1 Introduction

In this paper, we examine the ontological foundations of computer-generated music scores.⁽¹⁾ We focus on creative music systems that generate musical works written in scores to be performed, generally, by human players. Specifically, we will examine recent developments in genetic algorithms and evolutionary systems applied to musical composition to produce musical works for live performance. For this purpose, we take as empirical data the features of the Iamus computer, a system that follows an evo-devo approach, combining an evolutionary algorithm with an indirect encoding scheme. This approach allows Iamus to compose musical works autonomously in a contemporary original style. Iamus is autonomous in the sense that it simulates the full process of professional music composition in generating complete professional scores of new musical works (Díaz-Jerez, 2011, p. 14). In addition, Iamus does not imitate a style previously developed by any particular musician. Iamus produces its works in its own original atonal style, and employs disparate colour effects and contemporary resources in the orchestration of a piece (Sánchez-Quintana et al., 2013, pp. 100, 102). This point is what makes the difference between Iamus and knowledge-based systems, such as David Cope’s EMI Project. These are the two most salient features of Iamus that, in this article, lead us to take this creative system as a point of reference. The advances achieved in the Iamus computer have been acknowledged by Ball (2012), Coghlan, (2012), and Berger (2013), and its works have been recorded by renowned international soloists and orchestras. The conclusions drawn here could be easily extended to musical works not only generated by computers in scores, but also to those pieces generated in sound, as we will show below, despite this aspect being initially beyond the scope of this paper.

The ontology of music is structured around two logically independent questions: the categorial question and the individuation question. The categorial question aims to determine the kind of ontological category that musical works belong to. This task involves considerations concerning the existence and persistence conditions for musical works, and it has consequences for the determination of what it is to compose a musical work. The individuation question enquires into the conditions that settle the identity of musical works, and it is related to the way we appreciate musical works and their performances aesthetically. Since these two questions are logically independent, in this article we will focus on the categorial one. Our contention is that not all the possible answers to the categorial question in the ontology of music are equally compatible with the hypothesis that creative music systems, in general, and the Iamus computer in particular, compose musical works. The thesis defended here is that musical Platonism is the proposal that best accommodates this hypothesis. We claim that musical Platonism is the answer to the categorial question that offers the most straightforward explanation for the possibility of considering creative music systems as genuinely composing musical works. Moreover, we uphold that the notion of creative-evaluative discovery, as the characterization of what it is to compose a musical work entailed by Platonism, is the simplest explanation of the process developed by a computer in generating musical works, either in scores or sounds.

The second section of this paper offers a brief explanation of the main features of Iamus that will be relevant for the theses defended here. In the third section, we will examine musical Platonism. Fourthly, we will show how musical Platonism can accommodate the hypothesis that creative music systems compose by means of the notion of creative-evaluative discovery. In the fifth section, we will show that Platonism is the proposal that best accommodates the hypothesis in comparison with the other alternative answers to the categorial question. Finally, we will consider the phenomenon of a work’s versions as a problem for the hypothesis that can be reconciled in an elegant way by Platonism.

2 The Iamus Computer

We analyze the ontological foundations of computer music in order to determine which answer to the categorial question is the most suitable to accommodate the hypothesis that creative music systems compose musical works. With this aim, we seek to avoid speculative reflection and thus start by considering some empirical data concerning creative music systems. Specifically, we will focus on computer-generated music scores, and we will take the Iamus computer as reference. The reason for this choice involves two salient features of Iamus: it is autonomous in generating its musical works – that is, Iamus produces them without human intervention – and it offers them on correctly written musical scores (Díaz-Jerez, 2011). In other words, Iamus is provided with all the tools needed for the simulation of the full process of professional music composition, and the result of this process is offered in professional scores that fit the technical constraints of the instruments involved.⁽²⁾ The sense of “autonomy” employed here is the same as that used by Nierhaus to characterize what he calls “agents”.⁽³⁾ Together with situation in an environment and interaction with other agents, autonomy is taken to be one of the three features that characterize an agent (cf. Nierhaus, 2009, pp. 252–254). An agent is said to be autonomous in the sense that “it performs some tasks of problem solving to the most part independent of other agents” (Nierhaus, 2009, p. 252). In generating its musical works, Iamus fits the three conditions for taking an agent to be autonomous (cf. Nierhaus, 2010, p. 252): it acts continuously for some time, it plays a role in the art world’s network, and it has uniqueness, to the extent that it does not imitate any previous style in its compositions. Due to these salient features, the relevance of the Iamus computer has been noteworthy, reflected in several articles in high-impact journals (Ball, 2012; Coghlan, 2012; Berger, 2013). Its works have been played in live concerts and some of them have been recorded on CD, featuring performers such as David Ballesteros, Sviatoslav Belonogov, Cristo Barrios, and the London Symphony Orchestra. Iamus’ pieces are saved in a repository (Infinitunes) in different file formats: standard MIDI Files, FLAC lossless audio, printer-friendly PDF and the MusicXML file format (Díaz-Jerez, 2011). In this section, we describe some technical data of Iamus, and we highlight features of the system that are relevant for an ontological account of computer music.

Iamus is a computer cluster composed of 352 AMD processors using the Debian GNU/Linux operating system. Iamus is based on an evolutionary algorithm and, as with other systems using evolutionary algorithms, it follows a common pattern of Population-Based systems, that can be described in this way: “a changing set of candidate solutions (a population of individuals) undergoes a repeated cycle of evaluation, selection and reproduction with variation” (Fernández & Vico, 2013, p. 546). The starting point of this pattern, shared by Iamus with other systems employing evolutionary algorithms, is the generation of a population of individuals (the candidate solutions of the initial set). In the case of Iamus, this initial population is randomly generated, but it can also be generated from user-specified examples. Each candidate is evaluated using a fitness function, a function that determines the adequacy or inadequacy of the candidate, i.e., the quality of the candidate. Once the quality of the candidates is determined, the best ones are selected, so that the diversity of the population decreases. The diversity can be restored by the application of operators of mutation and recombination to a fraction of the candidate solutions. This process is iteratively applied and, as a result, the fitness average tends to increase by degrees.

The differences between Iamus and other evolutionary algorithmic systems have to do with the selection rules, variation operators and solution encoding (cf. Fernández & Vico, 2013, pp. 546–555). Two main points differentiate Iamus from other systems using evolutionary algorithms: on the one hand, Iamus is programmed following an evo-devo (evolutionary developmental biology) strategy; on the other, in contrast to classical evolutionary algorithms, it uses indirect encodings.

According to the evo-devo view, “developmental processes can be described as self-organized choreographies of precisely timed events, with cells dividing and arranging themselves into layers of tissues that fold in complex shapes, resulting in the formation of a multicellular organism from a single zygote” (Sánchez-Quintana et al., 2013, p. 100). Accordingly, evolutionary changes are interpreted as mutations in the organisms’ genomes, which modulate their developmental processes, giving rise to altered forms and new features. As an application of the evo-devo strategy to the field of music composition, Iamus has been programmed following a bio-mimetic approach, the view of artificial intelligence that mimics the evolutionary and developmental processes typical of living beings. The creators assumed an analogy between music and living beings: the hypothesis that, structurally, the complexity of a musical work resembles that of a living being. Thus, the simulation in a computer system of the embryonic development of multicellular organisms is applied by Iamus to the composition of musical works.

The second feature that distinguishes Iamus from other systems, the use of indirect encodings, is what allows the implementation of the evo-devo approach by the algorithm used in Iamus. Conventional evolutionary algorithms employ direct encodings: they straightforwardly map genotypes (representations of solutions) to phenotypes (the solutions themselves). In a classical evolutionary algorithm, each part of the phenotype is mapped to a part of the genotype, so that genotypes can overgrow to be practical. By contrast, the Iamus algorithm employs indirect encodings: “formal abstractions of developmental processes that define complex mappings between genotype and phenotype” (Sánchez-Quintana et al., 2013, p. 100). In the case of indirect encodings, we can reach complex solutions (phenotypes) from very simple representations (genotypes) and, since small variations in genotypes can prompt a variety of changes in phenotypes, complex variations of the solutions (phenotypes) can be easily generated. Therefore, with conventional evolutionary algorithms, we should not go beyond the implementation of biological-evolutionary processes (artificial evolution), to avoid awkward problems.⁽⁴⁾ On the other hand, the use of indirect encodings in the Iamus algorithm enables the implementation not only of biological evolutionary processes, but also of developmental processes (artificial development). Thanks to indirect encodings, Iamus compositions develop from genomic encodings in a way resembling embryological development, achieving highly structurally complex entities at a low computational cost (cf. Fernández & Vico, 2013, p. 550).

Accordingly, Iamus is not only based on an evolutionary algorithm – that is, one that uses mechanisms inspired by biological evolution, such as selection, mutation, reproduction, recombination, and so on. It also merges bio-inspired techniques: on the one hand, its compositions evolve in an environment ruled by formal constraints and aesthetic principles; and, on the other, its compositions are developed from genomic encodings in a manner that resembles embryological development (Fernández & Vico, 2013, p. 550). Therefore, the process implemented by Iamus in composing a musical work is a genomic-evolutionary process that can be described as follows:

1. The inputs introduced in the computer are the duration of the work and the instrumentation, that is, the number and kind of instruments that we want to perform the piece.
2. Once these data are introduced, the system randomly generates different musical genomes. The notion of “musical genome” is equivalent to what in musical analysis is called “generating cell” or “musical motif”, the most basic formal element upon which a musical work is generated. A musical motif is a finite set of sounds, with a given pitch, rhythm, articulation and dynamics. Thus, the musical genome generated by the system consists of symbols for pitch, rhythm, articulation, and dynamics. Structurally, these symbols are taken to be analogous to four of the nucleobases of human DNA: adenine, thymine, cytosine, and guanine.
3. These musical genomes, randomly generated, evolve through genetic operators, such as mutation, selection, genetic recombination, etc. The genomes compete for the best fit to the starting requirements, i.e., the binomial of the work’s duration and instrumentation. Only the fittest genomes for these requirements survive. As happens in the evolution and development of living things, once the genome of the work is constituted, the process of evolution and development of the work from that genome is a deterministic process.
4. The complexity of this evolutionary process is projected by Iamus to musical parameters, such as instrumentation, notation, formal aspects (such as the configuration of beginning, peak, and end of a work), indications of phrasing, articulation, tempo, and so on.
5. Only the compositions that overcome the fitness function survive. Among the conditions or rules set by the fitness function are: (i) instrumentation conditions, according to which the work composed must be technically performable by musicians; (ii) notation conditions, requiring that the work’s score offered by Iamus must be notationally correct – for instance, scores in which a bar of 4/4 includes 10 quavers are ruled out; (iii) formal conditions, for example, the idea of a beginning, a climax point and a conclusion as general features of the structure of a piece; (iv) expressive conditions, determining the most suitable nuance for an instrument’s passage in the environment of the piece and in consideration of the technical requirements of the instrument involved (crescendo, diminuendo, ritardando, forte, mezzo forte, piano, etc.); (v) user conditions, of which there are only two: the duration of the piece and the work’s instrumentation; and (vi) aesthetic conditions as, for instance, avoiding an excessive concentration of dissonances, or finding suitable colour combination of instruments.

Therefore, in the Iamus computer, the evaluation is made by means of a fitness function. In this fitness function are included fixed rules, for example, the range that can be played by a French horn, by a violin, by a clarinet, etc. However, the use of indirect encodings allows Iamus to implement an artificial development following an evo-devo approach. In this sense, Iamus does not try to simulate either the behaviour of human composers’ brains nor a simple evolutionary process. It applies the bio-inspired process of artificial development to the composition of musical works. In summary, the process followed by Iamus in composing a musical work is said to be analogous to the development and evolution of living beings because there is an initial moment of randomness in which the musical genome is structured; afterwards the musical genome is subject to deterministic laws of evolution and development (through the function of performance); and finally the result is a well-formed musical individual – i.e., a score that is notationally correct and performable by the instruments prescribed.

Three further aspects reinforce the idea of considering Iamus as a composer. Firstly, the system is completely autonomous in producing a musical work. Once the data of duration and instrumentation of the work are introduced, it is impossible to know beforehand the final work that the system will offer. Also, it is impossible to control or influence Iamus while composing the work, and in this sense the final score is produced exclusively by the computer. The second relevant aspect is that Iamus has not been programmed to mimic the aesthetics of any previously existing style. For instance, by the addition of the necessary constraints to the performance function, Iamus could have been programmed to compose works in accordance with Baroque aesthetics. These constraints could have been implemented by parameterizing in probabilistic terms the most common melodic movements and chords employed in the Baroque style. However, Iamus has been designed to compose music in a contemporary atonal style, thereby avoiding imitation of the particular style of any previous composer. Finally, the scores offered by Iamus have the necessary and sufficient elements to be played by musicians. It is claimed that “Iamus’ scores are indistinguishable from any other written by a human composer”, and so the performer faces Iamus’ scores as any other score written by a human being (Vico & Díaz-Jerez, 2012).

These are the features of the Iamus computer that will be relevant in the following sections of this article. Although the aim of the article is to provide an ontological account of computer-generated music (scores) from a general perspective, we will take the characteristics of Iamus as the empirical data to serve as the starting point for our considerations and as a point of reference with which to compare the results achieved.

3 The Categorial Question: Introducing Musical Platonism

The categorial question is the inquiry concerning what kind of entity musical works are. To answer the categorial question is to assign an ontological category to musical works. For instance, musical works can be said to be abstract objects (types), concrete objects (fusions, classes, sets), action types, action tokens, mental entities, and so on. The relevance of the categorial question lies in the interest of knowing what kind of existent are musical works (Dodd, 2008, p. 1114). By placing musical works within a given ontological category, we get a set of features that help us to characterize their nature. The answer to the categorial question has consequences for the existence and persistence conditions that we ascribe to musical works. If, for example, musical works are mental entities, they cannot exist before a being with mind has thought about them. Or, if musical works are platonic abstract entities, they have no temporal or spatial origin, and thus they are eternal. Therefore, since the answer to the categorial question has consequences for the existence conditions of musical works, it also determines what is to compose a musical work. Roughly, if we claim that musical works are mental entities, we are committed to the idea that musical works are created by mental activity; and if we state that musical works are platonic abstract entities, we must say that musical works cannot be created at all. In this section, we are going to examine in some detail musical Platonism, the view that we take as the most suitable account for accommodating the hypothesis that creative music systems compose musical works.

Musical Platonism is a variety of ontological realism about abstract objects. Applied to the ontology of music, ontological realism about abstract objects claims the following thesis:

REALISM: Musical works are types, i.e., abstract objects that can be exemplified in particular performances.

Realism assigns to musical works the ontological category of types. Types are abstract objects – that is, objects which are neither physical nor mental in that they are neither located in space nor are mind-dependent. The peculiarity of types among the variety of abstract objects is that types can be exemplified in other objects, called the tokens of the type. Tokens are concrete particulars. The relation between types and tokens is usually taken to be that of exemplification: a token is not a copy that resembles a type, but an exemplar of it where the type is manifested. Having tokens is what makes types repeatable, and this is the feature (repeatability) usually taken to distinguish types from other kinds of abstract objects (Wetzel 2009, p. xi). Different performances of the same musical work are said to be tokens of the same type.

Within the realm of realist answers to the categorial question, Platonism adds a thesis concerning the existence condition for types, giving voice to the intuition that types do not have temporal origin. Following Dodd (2007),⁽⁵⁾ the Platonist thesis can be defined in the next way:

PLATONISM: If musical works are types, they are not the sort of thing that can be brought into existence.

A type is individuated by the condition that something must satisfy in order to be a properly formed token of that type. This condition is a property associated with that type. Dodd derives the existence conditions of types from the existence conditions of their associated properties: since properties are eternal, types are also eternal (Dodd, 2007, p. 60). This approach seems to do justice to a very old tradition in philosophical thought that draws a link between music and mathematics: the Pythagorean view of music as a science of proportions.⁽⁶⁾ Under this perspective, musical works can be reduced to numerical proportions between the tones and pitches compounding them. It makes sense to say that the essence of a musical work is the relation between the wave frequencies of the tones that comprise the work. This sequence of sounds can be expressed numerically and considered to be mathematical in nature. One of the most salient features of mathematical entities is that they seem to be ontologically independent of any mental process and of their being instantiated in the physical world. For instance, the existence of the square as a geometrical entity does not depend on the existence of square things in the physical world. Nor does it depend on being conceived of by any mind. Therefore, it is plausible to take mathematical entities as existing before there were beings with minds in the world. These are, roughly sketched, some of the motivations supporting the intuition that mathematical entities and musical works have no origin.

Thus, if musical works are types, they exist for eternity and have no origin. This claim entails the consequence that musical works are not the kind of things that can be created. However, if musical works cannot be created, what is it to compose a musical work? It might seem that the only alternative to the thesis that composing is to create an entity would be to say that composing is to describe, copy or transcribe an existing type. However, according to Dodd this is a false dilemma. Creating, on the one hand, and copying (transcribing), on the other, are not the only two options to characterize what it is to compose a musical work (Dodd, 2000, p. 431). According to Dodd, Platonism is compatible with another view that does more justice to the value that we attribute to composers: to compose a musical work is to make a creative-evaluative discovery.

First, note that Dodd distinguishes between two kinds of discovery: on the one hand, those cases in which what is found is the goal or culmination of an inquiry; on the other, those cases in which what is discovered is something other than the target or culmination of an inquiry (Dodd, 2002, p. 386). In the first case, research is guided by criteria of success and, consequently, there are possibilities of being mistaken. In this kind of inquiry, what is sought is a certain state of affairs, something that satisfies a factual description the world. This description is the intended purpose of the inquiry and is what determines the success criteria: if what is discovered does not fit the description, then our research has been unsuccessful. For example, Christopher Columbus thought he had discovered a new sea route to Asia, but he was mistaken because the territory that he reached was not Asia but America. Therefore, the salient feature of this first kind of discovery is that it allows for the possibility of error. However, it sounds strange to say that composers can be mistaken in composing their works. We can find in the history of music examples of awkward works or compositions that have been rejected in their original or subsequent contexts, but even in those cases we tend to resist the idea that the composer has been mistaken in writing this or that melody. Hence, if we wish to characterize composers as discovering the works they compose, we cannot appeal to this first kind of discovery.

Crucially, in the second class of discovery considered above, the research is not guided by criteria of success and, consequently, there is no possibility of error. In this case, since there is no goal conceptually determined beforehand, there is no instance that can determine a criterion of success. According to Dodd, this kind of discovery is the one that corresponds to the act of composing a musical work. When Beethoven wrote the “Archduke” Trio there was no possibility for him to be mistaken. Although the type of this work already existed from eternity, neither Beethoven nor anyone else had a clear representation of that work before the score of the work was written. Beethoven only began to get a clear representation of that work when he was advancing in the process of composition of that piece. Thus, Beethoven could not have any particular or completely determinate goal before carrying out the act of composition of the “Archduke” Trio (Dodd, 2002, p. 387). The process of gaining a clear picture of the work coincides with the compositional act itself and, consequently, there is no gap between representation and inquiry that allows for the possibility of being mistaken, in contrast to the case of Christopher Columbus.

For the Platonist, to compose a musical work is not merely to make a simple discovery, but also a creative discovery. Within the Platonist framework, creativity cannot be attributed from an ontological point of view to the process of composition of musical works. Indeed, from an ontological perspective, the compositional process is not creative because types exist from eternity and, therefore, composers cannot be considered as adding any new entity to the world through their activity. Rather, Platonism ascribes creativity to the compositional process from an epistemological viewpoint. From this perspective, the process of composition itself is creative, because the composer, through the discovery of a type, is giving us news of an entity that we did not know before. In composing a musical work, a composer is adding something new to our culture (Dodd, 2000, p. 430). Thus, the composer comes across something that was already there, a type, but the way to meet it requires creative thought and the use of imaginative skills (Dodd, 2002, p. 382). Therefore, composers are not creative because they add new entities to the world, but due to the imaginative ability, that other people lack, to find, and let us know about, a previously existing entity (the musical work). For instance, Dodd claims that our use in ordinary language of expressions such as “the composer of the Fifth Symphony” or “the inventor of the steam engine” does not signify that those described as “composer” or “inventor” are really bringing into existence the type of the Fifth Symphony or the type of the steam engine, respectively. With the use of the expression “the composer of the Fifth Symphony”, as with the use of the expression “the inventor of the steam engine”, we are referring to the ingenious individual who was first in reaching the idea of this type of music work (or steam engine), and whose imaginative act began the process that led to the creation of the first exemplar of that type (Dodd, 2000, p. 429).

Moreover, the process of musical composition for the Platonist is not only a creative, but also an evaluative discovery. The process of discovering a type is evaluative because, according to Dodd, the composer evaluates what structure of sound types, once executed, will achieve the effect that the composer aims to achieve, and the result of that assessment is the indication by the composer of that structure in a score (Dodd, 2000, p. 431). What the composer writes in the score refers to something that already existed before, but it is also something he or she has selected evaluatively. Therefore, to carry out an evaluative selection, in the way Dodd is using this notion, implies:

1. having different possibilities from which to choose one; and
2. having a criterion by which to make that choice.

Platonism claims that both aspects take place in the process of composing a musical work. The main Platonist thesis is that if musical works are types, they exist from eternity. With this claim, Platonism assumes the independence between the ontological and the epistemological levels. All the possible types exist from eternity, regardless of whether we know them or not. As an audience, we have epistemic access only to those types that have already been indicated by composers. However, thanks to having superior imagination and musical knowledge, composers have the chance to grasp different types that have not yet been identified by any other composer (this is the creative character of their discovery). Accordingly, in the first place, composers have the possibility to choose between different possible types of sound-sequence events, which satisfies the first requirement of an evaluative act. And secondly, the composer has to choose one of them by analysing which of these types, epistemically available to him or her, is more likely to achieve the intended effect on listeners. Therefore, what the composer writes in the score is something that already exists before, but that he or she has evaluatively selected (Dodd, 2000, p. 431).

In this section, we have introduced the main features of types, the ontological category that Platonism assigns to musical works, and the characterization of what it is to compose a musical work according to Platonism. In the next section we will show how these two aspects of Platonism offer a suitable accommodation of the hypothesis that creative music systems compose musical works.

4 Platonism and Creative Music Systems

In this section, we are going to examine the compatibility between the Platonist account of musical works and the hypothesis that creative music systems are genuine composers. For this purpose, we will take into consideration the most salient features of the Iamus computer described above, and we will try to show how musical Platonism can accommodate them in a simple and direct way. Specifically, we will try to show:

1. That the Platonist thesis considering musical works to be a kind of abstract entity without an origin is intuitively close to the idea that music is mathematical in nature. This closeness allows for an easy ontological explanation of the compositions made by creative music systems that use mapping techniques.
2. That the characterization of the process of composing musical works as a creative-evaluative discovery allows us to account for systems which, like Iamus, do not employ mapping techniques.

Musical Platonism claims that musical works are eternal abstract entities. Meanwhile, numbers are also taken as eternal abstract entities by Platonism. This similar nature between types and numbers makes plausible the idea that types can be treated as mathematical entities. Specifically, this perspective allows for the possibility that musical works qua types can be completely expressed in terms of numerical relations because numerical relations and musical works are similar in nature. Under this view, we can numerically express the relations between the different pitches of the sounds involved in the sound structure of a musical work, and this numerical expression of the sound structure exhausts what the musical work is. If we took musical works as being, say, concrete objects, we could not operate such a reduction because concrete and abstract entities present very different ontological features that cannot be assimilated between them: while concrete objects are spatially located, abstract objects are not; and while concrete objects cannot be instantiable in other entities, abstract objects such as numbers can. Therefore, if musical works qua types can be reduced to numbers, what a creative music system would need to compose a musical work would be to make a numerical calculation that can be translated into musical notation. This approach accounts for algorithmic and fractal music that uses the method of mapping. Mapping is a mathematical operation that transcribes the numerical output of an algorithm to musical events.⁽⁷⁾ The idea of translation or mapping has been commonly used in creative music systems. Platonism can straightforwardly explain the idea that creative music systems are genuine composers in claiming that this translation of numerical relations into musical notations results in the discovery of a type, a possible combination of sounds that exists from eternity. Sound structures are mathematical objects consisting of sequences of sonic elements (tones, timbres, durations, etc.) that are reducible to numerical quantification. Hence, sound structures have no origin. The discovery of a mathematical structure results in the discovery of a musical work when we translate the mathematical structure into sonic elements.

However, to defend such a view, we need to complement musical Platonism with musical empiricism.⁽⁸⁾ Musical empiricism is a thesis concerning the individuation of musical works that claims that all that we can aesthetically appreciate in a musical work is reduced to the things we can hear in listening to that musical work. Musical empiricism gives rise to anti-contextualist accounts, according to which the only thing that matters in the individuation of a musical work is its sound structure. According to anti-contextualism, the sound structure of a musical work is composed only by the sonic or hearable elements belonging to the piece.⁽⁹⁾ In summary, we need to say that a musical work is not only an abstract entity but also that the only parameter to be considered in the individuation of musical works is their sound structure.

It is important to highlight that the choice of musical elements for the mapping process is ultimately determined by the human composer using the system (Díaz-Jerez, 2000, p. ix). In contrast to such systems, the use of evolutionary algorithms, in combination with the use of a sophisticated indirect encoding scheme, enables Iamus to develop an autonomous process in the production of musical works in which, as we will see, a kind of evaluation is involved. Accordingly, it can be pointed out that we are not doing justice to the Iamus computer by considering systems based on mapping techniques as composers with the same status as Iamus. We might not consider systems using mapping techniques to be genuine composers because the mapping process is ultimately determined by a human being and, consequently, they are not autonomous in the production of their works. Therefore, it would be ontologically more interesting to account for those creative music systems that do not employ mapping techniques and that, as it happens with Iamus computer, are autonomous in composing works of music. Our thesis is that, by means of the notion of creative-evaluative discovery, the Platonist can accommodate the hypothesis that the creative systems of this second kind compose musical works. What is also ontologically interesting is that, in this case, Platonism can accommodate the hypothesis without requiring an additional thesis concerning the individuation of musical works. Accordingly, we will show how the Platonist notion of creative-evaluative discovery can offer a satisfactory explanation of the process developed by Iamus in composing musical works.

4.1 Composition as Discovery

We recall that, according to Platonism, to compose a musical work is to carry out a kind of discovery in which what is discovered is not the goal of the inquiry. It is a process in which what is sought is not any conceptually determined goal by any description, and hence there is no instance to determine a criterion of success. Due to the absence of a success criterion, in this kind of discovery it is not possible to make a mistake. Analogously, it is impossible to miss a penalty shot if nobody knows what scoring a goal is. This is the feature that distinguishes the discovery of types from the class of discoveries that includes the one made, for example, by Christopher Columbus, or those made in the empirical sciences. Therefore, the Platonist account requires that there be no possibility of error in the process of composing a musical work.

This requirement is fulfilled by the Iamus computer in three respects. Firstly, scores produced by Iamus are notationally correct and technically performable. Thanks to the fitness function implemented in the system, it is not possible for Iamus to write a passage that cannot be performed by a competent musician, either because the passage is out of the performable register of the instrument (for instance, a C₂ for a piccolo flute) or because it requires non-existent resources for that instrument (for example, a pizzicato for a tuba). Secondly, Iamus does not carry out its activity guided by any conceptually determined goal. Iamus composes following a genomic-evolutionary process. At the beginning of that process, Iamus has no preconceived idea of ​​the work it will compose, and it does not intend the final product of this process to correspond with a description of a state of affairs previously stipulated. The process carried out by Iamus, which emulates the process that takes place in natural selection, is not teleological. And thirdly, Iamus’ products are taken as final (not provisional). Iamus is not provided with any mechanism of correction of its resulting products. Iamus cannot perceive any mistake or error in the works it composes, and consequently it cannot revise any supposedly improvable features of its works to produce new versions of those pieces. Once Iamus has produced a work, this work is not susceptible to changes operated by the composer, the system itself. Therefore, Iamus cannot be mistaken, and thus the hypothesis that Iamus composes musical works is compatible with the Platonist view, according to which to compose a musical work is to make a discovery in which there is no possibility of error.

4.2 Composition as Creative Discovery

Now we consider the second feature of what it is to compose a musical work according to Platonism: creativity. According to Platonism, to compose a musical work is to carry out a creative discovery. When we say that Dvořák is the composer of the “New World” Symphony we are not saying that he created a new entity in composing that work. Rather, we are saying that he was creative, in the sense that he was the only person capable of discovering and selecting the type of the “New World” Symphony. He was creative because he added something new to our shared knowledge; he introduced something new to our culture and our musical practices. Analogously, when we say that Iamus is the composer of Nasciturus we are not saying that it has created a new entity in composing that work. Rather, we are saying that it has been creative, in the sense that it has been the only entity capable of discovering and selecting the type of Nasciturus. Iamus is creative because it introduces something new into our shared knowledge and musical practices. By generating the score of Nasciturus, Iamus discovers a new type and, through this, a new and specific way of making a kind of performances is introduced.

In general, creative music systems are creative because they introduce knowledge of new kinds to perform music. We attribute special value to creative music systems because, in some cases, they introduce knowledge of types that, due to their high level of complexity, human beings, who have limited capacities, would never be able to discover: e.g., some cases of fractal music and other works derived from chaotic systems. However, it is important to note that the creativity we attribute to Dvořák or Iamus is ascribed from an epistemological standpoint and not from an ontological one. Both bring to our knowledge things that previously existed. In the same way, according to Platonism, just as human composers do not create their compositions, neither do creative music systems: they do not create anything, from an ontological perspective; rather, they are creative from an epistemological viewpoint. In contrast to what happens regarding compositions by human beings, it seems intuitive to resist the idea that computers create when they compose musical works. However, Platonism eliminates this difference by holding that human composers do not create new entities when they work. Platonism here offers a rich and simple account that grants computers the same status and value as human composers.

4.3 Composition as an Evaluative Discovery

Finally, we will attend to the third feature of the Platonist characterization of what it is to compose a musical work: we will focus on the notion of evaluative selection. According to Platonism, musical composition is a creative-evaluative discovery. However, the notion of evaluative selection could constitute a challenge when attempting to account for the activity of creative music systems, especially in the terms in which this notion is described by Dodd: “The composer evaluates which combination of sounds, once performed, will achieve the effect she wants to achieve and, as a result, comes to indicate a certain sound structure” (Dodd, 2000, p. 431).

In characterizing the evaluative selection that takes place in the composition of musical works, Dodd employs an intentional vocabulary that can raise some problems. Dodd’s words regarding the composer “want[ing] to achieve” can be easily regarded as committed to the idea that an evaluative selection involves a kind of teleological act: the composer chooses this sound structure x instead of any other, thinking that by means of x the result will be better than with any other sound structure with respect to the response of the audience. The effect intended by the composer can be considered as an a priori conceptually determined goal of the composition process. If this interpretation is correct, then:

1. Dodd is contradicting his own Platonist view, according to which to compose a musical work is to make a discovery that is not directed to any previously conceptually determined goal; and
2. the Iamus computer could not be considered as a composer because it seeks no conceptual goal in its process of composing a musical work.

However, there are other possible characterizations of the notion of evaluative selection that avoid any intentional vocabulary and, hence, are less problematic for the Platonist account.

Evaluation does not require keeping in mind any conceptual target. In a minimal sense, evaluation only requires, first, to have different possibilities among which to choose and, second, to have a choice criterion. This criterion need not be a conceptual goal but indeed can be a comparative criterion of the salient properties of the possibilities being evaluated. For instance, in evaluating moral norms, we do not need an absolute idea of goodness as a goal that provides a referent for making the evaluation. Instead, we can simply test the factual properties of the commitments for the action entailed by those norms and compare which is best in different respects (cf. Field, 2009, pp. 256–257). However, the evaluation paradigm without finality that is highly relevant for this article is natural selection.

Natural selection is a physical process in which biological organisms evolve. These biological organisms work as if they had been intelligently designed for some goal. However, natural selection in fact acts as a blind and random designer (Dutton, 2009, pp. 125–126). Despite not being aimed at any target, natural selection is an evaluative selection which, from initial variety, determines which individuals are fit to survive in a specific medium. Analogously, the Iamus computer proceeds with an evaluative selection that is not aimed at any pre-conceived goal. Iamus composes its works following a genomic-evolutionary process. The first step in the production of Iamus’ works, once the data of instrumentation and duration of the piece are set, consists of formulating a musical genome. Iamus randomly chooses several musical genomes, which compete with each other and mutate to adapt to the technical possibilities of the instrumentation established at the outset (the musical medium).⁽¹⁰⁾ Only the fittest genomes for these instruments (i.e., for this medium) survive and undergo a deterministic process in the formulation of a musical work. Therefore, the compositional process of the Iamus computer is analogous to natural selection. Like its natural analogue, this selection process is not guided or led by any preconceived goal. Moreover, Iamus’ selection is also evaluative: while natural selection filters the initial variety to leave the fittest individuals in a specific medium, Iamus’ selection determines from an initial variety which are the fittest musical genomes for a specific musical medium (instrumentation plus duration). Therefore, in evaluatively selecting between musical genomes, Iamus is evaluatively selecting between the types associated with those musical genomes. Thus, the evaluative process undertaken by Iamus in composing musical works can be accommodated in an unproblematic way by Platonism.

In this section, we have argued that musical Platonism is an answer to the categorial question in the ontology of music that accommodates in a simple and elegant way the hypothesis that creative music systems are genuine composers. The notion of musical works as eternal types (abstract ontologically thin, temporally and modally inflexible entities), and the characterization of composing a musical work by means of the notion of creative-evaluative discovery, offer a satisfactory explanation of, on the one hand, those creative music systems that use mapping processes (because the mathematical intuition concerning the nature of musical works is preserved); and, on the other, those creative music systems that, like the Iamus computer, avoid mapping processes and that could seem prima facie more challenging to an ontological explanation. It is noteworthy that, according to Platonism, when a composer generates a musical work, what is discovered is a type of sound-sequence-events, i.e., a structure of sound types, regardless of the way in which composers present or indicate the types discovered by them. These can be indicated either notationally, writing the sound structure in a score, or in sounds, by means of a first performance of this sound structure. In a similar vein, when a performer is improvising a melody with an instrument, he or she is ipso facto discovering a pre-existent type of sound-sequence-events. Therefore, Platonism is able not only to offer an explanation of the process of composition carried out by systems that generate scores of new musical works, but also by those systems that generate musical works only in sounds. Consequently, the scope of our thesis could be expanded: we posit that Platonism is the best explanation of the phenomenon of computer-generated music in a broad sense, including both music generated in scores and in sounds.

5 The Advantages of Musical Platonism versus its Alternatives

This section seeks to show the advantages of Platonism, as an answer to the categorial question regarding computer music. We propose here an inference of the best explanation in favour of musical Platonism. For this purpose, we synthesize the most outstanding alternatives to Platonism with respect to the categorial question in the ontology of music. Our contention is that these alternatives, when applied to the phenomenon of computer-generated music scores, are problematic or lack explanatory power. The alternatives to be considered are: idealism, Aristotelianism, nominalism, perdurantism, nihilism, historical particularism, the performance theory, and the phenomenological theory.

For clarification, we offer the following table, which we will explicate below:

5.1 Idealism versus Platonism

We shall start with the comparison between Platonism and musical idealism, the view that supports the following thesis:

IDEALISM: a musical work is a fluctuating and dynamic entity composed of the complex of conceptions to which a certain sound sequence or imaginary sound sequence gives rise (Cox, 1986, p. 136).

In examining this position, we will focus on two points: the ontological category that idealism ascribes to musical works, and the characterization of composing a musical work that follows from this theory. According to idealism, musical works are mental entities, i.e., entities that exist only in human minds. This view claims that sounds symbolize music only when they are perceived by those individuals that conceive them as music. Consequently, a musical work cannot be a sound structure simpliciter, but a sound structure conceived as a musical work. Accordingly, musical works cannot exist independently of human beings because they exist only in the consciousness of human beings (Cox, 1986, p. 133). Since musical works have a mental nature, they can exist in the mind of the composer without being written in a score or being played in a performance. The only requirement for the existence of a musical work is that the conception or idea of the work exists in the mind of the composer. Therefore, it is claimed by the defenders of this approach that “musical works are constructed when composers conceive and group tones in a systematic fashion” (Cox, 1986, p. 134). Thus, according to musical idealism, to compose a musical work is to conceive a group of tones in such a manner that they constitute a structured unity.

The first response to this view is that if to compose a musical work is to create the conception or idea of that work, then, since creative music systems have no ideas, they cannot compose musical works. Moreover, if musical works exist only in human consciousness, then, since computers have no consciousness, they cannot deal in any sense with musical works and, thus, they cannot compose musical works. In addition, the idealist account loses the mathematical intuition concerning the nature of musical works. While mathematical entities would be abstract, musical works would not, and thus mathematical and musical entities would be different in nature, so that we could not straightforwardly say that systems using mapping techniques would be composing musical works. Thereupon, musical idealism seems to be prima facie an answer to the categorial question in the ontology of music that is incompatible with the hypothesis that creative music systems are genuine composers. And if it is not incompatible, it would require the inquiry of spurious issues, such as whether computers have consciousness, what consciousness is, what an idea or a conception is, what it is to have an idea, and so on. However, none of these awkward explanations are required if we adopt the Platonist view. In contrast to idealism, Platonism does not require a theory of consciousness in order to account for the phenomenon of computer music. Consequently, in order to approach creative music systems, Platonism is a simpler, unencumbered, and more direct option than idealism.

5.2 Aristotelianism versus Platonism

The second view that we take into account is musical Aristotelianism, which maintains the following thesis:

ARISTOTELIANISM: A musical work is an initiated type, a sound structure and means for performing as indicated by a composer at a time (Levinson 1980, p. 20).

Aristotelianism is an answer to the categorial question that, like musical Platonism, characterizes musical works as abstract entities. The main difference with the Platonist account is that Aristotelianism considers those abstract objects not to be eternal. Initiated types have a temporal origin given by the act of indication made by the composer of the musical work. To compose a musical work is to indicate a sound structure and means of performing within a historical context. Aristotelianism claims that this indication is not a simple but an artistic indication, in which the composer is not only indicating, in a particular order, “certain individuals of the tonal realm that existed before the act of composition”, but also he is intending “to insert something new into the musical culture that precedes and surrounds him” (Levinson, 2013, p. 53). This second statement implies that the composer is “establishing a rule to reproduce sounds in a certain way following the particular indication of a particular historically-situated musical mind” (Levinson, 2013, p. 54). Therefore, the artistic indication, and hence the composition of a musical work, involves the establishment of a rule according to the Aristotelianist stance.

Although the Aristotelianist preserves the mathematical intuition about musical works in claiming that musical works are abstract entities, the characterization made by this approach of what it is to compose a musical work raises some problems in order to account for the phenomenon of computer music. First, according to Aristotelianism, if autonomous creative music systems compose musical works, they should have the intention of inserting something new into the musical culture. However, it is difficult to ascribe intentions to non-rational individuals, so we would need to complement Aristotelianism with a complex theory of intentionality, which is not required if we endorse Platonism. Secondly, for the Aristotelianist, the act of composition is a normative act where a rule for performance is established. However, normativity is bound to action. Normativity can be understood in terms of oughts, and oughts in terms of plans (Gibbard, 2012, pp. 19, 170). Accordingly, normativity is bound to actions in the sense that plans are liabilities with things that we have to do given certain circumstances. For instance, if the act of composing a musical work is essentially a normative act, as Aristotelianism claims, when a performer intentionally changes notes in making a performance of the score indicated by the composer, the composer ought to punish or sanction this performance, saying that throughout this performance his or her work has not been performed. Accordingly, if composing a musical work is essentially a normative act, any composer ought to be committed to plans for action similar to the one described above, given similar circumstances. However, creative music systems are not able to acquire such practical commitments when they compose musical works. Consequently, if composing a musical work is essentially a normative act, as Aristotelianism holds, then Aristotelianism is incompatible with the hypothesis that autonomous creative music systems such as Iamus compose musical works. With Platonism, we can preserve the intuition of musical works as abstract entities, avoiding the problems entailed by Aristotelianism. Normativity is not involved in the Platonist characterization of what it is to compose a musical work. Thus, the Platonist characterization of what it is to compose a musical work, as a creative-evaluative discovery, offers a more powerful and unproblematic explanation of the phenomenon of computer music than does the Aristotelian notion of artistic indication.

5.3 Concrete objects versus Platonism

Next we will consider two approaches that treat musical works as concrete objects: nominalism and perdurantism. Nominalism holds the following thesis:

NOMINALISM: a musical work is a class of performances.

The most extended version of nominalism is the one defended by Goodman (1968) and Predelli (1999), according to which a musical work is a class of performances whose members are the implementation of the characters of pitch and rhythm of a score (Goodman, 1968, pp. 117–118).⁽¹¹⁾ A musical work is nothing over and above the performances that meet the conditions set by the score. In this ontology, there are only concrete objects: performances that belong to different classes in virtue of being the implementations of different scores. Meanwhile, musical perdurantism claims the following thesis:

PERDURANTISM: A musical work is the fusion of its performances (Caplan and Matheson, 2006, p. 60).

According to Perdurantists, a musical work is a fusion: a concrete object that has the performances of the work as temporal parts.⁽¹²⁾ The different temporal parts (the performances) of the work are related via the appropriate continuity relation for musical works (Caplan & Matheson, 2006, p. 60). A musical work begins to exist only when its first performance take place, which gives rise to the first temporal part of the work. For instance, Schubert’s 5^th Symphony was premièred on 17 October 1841 in Vienna. This first performance gave rise to the first temporal part of this work, and the work did not exist before this first temporal part. This work was also performed by the Orquesta Ciudad de Granada on 8 February 2013. This performance is something that only exists on 8 February 2013, and that overlaps with every other performance of this work on that date, giving rise to the temporal part of the 5^th Symphony at that time. The two performances that give rise to these two different temporal parts are related to each other and to the other temporal parts of the symphony via the appropriate continuity relation for musical works.

Both views are neutral prima facie with respect to any consideration concerning creative music systems. Since a musical work is nothing besides its performances, all the ontological weight is put on the performances of the work, and issues concerning the composition of musical works have no place in this ontological approach. Under these views of musical works as concrete objects, musical works come into existence by means of their first performance, and no appeal to the composer’s activity is needed here. Therefore, being neutral with respect to what it is to compose a musical work, nominalism and perdurantism are answers to the categorial question that are unproblematic when applied to the phenomenon of computer music. However, and for the same reason, these views lack explanatory power in comparison with Platonism. Since they pay no attention to what it is to compose a musical work, they offer no explanation concerning the activity of creative music systems. If musical works are concrete objects and they come into existence through their first performance, then the performers, not the composers, are the individuals that create or discover musical works. The performer, playing a work for the first time, is giving rise to the first element of a class of performances or, alternatively, is giving rise to the first temporal part of a perduring entity, and in both cases we can ascribe to that performer the creation of the work. If so, what is then the role of composers if they are not the creators or the discoverers of the work? Perdurantism has no answer to this question. Nominalism could claim that the role of the composer is to create a score. However, in creating the score, the composer is not creating the musical work but merely giving some instructions for making a certain class of performances. Nonetheless, this is a poor account of the activity and role of composers in musical practices, and offers no explanation of their originality and creativity. These views could explain, at best, something concerning computer-generated music in sounds, but they say nothing about the phenomenon of computer-generated music scores. By contrast, musical Platonism provides an explanation of the activity, role and status of composers by means of the notion of creative-evaluative discovery. Therefore, although nominalism and perdurantism are unproblematic views in approaching creative music systems, Platonism is a preferable alternative because it is a view that is more powerfully explanatory.

5.4 Nihilism versus Platonism

Similar disadvantages are faced by musical nihilism. Musical nihilism holds the following thesis:

NIHILISM: At the ontological level, musical works do not exist, only sound structures that play the role of musical works.

Nihilism as a general account in ontology is the attempt to minimize the number of entities we have in our ontology. According to nihilism, there are no complex objects in the world but only collections of simple ones “arranged a certain way for a while, and then arranged a different way as a result of the intentional action of agents” (Cameron, 2008, p. 299). In music, sound structures are claimed to be the simplest entities, while musical works are taken to be complex entities. Therefore, at the fundamental level there are no musical works (Cameron, 2008, p. 304); there are only sound structures that play the role of musical works. Sound structures are considered to be abstract entities that exist eternally. Therefore, according to nihilism, to claim that it is true that “Beethoven’s 9^th Symphony exists” does not commit us to accept that there was an increase of entities in the world when Beethoven composed it. Composers do not create new entities. To compose a musical work consists of making certain simple pre-existing entities (sound structures) play the role of musical works. The composer gives a sound structure the role of a musical work by indicating it – that is, by giving us instructions on how to perform it (Cameron, 2008, pp. 305–306).

This characterization of composing musical works, as making sound structures play the role of musical works, can give rise to some problems when applied to creative music systems. The theory requires the existence of intentional agents to operate this action. The problem is that we would need to complement nihilism with a theory of intentionality and to examine whether creative music systems are intentional agents. This additional work is not necessary if we endorse musical Platonism. Moreover, there are creative music systems, such as Iamus, that we could hardly characterize as intentionally acting when they are composing. On the contrary, as we pointed above, the activity of Iamus is not guided by any previously determined target. Nevertheless, we might charitably think that nihilism does not in fact require intentional agents for making sound structures play the role of musical works. We could strip away the indication’s act of any intentional element. We could say minimally that in indicating a sound structure the composer is establishing a rule to reproduce sounds in a certain way, and that this is enough to make a sound structure play the role of a musical work. However, this normative characterization of the act of indication raises problems discussed above when we addressed Aristotelianism.

5.5 Particularism versus Platonism

The next approach we will consider is historical particularism, which answers the categorial question in the same way:

PARTICULARISM: a musical work is a historical particular, a real high-level object that is ontologically dependent upon its incarnations (Rohrbaugh, 2003, pp. 198–199).

According to particularism, musical works are real objects, in the sense that they are ontologically dependent upon their instances – their incarnations – and, in this way, their existence is rooted in the physical world. They exist in time and are temporal entities because they begin to exist at a certain point in history and cease to exist at a later point in time, depending on the existence of their incarnations. They are also temporally flexible entities because they can change over time and, on account of this, they have a life story. They are also modally inflexible entities, because they could have been different from what they really are (Rohrbaugh, 2003, p. 199). Moreover, particularists claim that the occurrences of a repeatable artwork are among the wider class of embodiments of a work. The embodiments of a work are the things on which the work depends ontologically for its continued existence (Rohrbaugh, 2003, p. 198). Not only are the performances of a musical work its embodiments, but also its scores, recordings, and so on. Musical works begin to exist when their first embodiment comes into existence. Consequently, we can claim that, from the particularist viewpoint, musical works are created by composers when they produce the first score for those works.

The characterization of composing a musical work entailed by particularism is compatible with the hypothesis that computers compose musical works. The only thing required is to give rise to the first embodiment of the work, and creative music systems such as Iamus provide notationally correct scores of the works they compose. However, there are some features of the ontological category ascribed by particularism to musical works that turn out to be problematic when we take into consideration creative music systems. The most problematic feature is temporal flexibility. In contrast to musical works composed by human beings, the works composed by Iamus seem not to be susceptible to changing over time. Changes in a musical work produced by the work’s composer give rise to different versions of that work. Bruckner, for instance, composed four versions of his Third Symphony, and these versions can be taken as different modifications of the work over time. Nevertheless, since computer music systems are not provided with any perceptual or proof-reading mechanism, the works produced by an autonomous computer such as Iamus must be taken as final products without the possibility of being changed by the composer. Another feature that could be problematic is modal flexibility, especially when considering creative music systems employing deterministic processes. In the case of Iamus, the process of evolution and development of the work from the musical genome is a deterministic one. Once the musical genome is selected, Iamus’ works could not have been different from how they are in the real world. Thus, Iamus’ works are not modally flexible once its genome is fixed. With the category of types as ontologically thin, temporally and modally inflexible eternal abstract entities, Platonism avoids these problems raised by musical particularism.

5.6 Performance Theory versus Platonism

This section is devoted to considering performance theory. In answering the categorial question, we find that performance theory makes the following statement concerning artworks in general:

PERFORMANCE THEORY: an artwork is a performance that specifies a focus of appreciation (Davies, 2004, p. 146).

A focus of appreciation is the product of a generative act made by an artist in producing an artwork (Davies, 2004, p. 26). For instance, the focus of appreciation of Michelangelo’s David is the physical object of white marble; the focus of appreciation of Beethoven’s 5^th Symphony is the sound structure indicated by Beethoven. However, for performance theory the artwork is something more than the focus of appreciation. The main difference between performance theory and the other answers to the categorial question is that, while these take the focus of appreciation as the complete artwork, for performance theory the focus of appreciation is only a part of the artwork, which also involves the generative act in the focus of appreciation. According to performance theory, the artwork is the concrete (spatially and historically situated) performance whereby a work-focus is specified (Davies, 2004, p. 147). For instance, Michelangelo’s David is not only the physical object of white marble, but also all the actions taken by Michelangelo in sculpting it. In specifying the focus of appreciation through a performance, the artist is articulating an artistic statement in an artistic medium by manipulating or acting over some material, the vehicular medium. The artist manipulates the vehicular medium guided by some intentions in order to articulate some meaning-properties of the work.

Each process carried out by Iamus in composing a musical work is a token of the same kind of process: the genomic-evolutionary process described in Section 2. In specifying the focus of appreciation of Nasciturus, the process followed by Iamus is an action that is a token of the genomic-evolutionary process, a type of action. Therefore, Iamus’ actions for composing musical works can prima facie fall under the category of action tokens. However, the type of action of which Iamus’ actions are tokens seems to be qualitatively different from the type of action of which artworks are said to be tokens according to the action token theory. One of the virtues of creative music systems is that they are able to develop complex compositional processes that exceed human abilities and limitations. Therefore, the compositional processes followed by creative music systems are qualitatively and quantitatively different from those followed by human beings. Moreover, the complex structure of the focus of appreciation can be seen as hardly applicable to the products of computer music systems. Although performance theory rejects explicitly the notion that the artistic statement has to be characterized in a propositional way, it is difficult to ascribe an artistic statement to creative music systems, since such attributions usually involve the attribution of some kind of intention. Moreover, the notion of “artistic medium” involves the understanding of practices, theories and notions of a particular artistic context. However, we would need an explanation of how creative music systems can have epistemic access to those elements involved in an artistic medium. Nothing of this is required by Platonism. The notion of creative-evaluative discovery developed by Platonism requires neither understanding nor epistemic access to the elements of the context of the discovery. Therefore, the approach presented by Platonism is once again a more direct and unproblematic view to account for the phenomenon of computer music.

5.7 Phenomenological Theory versus Platonism

Finally, we end this section by considering phenomenological theory. We take Roman Ingarden’s work (1986) as a reference because we consider it an intermediate step between Husserl’s phenomenology and other major supporters of the phenomenological view, such as Hartmann, Dufrenne, or Iser (cf. Chojna, 1990, pp. 86–87). The thesis of the phenomenological theory can be summarized as follows:

PHENOMENOLOGICAL THEORY: a musical work is an intentional object, an object that is neither mental nor physical but whose existence depends on acts of consciousness of the composer (Ingarden, 1986, p. 117).

The phenomenological theory assigns musical works to the ontological category of intentional objects. Despite the difficulties in determining the very nature of intentional objects (Kivy, 1987), it is clearly stated that they are neither physical nor mental objects (Ingarden, 1986, p. 120). On the one hand, the musical work is not identified with its performances and it is not reduced to its score; on the other, the musical work is neither the idea nor part of the conscious experiences of its composer, since it continues to exist after the composer’s death (Ingarden, 1986, p. 2). Ingarden’s point is that musical works have an origin: they are created by the composer’s specific, creative and psychosomatic acts (Ingarden, 1986, p. 116). One of the ways in which these acts may culminate is writing a score of the work. However, according to Ingarden, the score is always incomplete: it is a schematic prescription (set of rules) for performance. The score is incomplete because it has two kinds of elements: a) fixed elements, i.e., characters that refer univocally to the sound-base aspects of the piece; and b) elements open to various interpretations, which are related to aspects of the piece other than the sound-base features. The other way in which creative acts can be culminated is through an immediate performance made by the composer. However, a work is never identical to any of its performances, and even if this immediate performance is recorded, the indeterminacy of the work does not disappear, since recording techniques are never perfect and are limited to a point of listening (Ingarden, 1986, pp. 117–118). The indeterminacy found in musical works leads Ingarden to assign them the ontological category of intentional objects. The musical work is an “ideal boundary” aimed by the creative acts of the composer and by the perceptual acts of the listeners (Ingarden, 1986, p. 119). It is an object that we cannot obtain in its entirety and that can only be pointed out by us. The musical work is an intentional object, not a real one, since it lacks the kind of autonomy possessed by real objects. It has a heteronomous existence, depending on the existence of the composer and on his or her physical and mental acts. A real object is something that it is here or there, and that is reduced to its ontic base. Musical works as intentional objects are not located in space or time (they are supratemporal and supraindividual structures) and thus they go beyond their ontic bases (scores or performances). Musical works, hence, are things that can only be pointed at by composers and listeners by means of the ontic bases of these works and their mental states. Nevertheless, intentional objects are not subjective: they are not a mental or conscious experience (i.e., a mental entity), but something given in those experiences. The work is intersubjectively accessible by means of acts called aesthetic experiences or aesthetic perceptions (Ingarden, 1986, p. 122). Consequently, Ingarden distinguishes between musical works and aesthetic objects. The musical work is a schematic or incomplete object (and thus an intentional object), with gaps or places of indeterminacy that are filled in during aesthetic perception, where the aesthetic object is constituted.⁽¹³⁾ The musical aspect remains always the same, although it can give rise to very different aesthetic objects, depending upon the aesthetic experiences of the perceivers. Aesthetic objects are the bearers of aesthetic values.

Intentional objects depend on intentional acts in order to exist. The acts of composing a musical work are characterized by Ingarden as intentional acts. The work thus belongs to a “whole variety of intentional acts” (Ingarden, 1986, p. 119). These acts may result in the work’s score or in the first performance of the work.⁽¹⁴⁾ Ingarden claims that these acts “are formed by real people possessing real sense organs, who employ these organs either in the composition of a musical work or in its realization in new performances or in listening to successive new performances” (Ingarden, 1986, p. 119). By means of these acts, the composer conceives an intentional object that is consciousness-dependent for its existence, but that is mind-independent for its persistence through time.

Clearly, the statement quoted above is prima facie incompatible with any simulation of the process of composition of musical works in entities other than human beings. Moreover, putting aside Ingarden’s claim, we have to face two main difficulties in approaching the categorial question from the phenomenological theory if we take into account compositions made by creative music systems and, more specifically, the phenomenon of computer-generated music scores. The first difficulty is that it rules out as musical works the products generated by systems using evolutionary algorithms in general, and the products generated by Iamus in particular. According to what we claimed in Sections 4.1 and 4.3, the simulation of processes inspired by biological evolution are generally not teleological: the very process of natural selection is described as a blind and random design, not directed to any goal or end. The process of natural evolution is not directed to a particular outcome. It is not an intentional process, and hence the results of this process cannot be characterized as intentional objects. However, according to Ingarden’s view, musical works are intentional objects, i.e., objects that result from intentional acts. The products generated by systems using evolutionary algorithms and, particularly, the products generated by Iamus, are not the result of intentional acts; therefore, they are not intentional objects, and consequently they would not be musical works. The second difficulty is a comparative disadvantage of phenomenological theory with respect to musical Platonism. Some agent-based A-Life generative systems can display intentional acts, and thus they are good candidates for being characterized by phenomenological theory as composers, and their generated products as musical works. However, the physical bases of these intentional acts, and probably some of their qualitative features, are different from the physical bases of human beings’ intentional acts. The defenders of phenomenological theory owe us an explanation as to why such differences are irrelevant for the generation of an intentional object, and hence for the generation of a musical work. In other words, phenomenological theory must be supplemented with an explanation of why physical differences in mental states do not imply differences in the causal role of such states, which is not an easy task if we want to preserve a minimal materialism (cf. Lewis, 1974, p. 111). By contrast, the Platonist does not need this extra bit of explanation, since the existence conditions of the ontological category assigned to musical works from this view – i.e., types – are not taken to be dependent on intentional acts made by the work’s composer.

In this section, we have addressed the categorial question in the ontology of music, defending the thesis that musical Platonism is the most direct, unproblematic and powerful explanation to account for the phenomenon of computer music. For this, we began by presenting musical Platonism; next we showed how Platonism can account for computer music by considering the most salient features of the Iamus computer; and finally we compared Platonism with other alternative answers to the categorial question (idealism, Aristotelianism, nominalism, perdurantism, nihilism, historical particularism, performance theory and phenomenological theory), and we concluded that none of these views is preferable to Platonism, because either they all present problems when creative music systems are taken into consideration or they do not offer a satisfactory explanation of the phenomenon of computer music.

6 A Work’s Versions: A Possible Difficulty for Platonism

In this last section, we will address a difficulty that we must face in order to accommodate in the ontology of music the hypothesis that computer music systems in general, and Iamus in particular, compose musical works: the phenomenon of versions of musical works. Versions are revisions of a previous work, generally made by the work’s composer, without departing significantly from it. For instance, Sibelius’ 5^th Symphony has three versions. The piece was premièred in 1915. However, Sibelius modified his 5^th Symphony twice – in 1916 and 1919 – in an effort to improve the previous versions. As we have seen in Section 3, since Iamus is not provided with any mechanism to perceive a posteriori its products, we should consider these products as being final, in the sense that Iamus cannot revise the works it composes, and thus cannot give rise to new versions of them. It could be objected that the impossibility of making revisions and versions of its works is a qualitative lack of Iamus with respect to human composers. Accordingly, this qualitative lack should lead us to regard the process followed by Iamus as being qualitatively different from the process followed by human beings in composing musical works, so that we could not claim that Iamus composes in the same sense in which we assert that human beings compose music. However, Iamus’ inability to make new versions of its works can be accommodated within the Platonist theory, since this inability fits the nature of types and the explanation of a work’s versions offered by Platonism.

An ontological feature of types is that they are ontologically thin entities – that is, a type is individuated by the condition which something must satisfy in order to be a properly formed token of that type (Dodd, 2007, p. 54). This condition is an associated property of the type. Any change in this property – the condition that must be fulfilled by the proper tokens of the type – will always imply the individuation of a new and different type. This feature of being ontologically thin entities implies that types are modally and temporally inflexible entities (Dodd, 2007, p. 53). An entity is modally inflexible if and only if there is no possible world in which this entity has intrinsic properties different from the intrinsic properties it has in the actual world. Types and, hence, musical works, could not have been different from how they are in the actual world. On the other hand, an entity is temporally inflexible if and only if it cannot undergo any change in its intrinsic properties through time. A change in the intrinsic properties of a type would give rise to a different condition for something being a properly formed token of that type. However, if the identity of a type is given by the condition that must be satisfied by its tokens, any change through time in the intrinsic properties of a type will give rise to a token that exemplifies a new and different type. Consequently, according to Platonism, cases in which a type seems to be temporally flexible must be explained as cases where more than one inflexible type is involved.

This is precisely the case of versions of musical works. A version is, let us say, the result of the revision by the composer of a previous work. Once premièred in 1873, Bruckner modified his 3^rd Symphony three times (in 1877, 1878 and 1889) and altered the sound structure of the original version by changing notes, adding new parts and deleting others. Thus, the condition for something being a properly formed token of the 3^rd Symphony in 1873 is different from the condition that must be satisfied in 1889. It might be thought that if musical works are types, this case would show that types are temporally flexible. But this is not the analysis made by the Platonist. According to Platonism, to claim that a work has been revised by its composer does not imply that the work has changed. If the score of a later version is different from the score of an earlier version in any respect not explicitly permitted by this last one, then the two scores represent different types (Dodd, 2007, p. 90). That is, two scores specifying even slightly different conditions that correct performances of those scores must satisfy – for instance, a change in one or two notes – are scores of two different musical works. Within the Platonist framework, cases in which the composer revises a score cannot be regarded as cases of changes through time of the properties of a work, but cases in which the composer is giving rise to a new but very similar musical work.

While the Platonist analysis of the phenomenon of versions as new but similar musical works is far from being obvious when applied to human composers and involves a kind of revision of our intuitions, it has a direct and evident application to the activity developed by the Iamus computer. Iamus does not have any perceptive or corrective mechanism that allows it to revise a posteriori its products. Each score produced by Iamus is a different act of indication of a type. Let us imagine that, after introducing the data of “organ” (instrumentation) and “10 minutes” (duration of the piece), Iamus produces today (26 December 2015) a score P that indicates the work X. Let us also imagine that in ten years’ time we again introduce the same data to Iamus and it produces a score P₁ that indicates the work X₁. P₁ is almost exactly the same as P, differing only in the first and last notes of the piece. Moreover, suppose that during those ten years we had introduced the same data several times to Iamus, but it never produced a score slightly similar to P. Would we say that through P₁ Iamus has modified P in order to produce a new version of the work X? Since Iamus does not possess any mechanism to perceive its products, there is no causal link that connects the production of the score P₁ with P and, therefore, we would not say that Iamus has modified the work X by producing the score P₁. Rather, we would say that it has produced a new work X₁ indicated by the score P₁ that is very similar to the work X indicated by the score P. Even if Iamus produces very similar scores, since every act of indication made by Iamus is independent from its previous acts, we will always say that it has produced different musical works, except in the case in which the scores produced were exactly coincident and specify the very same condition to be fulfilled by the correct performances of the piece. This phenomenon can be completely accommodated by the Platonist approach, which states that a type is an ontologically thin entity, in the sense that any change introduced in its associated property results in a change in the condition that must be satisfied by the properly formed tokens of that type, which is enough to give rise to a new type. Thus, Platonism offers a direct and clear explanation that can accommodate the final character of the works composed by such creative music systems as Iamus and the phenomenon of versions.

7 Conclusion

In this article, we have tried to systematize the ontological foundations of computer-generated music. We take as empirical data the features of the Iamus computer, the first system to produce musical works autonomously in an original contemporary style. Next, we addressed the categorial question in the ontology of music, and argued that musical Platonism is an answer to the categorial question that can accommodate the hypothesis that creative music systems genuinely compose musical works. We claimed also that the notion of creative-evaluative discovery, the characterization of what it is to compose a musical work, according to Platonism, offers a satisfactory explanation of the process followed by a computer in producing musical works. We compared Platonism with other alternative answers to the categorial question (idealism, Aristotelianism, nominalism, perdurantism, nihilism, historical particularism, performance theory and phenomenological theory) and we concluded that none of these views proved preferable to Platonism because they either present problems when creative music systems are taken into consideration or they do not offer a satisfactory explanation of the phenomenon of computer music. It is noteworthy that in this article we do not defend Platonism as the best account concerning the categorial question in the ontology of music. This last point is beyond of the scope of this article. Our analysis is not an inquiry into the fundamental ontology of musical works, but an application of it to the phenomenon of computer-generated music, either in sound or in score. Nevertheless, consequences for the ontology of musical works could be extracted from the conclusions arrived at here. Consequently, we claim only that Platonism is the default position to explain what kind of entities musical works are when generated in score or audio by creative music systems or, in other words, that Platonism is the best way to account for the phenomenon of computer-generated music under the assumption that creative music systems can compose musical works.

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Notes

1. This article was funded by the Ministry of Education, Culture and Sport of the Government of Spain by means of the Programa Nacional de Formación del Profesorado Universitario (FPU13/00070) and by the research project Naturalismo, Expresivismo y Normatividad (FFI2013-44836-P). I wish to express my deep appreciation to my PhD supervisors, Juan José Acero and Neftalí Villanueva, for their contributions in improving this article, and to Gustavo Díaz-Jerez and Francisco J. Vico, for their help in technical and musical issues concerning computer music. I extend my gratitude to all the members of the research project Naturalismo, Expresivismo y Normatividad (FFI2013-44836-P), especially to José Ferrer, with whom I have had the opportunity to discuss many of the ideas developed in this article.
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2. A non-correctly written score would be one that demands resources that cannot be performed by the instrument player: for instance, a piano chord of eight notes to be played by a single hand (cf. Sánchez-Quintana et al., 2013, p. 102).
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3. I am grateful to an anonymous referee for its contribution on this issue.
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4. Two of the most prominent problems are problems of scalability and fragility on the solutions (cf. Sánchez-Quintana et al., 2013, p. 100).
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5. Dodd’s work is the most recent and elaborated approach to Platonism in the ontology of music. For this reason, in this section we will turn our attention to his papers for the explication of the Platonist view.
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6. This idea appears in Plato, who apparently inherited this idea from Pythagorean thought when, in the Republic, he states: “because [these men] do the same as those involved in astronomy. They look for numbers in those same chords listening” (Plato, 1992, 531c).
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7. As a complement of this brief definition, it can be noted that “Mapping consists of creating a one-to-one correspondence between the algorithm’s numerical output and a set of ordered musical events. Musical events can be single pitches, motives, or even fully fledged phrases” (Díaz-Jerez, 2000, p. 49).
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8. “Musical empiricism” is a term coined by Dodd (2007, p. 205) to specify the application to the musical case of a more general thesis labelled by Currie “aesthetic empiricism”. According to Currie (1989, p. 17), aesthetic empiricism is a thesis concerning the appreciation of artworks that claims that the aesthetic properties of an artwork are those that are detected by means of our senses. As Davies (2004, p. 25) explains, in commenting on Currie’s work, aesthetic empiricism minimizes the role, in the artistic appreciation of an artwork, of resources not available in an immediate experiential encounter with that artwork or with the artwork’s instances.
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9. Other wider views of sound structures can be found in the literature (cf. Davies, 2001, pp. 47–71). According to this perspective, a sound structure can include not only sonic elements, but also non-sonic ones. However, the most extended account in the literature is of the narrow sense, according to which a sound structure is composed only by sonic elements.
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10. For more considerations concerning the musical medium, see Davies 2003, 2007, and 2008.
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11. Predelli also adds other requirements, such as a causal connection with the act of composition of the author and being performed by the instruments prescribed by the composer. We put aside these aspects because they are irrelevant for the discussion addressed in the article.
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12. These definitions could be helpful: x is a fusion of the ys = df each of the ys is a part of x, and every part of x overlaps one of the ys (x overlaps y = df there is a z such that z is a part of x and z is a part of y) (Caplan & Matheson, 2008, p. 80).
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13. Since musical works cannot be performed schematically, the performers must fulfil the places of indeterminacy by interpreting it (cf. Ingarden, 1986, pp. 54–55; Chojna, 1990).
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14. “The score itself is intentionally designated by the composer’s creative acts …. Where the composer has not notated his work, however, has not fixed it in a score, the work is derived directly from his creative intentional acts, intentions that are sometimes immediately realized in a performance by the composer himself” (Ingarden, 1986, p. 40).
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Author contacts

• Nemesio García-Carril Puy
• nemesio@ugr.es
• Department of Philosophy I. University of Granada
• Facultad de Filosofía y Psicología
• Campus de la Cartuja
• 18011 Granada (Spain)