Future work may focus on investigating other timbre-related psychoacoustic descriptors in the context of the proposed analysis, to verify whether they contribute to142Proc. of the 15th International Symposium on CMMR, Online, Nov. 15-19, 2021

a better understanding of the perception of similarity of sound masses [22]. The studyof other audio descriptors in the context of sound mass music could also foment applications in the field of creative processes, particularly in computer-aided composition
and musical modeling. Exploration of perceptual features of a musical work throughcomparative analysis of different recordings of the same piece is also an interesting avenue for future work. It would be useful to investigate how the interpretative choices
in different performances could reveal the invariant properties of a musical work [35],as expressed in the score. Finally, musical analysis with audio descriptors might helpin empirical studies with musical excerpts [12], offering exploratory ways to represent
perception attributes of non-expert listeners.

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