Composing with Multidimensional

Timbre Representations

L e A h R e i d

t
C
A
R
t
S
B
A

The author discusses her work and approach to timbre-based
composition. Emergent in her works are a common theme and
exploration of “timbre spaces” and “timbre in space.” She discusses
two pieces: Ostiatim, for string quartet, and Occupied Spaces,
for two pianos and percussion.

descriptive factors of timbre. Para esto, we must look at the
various parameters of timbre and observe how they interact.
I find that the multidimensionality and complexity of
timbre is best illustrated in the following list by Caroline
Traube [3]:

My primary objective as a composer is to write beautiful and
stimulating music. Para mí, “beauty” is embodied by temporal
y, En particular, timbral attributes. In my works, timbre
acts as a catalyst for exploring new soundscapes, tiempo, espacio,
perception and color.

The problem with timbre is that it is ill defined. It is more
often defined by what it isn’t rather than what it actually is.
Unlike pitch and loudness, timbre does not have a simple,
objective or single dimensional scale. One can, sin embargo, de-
scribe timbre as a multidimensional attribute of sound, dónde
“continuous perceptual dimensions correlate with acoustic
parámetros, corresponding to spectral, temporal, and spec-
trotemporal properties of sound events” [1]. As timbre be-
came increasingly central in my composition, I adopted a
hybrid model that integrates both the “color” and “texture”
of sound and incorporates both static and dynamic attributes
of timbre. The “color” of sound is described in terms of an
“instantaneous snapshot of the spectral envelope,” while the
“texture” of a sound describes the “sequential changes in
color with an arbitrary time scale” [2].

Hiroko Terasawa and Jonathan Berger developed this
model of timbre at Stanford University’s Center for Com-
puter Research in Music and Acoustics (CCRMA). Este
view hints at two major compositional elements in a piece:
(1) static, vertical pitch and chordal structures and (2) dy-
namic, horizontal temporal processes. While these elements
are significant, this definition is still rather vague as to the

Leah Reid (composer, educator), University of Virginia, McIntire Department of Music,
112 Old Cabell Hall, PO Box 400176, Charlottesville, Virginia 22904, U.S.A.
Correo electrónico: leahcreid@gmail.com. Website: www.leahreidmusic.com.

Ver https://direct.mit.edu/leon/issue/54/3 for supplemental files associated
with this issue.

• temporal envelope

• spectral envelope

• absolute frequency position of spectral envelope

• variations of harmonic contents
• position of spectral centroid → brightness or

sharpness

• harmonic and noise components ratio

• inharmonic ratio

• odd/even harmonic ratio

• synchronicity of partials

• onset effects: rise time, presence of noise or

inharmonic partials during onset, unequal rise of
partials, and characteristic shape of rise curves

• steady state effects: vibrato, amplitude modulation,

gradual swelling, and pitch instability

What we notice from these parameters is that the spectrum
of the sound is critical, as are the individual frequencies,
the way the sounds change over time, their amplitudes and
the way these components interact with each other. Estos
parameters begin to give one a better idea of what timbre
actually is, but they still do not give a full view of how they
interact. This is where a spatial or geometric model of timbre
is beneficial.

Since timbre has no single dimensional scale that describes
él, when one reviews the research completed on timbre, one is
most likely dealing with a multidimensional space, or rather
a timbre space. A timbre space is “a model that predicts the
perceptual results of auditory stream formation and timbral
interval perception” [4]. Depending on the stimuli tested,
different correlates are produced.

https://doi.org/10.1162/leon_a_02034

LEONARDO, volumen. 54, No. 3, páginas. 337–343, 2021 337

Descargado de http://direct.mit.edu/leon/article-pdf/54/3/337/1925081/leon_a_02034.pdf by guest on 07 Septiembre 2023

t
r
a

d
norte
tu
oh
s

d
norte
a

s
tu
metro

Timbre space studies have used a variety of impulse
sounds, ranging from FM-synthesized simulations to re-
corded instrumental tones. The aim of these models is to
“find robust descriptors that explain perceptual data across
estudios, [a] develop perceptually relevant acoustic distance
models for measuring similarity objectively, [y para] find
powerful descriptors for sound categorization and source
identification” [5].

While there are many fantastic perceptual timbre mod-
els worth studying, including those of Howard Pollard and
E.V. Jansson [6], John M. Grey [7], Stephen McAdams et al.
[8] and many others [9], they have their limitations. por ejemplo-
amplio, the aforementioned studies do not explain unpitched
percussion or noise elements.

From a composition viewpoint, there haven’t been that
many composers who have made timbre the primary con-
cern in their music. While the first composers that often
come to our minds are from the spectral school, notably
Gérard Grisey [10] and Tristan Murail [11], the timbral sys-
tems of Krzysztof Penderecki [12], Kaija Saariaho [13], Pierre
Schaeffer [14] and Mathias Spahlinger [15] have particularly
fascinated me [16].

I have sought a model for my own purposes that both ac-
counts for the way we perceive timbre and allows one to work
with any sound/instrumentation. In this article, I outline the
conceptual timbre model I use when composing and give
examples from two recent instrumental works.

TiMBRe ModeLS in My MuSiC

I structure my works using six parameters, which I organize
into a set of two interlocking spaces or “cubes,” as I like to
visualize them (Higo. 1). The first cube essentially controls the
frequency components of the sound and has the following

three dimensions: spectral flux, spectral centroid and noise-
to-pitch ratio.

The first dimension, spectral flux, measures the Euclidean
distance between two spectra, or rather the change of spectral
energy over time. By extension, this dimension can be used
to control rhythms or the rate of pitch changes. This analogy
provides a measure of density in time analogous to spectral
flux at the intra-event level. Por ejemplo, in the model, a
sound with high flux indicates a high rhythmic activity or
that pitches are changing quickly, while a sound with low flux
would be one in which either there is a low rhythmic activity
or the pitches are stagnant.

The second dimension controls the noise-to-pitch ratio
and is similar to Kaija Saariaho’s “timbral axis,” a structur-
ing device used to create tension and replace functional har-
mony. On one end of the axis are sounds that are mostly
“pure” pitch—that is, sounds that are close to sine waves.
Por el contrario, the other end of the axis is “mostly noise” [17].
The third dimension controls the spectral centroid, o
bastante, the average centroid over time, and controls the
brightness and darkness of the sound. Por ejemplo, if the
space was evaluating the spectral centroid for a violin sound,
this axis would have four reference points—con sordino, sobre el
tasto, normale and sul ponticello—plus every shifting pos-
sibility in between.

The first cube is, sin embargo, missing key information,
namely the quality of the attack, the dynamic level and the
length of the event entering into the space. To solve this di-
lema, I use a second cube to inform these decisions. El
second space controls the evolution of the sound and works
in conjunction with cube I.

The first dimension—attack—controls how the sound or
gesture’s articulations are treated, ranging from no attack (o

Higo. 1. Timbre spaces used in my own works. (© Leah Reid)

338 Reid, Composing with Multidimensional Timbre Representations

Descargado de http://direct.mit.edu/leon/article-pdf/54/3/337/1925081/leon_a_02034.pdf by guest on 07 Septiembre 2023

t
r
a

d
norte
tu
oh
s

d
norte
a

s
tu
metro

a smooth onset) to a sharp attack (sharp onset); the second
dimension controls the length of the event, sound or gesture
that enters into the timbre cube; and the third dimension
controls dynamics.

With this conceptual model, each dimension scales, de-
pending on the source material and the function of the de-
sired result. One could use this model to learn more about a
sound’s timbral characteristics or map a composition’s instru-
mentation onto the space, thereby creating spatial coordi-
nates for every sound they wish to use and “see” the possible
relationships among them. This model can be used to derive
rhythms; generate a form, harmony and rate of material; o
simply inform the orchestration of the piece. With this ap-
proach, one can work with any sound or instrumentation.
One can use programs such as SPEAR [18], AudioSculpt [19],
OpenMusic [20], Orchids/Orchidea [21], Bach [22], etc., a
analyze these parameters, or one can work with the dimen-
sions intuitively. In either case, the model allows the per-
ceptual properties of timbre to address many compositional
elements across multiple dimensions.

To give an example of how one might use these spaces in
a composition, I outline below how I used the model in two
recent pieces.

Ostiatim

Ostiatim, for string quartet, comprises 15 fragments that ex-
plore the sounds produced by doors and the emotional in-
flections of people who interact with them. El título, significado
“door-to-door,” is meant to depict the timeline of the piece.
Each fragment is meant to be treated like a fleeting memory.
Sometimes connections are made, and other times, the mo-
ment slips away.

In this piece, the spectral flux dimension controls the fre-
quency and rhythm of pitch changes; the spectral centroid
controls bow placement and mute usage; the noise-to-pitch
ratio controls bow and finger pressure; the attack dimension
controls the attack quality, ranging from crescendo dal niente
to Bartók pizz.; the length of event ranges from short to long;
and dynamics range from niente to very loud. Cifra 2 de-
picts the way materials were viewed inside the space.

One can use the model to examine a static selection of
parámetros. Por ejemplo, fragment 1 comprises small bursts
of material with sharp onsets (Higo. 3). This point can be de-
scribed as having a mid-spectral centroid, a mid-high noise-
to-pitch ratio and a mid-high spectral flux.

One may also explore moving trajectories in segments of
material. Fragment 2 exemplifies some of the possible trajec-
tories that can be created with my timbre model (Higo. 4). El
fragment has two parts: measures 8–14 and measures 15–17.
In terms of articulations, the first part juxtaposes aggres-
sive pizzicati with arco sounds, and the second part features
delicate pizzicati and soft mid-noisy tremolos. Each part has
differing spectral flux coordinates. The first part of the frag-
ment has a high spectral flux, while the second part has a
mid-low flux.

The spectral centroid has multiple trajectories. One can
observe the motion in the second violin and the violoncello.
Por ejemplo, in measure 8 they move from sul ponticello to
ordinario, which can be viewed as a movement from a high
to a mid-spectral centroid. Another example can be seen in
measure 12 with a movement back to sul ponticello. Aquí,
the spectral centroid shifts back to high. In measure 13, ellos
shift to sul tasto, which can be viewed as a movement to a low
spectral centroid. The violoncello then does one more move-

Higo. 2. Timbre cubes as they relate to Ostiatim. (© Leah Reid)

Descargado de http://direct.mit.edu/leon/article-pdf/54/3/337/1925081/leon_a_02034.pdf by guest on 07 Septiembre 2023

Reid, Composing with Multidimensional Timbre Representations 339

t
r
a

d
norte
tu
oh
s

d
norte
a

s
tu
metro

Higo. 3. Ostiatim’s fragment 1. (© Leah Reid)

ment to sul ponticello before playing ordinario in measures
13-15. This motion can be viewed as a trajectory of a high to
low spectral centroid.

In terms of the noise-to-pitch axis, in measure 8, both the
second violin and the violoncello move from overpressured
bowing to normale bowing. This can be viewed as a move-
ment from a high noise-to-pitch ratio to a mid-low one.
The opposite motion can be seen again in measures 11–12
and 13–14. Además, in the second part of this fragment
(measures 15–17), the second violin and viola explore a mid-
high noise-to-pitch ratio while the first violin (measures
15–17) and the second violin (measure 17) explore a mid-
noise coordinate.

There are also overarching timbral poles/extremes and
large-scale trajectories occurring in the piece. Por ejemplo,
the “brightest” fragment is number 12, while the “darkest”
one is fragment 14. También, the noisiest fragment is number 10
while the “purest” one is fragment 14.

The composition is a series of abstracted door sounds that
explore both the gritty noisy aspects of these sounds and the
beautiful “emotional” side of them. The finished product is
not meant to be a replica of the original but rather an inter-
pretation of it.

Occupied Spaces

My next example, Occupied Spaces, for two pianos and per-
cussion, explores a series of timbral spaces, presented as
“rooms,” which grow, shrink and shift in shape. This piece
explores the concept of timbre in space.

The idea for the piece originated through my interest in
spatializing timbre, convolution and the topic of Normal-
ized Echo Density (NED) as defined in architectural acous-
tics [23]. NED describes how the reflections of a sound in a
given architectural space interact over time and the texture
that results. Some of the key terms and components associ-
ated with NED are: the sound’s clarity; focus and blur; el
perception of smoothness and roughness, or rather, the de-
gree of granularity of the sound; the ratio of direct to reflected

340 Reid, Composing with Multidimensional Timbre Representations

Descargado de http://direct.mit.edu/leon/article-pdf/54/3/337/1925081/leon_a_02034.pdf by guest on 07 Septiembre 2023

Higo. 4. Ostiatim’s fragment 2. (© Leah Reid)

t
r
a

d
norte
tu
oh
s

d
norte
a

s
tu
metro

Higo. 5. Example of an impulse
filtered to various degrees in
Occupied Spaces—measure 7,
depicting a single frequency in
a “room” vs. measure 289 con
encima 43 partials. (© Leah Reid)

signal in the sound; the dryness or wetness of a signal; y
the description of the number of reflections per second of an
acoustic signal. Por ejemplo, noises with low NED would be
perceived as “sputtery” and noises with high NED would
be perceived as “smooth.”

The work explores timbre through a series of 11 “rooms”
or conceptual spaces. Some of these spaces were modeled
after physically existing rooms; others were imagined and
do not follow the rules of physics and/or occur inside one’s
mind/head.

There are three impulses in the piece: a zipper, a clap and
a balloon pop. These impulses form the material that is in-
serted into the various rooms. These sounds are filtered to
various degrees, and over the course of the piece frequen-
cies are added to the impulses, thereby creating an increas-
ingly dense and, by analogy, noisy texture [24]. Por ejemplo,
in measure 7, only a single frequency is present within the
“room.” By contrast, encima 43 partials are present during the
climax in measure 289 (Higo. 5).

In my research, I looked at impulse responses of various
rooms, analyzed reverbs, created delay patterns and consid-
ered the resonant properties of different spaces. Similar to
the NED properties discussed above, I came up with room
classifications that I based on the following specifications: el
dryness/wetness of the sound, the number of reflections, el
degree of granularity, the characteristics of the overall sound
and the resonance of the space. To create clear timbral poles,
I decided that the two room-extremes would be an anechoic
chamber and an imaginary room with infinite reverb. El
other rooms fit between these extremes. By convolving im-
pulse responses with my original clap, balloon pop, zipper
sound and a single pitch (B4), I found each room’s specific
resonant properties, determined the rhythm of reflections

(if there were any) and analyzed the rooms’ dynamic curves.
After completing this process, I orchestrated the results,
choosing the instrumentation that best followed the rooms’
characteristic properties. Cifra 6 shows the resulting analy-
ses with notes on orchestration.

The piece’s overall form is divided into an introduction
and six main sections. Each section determines which rooms
are used, how many rooms can be present at any one time
and the degree of the noise-to-pitch ratio. Cifra 7 shows a
visualization of the piece’s form and timings of each room.
In Occupied Spaces the impulses interact with the rooms.
Both are essentially convolved. The rooms morph the in-
serted material and provide their own timbral trajectories.
The finished piece is the result of the collision of two formal
elementos: the rooms themselves and the material inserted
into them.

ConCLuSion

I am fascinated with how we perceive timbre, “timbre
spaces,” and the relationship between reverberant space and
timbre, or rather the concept of “timbre in space.” Over the
pasado 13 años, I have worked toward a conceptual composi-
tional model in which the “color” and “texture” of available
sounds are derived from multidimensional perceptual timbre
representaciones.

This model is essentially six parameters, organized into
two interlocking spaces, or cubes. The first cube controls the
spectral flux, the spectral centroid and the noise-to-pitch
ratio; the second cube controls the quality of the attack, el
dynamic level and the length of the event entering into the
first cube.

This method is a result of my admiration of and research
into spectral and postspectral concepts, perceptual studies,

Descargado de http://direct.mit.edu/leon/article-pdf/54/3/337/1925081/leon_a_02034.pdf by guest on 07 Septiembre 2023

Reid, Composing with Multidimensional Timbre Representations 341

t
r
a

d
norte
tu
oh
s

d
norte
a

s
tu
metro

Higo. 7. Graphical illustration of the temporal room spatialization in
Occupied Spaces. (© Leah Reid)

Schaefferian concepts and many composers’ approaches to
timbre. It expands upon and combines these ways of think-
En g. It allows composers to use sounds as acoustic models and
to structure both small- and large-scale elements in a work
using timbre perception as a guide. With this approach, tim-
bre may be used as a lens through which many compositional
elements may be explored.

With each composition, I find new ways to approach my
modelo. Ostiatim explores the orchestration of noise, and Oc-
cupied Spaces explores timbre in space through filtered im-
pulses and a series of rooms or spaces.

I have also explored these concepts with electronic media
(see Ring, Resonate, Resound and Crumbs), used timbre as a
structuring device (see Clocca) and developed new ways to
work with timbre and the voice (see Apple and Single Fish).
My interest in “timbre in space” has also led to significant ex-
periment with sound spatialization (see Sk(etch) and Reverie)
and collaborations with dancers—exploring relationships
between physical and perceptual spaces. Further informa-
ción [25], examples and recordings may be found at www
.leahreidmusic.com.

References and Notes

1 Stephen McAdams et al., “A Meta-Analysis of Acoustic Correlates of
Timbre Dimensions,” The Journal of the Acoustical Society of America
120, No. 5, 3275 (2006): www.doi.org/10.1121/1.4777215.

2 Hiroko Terasawa and Jonathan Berger, “A Hybrid Model of Timbre
Percepción,” The Journal of the Acoustical Society of America 124,
No. 4, 2448 (2008): www.doi.org/10.1121/1.4782593.

3 Caroline Traube, “Instrumental and Vocal Timbre Perception”
(2006): www.academia.edu/38557836/Instrumental_and_vocal
_timbre_perception (accedido 1 Puede 2020).

4 McAdams et al. [1].

5 McAdams et al. [1].

6 Howard Pollard and E.V. Jansson, “A Tristimulus Method for the
Specification of Musical Timbre,” International Journal of Acoustics
51, No. 3, 162–171 (1982).

John M. Grey and James A. Moorer, “Perceptual Evaluations of Syn-
thesized Musical Instrument Tones,” The Journal of the Acoustical
Society of America 62, No. 2, 454–462 (1977).

8 Stephen McAdams et al., “Perceptual Scaling of Synthesized Musi-
cal Timbres: Common Dimensions, Specificities, and Latent Subject
Classes,” Psychological Research 58, No. 3, 177–192 (1995).

In addition to the timbre models outlined in the article, I recom-
mend studying those of Peterson and Barney [26], Singh and Woods
[27], Von Bismarck [28], Pratt and Doak [29], wessel [30], Krum-

Higo. 6. Analytic transcriptions of the 11 “rooms” in Occupied Spaces.
The image depicts what results when a 16th note B4 is inserted into
each room. Pitches are altered, orchestration is informed and rhythms
are generated [43]. (© Leah Reid)

342 Reid, Composing with Multidimensional Timbre Representations

Descargado de http://direct.mit.edu/leon/article-pdf/54/3/337/1925081/leon_a_02034.pdf by guest on 07 Septiembre 2023

t
r
a

d
norte
tu
oh
s

d
norte
a

s
tu
metro

shansl [31], Iverson and Krumhansl [32], Lakatos [33], the IPA vowel
espacio [34] and the Timbre Is a Many-Splendored Thing conference
proceedings [35].

27 Sadan Singh and David R. Woods, “Perceptual Structure of 12 Ameri-
can English Vowels,” The Journal of the Acoustical Society of America
49, No. 6, 1861–1866 (1971).

10 Gérard Grisey, “Tempus ex Machina: A Composer’s Reflections on
Musical Time,” Contemporary Music Review 2, No. 1, 239–275 (1987).

11 François Rose, “Introduction to the Pitch Organization of French
Spectral Music,” Perspectives of New Music 34, No. 2, 6–39 (1996).

12 Danuta Mirka, “To Cut the Gordian Knot: The Timbre System of
Krzysztof Penderecki,” Journal of Music Theory 45, No. 2, 435–456
(2012).

13 Kaija Saariaho, “Timbre and Harmony: Interpolations of Timbral
Structures,” Contemporary Music Review 2, No. 1, 93–133 (1987).

14 Pierre Schaeffer, Traité des Objets Musicaux: Essai Interdisciplines

(París: Éditions du Seuil, 1966).

15 Philipp Blume, “Mathias Spahlinger’s 128 erfüllte augenblicke and
the Parameters of Listening,” Contemporary Music Review 27, No. 6,
625–642 (2008).

16 This list is not exhaustive. For a few additional examples, I recom-
mend the reader refer to research by Cogan [36], Erickson [37],
Lerdahl [38], Slawson [39], Terasawa [40], Thoresen [41] and Wishart
and Emmerson [42].

17 Saariaho [13].

18 SPEAR is a sinusoidal partial editing analysis and resynthesis tool,

available at www.klingbeil.com/spear (accedido 1 Puede 2020).

19 AudioSculpt is an IRCAM software for viewing, analyzing and pro-
cessing sounds described at http://anasynth.ircam.fr/home/english
/software/audiosculpt (accedido 1 Puede 2020).

20 OpenMusic is a visual programming language based on Common
Lisp and developed at IRCAM. The program is a useful environment
for music composition and is described at http://openmusic-project
.github.io (accedido 1 Puede 2020).

21 Orchids/Orchidea is a computer-assisted orchestration program de-
veloped at IRCAM and available at http://forum.ircam.fr/projects
/detail/orchidea (accedido 1 Puede 2020).

28 Gottfried Von Bismarck, “Timbre of Steady Sounds: A Factorial
Investigation of its Verbal Attributes,” Acustica 30, No. 3, 146–159
(1974).

29 R.L. Pratt and Philip Ellis Doak, “A Subjective Rating Scale for Tim-
bre,” Journal of Sound and Vibration 45, No. 3, 317–328 (1976).

30 David Wessel, “Timbre Space as a Musical Control Structure,” Com-

puter Music Journal 3, No. 2, 45–52 (1979).

31 Carol Lynne Krumhansl, “Why Is Musical Timbre So Hard to Un-
derstand?” in S. Nielzén & oh. Olsson, editores., Structure and Perception
of Electroacoustic Sound and Music (Ámsterdam: Excerpta Medica,
1989) páginas. 43–53.

32 Paul Iverson and Carol Lynne Krumhansl, “Isolating the dynamic
attributes of musical timbre,” Journal of the Acoustical Society of
America 94, No. 5, 2595–2603 (1993).

33 Stephen Lakatos, “A Common Perceptual Space for Harmonic and
Percussive Timbres,” Perception & Psicofísica 62, No. 7, 1426–1439
(2000).

34 IPA Vowel Chart: www.internationalphoneticassociation.org/sites

/default/files/IPA_Kiel_2015.pdf (accedido 1 Febrero 2021).

35 Etienne Thoret, Meghan Goodchild and Stephen McAdams, editores.,
Timbre 2018: Timbre Is a Many-Splendored Thing (Montréal, QC:
Universidad McGill, 2018).

36 Robert Cogan and Pozzi Escot, Sonic Design: The Nature of Sound
and Music (Cambridge, MAMÁ: Publication Contact International,
1984).

37 Robert Erickson, Sound Structure in Music (berkeley: Universidad de

California Press, 1975).

38 Fred Lerdahl, “Timbral Hierarchies,” Contemporary Music Review 2,

No. 1, 135–160 (1987).

39 Wayne Slawson, Sound Color (berkeley: Universidad de California

Prensa, 1985).

22 Bach is a source library providing Max/MSP for computer-aided
composition, available at www.bachproject.net (accedido 1 Puede
2020).

40 Hiroko Terasawa, “A Hybrid Model for Timbre Perception: Quan-
titative Representations of Sound, Color, and Density” (stanford
Universidad, PhD thesis, 2009).

23 Patty Huang et al., “Reverberation Echo Density Psychoacoustics,"
Proceedings of the Audio Engineering Society’s 125th Convention
(San Francisco, 2008).

24 While the densification of frequencies in itself does not equate with
an increased level of noisiness, in the case of Occupied Spaces, el
impulses themselves are different noises. Por lo tanto, as more frequen-
cies are added, by analogy, the true “noisy” nature of the sound is
revealed, thus creating an increasingly noisy texture.

25 Leah Reid, “Composing Timbre Spaces, Composing Timbre in
Space: An Exploration of the Possibilities of Multidimensional
Timbre Representations and Their Compositional Applications”
(Universidad Stanford, DMA final project, 2013).

26 Gordon E. Peterson and Harold L. Barney, “Control Methods Used
in a Study of the Vowels,” The Journal of the Acoustical Society of
America 24, No. 2, 175–184 (1952).

41 Lasse Thoresen, Andreas Hedman and James Grier, Emergent Musi-
cal Forms: Aural Explorations (Londres, ON: Department of Music
Research and Composition, Don Wright Faculty of Music, universidad-
sity of Western Ontario, 2015).