Università degli Studi di Torino

Dipartimento di InformaticaScuola di Dottorato in Scienze della Vita e della Salute

Dottorato in Neuroscienze – XXIV ciclo

The effect of music.Towards a Cognitive and Computational Model

of Music Relevance.

Tesi presentata da:Edoardo Acotto

Tutor: Prof. Leonardo LesmoDott. Daniele P. Radicioni

Coordinatore del dottorato: Prof. Filippo BogettoSettore scientifico-disciplinare di afferenza: INF/01

Anni Accademici: 2008–2009/2012–2013

2

To my beloved son Agostino, who is now four and a half years old

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Acknowledgements

Without Daniele Radicioni I would never have started my PhD and this workwould not exist: a great part of the merit is his, the demerit is only mine. Isincerely thank him for his expert and precious help and for his great patiencewith my idiosyncratic style of research and communication. I know that I amnot the best kind of disciple, insofar I appreciate his guide as I cannot say.

Francesca Garbarini, gave me a very precious help for analysing data ofExperiment 3. I sincerely hope that she will continue to participate to myresearch project.

I cannot say the importance of having known Carlo Geraci at the beginningof my PhD: since the first moment we met, he spoke me of scholars that arenow at the center of my interest. He constantly enlarged my scientific andcultural horizon. I thanks him once more for having invited me at Jean Nicodin november 2012, when I knew Fred Lerdahl. He helped me to organiseExperiment 2 and 3 and for analysing data of Experiment 2.

A very special thank is for my dear friend Jelle Gerbrandy: he has not onlyread, annotated and corrected almost the entire thesis but I cannot distinguishif his help was more important for the language, or the style, or the content,or the counter-examples, or the brilliance he naturally placed in all of hiscomments. I strongly hope that Jelle will help me in the future developmentof this project, as I think that he has perfectly understood the aim and theimplications of my work.

Mark Wiklund, my friend from Seattle, known in Sevilla at Epics 2012,has made the English of some parts of this work more similar to English.

Thanks to my mother, Adriana: she too read a part of the thesis andcorrected my English. Thanks for having spent so much time with Agostino,allowing me to advance with my work.

Last acknowledgement is the most difficult for me: Leonardo Lesmo, mydear professor and friend is no more with us. He could not read my final work,and amongst all my regrets this is the most serious one. In 2008 Leonardosuggested me to try to do a Cognitive Science PhD at the Turin Computerscience department. When I started my PhD I understood that Leonardowould have wished to make me study computational linguistics, his theoreticalfields, in which he was an important Italian pioneer. I certainly disappointedhim with my unwillingly to exchange music with verbs, syntactic structures,frames and thematic roles. But I started to study his beloved LISP. After hehad accepted my rebellion, we were friends as before: he was one of the mostliberal persons I have ever met, and also one of the most brilliant thinkersand researches. Every time we spoke about my work he understood all theproblems in a few seconds and he always had smart and important suggestions

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for me. I would have needed many more suggestions from him. I knew abouthis sickness but I never thought he would not have read my thesis. If thiswork is incomplete, this is at the maximum degree because it lacks the finalreading of Leonardo.

Finally, thanks to Viviana, for everything.

Contents

1 Introduction 11.1 Cognitive Musicology . . . . . . . . . . . . . . . . . . . . . . . 3

1.1.1 Pure music . . . . . . . . . . . . . . . . . . . . . . . . 31.2 Cognition and culture . . . . . . . . . . . . . . . . . . . . . . 41.3 Understanding music . . . . . . . . . . . . . . . . . . . . . . . 51.4 Musical universals . . . . . . . . . . . . . . . . . . . . . . . . . 61.5 Capacity for music: the modularity of the musical mind . . . . 71.6 Neuroscience of musical syntax . . . . . . . . . . . . . . . . . 101.7 Music, language, syntax . . . . . . . . . . . . . . . . . . . . . 111.8 Mental representations of music . . . . . . . . . . . . . . . . . 12

1.8.1 Intentional sound objects . . . . . . . . . . . . . . . . . 161.8.2 Representing sounds expectation . . . . . . . . . . . . 171.8.3 Conceptual spaces . . . . . . . . . . . . . . . . . . . . 181.8.4 Naive concepts . . . . . . . . . . . . . . . . . . . . . . 19

1.9 But what is music? . . . . . . . . . . . . . . . . . . . . . . . . 20

2 State of the Art 212.1 A Generative Theory of Tonal Music: GTTM . . . . . . . . . 22

2.1.1 Grouping structure . . . . . . . . . . . . . . . . . . . . 252.1.2 Metrical structure . . . . . . . . . . . . . . . . . . . . . 262.1.3 Time-span structure . . . . . . . . . . . . . . . . . . . 282.1.4 Prolongational structure . . . . . . . . . . . . . . . . . 282.1.5 Tonal Pitch Space . . . . . . . . . . . . . . . . . . . . . 31

2.2 Other related works . . . . . . . . . . . . . . . . . . . . . . . . 312.2.1 Cue abstraction theory . . . . . . . . . . . . . . . . . . 322.2.2 A General Computational Theory of Musical Structure 332.2.3 Schenkerian analysis . . . . . . . . . . . . . . . . . . . 342.2.4 Expectational theories . . . . . . . . . . . . . . . . . . 352.2.5 Temperley’s Melisma Music Analyzer . . . . . . . . . . 37

3 Model 393.1 Relevance Theory . . . . . . . . . . . . . . . . . . . . . . . . . 40

3.1.1 What is relevant? . . . . . . . . . . . . . . . . . . . . . 403.1.2 Defining relevance . . . . . . . . . . . . . . . . . . . . . 423.1.3 Musical Relevance . . . . . . . . . . . . . . . . . . . . 433.1.4 Effect and Effort . . . . . . . . . . . . . . . . . . . . . 443.1.5 Contextual effects . . . . . . . . . . . . . . . . . . . . . 46

vi Contents

3.1.6 Musical communication . . . . . . . . . . . . . . . . . . 483.1.7 Aesthetical relevance . . . . . . . . . . . . . . . . . . . 54

3.2 Processing Effort . . . . . . . . . . . . . . . . . . . . . . . . . 583.2.1 Hierarchical structures and effort . . . . . . . . . . . . 593.2.2 Computing the Processing Effort . . . . . . . . . . . . 603.2.3 Grouping rules . . . . . . . . . . . . . . . . . . . . . . 613.2.4 Reduction algorithm . . . . . . . . . . . . . . . . . . . 63

3.3 Musical Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . 643.3.1 Effect and affects . . . . . . . . . . . . . . . . . . . . . 653.3.2 Similarities and repetitions . . . . . . . . . . . . . . . . 683.3.3 Musical Forces . . . . . . . . . . . . . . . . . . . . . . 763.3.4 Melodic attraction rule . . . . . . . . . . . . . . . . . . 793.3.5 Attraction, tension and expectation . . . . . . . . . . . 813.3.6 Global Musical Effect grounding . . . . . . . . . . . . . 83

4 Experimental Validation 874.1 Experiment 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

4.1.1 Experimental setting . . . . . . . . . . . . . . . . . . . 894.1.2 Results and discussion . . . . . . . . . . . . . . . . . . 914.1.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . 92

4.2 Experiment 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 934.2.1 Materials and stimuli . . . . . . . . . . . . . . . . . . . 944.2.2 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . 954.2.3 Participants . . . . . . . . . . . . . . . . . . . . . . . . 954.2.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 964.2.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 984.2.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . 100

4.3 Experiment 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . 1014.3.1 Materials and stimuli . . . . . . . . . . . . . . . . . . . 1014.3.2 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . 1024.3.3 Participants . . . . . . . . . . . . . . . . . . . . . . . . 1034.3.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 1034.3.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 1044.3.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . 105

5 Conclusions and future work 1075.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

5.1.1 Musical Effect and Musical Relevance . . . . . . . . . . 1085.2 Future works . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

5.2.1 Refining parameters . . . . . . . . . . . . . . . . . . . 1095.2.2 Interactions between parameters . . . . . . . . . . . . . 111

Contents vii

5.2.3 Adding parameters . . . . . . . . . . . . . . . . . . . . 1115.2.4 Adding the tendency to the attraction/tension . . . . . 1115.2.5 Conceptual sound space . . . . . . . . . . . . . . . . . 1125.2.6 The Processing Effort model . . . . . . . . . . . . . . . 1125.2.7 Musical Relevance model . . . . . . . . . . . . . . . . . 1125.2.8 Relevance and creativity . . . . . . . . . . . . . . . . . 113

6 Appendix 1 115

Bibliography 117

List of Figures

1.1 Hypothesis of the modular architecture of the musical mind,from Peretz and Cortelhart [2003] . . . . . . . . . . . . . . . 8

1.2 Taxonomy of representations, reproduced from Dretske [1995] 13

2.1 Simple grouping of figures and a case of conflict, reproducedfrom Lerdahl and Jackendoff [1983, p.42] . . . . . . . . . . . . 24

2.2 Simple grouping of figures and a case of conflict, reproducedfrom Lerdahl and Jackendoff [1983, p.42] . . . . . . . . . . . . 25

2.3 Grouping structure of the opening of Mozart, K. 550, fromJackendoff [1987] . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.4 Overlapping groups, from Temperley [2001] . . . . . . . . . . 262.5 Alternative grouping of Bach’s Invention No. 1, mm. 1-4, from

Temperley [2001, p.65] . . . . . . . . . . . . . . . . . . . . . . 272.6 Metrical structure of the opening of Mozart, K. 331, from Jack-

endoff [1987] . . . . . . . . . . . . . . . . . . . . . . . . . . . 272.7 Time-span stracture, from Lerdahl and Jackendoff [1983] . . . 292.8 Three types of prolongational branching, reproduced from Ler-

dahl and Jackendoff [1983, p.182] . . . . . . . . . . . . . . . . 302.9 Secondary notation for prolongational structure, reproduced

from Lerdahl and Jackendoff [1983, p.201] . . . . . . . . . . . 302.10 Tonal space of C major (a) and of C minor reproduced from

[Jackendoff and Lerdahl, 2006] . . . . . . . . . . . . . . . . . 322.11 ITPRA theory, reproduced from Huron [2006, p.16] . . . . . . 37

3.1 Our reductional levels of Katz and Pesetsky [2009]’s toy melody 613.2 The sliding window used to score inter-event boundaries βt,

with t ∈ {1, 2, . . . , n − 1}: the bold formatted bar betweenevents e2 and e3 is the boundary currently being evaluated. . . 62

3.3 The events e in the toy melody are listed with their MIDI num-bers. Above the line, the 7 reduction levels in the toy melody,r1, . . . , r7. At the bottom the contribution re of each elementin the sequence. . . . . . . . . . . . . . . . . . . . . . . . . . . 65

3.4 Two couple of intra-textual similar passages, from Cam-bouropoulos [1998a, p.54]. . . . . . . . . . . . . . . . . . . . . 73

3.5 The Wundt curve, reinterpreted by Berlyne [1971], describingthe increasing arousal and its decreasing . . . . . . . . . . . . 75

3.6 Terry Riley, In C. . . . . . . . . . . . . . . . . . . . . . . . . . 76

x List of Figures

3.7 The anchoring strength discriminates the stability of a pitchrelative to a given key, in the context of a 4 levels tonal space.In this example, we illustrate the anchoring strength of pitchtones in the context of C major. . . . . . . . . . . . . . . . . . 80

4.1 Excerpt from the Piano Sonata in C minor (KV. 457) by W.A.Mozart. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

4.2 Excerpt from the “Petit pièce” from the Opus 68 n.5 by R.Schumann. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

4.3 a) variations of the Mozart excerpt; b) variations of the Schu-mann excerpt. . . . . . . . . . . . . . . . . . . . . . . . . . . 90

4.4 The six melodies used to build the experimental stimuli.Melodies in frame a) are featured by higher attraction score,while melodies in frame b) are featured by lower attractionscore, i.e., by higher tension. . . . . . . . . . . . . . . . . . . . 94

4.5 The twelve melodies used in Experiment3 . . . . . . . . . . . 1024.6 The effect of the Modulation factor. . . . . . . . . . . . . . . . 1044.7 The effect of the Condition factor. . . . . . . . . . . . . . . . . 104

6.1 Istruzioni . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

Chapter 1

Introduction

Contents1.1 Cognitive Musicology . . . . . . . . . . . . . . . . . . . 3

1.1.1 Pure music . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2 Cognition and culture . . . . . . . . . . . . . . . . . . . 4

1.3 Understanding music . . . . . . . . . . . . . . . . . . . 5

1.4 Musical universals . . . . . . . . . . . . . . . . . . . . . 6

1.5 Capacity for music: the modularity of the musicalmind . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.6 Neuroscience of musical syntax . . . . . . . . . . . . . 10

1.7 Music, language, syntax . . . . . . . . . . . . . . . . . 11

1.8 Mental representations of music . . . . . . . . . . . . . 12

1.8.1 Intentional sound objects . . . . . . . . . . . . . . . . 16

1.8.2 Representing sounds expectation . . . . . . . . . . . . 17

1.8.3 Conceptual spaces . . . . . . . . . . . . . . . . . . . . 18

1.8.4 Naive concepts . . . . . . . . . . . . . . . . . . . . . . 19

1.9 But what is music? . . . . . . . . . . . . . . . . . . . . 20

Music is an aenigma (Steve Pinker)Music really is something of an aenigma (David Huron)

This study is a first step toward formalizing the technical notion of relevancefrom a cognitive and computational perspective. Cognitive and computa-tional musicology extensively investigated at least the fundamental conceptsof musical meaning, musical communication and emotions implied in music,but the concept of relevance remains largely unexplored in the recent musi-cology. One could comment like Fodor [2000] that the a theory of relevanceis impossible (see Section 3.1.4). Nonetheless relevance theories do exist, andwe will argue that the version given by Sperber and Wilson [1986] is a work-ing theory. The enterprise to formalize a concept as broad and general as

2 Chapter 1. Introduction

relevance might seem an ambitious and groundless enterprise if a RelevanceTheory for language cognition and communication did not already exist, com-plete with a large community of consensus (for a bibliographical reference seethe Relevance Theory bibliography online.1 And although scholars often makeanalogies between music and language, Relevance Theory has not been appliedto music until now.

The work presented here is grounded on the intuition that Relevance The-ory is a powerful theory that can aptly explain some aspects of music cog-nition.2 The central idea is that by constructing a formal theory of MusicalRelevance, validating empirically with each stage of construction, it is possibleto partially unify two different cognitive theories (or two subsets of them), eachinitially aimed at different objects of study, but each sharing the same (Chom-skyan)3 computational-representational framework: Relevance Theory [Sper-ber and Wilson, 1986] and A Generative Theory of Tonal Music [Lerdahl andJackendoff, 1983]. This work builds on Relevance Theory, in order to accountfor musical cognition, which involves listening, understanding, and composingmusic. The claim is that the application of the concept of Cognitive Relevanceto music would partially explain listeners’ behaviour and composers’ choices.This kind of explanation has been a target of recent cognitive musicology,of course, and we take this into account in this work. In particular, we areconcerned with investigating the dynamics of the cognitive meaning of music.Albeit the investigation about “musical meaning” —whatever it can be— isan ancient philosophical and musicological question, the notion of music rel-evance can be used to posit ancient questions in a quite new perspective. Inthis work we do not speculate deeply on aesthetic consequences, but a MusicRelevance Theory would suggest some answers to problems created by othermusicological frameworks like e.g., by Lerdahl [1988a] (see Section 3.1.7).

Concerning the computational paradigm of this theory, there were goodreasons to ground this work on Relevance Theory. A computational modelof music relevance would be useful to the formulation of a general computa-

1 http://www.ua.es/personal/francisco.yus/rt.html.2 The expression “music cognition” normally refers to the discipline consisting in “un-

derstanding the mental processes that support musical behaviors, including perception,comprehension, memory, attention, and performance” (http://en.wikipedia.org/wiki/Music_cognition). Nonetheless, in order to avoid ambiguity between “the thing-in-itself”of the mental activity and the related meta-activity, in this work we will normally referto the discipline by the rarer expression “cognitive musicology” and to mental faculty as“music cognition”, in analogy with “social cognition”.

3 Ray Jackendoff (together with George Lakoff and David Ross) is one of professorNoam Chomsky’s first Ph.D. students; Dan Sperber is a cognitive anthropologist who hasprogressively differentiated himself from his mentor Lévi-Strauss by moving in the directionof a cognitive anthropology based on the hypothesis of mental modularism.

1.1. Cognitive Musicology 3

tional theory of musical cognition, which is a passionate and challenging col-lective enterprise (see, for example, the reviews in Cambouropoulos [1998b],and Rohrmeier and Koelsch [2012]). It could also be said that since we areat the beginning of the cognitive musicology, research on basic notions can bea resource. In turn, the investigation of the concept of music relevance caneventually shed light on the computational nature of the broader cognitiveprinciple of relevance.

1.1 Cognitive Musicology

Cognitive musicology could be considered an interdisciplinary field mixingperspectives, methods, and themes from cognitive psychology, neuropsychol-ogy, computer science, Artificial Intelligence, linguistics, and anthropology,i.e. the “hexagone” of the cognitive sciences [Bara, 1999]. For a recent surveyof cognitive musicology, see Pearce and Rohrmeier [2012].

Scientific psychology and computer science treated some problems of mu-sic cognition decades ago, but the development of cognitive science in the60s and 70s produced an increased interest in the cognitive basis of music.One innovation in cognitive musicology was the idea that formal instrumentsfor language analysis like Chomsky’s theories could be suitably adapted foranalysing music, too. Bernstein [1976] is generally considered the first scholarto view music as a kind of language, starting from a Chomskyan point of viewbut developing his theory in an innovative way. Some years after Bernstein’spioneering exploration, Lerdahl and Jackendoff [1983] published their cogni-tive model of music perception with the title “A Generative Theory of TonalMusic” (GTTM). Since this model is one of most famous in the history ofcognitive musicology, and it represents one of the two theoretical foundationsof our work (the other being Relevance Theory), we will present it in detailin Section 2.1.

As earlier stated, cognitive musicology is currently in a rich moment ofdevelopment, producing a great deal of theoretical, experimental, and com-putational results. Nonetheless, most of the early questions remain open.

1.1.1 Pure music

The object of the present work is what musicologists call pure music, i.e.instrumental music without words, choreographies, images, programs, etc.[Kivy, 2002, Jackendoff and Lerdahl, 2006, Davies, 2011]. It is true thatmusic is (or was) a complex social activity, and for this reason it is commonlyassociated with other social activities: attending a concert, a party, a theatre

4 Chapter 1. Introduction

performance, etc.. The aim of a general cultural relevance theory is thenexplaining different complex phenomena from a cognitive standpoint. Butthis is only a theoretical idea, not a research program.

Cognitive musicology, like philosophy of music, deals primarily with puremusic. We do not have any complete theory for apparently simple objects likesongs or the effect of musical timbre. The reader has to constantly considerthat in the following we will refer uniquely to pure music.

1.2 Cognition and culture

Aristotle had already observed that familiar music sounds betterthan unfamiliar music, and wondered why this was so. (DavidHuron)

In stark contrast to their ideological adversaries,4 cognitive sciences and neuro-science are more and more attentive to the cultural aspects of their respectivefocuses of study (see for two recent examples Choudhuri and Slaby [2012] andCross [2012].)

With apologies to 19th century idealist philosophers, the issue at stakehere is not a metaphysical opposition between mind and nature or betweensciences of mind and sciences of nature. Rather, it is the possibility of identify-ing music cognition as a hard-wired biological cognitive device almost uniqueto human kind (with something innate and something acquired). If this bio-logical core is identifiable –as the results of experiments investigating generalcompetencies (implicit knowledges) regarding rhythm, tonality, harmony, etc.suggest– the question of how cultural systems can form and influence partic-ular musical competences is still largely an unexplored one. The analogy tolanguage acquisition is evident: the notion of a universal grammar does notrule out the existence of deep cultural effects on language acquisition and use.

As a matter of fact, researchers in cognitive musicology have studied mu-sic from the standpoint of a Western scientific group of theories whose objectis Western music, i.e. “art music,” as well as popular music or jazz, bothof which are much less treated in the literature than classical music. Popu-lar music in 20th century century western societies has to be understood inthe context of the age of mechanical reproduction of the artwork [Benjamin,1977]: this is a historical period in which also a great 19th century centuryromantic symphony has become a common object for all the people. Western

4 John Searle being evidently the paradigm of this kind of misunderstanding critics, withwhom discussion seems frankly impossible: see for an example what Chomsky [2000] saysabout this issue.

1.3. Understanding music 5

social systems have influenced our conception of music, and, as a consequence,“the vast majority of studies have focused on music as an aural phenomenon,something that is listened to; they have tended to treat music as embodyingtypes of structures that are salient in Western theories of music; and theyhave, often implicitly, conceived of music as fulfilling only one and simplefunction, that of affording pleasure” [Cross, 2012]. In that work Cross citesnon-Western societies that use music differently from the West. He suggeststhat the general function of music can be to assist people in dealing with am-biguous social situations, having as a fundamental attribute the appearanceof a “raw, basic and unmediated” yet ambiguous meaning. In this perspectivemusic is much less the communicative phenomenon that it is normally seen as(see Section 3.1.6), and the object of information is the temporal frameworktoward which is directed the “floating intentionality” [Cross, 2012].

1.3 Understanding music

What does it mean to understand a piece of music? There are many answersto this simple question, and they all depend on the philosophical perspective ofthe answerer. As we have seen in Section 1.2, music cannot be fully explainedfrom cultural studies, which completely lack of a “naturalistic” explanation ofthe musical cognition, nor from cognitive musicology, that has great problemsin explaining the cultural and subjective aspects of the musical phenomenon.

Davies [2008] analyses the different points of view of skilled listeners, per-formers, analysts, and composers, reporting characteristic proper of each ofthese kind of subjects. Insofar in this work we are committed on designinga general model of music cognition we aim at explain the fundamental fea-tures of the skilled (idealized) listener, assuming that the others modalitiesof understanding are more complex but imply the first level as their naturalground.5 In this work we do not account for children musical comprehension,even though studying children sensibility to musical relevance would be veryimportant for our project.

From our perspective, grounded on GTTM/TPS ([Lerdahl and Jackendoff,1983, Lerdahl, 2001, Jackendoff and Lerdahl, 2006]), when a listener listensto a piece of music she constructs cognitive structures (i.e., mental represen-tations) in response to the music: so, from a cognitive point of view, the

5 This is the some opinion expressed by Jackendoff and Lerdahl [2006, p.34] “concentrateson the listener rather than on , because the experience of listening is more universal than[that of the performer and/or composer], and because the acts of performing and composingmusic require listening as well (including generating and attending to musical imagery inthe “mind’s ear”).”

6 Chapter 1. Introduction

understanding of a piece of music is “the organization that the listener un-consciously constructs in response to the music, beyond hearing it just as astream of sound” [Jackendoff and Lerdahl, 2006, p.34]. It is clear that thisperspective avoids hermeneutic as well as psychological, historical or culturalquestions. But this is only a methodological and preliminary avoidance: oncethe cognitive analysis is grounded, it is perfectly possible and even necessaryto enrich it with further points of view.

1.4 Musical universals

As cognitive psychology is interested in general capacities of human mind,cognitive musicology does not account for subjective music effects, ineffablequalia [Raffman, 1993] and associative representations at the basis of one’spersonal experience of music. Cognitive musicology aims at finding the uni-versal core of music cognition, just as like generative linguistics postulates theexistence of a Universal Grammar. Thus, the search for some musical uni-versals is (or should be) a core project of cognitive musicology: as we defineMusical Relevance as a discriminative criterion between inputs, active in anyidiomatic musical context, it could be one of those universals.

GTTM and its expansion, Tonal Pitch Space (TPS: Lerdahl [2001]), aimto enucleate some of these musical universals. Even though the original theorywas explicitly conceived to account only for western tonal music, Lerdahl andJackendoff [1983]’s four structures seem general enough to account for any kindof music in the world. (For having music it seems necessary and sufficient tohave at least one of them: Steve Reich’s Drumming, Part I, for example, isconstructed with pure rhythms, with no pitches at all). All music seems tohave at least some form of grouping structures (see Section 2.1.1) and metricalstructure (see Section 2.1.2); many kinds of music have a (broadly speaking)tonal pitch space (see Section 2.1.5); some kind of music have prolongationalstructure (see Section 2.1.4).

Although we are investigating about the existence of musical universals,this should not be interpreted as a criticism to Bharucha et al. [2006]’s asser-tion that there are no necessary conditions for music. Some music systemshave no rigid rhythmical structure, such as Japanese classical music [Galliano,2005]. Javanese gamelan, a particular kind of ritual group music, has no tonalstructure, because it is performed only with percussion instruments (metal-lophones) with no precise intonation. Of particular importance is the “tonalpitch space” [Lerdahl, 2001], which can assume several different forms even inWestern tradition, including jazz scales and ancient modes of gregorian chantand jazz scales. Pitches can be accorded also with microintervals, given that

1.5. Capacity for music: the modularity of the musical mind 7

well-tempered tonality is a recent acquisition, gradually consolidated after18th century Bach’s musical work [Piana]. In this sense, tonal space could beseen as a music universal. Granted, a precise tonal space, as that of majormode or minor mode in Western music, is not universal, but virtually all mu-sic has a tonal space, i.e. a regular segmentation of the sounds continuum.Other universals are likely to be found in the temporal processing of music[Drake and Bertrand, 2003].

1.5 Capacity for music: the modularity of themusical mind

One of the major assumptions of cognitive musicology is that music percep-tion does not depend exclusively on culture, but also on a particular deviceof mind/brain, an ability corresponding to neural circuits. Some scholars hy-pothesize of one or more dedicated mental modules for music [Peretz, 2012],possibly intertwined with language modules [Patel, 2012]. As the Fodorian no-tion of mental module has a lot of rigid theoretic implications [Fodor, 1983],other scholars speak more loosely of “musical mind” [Sloboda] or “capacity formusic” [Jackendoff and Lerdahl, 2006].

Even the scholars that theorize the modularity of musical mind do not sub-scribe necessarily to the Fodorian version of it. There are at least two reasonsfor this: The cultural dimension of music cognition would in fact make it veryhard to attribute to the musical faculty the mandatory character of Fodor-ian modularity, i.e. domain-specificity, informational encapsulation, rapidity,automaticity, restricted access and neural specificity. More important, Peretzand Cortelhart [2003] underline that even for Fodor these characteristics aremore prototypical than necessary or sufficient: they do not have to be presentfor the ascription of the modularity.

The property of the neural specificity of music modules seems to be con-firmed by the selective deficit of musical abilities in brain damaged people:there should be at least two different processing modules, one for speech andone for music [Peretz and Cortelhart, 2003, p.688]. Nonetheless, there are neu-roimaging data partially contradicting neuropsychological data. Patel [2012]addresses this contradiction with her “resource-sharing framework” (RSF, seeSection 1.6).

Given the recent development of the music/language comparison citepre-buschat12music, a theoretic framework like the RSF encourages the hypothe-sis that language and music modules differ in their representations but shareprocessing resources. Despite the interesting criticisms of Patel’s hypothesis[London], this framework is compatible with a different and more formal im-

8 Chapter 1. Introduction

Figure 1.1: Hypothesis of the modular architecture of the musical mind, fromPeretz and Cortelhart [2003]

portant work coming from generative linguistics: Katz and Pesetsky [2009]’s“identity theory”, which posits that music and language differ for the compo-nent blocks (concepts for language, sounds for music) but are identical in howthese blocks are processed. The hypothesis of a mental music module givesspace to the auxiliary hypothesis of the existence of sub-modules composingthe macro-module. For example, in psycholinguistics it is common to speak ofthe language module as comprising lexical and phonetic modules [Peretz andCortelhart, 2003, p.688]. In the case of music, rhythm and pitches are parsedfrom distinct mental and neuronal resources, as illustrated in Figure 1.1.

As Peretz [2012] says, the debates on modularity concerning language, faceprocessing, and also music are unresolved, and many issues have been con-founded beginning with Fodor [1983]’s seminal book: specialization, domain-specificity, brain localization, and innateness are not a block of propertiesnecessary and sufficient for modularity. While Fodor [1983] insisted mainlyon the informational encapsulation –intended as the perfect separation of the

1.5. Capacity for music: the modularity of the musical mind 9

peripheral modular informations from the activity of the central cognitivesystems– the property of domain-specificity, i.e. the exclusive operation of amodule on restricted domain of input or output, has probably remained themost central in the debate [Peretz and Cortelhart, 2003].

Even Bharucha [1984], who has himself designed an important connection-ist model of the tonal and harmonic perception, theorizes in his recent workstheorizes that music perception depends on “formal eliciting codes” (see Sec-tion 3.1.6) that are modular “in Fodor’s narrow sense of being informationallyencapsulated, cognitively impenetrable and automatic” [Bharucha et al., 2006,p.134]. Nonetheless, there is a great difference between Bharucha’s modularcodes and the Fodorian modules, particularly because Bharucha does not sub-scribe Fodor’s nativism. In contrast, he postulates mental informational codes“within a causal neural system that can learn some of its connectivity, basedon some innate constraints” [Bharucha et al., 2006, p.134].

More close to the model presented in this work, Jackendoff and Lerdahl[2006] make a comparison between the faculty, or capacity, for language andthe capacity for music. They follow five main general questions concerningthe musical structure: the mental representations that constitute the compre-hension of heard music; the musical grammar, i.e. the unconscious principlesthat allow the construction of the mental representations; the acquisition ofthe musical grammar or the learning of the musical understanding; the innateresources for music acquisition; and the broad vs. narrow musical capacity.6

These questions articulate the issue of the parallels between music and lan-guage, more properly focused on Jackendoff [2009]. The result of this paper,in which the question of music and affects is treated (see 3.3.1) is the im-possibility to separate the narrow musical capacity from the mental facultiesshared with other art forms, from general auditory perception, vocal commu-nication, and from the central processes of the general cognition [Jackendoff

6 These are the five questions in extenso:“Q1 (Musical structure): When a listener hears a piece of music in an idiom (or style) withwhich he/she is familiar, what cognitive structures (or mental representations) does he/sheconstruct in response to the music?Q2 (Musical grammar): For any particular musical idiom MI, what are the unconsciousprinciples by which experienced listeners construct their understanding of pieces of musicin MI (i.e., what is the musical grammar of MI)?Q3 (Acquisition of musical grammar): How does a listener acquire the musical grammar ofMI on the basis of whatever sort of exposure it takes to do so?Q4 (Innate resources for music acquisition): What pre-existing resources in the humanmind/brain make it possible for the acquisition of musical grammar to take place?Q5 (Broad vs. narrow musical capacity): What aspects of the musical capacity are conse-quences of general cognitive capacities, and what aspects are specific to music?” [Jackendoffand Lerdahl, 2006, p.34-36]

10 Chapter 1. Introduction

and Lerdahl, 2006]. This skeptical conclusion does not affects the results ofthe neuroscience of music but repeats the purely cognitivist point of view ofthe authors of GTTM, underlining the well-known complexity of music as acognitive phenomenon. We completely agree with the respect for the manydimensions of musical complexity: the present work does not aim at all toreduce that complexity to a simple model of music cognition.

Concerning mental modularity, if we succeed in demonstrating the plau-sibility of a mental device detecting musical relevance (see Section 3.1.3) weshould not be committed to formulate the strong hypothesis of the modular-ity of the musical mind, as Sperber and Wilson [1986] do not hypothesize aspecific mental module for relevance. As [Mercier and Sperber, 2009, p.150]say: “In the human case, most innate modules are learning modules (e.g. thelanguage faculty) and perform their function by using environmental inputsto construct acquired modules (e.g. the grammar of a particular language)”.So could be for music module.

1.6 Neuroscience of musical syntax

During the past twenty years, while the validity of classical cognitive sciencewas more and more a philosophical matter of discussion, neurosciences havemade great progresses in all the fields of the research concerning human brain.Also music has become an important topic of this experimental scientific do-main. Patel [2008] for example is one of the first works aiming at a completeexplanation of the music from a neuroscientific standpoint, comparing musicand language in a systematic way.

One of the most relevant result of Patel’s works is the presentation of theso-called shared syntactic integration resource hypothesis (SSIRH) or resource-sharing framework, conceived for reconciling contradictory data concerninglanguage syntax and music syntax (or pseudo-syntax: see Section 1.7). TheSSIRH is the hypothesis suggesting that “the two domains have distinct anddomain-specific syntactic representations (e.g., chords vs. words), but thatthey share neural resources for activating and integrating these representa-tions during syntactic processing” [Patel, 2008, p.268]. As a matter of factneuropsychological data suggest separation between brain resources for mu-sic and language, although neuroimaging data suggest commonalities in theuse of these resources. According to the SSIRH, which recently was proposedagain [Patel, 2012] and is consistent with current research on language process-ing, the brain networks integrating linguistic and musical syntax are resourcenetworks situated “in frontal brain regions that do not themselves contain syn-tactic representations but that provide resources for computations in posterior

1.7. Music, language, syntax 11

regions where syntactic representations reside” [Patel, 2008, p.283].As he is one of our reference authors concerning the musical cognition

and its psychological framework, it could be worth noting that Jackendoff[1995] assert that instead of the “language of thought” [Fodor, 1975] it wouldbe more appropriate to speak of “syntax of thought”. If computationalism-representationalism guarantees at least the syntactic nature of thought, withno regards for its semantic nature, that framework is appropriate for a purelysyntactic language as music is. We discuss the syntactical nature of musicalthought in the next section.

1.7 Music, language, syntax

Even if most of the scholars admit some commonalities between music andlanguage, they differ for their judgements about the nature of the relation be-tween them. Grounding on GTTM and Jackendoff [2009], Katz and Pesetsky[2009] recognize formal similarities between language and music concerning:

• the representation of metrical structure and certain linguistic represen-tation of linguistic stress ;

• Time-span Reduction (see Section 2.1.3) and the linguistic represen-tation of prosodic structure (“both are characterized by hierarchicallynested phrasal domains, each headed by a unique event at every hierar-chical level. In both systems, the property of being a head involves somenotion of rhythmic prominence, associated with the percept of stress inlanguage, and with rhythmic and harmonic properties in music”);

• prolongational reduction (see Section 2.1.4), whose binary-branching hi-erarchical structures are “in many respects formally identical to repre-sentations currently posited for linguistic syntax”.

Katz and Pesetsky [2009] enumerate then some major differences. Music isorganized sounds, and because the linearisation of sound implies a hierarchicalorder, all understandable music7 must have a hierarchical structure. Music isconceivable as an implicit hierarchical organization of sound events, who ap-pears linearly in the time, just as the sounds of the language. Some scholars

7 With “understandable music” we mean no aesthetic judgement, but We refer to thenow experimentally well known fact that some musical ideas are not perceivable from anormal hearer, and also from an expert listener [Raffman, 2003]. Of course 20th century“art music” has yielded a great amount of music with no hierarchical well-formed structuresgoverning sound events, but to explain this fact it historical, aesthetical, philosophical andsociological reasons are needed that are not included on a strict cognitive musicologicalstandpoint).

12 Chapter 1. Introduction

think that the most important analogy between music and language is basedon the common syntactic nature of both. It must be noted, however, thatlinguistic syntactic structure “is a hierarchical structure in which each nodebelongs to a syntactic category such as Noun or Adjective Phrase” [Jackend-off, 2009] while there are no precise musical analogues of such categories.8 AsPatel statues: “The key to successful comparison [between linguistic and mu-sical syntax] is to avoid the pitfall of looking for musical analogies of linguisticsyntactic entities and relations, such as nouns, verbs, and the constituentstructure of linguistic syntactic trees. Once this pitfall is avoided, one canrecognize interesting similarities at a more abstract level, in what one mightcall the ‘syntactic architecture’ of linguistic and musical sequences.” [Patel,2006], cited in Katz and Pesetsky [2009, p.1]. The analogy music/language isthus incomplete but not ungrounded. According with GTTM, the closest mu-sical structure to syntax is prolongational structure (see Section 2.1.4). Otherscholars maintain that music has got a real syntax: in an influential paper(draft) Katz and Pesetsky [2009] argue that music and language are identical(Identity Theory), except for the building blocks of music and language.9

The present work is based on the assumption that the hierarchical levels(structure) of sound events are the relevant dimension concerning processingeffort in music perception (see Section 3.2.2). In this framework, the musicalpseudo-syntax accounts for the non-linearity of the understanding process ofmusic.10

1.8 Mental representations of music

In cognitive musicology the use of the concept of mental representation iswidespread. Nonetheless it seems quite ambiguous and vague. The main-stream cognitive musicology maintains that mental representations of music

8 See also [Katz and Pesetsky, 2009, p.4]: “The building blocks of linguistic syntax arelexical items (arbitrary pairings of sound and meaning)–which have no obvious counterpartin music.”

9 “Identity Thesis for Language and Music All formal differences between language andmusic are a consequence of differences in their fundamental building blocks (arbitrary pair-ings of sound and meaning in the case of language; pitch-classes and pitch-class combinationsin the case of music). In all other respects, language and music are identical.” [Katz andPesetsky, 2009, p.5]

10 That’s a standpoint antithetic to that of the so-called “sequentialism”, the philosoph-ical theory affirming that to comprehend music is to follow the sounds-blocks one by one,without any interpretation of the structure [Davies, 2011]. That’s a point of view not so dis-tant from a comprehension of music à la Wittgenstein (see Bertinetto [2012]) that has alsosome experimental basis [Bigand and Parncutt, 2012] contradicting Lerdahl and Krumhansl[2007].

1.8. Mental representations of music 13

Figure 1.2: Taxonomy of representations, reproduced from Dretske [1995]

are non-conceptual, i.e that kind of sensory mental states that Dretske [1995]lists as experiences, sensations and feeelings (see Figure 1.2).

In Lerdahl and Jackendoff [1983] the term “representations” is used withoutany particular specification about their nature (syntactic, not semantic, car-rying a non-conceptual content). As it is well-known that in the Chomskyanapproach to the question, mental representations are assumed as “internal con-cepts” (I-concepts)–if they are conceptual–without regard to the philosophicalproblem of their reference to the world. In many cognitive theories, mentalrepresentations of music are considered to be implicitly construed by the mindaccording to the perception of musical flow, as tacit–or implicit–knowledge.By contrast, in GTTM the mental representations of music are considered inthe framework of a final-state theory, and the authors consider themselves notcommitted to explain musical cognition as a real-time process:

Our approach to music theory has not been concerned with ques-tions of memory capacity, real-time processing, brain localization,and the like. We have restricted ourselves to a formal character-ization of the listener’s intuitions about musical structure (thatis, of his mental representation of music) [Lerdahl and Jackendoff,1983, p.332].

The static nature of the account of music perception offered by GTTM is ofcourse a serious limitation of this theory, but today’s more adjourned cognitivemusicology has not really overtaken this limitation. The symbolic representa-tions of GTTM are alleged to represent the (final) mental representation of apiece of music, like a kind of natural and spontaneous musical analysis madeby the mind. So the standard musical notation plus the binary branching

14 Chapter 1. Introduction

trees notation would represent a graphic analogon of mental representationsof music. Of course, GTTM has to assume that symbolic representations ofmusic (notes on a pentagram) have a content analogous to that of the mentalrepresentations of music.

According to DeBellis [1995], GTTM representations of music would benot true representations, insofar they do not have–as true representationshave–truth conditions [DeBellis, 1995, p.21]. DeBellis’s critical point of viewfalls in the philosophical side of the opposition that Jackendoff [1995], evokinga Kuhnian “paradigm split”, calls the Philosophical Version of the theory ofmind:

What is the relationship of the mind to the world, such that wecan have knowledge of reality, such that we can have beliefs anddesires about things in the world, and such that our sentences canbe true or false? [Jackendoff, 1995, p.158]

But according to Jackendoff, the philosophical position does not fit the scien-tific standard of cognitive science, thus he strongly prefers the PsychologicalVersion of the philosophy of mind:

How does the brain function as a physical device, such that theworld seems to us the way it does, and such that we can behaveeffectively in the world? [Jackendoff, 1995, p.158]

Jackendoff’s position against philosophical explanations of reference de-rives from the Chomskyan notion of I-concepts (“internal concepts”) that al-lows science to inquire on concepts, rules and representations present in mind,but not to investigate their referential genesis and connection with world.11

11 “[According to Chomsky] rationalists hold that the mind is both structured and pro-vided with rich and extremely useful “content” at birth. Rationalists are “nativists.” Therationalist recognizes, of course, that experience and “external” factors play a role in themind’s “choosing” which concepts to activate or develop. But the rationalist denies thatexternal elements shape and constitute concepts via the operations of some sort of domain-general learning procedure such as hypothesis formation and testing. Circumstances serveto “occasion” or “trigger” the introduction of a concept; crucially, the mind’s own machinerydictates what “patterns” in the data count as appropriate “occasions.” The patterns are,in a sense, built into the mind all along. [...] rationalists think that the most fruitful wayto study the mind and its elements and “contents” is to focus on its internal structure andoperations (“internalism”). For them, a study of language’s various contributions to cog-nition, including the concepts that language expresses and the terms it puts in “referringpositions” in sentences, is a study of internally constituted “tools” that people can use forvarious purposes. The ways people use these word-tools to say what they intend, or to referto various things, are matters of free human action. Trying to deal with free action in anaturalistic science is for the rationalist hopeless.” [Mcgilvray, 2005, p.14]

1.8. Mental representations of music 15

DeBellis [1995] burdens on Jackendoff alone the weight of his mentalisticposition, according to which the problem of the right reference of representa-tions to the world is not a problem for semanticists but for general psychology.Indeed, Jackendoff makes musical objects a kind of mental-dependent objects[Bullot and Égré, 2010]: “the constancy and reality of a piece of music arepurely mental” [Jackendoff, 1995, p.165]. Jackendoff criticizes the very no-tion of “mental representation” as it is normally used implying intentionality:for him, as for Dennett [1987, 1991], the notion of representation should beconstructed as a non-intentional and perfectly computational notion:

A representation is not necessarily about anything; if you like,it does not strictly speaking represent anything. (Hence my hes-itation in using the term except as a rigid designator for whatcognitive scientists believe the mind has in it.) The point of thisnotion of representation is that it can in principle be instantiatedin a purely combinatorial device like the brain as I understand it,without resort to any miraculous biological powers of intentional-ity such as Searle [2003] wishes to ascribe to the brain. [Jackendoff,1995, p.160]

Jackendoff proposes also a possible alternative term for indicating the rela-tional character of “mental representations” in his views: “If one wishes toreserve the term mental representation for brain-states-with-intentionality, Ihave no objection to introducing a new term, say mental distinctions, for thenonintentional states that I am calling mental representations here” [Jack-endoff, 1995, p.182]. For Jackendoff, mental representations of music havedefinitely no truth value: “It hardly makes sense to say that the representa-tions one constructs in response to hearing a performance of the Eroica aretrue or false. Nor does it make sense to claim one has propositional attitudestoward musical representations, which are not, as far as I can tell, proposi-tions” [Jackendoff, 1995, p.165].

Jackendoff uses mental representations of music against the Fodorian posi-tion which maintains semantic content at the core of mental representations:“the factors that make a piece of music cohere for a listener into somethingbeyond a mere sequence of notes involve complex internal computations overabstract mental representations of the piece. Fodor’s insistence on respect-ing semantic relations seems out of place here: these abstract structures arepart of mental life, but one would hardly want to make a metaphysical claimabout there being something “real” in the world, propositional or otherwise,that they are representations of ” [Jackendoff, 1995, p.29-30]. Here the ques-tion of mental representation of music risks to become puzzling: we can easily

16 Chapter 1. Introduction

allow that musical structures are not out there in the world; but what aboutsound objects at the basis of musical structures? It seems implausible thatsound objects could be nonintentional objects, in the sense of Jackendoff’snonintentional mental representations [Bullot and Égré, 2010].

1.8.1 Intentional sound objects

The non-intentional character of mental representations à la Jackendoff raisesproblems, not only for the cognitive psychologist who does not want to cutoff with a theoretic guarantee of the reference to the world, but also for philo-sophical accounts of sound events as intentional objects. The non-semanticalcontent of a mental representation of musical sounds is “a content that rep-resents a sort of tension” [Luntley, 2003]. We assume that this mentally rep-resented tension is the same psychophysical feeling investigated in many cog-nitive musicological works: in Section 3 we will illustrate Lerdahl’s version ofthis notion.

Is the content of mental representations of music conceptual or non-conceptual? The intentionality of mental representations of sound objectsdoes not need to be conceptual, since, as observed by DeBellis [1995, 2005]and Luntley [2003], mental non-conceptual representations of music are veryplausible, and they are very likely to cause behaviour even if this behaviourcould not be rationally (linguistically) explained by the subject. Launtley’sexemple is: to hear the tension of a dominant chord without knowing thatit is a dominant chord. Sound objects can be easily thought as intentionallyrelated to the world:

Regardless of the exact status of its targets, auditory experiencemay be characterized as intentional, in the sense that it is aboutthat which is heard, or that which determines whether our demon-strative judgements based on auditory experience are true or false(their truth conditions). In accordance with the terminology in-herited from Phenomenology, the contents of auditory experiencecan therefore be described in terms of “intentional objects”, in thebroad sense of that which the state is about. [Bullot and Égré,2010, p.7].

If mental structures postulated in Lerdahl and Jackendoff [1983] are necessaryto explain musical cognition, concerning non-musical sounds it seems possibleto have a not representationally mediated perception of the sound object: adirect perception, in Gibson [1979]’s sense of sound objects.12 Huron [2006]’s

12 An important recent psychoacoustical theory of harmony, that of Parncutt [1989] isexplicitly grounded on Gibson [1979]’s theory.

1.8. Mental representations of music 17

discussion of the complex cognitive process for localizing sounds in the space isa good example of a realist approach to the mental representations of sounds.

1.8.2 Representing sounds expectation

The now well-known concept of “expectation” was introduced in musicologyby Meyer [1956]: sound events cause certain kinds of expectations of othersound events, and the satisfaction or the delusion of the expectancy is com-monly considered as “a generator of musical affect” [Margulis, 2005, p.663].We discuss in Section 3.3.5 the cognitive and computational implications ofthis concept and of the theories that are constructed on it, and we only presentit now from the representational point of view.

More recently, Huron [2006] has sketched a complete theory of psycholog-ical expectations, starting from Meyer’s seminal study. To expect somethingis to mentally represent something as coming, so expectation is a kind of men-tal representation: “These expectations can be satisfied or not; it is this thatmakes them representational” [Luntley, 2003, p. 414]. Huron [2006] discussesthe evolutionary origin of sound representations, starting from the specificexample of the localization of sound in which three levels of perception areinvolved: unconscious (implying interaural time, amplitude differences andspectral shape), subconscious (involving horizontal azimuth of sounds, eleva-tion or perception of their vertical position, and perception of distance) andconscious (place, speed and trajectory, i.e. more “macroacoustic” dimensions).As it easily seen, all these representational dimensions are psychoacoustic andpre-cognitive, i.e not musical per se.

These kinds of representations are predictive of future events, so theyimplement the “where-next function”, necessary both for survival and for themusical understanding. For Huron, mentally represent sounds has a biologicalfunction, but different forms of representation are allowed. The canonical caseof pitch representation is canonical under this respect: for a listener hearingmusical sounds there are no a priori reasons to expect the next sound eventas an absolute pitch, or a particular pitch-class, or a contour, or an interval,or a scale degree, or a particular member of a specific chord, etc. There aremany representational (categorizing) possibilities: which is the effective oneis for Huron a difficult empirical question. It is a difficult question becausethere are no known methods for discriminating in which format the humanmind processes the sound information. It is plausible in fact that “a profu-sion of different representations might be useful for a listening brain” [Huron,2006, p.107]. Huron subscribes to “neural Darwinism” [Edelman, 1987]. Fromthis perspective “a good mental representation would be one that captures orapproximates some useful organizational property of an animal’s actual envi-

18 Chapter 1. Introduction

ronment” [Huron, 2006, p.107]. So the choice of the good format for a mentalrepresentation of sound is motivated from natural evolution. But how couldwork the selection of the best mental representations? Provided that selectedrepresentations should not be the best ones, but only the most adaptive in aparticular context, it is possible that other representational possibilities wouldabstractly be better. Nonetheless, if the evolution of human mind has “cho-sen” that specific representational format, it means that it was contingentlyfavorable, and probably the least expensive solution (the most “relevant” inthe sense of Sperber and Wilson [1986]).

Here the concept of “expectation” is central: a mental representation that isnot adequate to the real world is more likely to cause wrong predictions. Huronhypothesizes four general principles, or preference rules (see Section 2.1), forthe representation of pitch [Huron, 2006, p.122]:

1. lower-order relationships;2. neighbouring over distant relationships (preferred for the same reason

of 1);3. lower-derivative states;4. event-related binding.

Those types of relationships and cognitive objects would be probably preferredbecause they are simpler to compute. In each case, these principles would beoriented by the preference for useful (relevant) simplicity over equally usefulcomplexity, as in a consolidated tradition of the evolutionary inspired cogni-tive science [Chater and Paul Vitányi, 2003]. These principles are generallyunderstandable as a preference for events or objects, more than for relations :mind/brain can represent relationships, but representations are easier to pro-cess “when they are mentally attached to events or objects” [Huron, 2006,p.124].

From a neurological point of view, Huron’s four principles are plausible interms of neural networks because they favour the computational simplicity.These principles are fully compatible with neural Darwinism, implying thatthe initial mental representations of sounds are simple, low-order and freefrom contextual information.

1.8.3 Conceptual spaces

Concerning the symbolic/connectionist divide, Gärdenfors [2004] says that“it has been a common prejudice in cognitive science that the brain is ei-ther a Turing machine working with symbols or a connectionist system usingneural networks”. According to Gärdenfors, neither the symbolic nor the

1.8. Mental representations of music 19

associationist-connectionist approach can fully explain and model the mecha-nism of concept acquisition, which needs a formalization of similarity (recallChomsky [1959]’s criticisms against the behaviouristic notion of “similar stim-uli”).

According to Gärdenfors, the solution is a third form of representing in-formation, based on geometrical structures. Gärdenfors elaborated a theoryof conceptual spaces in which concepts are considered as multidimensionaldomains with a multiplicity of quality dimensions. The conceptual level ofcognition is the second level of Marr [1982] famous three levels of cognition,the level of “Representation and algorithm” between the symbolic (Compu-tational) and the connectionist one (for Marr, that of Implementation). Aconceptual space consists of a number of quality dimensions, where commonexamples of dimensions are “temperature, weight, brightness, pitch and thethree ordinary spatial dimensions height, width and depth”. But, if musicalpitch were represented in a conceptual space, what about the relations be-tween pitches and other musical dimensions that constitute musical relationsand objects? Also the sub-musical (sound object) level is a matter of mentalrepresentation. Sound objects are intentional objects (see Section 1.8.1), sothey are mental representations of the sounds of the world: that is plausiblythe evolutionary function of audition. Following Gärdenfors we hypothesizethat the representation of the sound object should be at the subsymbolic leveland the representation of musical object is at the symbolic level, that of Marr’s“representations”.

So simple sound perception cannot be identified with music perception.The status of the “musical object” has to be of higher level than sound ob-ject. The musical object supervenes on (i.e., depends on/covaries with/isirreducible to) the sound object, and its ‘supervenience’ should pass throughthe conceptual level of mental representations.

1.8.4 Naive concepts

In the experimental part of this work we grounded our experimental tests ona naive concept of Musical Effect. But what are we referring to, precisely,with “naive concept” of something? The attribution of “naive” for designingsome spontaneous–and also divergent from the scientific homonym discipline–is quite widespread [Bozzi, 1990, Smith and Casati].

Also non-expert listeners probably own some naive concepts, someone cer-tainly acquired through common culture, some other that may be innate.

20 Chapter 1. Introduction

1.9 But what is music?

We dare suggest only en passant some ideas about that embarrassing question.This is a good example of “unanswered question”, as said by the title of a sug-gestive Charles Ives’ short composition, than adopted as title for the Bernstein[1976]’s conferences at Harvard. Steve Pinker’s and David Huron’s opinions,quoted as epigraph at the beginning of this work, are ironic but not thatmuch. It is possible that before music we are confronted to something forthe comprehension of which our mind is not naturally equipped, as for visu-alizing multidimensional spaces, or understanding Quantum Mechanics in anintuitive way. Our species is evidently gifted for music but not for thinking tomusic. Someone can do it, as the theoretical speculation about music showsfrom the ancient Greeks and Chinese studies; nonetheless this speculation isthe result of a technical thought, not of a spontaneous one. It must be saidthat this is the same for all techniques the human mind has historically devel-oped: anyway, other scientific objects like language or physics do not appearas enigmatic like music does.

The well-known definition of the music is brilliant but philosophically un-satisfying: “music is auditory cheesecake, an exquisite confection crafted totickle the sensitive spots of at least six of our mental faculties” [Pinker, 1997,p.534], where the six (very general) faculties are the language, the auditoryscene analysis [Bregman A.S., 1990], emotions, habitat selection, motor con-trol and “something else”. A frequent answer says more or less that musicis organized sounds.13 That minimal definition could be accepted with thisremark: 20th century music has enormously enlarged the domain of soundsacceptable for music, with a huge research on the nature of “noise” and alsothe compositional methods for organizing sounds are nowadays much morefree than in all the music history until the end of 19th century.

Summary

In this Section we have illustrated the content at stake in our work, analysingsome fundamental concepts of cognitive musicology, choosing those most re-lated to our research about Musical Relevance. In particular, we have dis-cussed some aspects of the complex cognitive nature of music perception, inrelation with other classical and recent theories.

13 This is such a widespread notion that also the late poet, rockstar andcomposer Lou Reed (Lewis Allan Reed, 1942–2013) defined music as “orderedsounds”, during his last interview: http://www.rollingstone.com/music/videos/lou-reeds-last-words-watch-his-final-interview-20131108.

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E. Acotto and Radicioni D.P. Musical relevance: a computational approach.Sapporo, 2012. URL http://mindmodeling.org/cogsci2012/papers/0224/index.html. (Cited on page 88.)

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