Musical notation can be seen as a technological tool for thinking that enables us to conceive novel structures and gain access to relationships between sound events that otherwise would seem unapproachable. At the same time, writing music on paper raises certain puzzling questions about the nature of musical objects. How can a musical object exist simultaneously in different mediums? Is sound the image of the score or the score the image of sound? Consider, for instance, the beginning of Beethoven’s Fifth Symphony. Is it the same motif when performed by a professional orchestra as when whistled by someone in the street? Some may reply that in these instances, the motif is reproduced with various degrees of correctness, which is rightly represented in the score. In the same way that a triangle can be rigorously expressed by trigonometric functions but never perfectly drawn, the motif is a kind of a priori that exists in an ideal realm—and therefore we can only aim to execute it as accurately as we can. But if we then look at the score, we still face similar questions: is the motif the same when it appears in different instruments of the orchestra? Or when its rhythm is augmented or the melody harmonised? The same goes for more complex musical objects and transformations. When does a musical object stop being itself and become something else?
There is a long-standing disagreement in the Western tradition over the intrinsic nature of music and whether abstract conceptualisation or concrete phenomenal experience and practice should come first. Berio 1 traced what Earle called a “hoary dualism” 2—and Christensen described as an “invidious dichotomy” 3—back at least to the writings of Boethius, in particular his highly influential De institutione musica. Although mostly concerned with sound, music for Boethius was purely a mathematical science (part of the numerical sciences—the quadrivium, which included arithmetic, geometry, astronomy, and music theory), the task of which was to study rational relations between whole numbers. 4 Music was conceived above all as “a means of knowledge,” 5 “a path to philosophical wisdom, consisting in the passage from sensible knowledge to the highest achievements of the intellect.” 6
This Platonic conception of music “as an abstract science of discrete numerical relations” 7 persisted through centuries, and Boethius’s “highly sophisticated mathematical discussion of interval ratios and proportions remained authoritative … for medieval readers until at least the fourteenth century.” 8 However, the idea that music theory in the Middle Ages was hostile to practical aspects of music and its sensual enjoyment should be nuanced and received with caution. As Hentschel argued, the issue is much more rich and complex. Already before Boethius, deviations from Platonism in the Pythagorean tradition can be found, for instance, in Ptolemy (ca. 100–178), who provided a highly developed and refined description of the roles of reason and perception. 9 To quote Thomas Christensen, “the glory of much medieval theory is how it so brilliantly mediates these two epistemological extremes (if not fully reconciling them).” 10
By the end of the thirteenth century, the influence of Boethius showed signs of waning and the attention of several scholars shifted from an interest in abstract aspects of musical speculation (numerus sonorus) to the study of music as an acoustical phenomenon. 11 This reorientation is reflected, on the one hand, in the incorporation of music into the “middle sciences” (scientiae mediae), a term created to define sciences halfway between mathematics and physics, and, on the other hand, in a progressive transition of music towards the trivium’s territory, a “trivialisation” produced in particular because of the growing interest in studying music in connection with grammar and rhetoric. 12
Nevertheless, the invidious dichotomy has adamantly persisted in different forms until the present.
Berio’s generation witnessed several quarrels between proponents of opposing views (e.g., integral serialism versus chance music). Today (probably with less belligerence than in past decades), we can still find grouped under the same umbrella term of “contemporary music” composers such as Pierluigi Billone, who states that his material is sound, “Le son est ma matière,” 13 and Mark Applebaum, who has composed at least some of his work without sound in his head. 14 Also included are “Platonist” composers such as Tom Johnson, who is interested in “finding the music” in mathematical models. Sound, Johnson seems to concede, is not the music, but the image of it—“I want to find the music, not to compose it.” 15
As a composer, I find these issues fascinating, as they call into question the nature of musical objects and music itself. As Sloboda observed, “music is a constantly evolving product of human culture, whose forms, functions and discourses are not fixed. It is what we decide to make it.” 16 Or, in Cook’s words: “Music doesn’t just happen, it is what we make it, and what we make of it.” 17 Mediating between abstract and concrete and between intuition and formalism has been significant for my practice as a composer since the very beginning. In the following, I propose tackling the issue by using the notion of framing, which involves considering music to be not (only) about sound, nor (only) about notation, but mainly about understanding.
To start, I would like to point out what I believe is a particular feature that musical objects share, at least to some extent, with what Noam Chomsky calls the “atomic concepts” of language. 18 According to Chomsky, in ordinary language we do not have names for things; naming may indeed be seen as a kind of “worldmaking” in Nelson Goodman’s sense, 19 “but the worlds we make are rich and intricate and substantially shared thanks to a complex shared nature.” 20 A river can still be the same river (with the same name) even if the water in it is replaced by coffee or its course is reversed. Even an apparently transparent word such as “thing” cannot account for the notion of thinghood, because its identity condition cannot be clearly defined: “Suppose we see some branches strewn on the ground. If they fell from a tree after a storm, they are not a thing. But if they were carefully placed there by an artist as a work of conceptual art, perhaps given a name, then the construction is a thing (and might win an award).” 21 The atomic concepts of language have an abstract character in the sense that they do not refer to mental-independent entities in the world—and this is essential for their multiple instantiations and individuation. 22 I find this idea quite adequate to describe (at least metaphorically) the way I conceive musical objects, as their functions are never fixed and their meanings (whatever they may be) are intricate and complex.
For Goodman, Cook writes, musical objects are “allographic, instanced equally by scores, performances, or sound recordings.” 23 As with the atomic concept of language, musical objects do not necessarily denote actual things in the world; rather, they are instances of a certain mental notion that we have of them and that we share, which may vary depending on individual perceptual capacities, knowledge, and circumstances.
Framing sound and other objects is a kind of “worldmaking.” As Goodman remarked, frames of reference “seem to belong less to what is described than to systems of description.” 24 This is to say, as I understand it, that when we put something within a particular frame, we are not exhausting the possible ways of describing that object. In other words, we are not really referring to a specific thing in the world, but rather only providing a certain frame through which the object can be described according to a particular system. The same physical object, within different frames, can be something quite contrasting; therefore, it is the system of description that matters more than the nature of the object itself. A sound can be a musical note, an alarm, speech, noise, a “sound object” (in Pierre Schaeffer’s sense, or in any other sense), a “musical thing,” and so on. 25 But it is nothing (that we can name) without a particular frame of reference. The same applies to musical materials other than sound.
Goodman introduced the notion of the sample to explain how an object can exemplify some of its properties—but not all its properties, “for then the sample would be a sample of nothing but itself.” 26 A red book can then be a sample not only of red but also of a book, of English, of its author, or of a particular genre or subject; and, depending on its use and function, it could also be a sample of a doorstop or perhaps a fly swatter.
I find this idea useful for understanding how musical objects of different natures can relate to one another (e.g., by exemplifying the same property), and why their meanings can be so intricate (for they can simultaneously be a sample of several properties). Because of their abstract character, musical objects can be instantiated (allographically) multiple times; and, being mental-dependent entities, what they are a sample of depends on our command and understanding of the system of categories within the musical domain. Importantly, understanding here involves “understanding or cognition in all of its modes—including perception, depiction, and emotion, as well as description.” 27 I think that as practitioners we can also employ this idea to enable creative opportunities and to recognise affordances in different materials (sound, instruments, numerals, etc.). In what follows, I would like briefly to present examples from two of my own works.
Musical objects can be a sample of multiple things simultaneously. In a recent work, Reframing, I tried to define and formalise (without algorithmic sophistication, but rather through simple procedures) what different instances of musical objects could exemplify. Often, exemplification is something associated with reception and interpretation (after we are confronted with the object). Here I proceeded by deciding in advance what combination of properties each object would exemplify, as a kind of prompt for creativity (although I do not expect that the listener will perceive the process in exactly the same way that the work was composed).
Independent sets of properties (three for the violin, two for the bass clarinet) were defined and ordered in quasi-symmetrical tables (figures 1–5). These properties do not determine a unique output (there is plenty of room for interpretation), but impose some kind of constraint on what properties each instance of the object will exemplify. This allows me to create multiple instances of hybrid objects, in the sense that properties are mixed and recombined in each occurrence. Rhythms and durations (figure 6) were determined following an independent process.
Figure 1. First set of properties for the violin (bow techniques).
Figure 2. First set of properties for the bass clarinet (techniques).
Figure 3. Third set of properties for the violin (number of “pivot” pitches).
Figure 4. Second set of properties for the violin (sound qualities).
Figure 5. Second set of properties for the bass clarinet (articulation).
Figure 6. Durations were generated independently using the software Open Music.
The first instance of the violin [I, A, 1] is a sample of a sustained sound, with slow bow and no transitions, performed on the open fourth string and a high harmonic in the third string (example 1). What I find interesting in proceeding this way is that each of these properties are themselves intricate and complex—each of them may exemplify several things—which is emphasised by the constant variation and combination of the constraints (see example 2 for an illustration).
Example 1. First instances of musical objects in the violin part.
Example 2. Different instances of musical objects in the violin part.
This example is characteristic of my work. I often create self-contained objects, which I then transform in several ways. This idea is related to what Burge calls objectification, which is implemented in perception by perceptual constancies (also known as perceptual invariances), such as shape constancy, location constancy, and luminance constancy. 28 Consider for instance looking at a window, the shape of which you recognise as rectangular even though its actual profile might be trapezoidal from your position. 29 Analogously, in the passage shown below from my violin trio Difference Identities (example 3), a canon is fragmented and then each fragment is stretched and compressed in different proportions (as if the window from the previous analogy actually deforms when you move). Furthermore, each violin has a different scordatura (though notice that only the order of the pitches changes), which means that the same gesture produces a different result on each instrument. What interests me here is that the identity of the objects is not clearly defined, as it is modulated by the scordatura and constantly altered by the stretching and compression processes. I like to think of this being like perceptual constancies becoming unstable and variable while listening to the same object. Another way to see this example is to think that only certain features of the objects are shared—for example, each instance is a sample of the same instrumental gesture, rhythmic proportion, notation, sound quality, and so on—but that other properties, such as duration (or tempo) and pitch order, are unique to each instance.
Example 3. Difference Identities violin trio, fragmented canon.
In the Western musical tradition there has been a persistent invidious dichotomy characterised by the opposition between abstract and concrete, conception and realisation, notation and sound, formalisation and intuition, and so on. This chapter looked at the issue by considering musical objects as mental-dependent entities analogous to the atomic concepts of language, in the sense that they also have complex meanings and an abstract character that enable their multiple instantiations—which is consistent with Goodman’s conception of musical objects as allographic. Goodman’s notion of exemplification also helps us understand how musical objects of different natures can participate in a system of description belonging to the same domain. Objects exemplify different things in different circumstances; therefore, a sound, a gesture, or a movement or light on the stage can all be a sample of the same properties in a particular system. It follows that musical objects do not have “parameters,” but properties, which are variable and intricate. I use the term framing—which is a way of “worldmaking,” in Goodman’s sense—to designate the creative endeavour of enabling and exploring the potentialities of objects, independent of their nature, within the musical domain. In this view, music is not about sound, nor about notation, but about understanding—in a broad conception of the term, including cognition and perception in all their modes.
I used examples from two of my works to suggest that this way of thinking about musical objects could be valuable for both theorists and practitioners. These examples are not exhaustive, but suggest that conceiving musical objects as non-fixed entities (the motif from Beethoven’s Fifth Symphony, in different instances, can be a sample of different things, and by parity of reasoning, several objects can be a sample of it as well) may offer creative opportunities and alternative tools for understanding music, and perhaps also for imagining new ways of making it.
Cite as
Galaz Salamanca, Pablo. “Mental-Dependent Musical Objects: Framing and Objectification in My Musical Practice.” In Imagining the Non-Present: Thought Experiments on Rich Temporality in Sound, edited by Carlo Diaz. SONUS Series. Ghent: Orpheus Instituut, 2026. https://doi.org/10.47041/SONUS.2026.2.
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